- © 2016 Mineralogical Society of America
INTRODUCTION AND SCOPE
The platinum-group elements (PGEs; Os, Ir, Ru, Rh, Pt, Pd), along with rhenium and gold, are grouped together as the highly siderophile elements (HSEs), defined by their extreme partitioning into the metallic, relative to the oxide phase (> 104). The HSEs are highly refractory, as gauged by their high melting and condensation temperatures, and were therefore relatively concentrated in the feedstock for the terrestrial planets, as defined by the composition of chondritic meteorites (e.g., Anders and Ebihara 1982; Horan et al. 2003; Fischer-Gödde et al. 2010). However, the planetary formation and differentiation process has since acted on this chemical group to produce a rich variety of absolute and relative inter-element fractionations. For example, analysis of iron meteorites suggests a significant decoupling of the HSE in the cores of planetesimals, and likely Earth’s core, with Os, Ir, Ru (IPGE-group) and Re concentrated in the metal phase, and Pt, Rh, Pd (PPGE-group) plus Au usually concentrated in the residual liquid (Goldstein et al. 2009). In terms of the silicate Earth, analysis of mantle rocks reveals very low levels of the HSE, but relative abundances similar to chondrites (see review by Day et al. 2016, this volume), in part reflecting HSE segregation into core-forming iron (Ringwood 1966; Ganapathy et al. 1970). This is in contrast to mantle-derived melts, whose HSE abundances are highly fractionated, with relative depletions in the IPGE-group compared to PPGE-group, as well as Re and Au (Barnes et al. 1985). Resulting Re/Os and Pt/Os fractionation also influence the long-term evolution of the 187Re to 187Os and 190Pt to 186Os decay systems, and, hence, the development of distinctive Os-isotope reservoirs (Walker et al. 1997; Shirey and Walker 1998; Day 2013). The emplacement of mantle-derived magmas into Earth’s crust results in a further decoupling of the HSE suite. Crystallization of mafic and ultramafic magmas appears to leave the IPGE in magmatic cumulates, while concentrating the PPGEs, Re and Au in the more differentiated products (e.g., Brugmann et al. 1987; Puchtel and Humayan 2001, 2005). The onset of sulfide liquid saturation in these systems can produce a wholesale reduction of HSE concentrations in the silicate melt, reflecting the highly chalcophile nature of this element suite. Magmatic sulfide liquids may differentiate internally, with further concentration of the IPGEs and Re into accumulations of the early formed monosulfide solid solution (MSS), and subsequent enrichment in the liquid residue in the PPGEs and Au (Barnes and Ripley 2016, this volume). As the silicate magma differentiates further, an orthomagmatic fluid may develop, possibly disturbing the primary distribution of the HSE within the pile of accumulated solids (e.g., Boudreau et al. 1986; Boudreau and Meurer 1999). More evolved magmas emplaced at a high level in the crust, or even erupted, may have some of their remaining HSE collected into a low-density vapor phase, which may be deposited in a hydrothermal stockwork (Richards 2011), or dispersed into the atmosphere during volcanic eruptions (e.g., Naughton et al. 1976; Zoller et al. 1983; Toutain and Meyer 1989; Crocket 2000; Yudovskay et al. 2008). Hence, the HSE are not only fractionated during planetary differentiation, but during this process, these elements may exhibit four out of the five geochemical classifications originally proposed by Goldschmidt (1958; Table VI, page 25); concentration in the core, and magmatic sulfides (siderophile and chalcophile), partitioning into silicates/oxides (lithophile), and expulsion in volcanic emanations (atmophile). In order to make full use of this unique suite of elements to understand the planetary differentiation process, information on their partitioning amongst solid/liquid iron metal, sulfide, silicate, oxide phases, and vapour/fluid, as well as the stability of HSE-bearing accessory phases is required. The advent of procedures to detect very low concentrations of the HSE in these various phases has greatly expanded our empirical understanding of this behavior (Meisel and Horan 2016, this volume), but significant uncertainties still remain. Laboratory experiments offer a complimentary approach to the empirical studies, providing constraints on the nature of HSE fractionation involving specific phases, and variation with intensive parameters. This chapter provides a review of that work, with an emphasis on results pertaining to processes occurring mostly at the magmatic stage. For each of the experimental systems considered, we have provided some information on how the experiments are done, the methods of analysis and attempt to place the results in a theoretical framework.
SOLID METAL–LIQUID METAL PARTITIONING
Studies of the iron meteorites have shown large variations in both the relative and absolute abundances of the HSE (e.g., McCoy et al. 2011; see review by Day et al. 2016, this volume). In part, this variation may derive from differences in the bulk HSE composition of the meteorite parent bodies, but significant differences exist within groups derived from a single parent body, reflecting the role of internal differentiation processes (e.g., Scott 1972; Scott and Wasson 1976; Goldstein et al. 2009). So-called non-magmatic iron meteorites (Types IAB and IIICD) are thought to derive by impact melting of planetesimals, with the variation in HSE concentrations due to mixing of different melt fractions (e.g., Choi et al. 1995). In contrast, HSE variation in the magmatic iron group is consistent with crystal–liquid fractionation during solidification of the parent body core; as mentioned, segregating metal concentrating the IPGE and Re, with enrichments in the PPGE + Au in residual melt (e.g., Scott 1972; Pernicka and Wasson 1987; Walker et al. 2008; Goldstein et al. 2009). Studies of the magmatic iron group have also emphasized the possible role of non-metal components, such as S, C, Si, and P, in affecting the solid metal–liquid metal partitioning, as accessory phases containing those elements are ubiquitous (Goldstein et al. 2009). This is also consistent with the need for a light-element component in the cores of the terrestrial planets, in order to explain their density deficit, and to satisfy cosmochemical constraints (Dreibus and Wanke 1985; McSween 1994; McDonough 2003). Laboratory experiments of solid metal–liquid metal partitioning have provided the means to verify the core crystallization model for the magmatic irons, and also inform about the effects of non-metal components (Willis and Goldstein 1982; Chabot and Drake 1999; Goldstein et al. 2009) as well as the influence of the crystalline metal (Van Orman et al. 2008; Stewart et al. 2009; Rai et al. 2013) on HSE distribution during solidification. Also, a major focus of study in recent years has been the relative fractionation of Re/Os and Pt/Os arising from inner core solidification, which bears on the development of deep planetary reservoirs with distinct 187Os/188Os and 186Os/188Os isotopic compositions (e.g., Walker et al. 1995, 1997; Brandon et al. 1998). The following sections outline the parameterizations used to describe variation in the solid-metal/liquid metal partition coefficient, DSM/LM, as a function of either liquid metal composition or solid metal structure. Several considerations for experiments at both ambient and high pressure are first described.
EXPERIMENTAL APPROACH TO SOLID METAL–LIQUID METAL PARTITIONING (DSM/LM)
Past studies have focused on the separate roles of the liquid and solid phases on controlling the absolute and relative magnitudes of DSM/LM. The structure of solid Fe is expected to undergo changes due to both pressure and the incorporation of light elements. The consequences of increasing pressure are manifold, including control on the stable atomic arrangement (e.g., the FCC to HCP transition at high T; Komabayashi et al. 2009), unit cell volume, and effect on the solubility of light elements in the Fe-metal structure (e.g., Zhang and Fei 2008). Although temperature is likely to play a second-order role, most experimental data have been acquired at conditions significantly cooler than those expected to accompany core crystallization in larger planetary bodies. This makes T worthy of investigation in future work. Outlined here are several different experimental approaches that have been used to determine DSM/LM over a range of P–T–X conditions.
Most of the early experimental studies of HSE partitioning in solid metal–liquid metal systems were conducted at 0.1 MPa and temperatures corresponding to the Fe (+ Ni) – X liquidus, with X being C, S, O, Si, and P, with more recent work focusing on the effect of pressure. The primary concerns for experiments in the Fe-rich systems of interest here are the attainment of equilibrium and the potential for reaction between the container material and the charge. The compositional space that can be accessed is governed by phase relations in the chosen system and must also be considered in the experimental design. For experiments done at ambient pressure, there is the additional consideration of volatile element loss from the sample. With these in mind, the experimental protocol adopted for experiments to determine siderophile element partitioning at ambient pressure in the Fe ± S, P, C systems has remained essentially unchanged since the pioneering experiments of Drake et al. (1978). The light element components are typically introduced to starting materials as Fe-sulfide, elemental phosphorus and graphite powder, for S, P, and C, respectively, which are mixed and ground with metallic Fe, Ni, and typically one HSE dopant at the wt% level (e.g., Jones and Drake 1983; Malvin et al. 1986; Chabot et al. 2006), although multiple HSE can be added at ppm levels. As shown by Fleet et al. (1999), constant partitioning is obtained over the ppm to wt% concentration range. The most commonly employed crucible material is vitreous alumina, as it is unreactive with the alloy phase and stable to the required temperatures (e.g., Drake et al. 1978; Jones and Drake 1983). Owing to the volatile nature of the light element additives, most past experiments at low pressure have been done in evacuated and sealed silica glass ampoules (Fig. 1a), although some early results (free of S and P) were obtained with open crucibles in contact with an Ar–H2 atmosphere (Willis and Goldstein 1982; Jones and Drake 1983).
In order to aid sample homogenization and reduce the time required for equilibrium, some studies have employed a superliquidus step lasting for several hours, then cooling to the intended equilibration temperature of the experiment (Drake et al. 1978; Chabot et al. 2006, 2007). Typical experiment durations are between 12 and 200 h (e.g., Chabot et al. 2006, 2007), although runs as short as 5 h appear to be sufficient for equilibrium in the Fe–Ni–S–P system at 0.1 MPa and 1250 ºC (Malvin et al. 1986). Experiments are terminated by immersing the sample in cold water. Although the rate of heat loss is high, quenching an iron-rich liquid containing S, P or C by this method still results in precipitation of a heterogeneous intergrowth of Fe-rich metal with a light element-rich component (Fig. 1b). In order to obtain an average composition of the quenched melt phase, run product analysis by electron microprobe, or more recently by LA-ICPMS, employs a defocused or rastered beam.
Certain experimental systems offer unique challenges. Phase relations in the Fe–Si system show that for compositions more Fe-rich than the eutectic that exists between Fe and Fe2Si, the solid and liquid alloy phases contain similar quantities of Si (Kubaschewski 1982). Isolating the effect of liquid composition on partitioning is therefore not straightforward. To circumvent this problem, Chabot et al. (2010) conducted experiments in the Fe–S–Si system and monitored trace element distribution between immiscible melt pairs; one rich in the S and the other in Si. By comparison to the well-established effects of S on partitioning, the role of Si could be evaluated independently. The effect of oxygen on DSM/LM has also been difficult to evaluate, as the solubility of oxygen in molten Fe is diminishingly small at low pressure. However, work by Naldrett (1969), and later by Fonseca et al. (2008), has shown that the oxygen content of molten Fe–S can reach several wt%. Taking advantage of this effect, Chabot et al. (2015) measured partitioning in the Fe–S–O system, and again, by comparison to partitioning systematics in the Fe–S system, were able to evaluate the role of O.
Experiments done at elevated pressures have utilized both piston-cylinder and multi-anvil apparatus. Crushable MgO is often employed as a sample container, as it is unreactive with Fe-rich alloys over a broad spectrum of conditions, and promotes a homogenous pressure distribution (e.g., Jones and Walker 1991; Walker 2000; Lazar et al. 2004; Van Orman et al. 2008). In order to prevent leakage of the liquid alloy phase during the experiment, the crushable MgO is annealed at ~ 600–800 ºC for ~ 8–12 hrs at the target pressure (e.g., Jones and Walker 1991; Walker 2000). Hard-fired alumina crucibles have also been employed successfully to investigate partitioning in the Fe–S and Fe–C systems (Chabot et al. 2008, 2011; Rai et al. 2013), as well as graphite to study HSE partitioning in the Fe–S–O system (Fleet et al. 1991). At the low temperatures and high-sulfur content of the experiments done by Fleet et al. (1991), the solubility of carbon in the sulfur-rich liquid phase is negligible. However, partial closure of the Fe–C and Fe–S liquids miscibility gap with increasing pressure (Corgne et al. 2008), may result in significant levels of carbon in the resulting liquid, and therefore difficulty in isolating the separate effects of C and S. Graphite-saturated experiments in the Fe–S–C system may also become saturated in cementite (Fe3C), rather than Fe, as the solid phase coexisting with sulfur-rich liquids (Dasgupta et al. 2009; Buono et al. 2013).
Refractory Os–Ir ± Fe alloy grains, in some cases rimmed by Pt, were observed by Fleet et al. (1991) in experiments conducted in the Fe–S-O system at 1100–1200 ºC and 4.5–11 GPa. Some experiments done at ambient pressure and temperatures of 1000–1200 ºC in the Fe–Ni–S system also display evidence for heterogeneous Os concentrations in the solid metal phase (Fleet et al. 1999). A similar problem with Ir homogeneity was noted by Jones and Drake (1983). These grains result from the use of HSE-rich starting materials that are resistant to dissolution at the chosen experimental temperatures and durations. A factor which might have exacerbated the equilibration problem in the Fleet et al. experiments was the loading of several of the PGEs into each experiment, producing significant domains of Fe-poor, IPGE-rich alloy in which diffusion of all the PGEs is intrinsically slow (Watson and Watson 2003). To prevent the formation of refractory HSE grains in experiments done at 10 GPa and 1400–1500 ºC, Walker (2000) used a novel experimental arrangement to prevent alloying between the HSEs and Fe early in the experiment. This was achieved by taking advantage of the large thermal gradient intrinsic to the multianvil assembly, and positioning powdered Pt, Os, and Re metal in what would become the hot zone of the capsule, causing complete dissolution and precipitation with newly formed Fe–Ni crystals at the cold end. Experiments that exploit a thermal gradient have also been used to determine solid metal–liquid metal partitioning in the Fe–Si system (Morard et al. 2014). As the melting loop in the Fe–Si system is only a few tens of degrees, Morard et al. (2014) imposed a vertical temperature gradient across samples so as to increase the relative proportions of metal and liquid for a given bulk composition.
Effect of liquid metal composition on DSM/LM
The effect on DSM/LM resulting from changes to the liquid metal composition has been parameterized by Jones and Malvin (1990) in terms of a non-metal interaction model. Jones and Malvin (1990) consider partitioning of an element (i) between solid (SM) and liquid (LM) metal. At equilibrium, the chemical potential of i is equal in both phases:(1)
Expressing these chemical potentials in terms of the standard state chemical potential and the activity of element i in each phase (ai) yields:(2)
Recalling ai = γiXi (where γi and Xi are the activity coefficient and mole fraction of i respectively), the activity terms may be replaced to provide an expanded form of Equation (2):(3)
Equation (3) may be rearranged to yield:(4)
Substituting the molar partition coefficient (Di*SM/LM) into the left hand side of Equation (4) and the Gibbs free energy of reaction (ΔGrO) for μiLMO − μiSMO yields:(5)
From Equation (5) we see that for a system at constant pressure, the molar partition coefficient will depend upon temperature and changes to the activity coefficient of element i in both the solid- and liquid-metal phase. Jones and Malvin (1990) argue that both T and changes to γiSM have a negligible effect on Di*SM/LM relative to changes in γiLM.
The effect of T can be assessed by considering an ideal system, in which the ratio γiSM / γiLM is unity, and variation in Di*SM/LM depends only on the free energy term. ΔGrO in Equation (5) corresponds to the melting reaction for pure solid and liquid phases of element i, and can be written in terms of the heat of fusion (ΔHm) for the element of interest. Remembering that −ΔGrO = − (ΔHrO − TΔSrO) and replacing the subscript r with m, to denote the melting reaction, Equation (5) becomes:(6)
At the melting temperature of i, −ΔGrO = 0 and so ΔSm = ΔHm / Tm. Substituting this identity into Equation (6) yields the following expression:(7)
Equation (7) can be used to assess the variation in Di*SM/LM arising from changes in temperature. Table 1 lists the melting temperatures and enthalpies of fusion for the highly siderophile elements. Selecting osmium, which has the largest enthalpy of fusion, we calculate that Di*SM/LM will only vary by a factor of ~ 2.5 if T changes by 1000 ºC . The weak dependence of Di*SM/LM on temperature suggested by this analysis is borne out by the similar correlation coefficients (R2) obtained from simple regression of Di*SM/LM vs. liquid-metal composition and multiple linear regression vs. both liquid-metal composition and 1/T (Jones and Malvin 1990).
For systems at relatively low P, in which the solubility of light elements in solid Fe–Ni alloy is small, Jones and Malvin (1990) argue that changes in γiSM are negligible relative to changes in γiLM. They support this assertion by noting that values of Di*SM/LM in the light- element free system are typically close to unity, the solid Fe–Ni system is itself relatively ideal, and that their 0.1 MPa experimental data can be adequately modeled considering only the γiLM term. Chabot and Jones (2003) later used a modified version of the Jones and Malvin (1990) parameterization to successfully model a much larger database of 0.1 MPa partitioning data, providing further support for an approach that considers only changes in γiLM.
Accepting that changes in T and γiSM do not strongly drive changes to the solid metal–liquid metal partition coefficient, we can return to the relationship given in Equation (5) and simplify it to yield(8)
For geo- and cosmochemical purposes, the more useful independent variable is liquid-metal composition rather than γiLM. These are linked, however, through interaction parameters which describe the excess free energy of mixing. For a liquid-iron alloy containing solutes i through N in dilute concentration, the activity coefficient of i is often described using only the first-order interaction parameters (ɛ):(9)
where γi0 is the activity coefficient of i at infinite dilution in liquid iron and Xj is the mole fraction of the subscript component in solution. It should be noted that by ignoring interaction parameters greater than first order, Equation (9) is not thermodynamically rigorous and should only be applied to alloys in which the solutes are dilute (Ma 2001 and references therein). Despite this, the following model adequately describes the experimentally determined partitioning of several HSEs in systems containing up to ~ 30 wt% sulfur (Jones and Malvin 1990). Although Ni is also typically present in moderate concentrations, it’s relatively weak interactions with Fe, S, P, and C permit the simplification embodied by Equation (9) while still allowing most experimental data to be modeled successfully (Jones and Malvin 1990).
As an example, if we consider the case of iridium partitioning in an Fe–Ni–S alloy, the activity coefficient of Ir, as given by Equation (9) is:(10)
From Equations (8) and (10) it is apparent that the solid metal–liquid metal partition coefficient of Ir can be expressed in terms of the component mole fractions weighted by their corresponding interaction parameters. Jones and Malvin (1990) propose a further simplification, whereby the alloy is described as comprising only metal and non-metal domains, which either accept or reject the HSEs respectively. In this framework, changes to the activity coefficient as a function of liquid composition can be described by a single modified interaction parameter, termed the β factor. For Ir in the Fe–Ni–S system:(11)
where α is a constant specific to the compositional system being investigated and n is a stoichiometric coefficient related to the speciation of the non-metal component in the alloy. Equation (11) retains the linear dependence of the activity coefficient on composition inherent in Equation (10) and is subject to the same limitations discussed above. Substituting Equation (11) into (8), yields DIr*SM/LM as a function of the non-metal content of the alloy and the β factor:(12)
where C is a constant. As the sulfur (or other light-element) content of the alloy tends towards zero, ln DIr*SM/LM will tend towards C, such that in the limiting case of Xs = 0, C will equal the partition coefficient in the light-element-free system (ln Di0). Figure 2 provides an example of partitioning data for Au and Re in the Fe–Ni–S system plotted in the form of Equation (12), illustrating the overall linearity of the data. For partitioning of an element i in a system containing light elements j through N, the general form of Equation (12), therefore, becomes:(13)
The value of βi in Equation (13) for a system containing multiple light elements is related to the β factors in each of the individual light-element-bearing systems. Jones and Malvin (1990) express this relationship as a weighted average of the effects in the end-member systems:(14)
For example, the β factor for element i in the Fe–Ni–S–P system, where nS and nP are 2 and 4, respectively, is described as:(15)
Chabot and Jones (2003) develop further the parameterization outlined here, such that only a single beta factor need be determined in systems containing multiple light elements.
In order to implement predictive models of partitioning in light-element-bearing systems, the key parameters to determine from experiments are therefore DSM/LM and the β factors. Table 2 provides a summary of these values determined for the HSE at 0.1 MPa as defined using the Jones–Malvin formalism. Values of DSM/LM and β show a ~ 5-fold difference in magnitude amongst the HSE, with the strongest melt composition effects implied for Re–Os–Ir, and the least for Pd and Au. These differences serve to further decouple the HSE during core solidification as the light-element component builds up in the residual melt. Significantly, although values of β for Re, Os, and Pt are similar, there are resolvable differences in the values of DSM/LM, in the order Os > Re > Pt. This result was noted based on empirical estimates from magmatic iron meteorites (Walker et al. 1995), and used to develop the hypothesis that mafic magmas with anomalous enrichments in 187Os/188Os and 186Os/188Os contain an outer core component (Walker et al. 1995, 1997; Brandon et al. 1998). Subsequently, experiments have been done to document the effect of pressure on the relative partitioning of these elements (3–22 GPa; Walker 2000; Van Orman et al. 2008; Hayashi et al. 2009). Some of these studies suggest that DSM/LM becomes smaller, and more similar, likely due to an increased size misfit in Fe metal (Van Orman et al. 2008), as described below.
The role of the solid phase on DSM/LM
As described in the previous section, much of the available solid metal–liquid metal partitioning data can be adequately described using a parameterization which takes into account metal-solvent interactions in the liquid (e.g., Jones and Malvin 1990; Chabot and Jones 2003). This approach however, provides no theoretical explanation for the role of the crystalline Fe–Ni solid phase, as manifested by ~ 5-fold difference in values of DSM/LM between the HSE (Table 2). Several recent studies have sought to provide this theoretical framework through application of a modified form of the lattice strain model (Van Orman et al. 2008; Stewart et al. 2009; Chabot et al. 2011; Rai et al. 2013). This model, as commonly applied to silicate systems, quantifies the parabolic relationship between log DCrystal/Melt and ionic radius (Blundy and Wood 1994). This functional form arises because the variation in partition coefficients for a suite of isovalent cations originates purely in the elastic strain incurred by the size mismatch between the substituent cation and the optimal radius for that site. An analogous approach has been taken for application to metallic systems, with DiSM/LM cast as:(16)
where DoSM/LM is the partition coefficient for an element with the ‘ideal’ neutral atomic radius for site M (r0(M)), NA is Avogadro’s constant, EM is the apparent Young’s modulus for site M and ri is the radius of a neutral atom of element i. Some previous studies have used the neutral atomic radii of Clementi et al. (1967) for values of ri and fit the experimental data to Equation (16) by varying D0, r0, and EM (Stewart et al. 2009; Chabot et al. 2011; Rai et al. 2013). Application of this model by Stewart et al. (2009) to previous results for HSE partitioning in the Fe–S and Fe–C systems, at 0.1 MPa to 22 GPa (Chabot and Jones 2003; Chabot et al. 2006; Van Orman et al. 2008), suggests incorporation of these elements in the lattice does not occur through simple replacement of Fe. The large value of r0 (1.83 Å) for the parabola defined by the 3rd row transition elements, Au through W, is significantly greater than the atomic radius of Fe (1.56 Å) and may instead suggest the accommodation of these elements in defects resulting from the presence of light elements in the Fe lattice (Stewart et al. 2009). However, Van Orman et al. (2008) showed that the partitioning of Re, Os, and Pt was consistent with their relative increase in metallic radius compared to that of Fe in the FCC structure. Chabot et al. (2011) considered a larger suite of data in this context, and found that the systematic partitioning trends using atomic radii as the ordinate broke down for the 1st- and 2nd-row transition elements when plotted as a function of the metallic radius. The reason for these differences are unclear, but certainly bear on our interpretation of which sites the HSE partition in the solid-metal phase, and the fundamental controls on inter-element fractionation.
As a final point to this section, we note that the ~ 5-fold variation in β is similar to the differences in DSM/LM for the HSE, with the latter related to the elastic strain generated by size mismatch from the optimal site size in FCC iron. Values of β provide a measure of the affinity of a particular HSE for Fe-rich domains within the liquid structure, with larger values of β signifying enhanced sulfur avoidance (Jones and Malvin 1990). Thus, it seems reasonable that the extent to which a particular HSE will concentrate in more Fe-rich, non-metal-poor melts should be related to the size of the metal atom, provided Fe-solid and Fe-rich melt have similar structures. The structural similarity between liquid and solid metal is implied by the small ΔV for the solid-to-liquid metal transfer of components, as indicated by the relatively small effect of pressure on DSM/LM as documented in previous work (e.g., Van Orman et al. 2008; Chabot et al. 2011). As shown by Brenan and Bennett (2010), values of DSM/LM show a somewhat stronger dependence on metal, or atomic radius than β, but there is a sympathetic variation between the two, suggesting similar origins of the HSE “selectivity” for Fe-rich domains. As proposed by Van Orman et al. (2008), with increasing pressure the difference in absolute and relative values of DSM/LM for Pt, Re, and Os (and likely the other HSE) decrease due to the increased size mismatch between the substituent metal and Fe, and between individual HSE. If so, then we expect that not only will pressure decrease the absolute and relative values of DSM/LM (as per Van Orman et al. 2008), but, by analogy, pressure may also reduce the differences between individual values of β. The effects of increased pressure are not straightforward, however, as exemplified by the results of high-pressure experiments for Pt, Re, and Os done in the Fe–Ni–S system (vs. the Fe–S system studied by Van Orman et al.), which instead show a slight increase in DSM/LM with increasing P (Hayashi et al. 2009).
Soret Diffusion Experiments
The effect of liquid composition on solid metal–liquid metal partitioning can also be determined from experiments that impose a thermal gradient on non-ideal Fe-alloy solutions (e.g., Fe–S; Brenan and Bennett 2010). These experiments produce run-products with major-element compositional gradients that reflect the opposing mass fluxes of Soret and chemical diffusion. Soret diffusion arises when the system contains components that possess a different partial molar enthalpy when undergoing activated transport in the medium. A component with higher enthalpy in transport will migrate from hot to cold; transporting heat to the cold portion of the system and acting to ameliorate the imposed temperature imbalance. The opposite sense of migration is expected for components with a lower enthalpy in transit, thus also redistributing heat so as to reduce the thermal gradient. Details of the Soret process and its application to complex geologic systems are treated in detail by Lesher and Walker (1986, 1991). Chemical diffusion can limit the magnitude of segregation by Soret diffusion, due to the chemical potential gradients that arise from compositional differences along the sample length. In ideal systems, chemical diffusion may be quite effective in limiting compositional gradients due to the large change in chemical potential with composition. In strongly non-ideal systems however, which contain P–T–X regions where d μi/d X ≈ 0, and hence the driving force for chemical diffusion is negligible, experiments may exhibit large gradients in major-element composition. The magnitude of the compositional gradient is described by the Soret coefficient (σ), which for a binary system is given as (Lesher and Walker 1986):(17)
where XHot and XCold are the component mole fractions measured at the hot and cold ends of the sample respectively and X̄ is the average component mole fraction in the sample. Trace elements in the system are distributed to maintain a constant activity along the sample and concentration gradients therefore depend upon changes to the activity coefficient with major element composition (Jones and Walker 1990). The following derivation relates the compositional gradient for a trace element (i), measured in a Soret diffusion experiment, to β. Values of β obtained from these experiments may then be used to predict partitioning through the use of Equation (13) (Brenan and Bennett 2010).
Assuming a hypothetical solid Fe phase in equilibrium with the melt at all points along a Soret diffusion experiment, the solid metal–liquid partition coefficient for i can be defined at two points along the sample (T1 and T2) as:(18) (19) (20)
Substituting XiSM / XiLM for DiSM/LM :(21)
For adjacent positions along the sample, it can be shown that Xi,T1SM / Xi,T2SM ≈ 1, simplifying Equation (21) to give:(22) (23)
Or more simply:(24)
Values of β are therefore extracted from plots of ln XiLM vs. ln (1 − nαXl) and are assumed to be temperature independent. Evidence for the lack of a strong T dependence for β is provided by previous equilibrium experiments (Jones and Malvin 1990; Chabot and Jones 2003) and the linearity of data plotted in the manner described above (Brenan and Bennett 2010). An example of the major and trace element data produced by Soret experiments is provided in Figure 3.
Soret diffusion experiments are subject to the same design considerations as those described previously for ambient pressure and high pressure studies. The primary advantage of this approach is that a small number of experiments can provide information comparable to a large suite of isothermal solid–liquid partitioning experiments. A further application of this method is to determine the effects of light-elements that have a low solubility in Fe-rich melt. Phase relations in the Fe–O system for example, preclude large volume experiments to directly measure solid metal–liquid metal partition coefficients for liquids that span a broad range of O-contents (i.e., ≤ 2.2 wt% O at 15 GPa, Langlade et al. 2008). Soret experiments, however, can be performed at super-liquidus temperatures where light-element components more readily dissolve in the melt. This can provide access to compositional space that may be relevant to high-pressure planetary differentiation processes. A disadvantage of this approach, however, is the lack of information for the solid phase, which also exerts a strong control on inter-element fractionation, as noted above.
HSE SOLUBILITY EXPERIMENTS: IMPLICATIONS FOR METAL–SILICATE PARTITIONING
Accretion of the Earth from planetesimals of chondritic composition (McDonough and Sun 1995; Wood et al. 2006), with concurrent differentiation into a metal core and silicate mantle, is generally thought to have occurred over the first ~ 30 Ma of Earth’s history (e.g., Kleine et al. 2002; Yu and Jacobsen 2011). During accretion, heat generated by the decay of short-lived isotopes and the collision of large impactors is likely to have raised global temperatures sufficiently to cause widespread melting and the formation of a magma ocean, through which more dense Fe–Ni liquid could descend (e.g., Ringwood 1966; Karato and Murthy 1997; Wood et al. 2006; Rubie et al. 2007). In this scenario, the siderophile elements would be transported to the growing core, leaving a depleted silicate mantle with element ratios that depend upon the differing affinities for the metal phase (e.g., Chou 1978; Newsom and Palme 1984; Wänke et al. 1984). Past work has ascribed the behavior of the moderately siderophile elements (MSEs; Mo, W, Cr, V, Mn, etc) to a combination of metal extraction and accretion of compositionally distinct components (Wänke and Dreibus 1988; Schmitt et al. 1989; O’Neill 1991). More recently it has been shown that, if metal–silicate partitioning is appropriately parameterized, a match to mantle MSE abundances can be achieved at appropriately high pressure and temperature (e.g., Wade and Wood 2005; Righter 2011; Siebert et al. 2011; Wade et al. 2012). In contrast, metal–silicate partitioning of the HSE has provided a somewhat conflicting view on the accretion model. The majority of past work on HSE partitioning has been at 0.1 MPa and relatively low temperature (~ 1300–1400 ºC) and showed that at the relatively reduced fO2 attending core formation1 (i.e., 1.5 log units more reduced than the iron–wustite buffer; IW – 1.5) metal–silicate partitioning of all the HSEs is likely to exceed 105–108 (e.g., Borisov and Palme 1995, 1996; Ertel et al. 1999, 2001). Such results predict the quantitative removal of the HSEs from the silicate mantle, which is inconsistent with their estimated abundances in the primitive mantle (Becker et al. 2006). This apparent lack of mantle HSE depletion is a long-standing issue in geochemistry, and has come to be known as the “excess siderophile element problem”. Importantly, moderate to large differences in the relative mantle abundances of the HSEs are also predicted by the low- temperature partitioning data (compare Borisov and Palme 1996 to Ertel et al. 1999), in conflict with observed chondritic relative abundances (Becker et al. 2006) and a mantle Os-isotope time evolution requiring Pt/Os and Re/Os ratios to match those of chondritic meteorites (Meisel et al. 2001; Brandon et al. 2006). These combined observations support a model for late accretion of a small amount of dominantly chondritic material which post-dated core formation; the so-called later veneer (e.g., Kimura et al. 1974). The veracity of this model came into question, however, following the proposal of Murthy (1991) that there should be a convergence of metal–silicate partitioning values at the very high temperatures likely during core formation (i.e., > 2700 ºC), resulting in a mantle HSE composition set by metal–silicate equilibrium. Although the strategy to estimate high temperature partitioning was shown to be flawed (e.g., Capobianco et al. 1993) more recent results have indeed shown that temperature is a key variable to be considered, as is the importance of measurements at reduced conditions, at which some HSE may exhibit unanticipated and unusual redox behavior, as described in the subsequent sections.
CALCULATING THE METAL–SILICATE MELT PARTITION COEFFICIENT FROM SOLUBILITY DATA
Experiments that equilibrate silicate melt with an Fe-rich metal liquid usually result in vanishingly low HSE concentrations in the quenched silicate melt, owing to high values for metal/silicate partition coefficients, DiMet/Sil. For example, a sample doped with 200 ppm of element i and comprising equal fractions of metal and silicate melt will result in CiSil < 0.004 ppm for values of DiMet/Sil > 105. Hence, in order to generate run-products with measurable HSE levels in the quenched silicate phase, solubility experiments are performed. In this case, pure HSE metal, or an HSE-rich alloy, is equilibrated with silicate melt at the desired P–T–fO2 conditions and values of DiMet/Sil are calculated using the formulation of Borisov et al. (1994), described as follows. The dissolution reaction for a metal in silicate melt is:(25)
where n is the oxidation state of the dissolved metal cation. Two equilibrium constants can be defined for this reaction, one for an experiment at saturation in an HSE phase (KSat) and the other pertaining to a natural system with dilute HSE concentrations (KDil):(26) (27)
where aM and aMOn/2 are the activity of the metal and metal oxide and components. Substituting ai = Xiγi into Equations (26) and (27), where Xi and γi are the mole fraction and activity coefficient respectively, yields:(28) (29) (30)
The molar partition coefficient (D*Met/Sil = XMet / XSil) may then be substituted into the left-hand side of Equation (30), yielding:(31)
The very low solubility of HSEs in silicate melt, even when saturated in a pure metal phase, results in negligible changes to γMOn/2 over the possible range for XMOn/2 and the ratio γMOn/2 / γMOn/2Sat may therefore be treated as unity. After taking the exponent, Equation (31) then becomes:(32)
Typically. it is the concentration by weight rather than mole fraction of a trace element that is reported and conversion of Equation (32) to the weight-based, rather than molar, partition coefficient is accomplished using the following conversion factors (A and B):(33) (34) (35)
which simplifies to:(36)
where CMSat is the concentration of M measured in the silicate melt at the solubility limit and γM is the activity of M at infinite dilution in Fe metal. Values of A tend toward a constant value as the concentration of M in Fe-alloy decreases.
Controls on the metal–silicate partition coefficient
Temperature, pressure, oxygen fugacity and melt composition may all play a role in determining the value of DMet/Sil. The equilibrium constant for Reaction (26), describing the dissolution of a trace metal into silicate melt may be equated with the Gibbs free energy of reaction (ΔGr∘) as follows:(37)
Replacing the activity terms (ai = Xiγi) and rearranging yields:(38)
Expanding the free energy term (ΔGr∘ = ΔHr∘ − TΔSr∘ + PΔVr∘) and substituting the molar partition coefficient into the left hand side of Equation (38) reveals the variables that might be expected to affect HSE partitioning:(39)
where ΔHr∘, ΔSr∘ and ΔVr∘ are the enthalpy, entropy, and volume change of reaction respectively. Assuming these three parameters do not themselves depend strongly on P or T, Equation (39) can be simplified to yield the following relationship:(40)
where a, b, and c are constants determined by regression of the experimental data. The partition coefficient is therefore expected to depend on temperature, pressure, oxygen fugacity and the composition of both the silicate and metallic melt. Equation (40) provides the basis for the various approaches employed in past work to parameterize the results of either metal solubility measurements or direct determinations of metal–silicate partitioning. A summary of such work is provided in Table A1 in the appendix.
Whereas the dependence of solubility and partitioning on fO2 is reasonably well established under oxidizing conditions (i.e., > FMQ), experiments done at reducing conditions often display strongly disparate results. The origin of this variation is thought to arise from the presence of dispersed metal inclusions in silicate run-products2. This effect has introduced some uncertainty in the accuracy of past measurements, of both metal solubility and mineral-silicate melt partitioning (see Silicate and Oxide Control on HSE Fractionation). Hence, before reviewing the partitioning results for the various HSEs, it is instructive to briefly describe the inclusion problem, and efforts to overcome it in experiments.
Metal inclusions in experiments and the analysis of contaminated phases
The presence of a dispersed metallic phase contaminant in quenched silicate melts from solubility experiments has been recognized since the earliest efforts to determine values of DMet/Sil for the HSE (Kimura et al. 1974). An array of different particle sizes have been implied, ranging from ~ 0.05 μm to ~ 5 μm, also with varied spatial distributions (compare Ertel et al. 1999; Cottrell and Walker 2006; Fortenfant et al. 2006; Mann et al. 2012). Owing to their small size and dispersed nature, it has been difficult to fully document the characteristics of these inclusions, even by high resolution electron microscopy. Hence, the most commonly-used indication of their presence has been poorly reproducible solubility measurements and heterogeneous time-resolved LA-ICPMS spectra (e.g., Ertel et al. 2001, 2006). Any study of solubility and partitioning where metal inclusions are suspected must therefore assess their presence as either an exsolved, but once dissolved, component of the silicate melt, or instead a discrete metal phase at the conditions of the experiment (hereafter referred to as ‘quench’ and ‘stable’ inclusions respectively). If the metal particles have the latter origin, then their contribution to the analyses of silicate run-products whose intrinsic HSE concentration is very low will increase the apparent solubility. This issue embodies much of the ambiguity over the true solubility and partitioning of HSEs at reducing conditions.
Early efforts to determine HSE solubility used bulk analytical techniques (e.g., neutron activation analysis, scintillation spectrometry), which required extra care to ensure a minimum level of metal contamination, including reversal experiments, measurements on different aliquot sizes, thorough cleaning of the exterior portion of glass shards, etc. For the cases of Pd (Borisov et al. 1994) and Au (Borisov and Palme 1996), solubility determined by these methods produced reproducible results, and systematics with fO2 consistent with thermodynamic expectations. Other metals, such as Ir, Os, and Re, produced more scattered results, which is now suspected to be a result of metal contamination (Ertel et al. 2001; Fonseca et al. 2011). The arrival of LA-ICPMS as a readily available tool for trace element analysis (e.g., Jackson et al. 1992) provided an alternative, in situ, approach to solubility measurements. The time-resolved spectra produced during sample ablation revealed metal inclusions manifested as high count-rate ‘peaks’ separated by low count-rate ‘troughs’, the latter thought to more closely represent the intrinsic signal from metal dissolved in the silicate (Fig. 4). Under this pretext, several studies have filtered their analytical results by calculating concentrations from only the “trough” portion of the spectra, (e.g., Ertel et al. 2001, 2006; Laurenz et al. 2013), yielding reasonably systematic relations between solubility and fO2 at conditions at least as reducing as the FMQ buffer. How closely the low count-rate portions of spectra represent truly inclusion-free silicate however, will depend upon the nature of both the sample (inclusion size, spatial distribution) and the analytical conditions (spot-size, wash-out time of the ablation cell). Most importantly, solubilities determined using this method still rest upon assigning all of the heterogeneity to inclusions having a stable origin, which does not account for the possibly of some exsolved metal. The difficulty associated with analysis of inclusion-contaminated silicate run-products has driven attempts to suppress the formation of the metal particles (Borisov and Palme 1995; Ertel et al. 1999, 2001; Borisov and Walker 2000; Ertel et al. 2001; Brenan and McDonough 2009; Bennett and Brenan 2013; Bennett et al. 2014; Médard et al. 2015). Due to the success of these efforts, the database of inclusion-free solubility measurements is now sufficient to assess the oxidation state of most HSEs dissolved in silicate melt at reducing conditions, and derive accurate values of metal–silicate partitioning. The experimental and analytical approaches used to generate this database are outlined in the section Experimental methods to measure HSE solubility and metal/silicate partitioning.
Prior to describing the methods to measure partitioning, and their results, a brief review is provided of some of the proposed mechanisms for inclusion formation.
Possible mechanisms of metal inclusion formation
A diverse range of mechanisms have been proposed for the formation of dispersed metal inclusions in glasses synthesized at high temperature and low fO2. In the following discussion two categories of metal inclusions are considered: 1) ‘quench’ inclusions that form by exsolution from the silicate melt during the cooling step that accompanies the termination of an experiment and 2) ‘stable’ inclusions that are present as a discrete metal phase at the P and T of the experiment.
Quench metal inclusions
HSE solubility experiments are terminated by rapid cooling of the sample, so if the solubility of the HSE is prograde, then this step may cause oversaturation in HSE metal. In some instances, the silicate melt does not quench to a glass, so HSE metal may also form by local saturation due to a build-up in concentration in the residual melt by the crystallization of phases that exclude the HSE. The increase in solubility with temperature documented for nearly all of the HSE (See: Summary of experimental data) suggests that if quench rates are sufficiently slow, then HSE metal grains will begin to nucleate and grow. Cottrell and Walker (2006) outline several expectations for inclusions formed in this manner: an increase in diameter with decreased cooling rate, spatial variability in the distribution of inclusions due to differences in cooling rate across the sample, and a compositional difference between inclusions and the bulk HSE ± Fe source metal. Cottrell and Walker (2006) document all of these features in experiments to measure Pt solubility done at 2.2–2.3 GPa and 1940–2500 ºC, providing a strong argument that the inclusions observed in their silicate run-products were formed by exsolution when the sample was quenched. These authors also measured comparable Pt concentrations in portions of the sample both with and without visible contamination by metal inclusions; consistent with a spatial variability in the quench rate within the sample.
In the metal–silicate partitioning study of Mann et al. (2012), the silicate melt phase did not quench to a glass, but instead to a fine intergrowth of quench crystals. This is a common result for melt compositions which are poor in network-forming cations, as in this case. Metal particles were found to be concentrated along the boundaries of skeletal olivine crystals that formed during quenching. These particles were interpreted to form by HSE buildup during quench crystallization, and included as part of the original high P–T melt composition, on the basis of uniform element concentrations measured across the sample and smooth correlations between DMet/Sil and fO2. It is noteworthy that even if metal-inclusions in the Mann et al. (2012) study did not form exclusively upon quench, and values of DMet/Sil were thus underestimated, Re, Ir and Ru are still found to be too siderophile to account for their PUM abundance.
Although there is good evidence for the formation of a metal phase during quench in both these previous studies, it remains possible that experiments also contain stable inclusions. However, at the very high experimental temperatures, and associated high solubilities, the relative contribution of stable inclusions to the measured concentrations is likely to be small.
Stable metal inclusions
Unlike inclusions that form when the sample is quenched, stable metal inclusions are expected to display a relatively uniform spatial distribution and possess the same composition as that measured for the bulk metal source. Although cooling rate should not have any effect on the nominal size of stable inclusions, it is foreseeable that they may act as sites for heterogeneous nucleation of metal precipitated by over-saturation of the melt during quench. The small size of stable inclusions can render them undetectable by scanning electron microscopy, preventing their distribution and composition from being accurately determined and their origin confirmed. Conclusive evidence that metal inclusions can form as a stable phase in experiments has now been provided by Yokoyama et al. (2009) and Médard et al. (2015). Yokoyama et al. (2009) measured metal–silicate partitioning of Os using a natural meteorite starting material. The Os isotopic compositions of inclusion-contaminated run-product glasses define a mixing array between the meteorite starting material, and inclusion-free glass. This implies that inclusions in these experiments possess the same isotopic composition as the meteorite starting material. The measured array in Os concentration and isotope composition therefore reflects different glass to inclusion ratios in the individual aliquots. By contrast, inclusions formed upon quench should resemble the isotopic composition of the silicate melt and not define mixing lines that extend to the meteoritic starting material. Médard et al. (2015) performed solubility experiments in a centrifuge piston-cylinder, and found that the Pt content of melts subject to high acceleration was lowest in the top-most portion of the sample, suggesting partial segregation of stable metal particles to the base of the sample. Combined, these results confirm the assertions of earlier studies that suggest a stable origin for inclusions on the basis of sample heterogeneity (Borisov and Palme 1997; Ertel et al. 1999, 2006).
Perhaps the most obvious means to introduce metal particles into silicate melt is by erosion of the metal source. This mechanism was advocated by Yokoyama et al. (2009) based on the similarity in the isotopic composition of the metal contaminant with the metal phase added to experiments. In contrast, Ginther (1971) proposed that contamination of glass by platinum inclusions occurred via oxidation of the Pt container, caused by the dissociation and evaporation of alkali or alkali-earth oxide complexes in the melt. This mechanism was based on the observation that inclusions were restricted to surface layers of the unstirred melt and independent of the fO2 of the atmosphere within which the experiment was performed. Borisov and Palme (1997) noted that this mechanism would be most effective under reducing conditions, where alkali metal evaporation is enhanced, and may potentially explain the formation of Pt and Ir inclusions in their low fO2 experiments. Although this may be a viable process in open-system experiments performed using gas-mixing at ambient pressure, it cannot explain the formation of metal inclusions in experiments done at high confining pressure and is unlikely to afflict experiments performed in vacuum-sealed silica tubes.
Metallic Pt inclusions have been well documented during the synthesis of large volumes (> 0.5 L) of phosphate laser glass. Campbell et al. (1989) summarized previous studies of laser glass synthesized in Pt containers and concluded that thermal gradients were responsible for the formation of metal inclusions. The experimental design used in these studies involved induction heating of the sample in a Pt crucible. Once the sample was molten, more feedstock was added to increase the level in the crucible. Campbell et al. (1989) identify relatively large thermal gradients in this arrangement, and owing to the increase in Pt solubility with temperature, such gradients will force precipitation of metal inclusions. Most petrologic experiments done at 0.1 MPa however, are performed using small sample sizes (< 2 mL), in the absence of significant thermal gradients, suggesting that this mechanism does not account for the formation of inclusions in most of the studies discussed as part of the present work.
The formation of metal particles in experiments containing certain alloy-forming impurities is a mechanism proposed by Borisov and Palme (1997) that may potentially apply to both ambient- and high-pressure studies. In this scenario, dissolved oxide components in the melt react with the HSE source material to produce oxygen and an HSE alloy as the product. For example the reaction proposed by Borisov and Palme (1997) for Pd is:(41)
Decreasing fO2 therefore favours the formation of stable alloy grains. Borisov and Palme (1997) suggest that the presence of impurities that react more readily with HSEs than Si, such as As, Sb, Bi, Ge, Sn, and Pb, may increase the likelihood of alloy formation. In open-system gas mixing experiments, the volatile nature of potential alloying elements should lead to progressive loss at high T, resulting in metal inclusions free of these impurities by the end of an experiment (Borisov and Palme 1997). Borisov and Walker (2000) made use of these concepts and removed volatile contaminants from starting materials by fusion at controlled fO2 conditions. This resulted in inclusion-free run-product glasses produced at a fO2 lower than past work. Although it may have been the removal of contaminants from reagents that prevented inclusions from forming, pre-reduction of the sample may also have played a role (see below).
Fortenfant et al. (2006) found that erosion of the sample crucible or stirring spindle was an unlikely source of the Os inclusions in their experiments, after identifying components in an inclusion that were not present in the labware used to perform the experiment. On this basis, the authors instead suggested that inclusions originate as a result of exsolution from silicate melt, driven by changes in sample fO2. Bennett et al. (2014) developed this idea and proposed a mechanism for stable metal inclusion formation based on the time-evolution of fO2 during the initial stages of an experiment. Most metal solubility experiments use starting materials that are fully or partially oxidized (i.e., Fe present as Fe2+, Fe3+ and sample capsules loaded in air), but then subject to a reducing atmosphere or encapsulated in a reducing material (e.g., graphite). Once the sample is heated, reaction between the sample and the reductant occurs, and the initially high fO2, imposed by the starting materials, begins to fall. For the case of a graphite-encapsulated experiment initially undersaturated in a fluid phase, the redox reaction is:(42)
This reaction will proceed until an equilibrium CO32− concentration is obtained.3 With reference to Equation (25), the dissolution of HSEs in silicate melt requires oxidation of the metal phase, hence reduction of oxidized starting materials by Reaction (42) causes an accompanying decrease in metal solubility. If the kinetics of HSE dissolution are suitably rapid, the silicate melt may be endowed with elevated metal concentrations initially, but as fO2 drops, saturation occurs and HSE grains may precipitate. This process is portrayed schematically in Figure 5. Médard et al. (2015) note that in all past experiments in which stable metal inclusions are observed, the equilibrium fO2 of the experiment is lower than that of the starting materials, consistent with the operation of the proposed reduction mechanism. Borisov and Walker (2000) also reported that experiments in which starting glasses were synthesized at the same conditions as the subsequent solubility determination were less susceptible to contamination by Os metal inclusions—procedures that would have suppressed an initially oversaturated state.
Experimental methods to measure HSE solubility and metal–silicate partitioning
A simple method for measuring HSE solubility is by suspending a silicate melt bead within a wire loop, or encapsulated in foil, made of the pure metal, then equilibrating the sample in a gas-mixing furnace at high temperature. Samples are rapidly quenched, then analysed for the HSE by either bulk (e.g., Borisov et al. 1994; Borisov and Palme 1995, 1997) or in situ methods (Laurenz et al. 2013). Variations on this approach involve the use of alloys, whose composition either allow higher equilibration temperatures without melting (e.g., Pd–Au; Borisov and Palme 1996) or involve a combination of metals, one of which is wire-forming (e.g., Ni) with those that are not (e.g., Os; Borisov and Palme 1998; Borisov and Walker 2000). Borisov and Walker (2000) modified this technique to suppress the formation of stable Os metal nuggets by using Ni–Os alloy in the wire loop, and pre-saturating the silicate melt in Ni prior to the solubility experiment. This pre-saturation step was considered to suppress chemical erosion of the Ni–Os loop, and subsequent entrainment of metal particles in the melt. Note that for experiments employing alloy source material, HSE concentrations measured in the silicate melt must be corrected to solubilities corresponding to equilibrium with the pure HSE phase .
The mechanically assisted equilibration (MAE) method allows for the approach to metal–silicate melt equilibrium to be monitored over the course of an experiment, while the sample is subject to continuous stirring (Dingwell et al. 1994). In this technique, a relatively large mass of silicate melt is contained in a metal crucible within the hot zone of a gas-mixing furnace. The melt is subject to forced convection by a rotating metal spindle suspended axially, with material sampled from the crucible sequentially so as to obtain a solubility vs. time history. The purpose of the rotating spindle is to promote metal–silicate equilibration involving advective as well as diffusive exchange with the metal source. An extensive review of this technique as applied to HSE solubility measurements is given by Ertel et al. (2008). Despite this advance, however, it has been difficult to obtain reproducible solubility measurements at fO2 more reducing than FMQ.
Brenan and McDonough (2009) and later Bennett and Brenan (2013) were able to suppress the formation of stable Ir, Os, and Re inclusions in high-pressure (2 GPa) experiments by adding these metals encapsulated in a pre-melted gold bead. This approach yields a unique experimental geometry that changes the relationship between fO2 evolution and HSE in-diffusion during the early stages of an experiment. Molten Au strongly wets Re, Os, and Ir at high T to form a rind that physically separates the bulk HSE source in the experiments from the silicate melt (Fig. 6). This rind slows the diffusive transfer of the encapsulated metal into the silicate melt, thus allowing the melt to undergo reduction prior to the onset of metal dissolution. This technique has proved successful in suppressing metal inclusion formation under conditions as reducing as IW – 1.2 (Brenan and McDonough 2009). One tenet of the Au rind method is that the HSE of interest must be sparingly soluble in molten Au, so as to limit the HSE flux to the silicate melt. It is therefore unsuitable for investigating elements such as Pt and Pd, which display complete miscibility with Au at high temperature.
Bennett et al. (2014) performed experiments to measure Pt solubility in molten silicate by adding elemental Si to starting materials, which serves to strongly suppress any initial oxidation of the melt, and thereby inhibit the formation of inclusions by initial oversaturation. The veracity of this approach was tested in experiments done both with and without added Si, with the time-resolved analysis of run-products as a guide to inclusion abundance. Control experiments, which had no silicon added, display significant heterogeneity of the time-resolved spectra for Pt, in contrast to the uniform (and relatively low intensity) signal for Pt in experiments done with 0.75–2 wt% added Si. Although this technique was successful in producing uncontaminated samples as reduced as IW – 1.6 at temperatures ≥ 1900 ºC, inclusions were identified in experiments at 1800 ºC and ~ IW, suggesting this method may be less effective at lower temperatures.
The small size of stable inclusions and the low solubility of the HSE in general would seem to preclude the segregation of metal grains from silicate melt without the assistance of stirring; an effect not easily achieved in high pressure experiments. Subjecting the molten sample to high acceleration however, increases the settling velocity of dense particles from the silicate melt. With this in mind, Médard et al. (2015) used a piston-cylinder mounted in a centrifuge to perform Pt solubility experiments at accelerations of up to ~ 1500 g0. Run products from synthetic Fe-free melts achieved partial cleansing by this method. Experiments done with a natural FeO-bearing melt yielded similar solubility for static and high-g0 experiments, which was attributed to the role of dissolved FeO as an oxygen donor to facilitate.
In addition to experiments which have measured the solubility of pure metals, or binary metal alloys, then calculating partition coefficients from Equation (36), other work has focused on more direct determinations using Fe-rich alloy compositions. As gold is the most soluble of the HSE in molten silicate, it is possible to measure Fe metal–silicate melt partitioning for relatively dilute Fe–Au alloys (i.e., < 4 wt% Au), for which results have been reported by Brenan and McDonough (2009) and Danielson et al. (2005). A comparison of partitioning calculated from the solubility of pure Au with this more direct method has yielded very good agreement (see Effect of oxygen fugacity). Other experiments have also involved Fe-bearing multicomponent alloys, but with the HSE more concentrated (Mann et al. 2012). In that case, the challenge is access to an accurate solution model for extrapolating apparent partition coefficients to infinite dilution.
Summary of experimental data
The existing database of HSE solubility and partitioning data contains significant complexity, arising from the issues surrounding metal inclusions discussed above. To simplify the following overview of HSE behavior as a function of P, T, X, and fO2, only those data which are demonstrably free from contamination or have been shown to agree well with the data from such experiments (e.g., data from filtered LA-ICP-MS spectra) are presented. Unless otherwise stated, the oxidation states quoted below have been determined by linear regression of solubility vs. fO2 plots using the following relationship:(43)
Effect of oxygen fugacity–
Several studies have determined the solubility of Re as a function of fO2 and data now exists at 0.1 MPa to 18 GPa and 1400–2500 ºC (Fig. 7). At 0.1 MPa and above ~ IW + 1, Re is thought to be dissolved as a mixture of 4+ and 6+ species, with 6+ being dominant across most of the fO2 range (Ertel et al. 2001). This result is consistent with crystal–melt partitioning experiments that also indicate 4+ and 6+ species for Re above ~ IW (Mallmann and Neill 2007; see also Silicate and Oxide Control on HSE Fractionation). The lowest fO2 time-series experiment of (Ertel et al. 2001), however, does suggest a minor contribution from a more reduced species. In isolation, high P–T data acquired between IW + 2.5 and IW − 1.5 suggest Re is dissolved in silicate melt as a 2+ species (Mann et al. 2012; Bennett and Brenan 2013). Correction of the data at 1400 ºC from Ertel et al. (2001) to 2000 ºC for comparison with the data of Bennett and Brenan (2013), however, reveals moderately good agreement between these datasets above ~ IW + 1 but evidence for a more reduced species in the higher T dataset at lower fO2 (Bennett and Brenan 2013). At present, there is insufficient data to thoroughly assess at what fO2 Re2+ becomes the dominant dissolved species, or to what extent this transition may depend upon P or T.
Experiments at 0.1 MPa and 1350–1400 ºC using Fe-free melts suggest Os is dissolved primarily as a 3+ species between ~ IW + 1 and IW + 4, although the presence of Os4+ cannot be excluded on the basis of these data (Borisov and Walker 2000; Fortenfant et al. 2006). Data from 0.1 MPa experiments performed at more reducing conditions display evidence for contamination by metal inclusions, preventing straightforward measurement of Os concentrations. Filtering of time-resolved LA-ICP-MS signals was found to be impossible due to the very low concentration of Os dissolved in the melt and the high Os background associated with available sulphide standards (Fortenfant et al. 2006). Brenan and McDonough (2009) however, were able to measure Os solubilities by LA-ICPMS in uncontaminated Fe-bearing experiments performed at 2 GPa 2000 ºC and as reduced as IW −1.6. These authors suggest solution as mixed 1+ and 2+ species based on the slope of 0.38 defined by their data. Although neither of these oxidation states is suggested by the 0.1 MPa data, it is worth noting that a mixture of 1+ and 3+ species also yields an adequate fit to the high T data. Importantly, the high T, low fO2 experiments suggest there must be some contribution from a species more reduced that Os2+ (expected slope of 0.5).
O’Neill et al. (1995) determined the solubility of Ir in CaO–MgO–Al2O3–SiO2 (CMAS) melt at 1400 ºC between IW − 1.5 and IW + 10. At conditions more oxidizing than ~ IW + 4, the change in Ir solubility is consistent with solution as a 2+ species (slope of ~ 0.5). At more reducing conditions however, O’Neill et al. (1995) observed no change in solubility with fO2 and ascribe this to either contamination by metal inclusions or solution as either Ir0 or Ir-carbonyl species. More recent solubility measurements at 1500 ºC on a similar composition over a comparable fO2 interval, reported by Fonseca et al. (2011), yielded results consistent with Ir3+ (slope of 0.75). A possible reason for the discrepancy between the two studies is that the metal contamination suggested in the experiments of O’Neill et al. (1995) are largely avoided in the work of Fonseca et al. (2011), as that study employed LA-ICPMS for sample analysis. Borisov and Palme (1995) determined the solubility of Ir-poor alloys (Ir10Pt90) over a similar range of fO2 and melt composition at 1300 ºC and 1480 ºC. Their data are consistent with solution as a 1+ species between ~ IW − 1 and IW + 8 and mixed 2+ and 3+ species at more oxidizing conditions (slope of 0.68). Results from 2 GPa experiments at 2000 ºC also suggest Ir dissolves predominantly as a 1+ species between IW + 0.5 and IW + 2.7 in basaltic melt. Mann et al. (2012) determined Ir partitioning at high P–T conditions (3.5–18 GPa, 2150–2500 ºC) and their data suggest Ir2+ as the dissolved species between ~ IW − 1.5 and IW + 0.5, although the authors acknowledge that this trend is not well defined. Spinel–melt partition coefficients measured at ~ IW + 1 to + 6 are also consistent with Ir2+ in the crystal lattice (Brenan et al. 2012). It is therefore likely that Ir2+ persists as a subordinate species at these more reducing conditions.
Borisov and Nachtweyh (1998) investigated Ru solubility at 0.1 MPa and 1400 ºC in anorthite-diopside melts between ~ IW + 6 and IW + 10. Their results define a slope of 0.73, corresponding to a 3+ oxidation state (Fig. 7). These results are consistent with the crystal-melt partitioning of Ru in olivine and spinel, that also suggest Ru3+ is present over much of the terrestrial fO2 range (Brenan et al. 2003, 2012). Laurenz et al. (2013) measured Ru solubility in picrite melts at 1300 ºC, 0.1 MPa and IW + 3.5 to IW + 5.5, obtaining results consistent with Ru dissolved as a 4+ species (Fig. 7). These authors suggest the difference in their data is due to the use of Fe-bearing melt compositions, that stabilize more oxidized species through redox exchange reactions analogous to those observed for Pd (Laurenz et al. 2010):(44)
In experiments done using Fe-bearing melt compositions at 6–18 GPa, 2150–2300 ºC and IW −1.5 to IW + 0.5 measured solubilities suggest Ru2+ is the dominant species (Mann et al. 2012). This is consistent with evidence from chromite-melt partitioning experiments, done at lower P-T conditions, that Ru2+ becomes dominant at conditions more reducing than ~ IW + 2.5 (Brenan et al. 2012).
Ertel et al. (1999) determined the solubility of Rh in experiments performed at 0.1 MPa and 1300 ºC in melts with a composition close to the anorthite-diopside eutectic (Fig. 7). Between ~ IW + 6 and IW + 11, their data suggest Rh is dissolved primarily in the 2+ oxidation state, with a minor contribution from either a 3+ or 4+ species. Ertel et al. (1999) consider Rh3+ more plausible however, as the 3+ solid oxide is the stable phase at high temperature in air (Nell and O’Neill 1997). At more reducing conditions, measurements of Rh solubility at 0.1 MPa display evidence for contamination by stable metal inclusions. Regression of high P–T (6–18 GPa, 2150–2300 ºC) experiments at IW − 1.5 to IW + 0.5 yields a slope of 0.36, suggesting a mixture of Rh2+ and a more reduced species (Mann et al. 2012). Experiments to determine the olivine-melt (0.1 MPa, ~ 1330 ºC) and chromite-melt (0.1 MPa–2 GPa, 1400–1900 ºC) partitioning of Rh (see Spinel–melt partitioning of HSEs) are also consistent with the prevalence of a 2+ species between ~ IW + 5 and IW + 7 (Brenan et al. 2003, 2012).
At relatively oxidizing conditions (above ~ IW + 5), isothermal suites of experiments at 0.1 MPa define slopes of ~ 0.5 between 1300 and 1560 ºC, suggesting Pt is dissolved as a 2+ species (Borisov and Palme 1997; Ertel et al. 1999). Spectroscopic determination of Pt oxidation state in CAS glasses synthesized at 1630 ºC in air indicate the presence of 4+ species at highly oxidized conditions (Farges et al. 1999).
At more reducing conditions (~ IW −0.8 to IW + 3.4), in experiments which were demonstrably free of contamination by metal inclusions, Bennett et al. (2014) observed a slight increase in Pt solubility with decreasing fO2 in basaltic glasses at 2 GPa and 2000 ºC. They interpret these results as owing to the presence of both neutral Pt and an unidentified Pt cationic complex. The solution of Pt-carbonyl species at low fO2 is discounted however, as no correlation is observed between Pt solubility and the carbon content of the melt (Bennett et al. 2014). A similar increase in solubility with decreasing fO2 was found by Médard et al. (2015) at more reducing conditions (~ IW − 2.5 to IW − 0.5) in experiments at 1.2 GPa and 1900 ºC. At lower T (1400 ºC and 1600 ºC) but similar fO2, however, Médard et al. (2015) measure constant Pt solubility with changing fO2. They interpret data with approximately constant solubility as suggesting Pt0 dissolved in the melt. Results from both Médard et al. (2015) and Bennett et al. (2014), that define a trend of increasing solubility as conditions become more reducing, are more consistent with the presence of either anionic platinum or the formation of complexes such as PtSix.
Although solubilities are broadly consistent with past work at similar conditions, Mann et al. (2012) observe a slight decrease in Pt solubility with decreasing fO2 between IW + 0.5 and IW −1.5 at conditions of 3.5–18 GPa and 2150–2500 ºC. Isothermal, isobaric sets of experiments from that study define an average slope of 0.29, consistent with Pt1+ dissolved in the melt. It is unclear why these experiments yield a different result to the studies of Bennett et al. (2014) and Médard et al. (2015), as all were conducted using Fe-bearing melt compositions, and pressure appears to have little effect on Pt solubility (see Temperature and pressure). It is also unlikely that the higher temperatures employed in the Mann et al. (2012) study are responsible, as measurements of Au and Pt solubility both suggest that increased T favours the reduced species (Borisov and Palme 1996; Médard et al. 2015). Cottrell and Walker (2006) also investigated Pt partitioning over a similar range of P–T conditions to Bennett et al. (2014) and Médard et al. (2015), but measured Pt solubilities that are systematically higher. Between IW − 0.75 and IW − 5.32, these authors observe no systematic dependence of solubility on fO2. These experiments may represent a continued increase in solubility with decreasing fO2, as suggested by extrapolation of the trend defined by 2000 ºC data from Bennett et al. (2014).
In summary, Pt is dissolved in silicate melt predominantly as 2+ species above ~ IW + 5, with evidence for 4+ species at the most oxidizing conditions. At more reducing conditions the data is consistent with solution as Pt0, with either anionic species or non-oxide complexes becoming significant at the lowest oxygen fugacities investigated.
Borisov et al. (1994) measured Pd solubility in experiments at 0.1 MPa and 1350 ºC over a wide range of fO2 (~ IW to IW + 10) in anorthite-diopside melts (Fig. 7). These authors used a 3-species model to fit the data, comprising Pd2+, Pd1+ and Pd0. The data were found to be consistent with Pd1+ and Pd0 as the dominant species over the fO2 range investigated, with Pd2+ contributing most significantly to the dissolved Pd contents in experiments more oxidized than ~ IW + 7. Further experiments at 0.1 MPa using anorthite-diopside melts extended the database of Pd solubility measurements to lower fO2 (~ IW − 1) and temperatures of 1300, 1400, and 1480 ºC (Borisov and Palme 1996). These data are consistent with the oxidation states for Pd indicated by the earlier study of Borisov et al. (1994). Experimentally-determined olivine-melt partition coefficients at ~ IW + 7.8 and ~ IW + 3.0 (0.1 MPa, 1335 ºC) also indicate a change from Pd2+ to Pd1+ as conditions become more reducing, in agreement with the solubility measurements (Brenan et al. 2003; Origin of the variation in partitioning). In experiments employing Fe-bearing melts however, Laurenz et al. (2010) observe lower solubilities below ~ IW + 3.5 than either Borisov et al. (1994) or Borisov and Palme (1996), and a dependence of solubility on fO2 that suggests Pd1+ not Pd0 is the predominant dissolved species. Between ~ IW + 3.5 and + 5.5 the data of Laurenz et al. (2010) again suggest Pd is dissolved as a more oxidized species than Borisov et al. 1994 (Pd2+ vs. Pd1+), and report higher solubilities for this fO2 range accordingly. These authors attribute the higher oxidation state of Pd indicated by their data between ~ IW + 3.5 and + 5.5 to redox exchange reactions with Fe, analogous to those described above for Ru. However, it is important to note that it can be difficult to assess speciation in Fe-bearing experiments which cover the high fO2 range in which both Fe2+ and Fe3+ are present, as the melt structural role of Fe3+ is different than Fe2+ (Farges et al. 2004). Hence, changes in solubility may also derive from changes in the activity coefficient for a single HSE species in response to melt structure, instead of a change in speciation (see Role of silicate melt composition on melt structure effects).
Figure 7 displays the high pressure data of Righter et al. (2008) and Mann et al. (2012) collected at 1.5 GPa and 6–18 GPa respectively, corrected to unit activity of Pd. For data from the Mann et al. (2012) study, activity coefficients for Pd in the metal were taken as the values calculated in their activity model. Correction of the data from Righter et al. (2008) was made using the Margules parameters summarized by Borisov and Palme (2000) for the Pd-Fe system and ignoring the presence of Sb (< 7 wt%) in the alloy. Although only a limited number of isothermal high P data are available, those of Mann et al. (2012) (2150–2200 ºC) appear to be broadly consistent with the speciation model employed by Borisov et al. (1994). The lower T data of Righter et al. (2008) (1800 ºC) cover an insufficient range in fO2 for speciation to be reliably determined from only these datapoints. However, the solubilities recorded by their experiments are similar to those found by Mann et al. (2012) at similar fO2 but higher T. For temperatures > 1800 ºC, the experiments of Righter et al. (2008) suggest much greater Pd solubilities than measured by Mann et al. (2012). Although the reason for this discrepancy is not entirely clear, it is possible that the presence of Sb in the alloys used by Righter et al. (2008) affects the partitioning behavior of Pd, and subsequently, the solubilities at Pd saturation we calculate from their data.
At 0.1 MPa and 1300–1480 ºC, experiments performed between ~ IW + 10 and IW using anorthite–diopside melt suggest Au is dissolved as 1+ species (average slope of ~ 0.23; Borisov and Palme 1996). Results also showed that at fO2 below ~ IW, however, the positive relationship between fO2 and solubility expected for the solution of metal-oxide species is reversed and solubility instead increases as conditions become more reducing. Borisov and Palme (1996) proposed that dissolution by way of an oxygen-producing reaction, such as the formation of silicide or carbide species, was most likely responsible for the observed increase in solubility at reducing conditions. Au solubility has also been determined in basaltic melts at 2 GPa and 2000 ºC (Brenan and McDonough 2009; Bennett and Brenan 2013). These studies reveal a weak negative dependence of solubility on fO2 between ~ IW − 1.2 and IW + 2.6, suggesting Au is dissolved in the melt as Au0 with the possibility of an additional contribution from either a silicide or other cationic species. The formation of carbide or carbonyl complexes in the studies of Brenan and McDonough (2009) and Bennett and Brenan (2013) is considered unlikely, as no difference in solubility is observed between experiments performed in graphite vs. metal-alloy capsules. From the regression of partitioning experiments done at 3–23 GPa and 1750–2500 ºC, Danielson et al. (2005) found DMet/Sil decreases as conditions become more reducing, consistent with the results of solubility experiments. The fact that Au1+ is not suggested by the high P–T data is also consistent with the experiments of Borisov and Palme (1996), which indicate the transition to reduced species occurs at a higher relative fO2 at elevated temperatures. Results of gold solubility measurements in hydrous, S- and Cl-bearing compositions at low-P and -T are discussed in Concluding Remarks.
Role of silicate melt composition
Several studies have sought to determine the effect of silicate melt composition on HSE solubility. Borisov and Danyushevsky (2011) conducted a systematic investigation of Pt, Rh, and Pd solubility in air at 0.1 MPa and 1450–1550 ºC. Experiments performed in the CMAS system, with variable quantities of SiO2 added to an anorthite–diopside eutectic composition, reveal markedly different behavior for Pd compared with Pt or Rh. Pd solubility increases by ~ 55 ppm with increasing silica content between ~ 50 and 55 wt% SiO2. The addition of further silica to the system then causes a gradual decrease in solubility by ~ 75 ppm between ~ 55 and 70 wt% SiO2. Pt and Rh, however, display a monotonic decline in solubility as the SiO2 content increases from ~ 50 to 70 wt% SiO2. The change in both Pt and Rh solubility over this interval is linear and more pronounced for Rh than Pt. Wheeler et al. (2011) observed a decrease in the concentration of Pd in the silicate portion of their metal–silicate partitioning experiments with increasing bulk Pd contents. They rationalized this result, and its relationship to earlier studies, by positing the existence of a curved silicate saturation surface; which is intersected by tie-lines between co-existing liquids at progressively lower Pd concentrations as the metal alloy becomes more Pd-rich. Analogous behavior, in which a curved silicate saturation surface exists in the Pd–Si–silicate melt system, may explain the variation in Pd concentration observed by Borisov and Danyushevsky (2011) in the CMAS system. Borisov and Danyushevsky (2011) also performed experiments for Pt and Rh in the CA ± S system, and again observed a decrease in solubility for these elements with increasing silica content. Unlike the CMAS system, however, these experiments define a non-linear relationship between solubility and SiO2 content. After correcting their solubility data for CMAS melts to 1550 ºC for comparison with results from the CA ± S system, Borisov and Danyushevsky (2011) proposed the following relationships for Pt and Rh solubility as a function of melt composition:(45) (46)
The family of solubility vs. SiO2 curves produced by Equations (45) and (46) for different (CaO + MgO)/Al2O3 ratios are portrayed in Figure 8, with the accompanying experimental data. These results are qualitatively consistent with those of Dable et al. (2001), also obtained in the CAS system (0.1 MPa, 1227 ºC), who observe lower Pt solubility in melts with 70 wt% SiO2 than those with 40 wt% SiO2 for experiments done in air. In the experiments of Dable et al. (2001), however, this difference becomes less pronounced at low fO2, suggesting the compositional effect may be smaller for reduced Pt species in the melt. A negligible compositional dependence for Pt solubility at low fO2 is also supported by the agreement between high pressure experiments using basaltic to komatiitic melts (Mann et al. 2012; Bennett et al. 2014; Médard 2015). Nakamura and Sano (1997) conducted Pt solubility experiments at 0.1 MPa and 1600 ºC in air, using a variety of binary oxide melt compositions (BaO–Al2O3, BaO–SiO2, CaO–Al2O3, CaO–SiO2, Na2O–SiO2). These authors cast their solubility measurements as a function of theoretical optical basicity, a measure of the electron donation capacity of the melt components. Results show a linear increase in the logarithmic Pt concentration with optical basicity, where the slope of this trend is identical for each of the studied oxide pairs. The absolute Pt solubility however, is ~ 100 times greater for melts containing BaO as the basic oxide component. The results of Nakamura and Sano (1997) indicate a similar relationship between melt composition and solubility to those of Borisov and Palme (1997) and Borisov and Danyushevsky (2011), but also suggest that the identity of the acidic melt component (i.e., Al2O3 or SiO2) is unimportant relative to that of the basic component. Bond valence modeling of Pt in CAS melts suggests Pt is bonded to non-bridging oxygens surrounded by Ca second neighbors (Farges et al. 1999). This is also consistent with the observation that Pt solubility is enhanced in depolymerized melt compositions and tracks positively with CaO content. The study of Farges et al. (1999), however, also identifies Pt4+ not Pt2+ as the dissolved species in melts synthesized at 1630 ºC in air, contrary to that suggested by the dependence of solubility on fO2, albeit at lower T. Their model may, therefore, not apply directly to Pt in melts at low fO2. Most geologically important melt compositions contain iron, but most 0.1 MPa studies of HSE solubility have been performed using Fe-free melts. More recently, several studies have highlighted the role of Fe in both the solubility and speciation of HSEs in silicate melts (Laurenz et al. 2010, 2013). When compared with the solubilities of Pd and Ru measured in Fe-free melts, these authors observed the stabilization of more oxidized dissolved species at a given relative fO2. They suggest this difference results from redox exchange equilibria with Fe as described, for example, by Equation (44). Whether solubility in Fe-bearing melts is higher or lower than seen for Fe-free melts will therefore depend upon the fO2 conditions being investigated. Turchiaro (2013) investigated Pt and Rh solubility in basalt-rhyolite mixtures at 0.1 MPa, 1400 ºC and ~ IW + 6.8. The solubility of both elements was seen to decrease with increasing proportions of the rhyolite component. When plotted as a function of non-bridging oxygens over tetrahedrally coordinated cations (NBO/T), a measure of melt polymerization, the variation in solubility measured by Turchiaro (2013) is comparable to that measured by Borisov and Danyushevsky (2011) in CMAS melts. After correction of their data to account for differences in T and fO2 however, the absolute solubilities measured by Turchiaro (2013) are systematically higher than those of Borisov and Danyushevsky (2011) (Fig. 9). This is consistent with the idea that Fe may enhance HSE solubility through exchange equilibria of the type suggested by Laurenz et al. (2010). It should also be noted however, that the experiments of Turchiaro (2013) used natural starting materials containing several weight percent of alkali elements (Na2O, K2O) and TiO2 that may also modify HSE solubility (Borisov et al. 2004, 2006).
Borisov et al. (2006) investigated the effect of sodium content on the solubility of Pd by adding various quantities of Na2O to melts with an An–Di eutectic composition. In experiments done at 0.1 MPa, 1300 ºC and in either air or a CO2 atmosphere, Pd solubility was seen to decrease by 20–30% with increasing sodium content, up to ~ 4 wt% Na2O. Further addition of Na2O however, elicits no change in Pd solubility up to ~ 11 wt% Na2O, the most sodium rich composition investigated. The inverse behavior is observed for the addition of titanium oxide to CMAS melts, where little or no increase in Pd solubility is observed up to ~ 4 wt% TiO2, after which the log Pd solubility increases in a linear fashion up to ~ 25 wt% TiO2 (Borisov et al. 2004). A similar increase in solubility with TiO2 content is observed for Ni and Fe (Borisov et al. 2004). Furthermore, the dependencies of both Ni and Co solubility on melt SiO2 content are similar to that observed for Pd, but not Pt or Rh (Borisov and Danyushevsky 2011). These features suggest a similar structural environment might be shared by Pd, Ni, Fe, and Co, which is distinct from certain other HSEs such as Pt and Rh.
Sulfur may also affect HSE solubility by providing an additional ligand for the formation of dissolved species. In experiments saturated in an HSE metal phase, but undersaturated with respect to an immiscible sulphide phase, solubility may be enhanced through reactions with the form (Laurenz et al. 2013):(47)
Experiments for Ru at 1300 ºC, 0.1 MPa and log fS2 of −2.3 display an order of magnitude increase in solubility compared with sulfur-free experiments at otherwise identical conditions (Laurenz et al. 2013). It is possible that the addition of other complexing anions (e.g., Cl, P) may also enhance HSE solubility through reactions analogous to Reaction (47); however, Blaine et al. (2011) observed no increase in Pt solubility in Cl-bearing experiments.
Temperature and Pressure
It has been recognized for some time that the solubility of many siderophile elements in silicate melt increases with temperature (e.g., Murthy 1991; Capobianco et al. 1993; Walker et al. 1993; Hillgren et al. 1994). Recent studies have expanded the database for HSEs significantly and confirmed the presence of a T dependence for elements which previously had little or inconclusive data (e.g., Righter et al. 2008; Brenan and McDonough 2009; Mann et al. 2012; Bennett and Brenan 2013; Bennett et al. 2014; Médard et al. 2015). Measurements of HSE solubility are most often used to estimate metal–silicate partition coefficients, which can be calculated from Equation (36). This calculation however, depends not only on the HSE concentration in the melt at the solubility limit, but also on the activity coefficient for that HSE at infinite dilution in a liquid Fe solvent, γM. Values of γM may themselves vary with temperature and pressure, meaning an observed dependence of HSE solubility on these variables may not directly translate to similar behavior during metal–silicate partitioning. Where suitable thermodynamic data is available, γM may be calculated at the appropriate P–T conditions with a binary asymmetric mixing model (Thompson 1967):(48)
where WM and WFe are Margules interaction parameters for the HSE of interest (M) and Fe respectively, that are calculated at the required P and T from individual components relating to the excess enthalpy (WH), entropy (WS) and volume (WV) of mixing:(49)
where Pº is the reference pressure at which WH, WS, and WV were determined; typically 0.1 MPa (1 bar). The T dependence of W for most Fe–HSE binaries is relatively small, and Equation (49) provides a suitable value for W. For systems such as Fe–Pd and Fe–Pt, however, which have a greater dependence on temperature, it may be required to extrapolate values of W from the reference T at which the interaction parameters were acquired (Tº), to the conditions of the experiment (Mann et al. 2012). This can be accomplished using the following relationship (Japan Society for the Promotion of Science 1988):(50)
A summary of the available thermodynamic data for Fe–HSE and HSE–HSE systems, and more detailed discussion of modeling the activity-composition relationships in multi-component HSE–Fe alloys can be found in Mann et al. (2012).
With these considerations in mind, Figure 10 displays the variation in DMet/Sil for the HSEs as a function of inverse temperature. All data show a decrease in DMet/Sil with increasing T, in the order Pt > Os ≈ Ir > Pd > Ru ≈ Au > Rh > Re. The solid lines in each panel of Figure 10 represent fits to an isobaric dataset acquired at the conditions noted in the caption. For most elements the dependence of DMet/Sil on T appears independent of P and fO2. At low T however (< 1400 ºC), some data for Pt fall systematically below the trend defined by data at higher T and pressures ranging from 0.1 MPa to 18 GPa. For the data of Ertel et al. (1999) and Fortenfant et al. (2003), this is due to the higher fO2 of their experiments. It should also be noted that the weaker dependence of DMet/Sil on T indicated by the data of Fortenfant et al. (2003) is from experiments performed at the same absolute fO2 but different relative fO2, unlike data used to define the solid line in Figure 10 which represent experiments at a similar relative fO2.
For Pt, Re, Ru, Au, and to a lesser extent Pd, results from experiments done at 0.1 MPa to 18 GPa are generally well reproduced by a single linear regression, indicating only a weak or negligible effect of pressure on the partition coefficient. There are, however, several noteworthy exceptions. For Au, data collected at ≥ 21 GPa fall below the trend defined by results at 0.1 MPa to 13 GPa, suggesting pressure may cause a decrease in DMet/Sil at these conditions. Data for Pd also suggest little effect of P on DMet/Sil between 0.1 MPa and 3.5 GPa. Results from Mann et al. (2012) done at > 6 GPa however, fall systematically below the trend defined by 0.1 MPa data. Experiments from the study of Righter et al. (2008) done at 1.5 GPa to 15 GPa also suggest lower values of DMet/Sil for Pd than expected from the 0.1 MPa trend (Fig. 10), although this may be due to the presence of Sb ± Re ± S ± P ± C in the alloy phase used in those experiments.
The effect of P on DMet/Sil for Os is difficult to assess due to the use of Os–Ni alloys as the HSE source in experiments at 0.1 MPa. Activity–composition relationships in this binary system are unknown and the measured concentrations of Os in the silicate portion of experiments performed by Borisov and Walker (2000) and Fortenfant et al. (2006) have been corrected to those expected for the pure metal by assuming ideality in the Os–Ni alloy. This leads to rather high corrected Os solubilities, accompanied by low values for DMet/Sil. The presence of a miscibility gap in the Ni–Os system (Okamoto 2009), however, indicates the assumption of ideality for these alloys is an oversimplification and calculated values of DMet/Sil should therefore be considered minimum-values. The experiments of Yokoyama et al. (2009), done at 1–2 GPa yield values of DMet/Sil that lie between those of Brenan and McDonough (2009) done at 2 GPa, and the ambient pressure studies, but provide little extra constraint on the pressure effect.
There are no data for Ru partitioning at 0.1 MPa and conditions more reducing than ~ IW + 5.5, preventing direct comparison to the available high-P results of Mann et al. (2012) obtained at more reducing conditions (~ IW −1 to IW + 0.5). Correction of the solubilities obtained from 0.1 MPa experiments at oxidizing conditions to the average relative fO2 of high-P experiments, however, reveals good agreement between data at different pressures (0.1 MPa to 18 GPa). Correction of the 0.1 MPa data was done assuming either a 3+ (Borisov and Nachtweyh 1998) or 4+ (Laurenz et al. 2013) oxidation state for Ru dissolved in the melt, as found in the respective studies.
Metal–silicate partition coefficients for Au, Ir, Pd, and Rh, suggest a reduction in values with increasing P, for at least part of the investigated pressure range. For the case of Au, the effect of P is difficult to isolate, as the partitioning experiments of Danielson et al. (2005) that suggest a reduction in DMet/Sil at high P are also sulfur-bearing. Values of DMet/Sil for Au are expected to decrease with increasing S contents of the metal phase (e.g., Jones and Malvin 1990) and S itself becomes more siderophile with increasing P (Boujibar et al. 2014). Run-product compositions are not quoted by Danielson et al. (2005), making it difficult to quantify if the low values of DMet/Sil recorded by experiments at 21 and 23 GPa are the direct result of P or the coupled effects of P and composition. Values of DMet/Sil for Rh at high P appear to lie along the trend defined by 0.1 MPa experiments (Fig. 10), however, there is a significant difference (> 4 log units) in relative fO2 between these data. Plotting the same trend through an experiment done at 0.1 MPa, 1300 ºC and more reducing conditions (dashed line in Fig. 10), reveals the discrepancy between high and low pressure experiments. Fig. 11 displays DMet/Sil for Rh as a function of pressure for the experiments of Mann et al. (2012) (~ IW − 1.5 to IW + 1.5, 2150–2500 ºC) and the 0.1 MPa experiments shown in Figure 10, corrected to 2180 ºC and IW using the T dependence of Fortenfant et al. (2003) and assuming Rh2+ in the melt. Figure 11 portrays the negative dependence of DMet/Sil on P, which likely changes magnitude somewhere between 6 and 18 GPa (Mann et al. 2012). A similar comparison of DMet/Sil vs. P can be made for Ir, after correction of data at similar fO2 (~ IW + 0.5 to IW + 0.7) to the same T, using the trend found by Brenan and McDonough (2009). Although there is a dependence of DMet/Sil on P for Ir, its magnitude rests heavily on the datapoint at 6 GPa, which defines a minimum in the data. Further experiments are therefore required to better quantify the effects of P on DMet/Sil for Ir. Figure 11 shows DMet/Sil vs. P for Pd, from experiments done at conditions more reducing than ~ IW − 0.2. As observed for Rh and Ir, the magnitude of the P dependence changes above 6 GPa, although the difference is weaker for Pd than indicated for either Rh or Ir (Mann et al. 2012).
In summary, all of the HSEs display a decrease in DMet/Sil with increasing T. Compilation of the literature data also suggests that DMet/Sil for several elements decreases significantly with increasing P and the magnitude of this change may vary across the investigated P range (Mann et al. 2012).
Application of results to core formation
In order to apply the results of solubility and partitioning experiments to models of terrestrial accretion and core formation, values are parameterized according to Equation (40). To demonstrate this approach, we have chosen to parameterize DMet/Sil for Pt, Re, and Os as these elements comprise the long-lived Re–Os and Pt–Os isotope systems. The data summarized in earlier sections suggest that for reducing conditions, T and fO2 are the important controls on DMet/Sil. Equation 40 may thus be simplified to yield:(51)
Values for the coefficients a, n, and c and their sources are listed in Table 3. For equilibration between metal and silicate reservoirs at a chosen set of conditions, the concentration of trace element i in the silicate phase (CiSil) can then be calculated using the following relationship:(52)
where (CiTOT) is the concentration of i in the bulk system (typically chondritic concentrations when considering core formation) and f is the fraction of silicate melt being equilibrated. Figures 12a and b display the change in CiSil for a primitive upper mantle composition (PUM) following metal–silicate equilibrium over a range of T and fO2 conditions. It can be seen from these figures that the PUM concentrations of Re and Os are not reproduced by metal–silicate equilibrium over a wide range of T–fO2 space. Conversely, PUM concentrations of platinum can be accounted for if metal–silicate equilibrium occurs at high T and low fO2 (e.g., ~ 3250 ºC at IW − 2). Figures 12c and d display the change in Re/Os and Pt/Os ratio over the same T and fO2 interval as shown in 12a and b. Approximately chondritic Pt/Os, as required to account for the Os isotopic composition of PUM, is not reproduced under any conditions. The PUM Re/Os ratio is only reproduced at relatively low T (<1830 ºC) for redox conditions appropriate to core formation (<IW − 2). Values of DMet/Sil at these temperatures however, result in absolute PUM concentrations for all three elements that are many orders of magnitude lower than observed. It is observations such as these that have led to the conclusion that metal–silicate equilibrium is insufficient to account for the HSE budget of PUM.
SILICATE AND OXIDE CONTROL ON HSE FRACTIONATION
Studies of sulfide-undersaturated mafic and ultramafic igneous systems reveal that Re, Au, and PPGE-group elements (Pt, Pd, Rh) are incompatible in early-crystallizing phases, principally olivine and chromite (e.g., Brugmann et al. 1987; Barnes and Picard 1993; Walker, et al. 1999; Puchtel and Humayun 2001; Pitcher et al. 2009; see also summary in Day 2013), whereas Re may be compatible in titanomagnetite in more evolved magmas (Righter et al. 2001; Gleißner et al. 2012). This is in contrast to the IPGE-group elements (Os, Ir, Ru), which typically show decreasing levels with measures of magmatic differentiation, such as whole-rock MgO, Ni, and Cr abundances (e.g., Brugmann et al. 1987; Puchtel and Humayun 2001; Pitcher et al. 2009), suggesting removal by olivine and/or chromite. Compatibility of Os, Ir, and Ru in olivine and chromite has also been implied by the preferential concentration of these elements in mineral separates relative to estimates of the coexisting melt (Puchtel and Humayun 2001; Puchtel et al. 2004). There arises some ambiguity, however, as to whether olivine and chromite are indeed the host phases for these elements, as it is now widely recognized that both minerals may contain microinclusions of platinum-group minerals (PGMs), such as Os–Ir–Pt-bearing alloy and laurite–erlichmanite (RuS2–OsS2; (Legendre and Augé 1986; Talkington and Lipin 1986; Merkle 1992; Cabri et al. 1996; Garuti et al. 1999; Gervilla and Kojonen 2002; Zaccarini et al. 2002). Despite this, in situ LA-ICP-MS studies have shown homogeneous Ru, Ir, Os, and Rh concentrations in some chromites from komatiite, komatiitic basalt and oxidized arc basalt (Locmelis et al. 2011, 2013; Pagé et al. 2012; Park et al. 2012), suggesting that the IPGEs and Rh may substitute into the spinel structure under certain circumstances.
Given the evidence from natural systems, laboratory partitioning studies for the HSE have therefore focused on olivine and spinel, although limited results have also been obtained for other minerals. As summarized below, results suggest that olivine and spinel-structured minerals may selectively concentrate the IPGEs, Rh, and in some cases Re, while excluding Au, Pt, and Pd. Experimental studies also reveal the important role of oxygen fugacity to control the magnitude of partitioning, as this variable affects both the speciation of the HSE, and, for the case of spinel, the availability of favorable partitioning sites.
As described in HSE Solubility Experiments: Implications for Metal–Silicate Partitioning, a fundamental difficulty of experiments to measure the mineral/melt partitioning of the HSEs, is the very low solubility of some of these elements (ppb levels for Os, Ir, Pt, Rh, and Ru) in molten or solid oxide at the relatively reduced conditions relevant to terrestrial magmas (i.e., FMQ ± 1). To impose the maximum concentration allowable, experiments are usually done at saturation in the metal of interest. At such low oxygen fugacities, however, even trace amounts of undissolved metal (so-called micronuggets, as described in Metal Inclusions in Experiments and the Analysis of Contaminated Phases) incorporated into a phase analysis can completely obscure the intrinsic HSE concentration. To overcome this problem, most past partitioning studies have adopted two common approaches. First, experiments are done at relatively high fO2, corresponding to conditions at which all the HSE are significantly soluble (ppm levels and above) in the phases of interest. Oxygen fugacity is also an important parameter to control, as the oxidation state of the HSEs may change with fO2. Second, the HSE content of coexisting phases is determined using a microanalytical method with good spatial resolution, including electron microprobe, secondary ion mass spectrometry (SIMS) and LA-ICPMS. Although the latter technique is the most destructive of the three, it offers the combined benefit of good sensitivity (ppm to ppb detection limits), and significant sampling depth (10s of μm vs. sub-μm for SIMS) such that phase homogeneity, and the presence of HSE metal contamination, can be readily assessed. Application of the LA-ICPMS technique is optimized using a relatively large diameter laser spot, producing more ablated material, resulting in lower limits of detection. Hence, it becomes a challenge to the experimentalist to grow crystals of sufficient size to take full advantage of this technique (Fig. 13). This aspect can be optimized by employing an experiment time-temperature history which minimizes the nucleation density, usually by slow cooling over a small temperature interval from the pre-determined liquidus (Brenan et al. 2003, 2005). Methods to achieve metal saturation include the wire loop technique, in which the melt + crystals are held by surface tension in a loop of the HSE wire of interest (Ir, Pt, Rh, Pd, Au; Brenan et al. 2012), or contained in a metal capsule (Righter et al. 2008); Ru and Os are not readily available as wires or tubing, and hence are added as powders. Other experiments have contained samples in crucibles made from natural or synthetic minerals (e.g., olivine and spinel; Brenan et al. 2003, 2005; Capobianco and Drake 1990; Fig. 13), with the metal added separately as wire or powder. The most convenient way to control and vary oxygen fugacity in partitioning experiments done at low pressure and high temperature is to suspend samples in a sealed furnace with a controlled flow of gas (air, CO2–CO, O2, etc; Capobianco and Drake 1990; Brenan et al. 2003, 2005). As an added twist, however, Re and Os are quite volatile at high oxygen fugacity, with Os forming the toxic OsO4 gaseous species. Partitioning experiments involving these elements have been done at low pressure using gas-mixing, but at relative reduced conditions (Brenan et al. 2003), or with samples encapsulated with an oxygen buffer in vacuum-sealed silica glass ampoules (Righter et al. 2004), or done at high confining pressure (Righter and Hauri 1998; Righter et al. 2004; Mallman and O’Neill 2007) using internal buffers. A summary of the studies to measure silicate– and oxide–silicate melt partitioning of the HSEs is provided in Table A2 in the Appendix.
Spinel–melt partitioning of HSEs
Capobianco and Drake (1990) and Capobianco et al. (1994) measured spinel– and magnetite–silicate melt partition coefficients for Rh, Ru, and Pd at 0.1 MPa, 1250–1450 ºC and relatively high oxygen fugacities (i.e., FMQ + 1 to FMQ + 7), with their work revealing large partition coefficients for Ru (~ 20 to > 4000) and Rh (~ 80–300), and uniformly low values for Pd (i.e., < 1). These results have been confirmed for Cr-bearing spinel at similar conditions in the more recent work of Righter et al. (2004), who also report a Dmineral/melt for Ir of 5 to > 10,000, and that Au and Re are incompatible (Dmineral/melt of 0.08 and 0.0012–0.21, respectively). Results obtained by Brenan et al. (2012) for Cr-spinel at 0.1 MPa and 2 GPa, 1400–1900 ºC and more reduced fO2 (FMQ − 2 to FMQ + 4) yielded generally lower partition coefficients for the IPGE than previous work, with Ru as the most compatible (Dmineral/melt of ~ 4), followed by Rh and Ir, which are moderately incompatible to compatible (Dmineral/melt range of 0.04 to ~ 1), with Pt and Pd the most incompatible (Dmineral/melt < 0.2). Mallmann and O’Neill (2007) investigated the (Mg-Al) spinel–melt partitioning of Re at 1275–1450 ºC and pressure of 1.5–3.2 GPa with fO2 ranging from FMQ − 2.9 to + 5.6. Their results show a remarkably systematic decrease in the Dmineral/melt for Re over this fO2 interval, ranging from ~ 0.3 to < 3 × 10−5. A summary of partition coefficients measured in these studies is provided in Figure 14, with the logical abscissa being experiment fO2. Although there is significant scatter to the data, an overall consistent result is that Ir, Ru, and Rh are more compatible in spinel then Pt, Pd, Au, and Re. In contrast to the results for Re, partition coefficients for Ir, Ru, and Rh show an overall decrease as conditions become more reducing.
Silicate mineral–melt partitioning of HSEs
Aside from spinel, most of the previous mineral-silicate melt partitioning measurements for the HSE have been measured for olivine, with a generally similar sense of fractionation: Ir, Ru, and Rh moderately compatible, and Pt, Pd, Au, and Re incompatible. Results are summarized as a function of fO2 in Figure 15. Olivine melt partition coefficients measured at 0.1 MPa and 1330–1343 ºC for Ru and Ir increase from values of ~ 0.5 at FMQ > + 4 to ~ 2 at lower fO2. Values for Rh partitioning are ~ 2 over the entire fO2 range considered thus far (FMQ + 2 to + 7; Brenan et al. 2003, 2005; unpublished data). Partition coefficients for Au and Pt measured at similar conditions are uniformly low (0.12 or less), with no apparent change with fO2 (Righter et al. 2004 ; Brenan et al. 2005). Values for Pd measured by Brenan et al. (2003; unpublished data) decrease systematically with fO2: from 0.05 at FMQ + 7 to ~ 0.006 at FMQ − 0.5. The single value of ~ 0.1 reported by Righter et al. (2004) under oxidizing conditions is somewhat higher, but broadly consistent with this trend. In contrast to Pd, olivine-melt partition coefficients for Re measured by Mallmann and O’Neill (2007) increase with decreasing fO2, from 1.5 × 10−5 at ~ FMQ + 6 to ~ 0.5 at FMQ − 3, showing a similar trend to the results for spinel. Values for Re partitioning measured by Righter et al. (2004) are systematically larger than those measured by Mallmann and O’Neill (2007) at similar relative fO2, possibly reflecting some metal contamination in the run-product olivines. Re partition coefficients measured by Brenan et al. (2003) are significantly lower than the Mallmann and O’Neill (2007) determinations, which the latter authors attribute to a low abundance of charge balancing hydrogen-related point defects, present in their high pressure experiments, but absent in the 0.1 MPa, dry experiments of Brenan et al. (2003). Watson et al. (1987) did a reconnaissance study on clinopyroxene at 1275 ºC and 0.1 MPa, obtaining Dmineral/melt of ~ 0.04 for Re, and ~ 0.08 for Os, but fO2 was not controlled.
Results of other silicate mineral–melt partitioning experiments are summarized in Table A2. Aside from the extensive data for Re, of note is the Dmineral/melt for Pt of 1.5 determined for clinopyroxene by Righter et al. (2004). This value is somewhat unexpected, however, given that Pt2+ is the likely species at the fO2 of those experiments (Ertel et al. 1999), with an ionic radius of 0.8 in VI-fold coordination (Shannon 1976), and therefore an expected partition coefficient of ~ 0.1 based on the Blundy–Wood partitioning model (see next section). Results for Re partitioning include the measurements of Mallmann and O’Neill (2007) for clinopyroxene, orthopyroxene, and garnet (in addition to olivine and spinel mentioned above) determined over a significant range in fO2 (FMQ: 2.9 to + 5.6) at 1.5 to 3.2 GPa. Re was found to be highly incompatible in these phases at the most oxidized conditions, but values increase with decreasing fO2. Values of Dmineral/melt for Re involving clinopyroxene and garnet approach or exceed unity at ~ FMQ − 2, whereas Re is incompatible in orthopyroxene at all conditions studied. Righter et al. (2004) and Righter and Hauri (1998) also found Re to be incompatible in clinopyroxene and orthopyroxene at similar fO2, and Righter and Hauri (1998) measured DRe > 1 for garnet at FMQ − 2.9 to − 4.8.
Origin of the variation in partitioning
As described previously for solid metal–liquid metal partitioning (see The role of the solid phase on DSM/LM ), Equation (16) relates the mineral–melt partition coefficient to the degree of size misfit between the substituent cation, and the optimal value for the crystallographic site (Blundy and Wood 1994). This model accounts well for HSE partitioning into olivine and spinel, (Mallman and O’Neill 2007; Brenan et al. 2003, 2005), with the additional importance of crystallographic site occupancy, and its variation with composition, to fully account for the spinel partitioning data (Brenan et al. 2012). A further complication to the partitioning of the HSE is that the valence state for some changes over the fO2 at which partitioning has been investigated, thus influencing cation size misfit, and possible substitution mechanisms as well. A change in valence state with fO2 has been demonstrated by Mallmann and O’Neill (2007) to control Re partitioning into pyroxene, olivine and spinel, and suggested by Brenan et al. (2003, 2005) for Ru, Ir, and Pd substitution into olivine. In the latter case, the increase in D for Ru and Ir was interpreted to result in a shift from Ir3+ and Ru3+ in the melt to divalent species, as the ionic radius of Ru2+ and Ir2+ is estimated to be close to Mg2+, hence nearly optimal for substitution into the olivine structure, as predicted by the model of Blundy and Wood (2001). Estimates of valence state from Ir and Ru solubility experiments are somewhat conflicting, however, as it is possible to fit both 2+ and 3+ species to some data (Ru, Borisov and Nachtweyh 1998; Ir, Brenan et al. 2005), whereas other results suggest higher valence states (Ru4+, Laurenz et al. 2013; Ir3+, Fonseca et al. 2011). Partitioning experiments over a broader range of fO2 would be useful to better understand this behavior.
Changes in element partitioning involving a shift in valence state can be understood by considering the case for Re partitioning, in which there is very good agreement between partitioning systematics and valence state changes implied by the solubility data. Following the approach of Mallman and O’Neill (2007), the solution of Re metal into silicate melt can be described by the reaction:(53)
which has a solubility product of the form:(54)
As demonstrated by Ertel et al. (2001), the variation in the solubility of Re with fO2 in the basalt-analogue they investigated can be modeled by contributions from both Re4+ and Re6+ species. Hence, the total solubility of Re in the melt at a given fO2 can be expressed as:(55)
with square brackets denoting the melt phase. Substituting the individual solubility products yields:(56)
Values of Qx+ are calculated by fitting the experimental solubility data. An equation equivalent to Equation (55) can be written for the crystalline phase, yielding the following relation for the partition coefficient including all melt species:(57)
in which curly brackets denote the crystalline phase. Partition coefficients for the individual melt species can be written as:(58) (59)
and expressing [Rex+Ox/2] in terms of the solubility product yields:(60)
Hence, a full description of the partitioning in systems involving multiple valence states can be obtained with knowledge of the partition coefficients for the pure valence state, as well as the solubility product for the metal dissolution reactions. Mallman and O’Neill (2007) applied this analysis to their Re partitioning data, using values of Qx+ obtained from the Re solubility experiments of Ertel et al. (2001), and estimates for Dx+ that provided a best fit to their data. Results of fitting the Re partitioning data for olivine and spinel to Equation (60) are shown in Figures 14 and 15, with similar behavior for the other minerals studied. Re6+ is highly incompatible in olivine and spinel, owing to charge and size mismatch, with Re4+ much less so, behaving similar to Ti4+ (Mallmann and O’Neill 2007), accounting for the significant variation in partitioning with fO2. Following a similar approach, the olivine-melt partitioning for Pd (Brenan et al. 2003; unpublished data) can also be well fit to a form of Equation (60), but assuming Pd2+ and Pd1+ (Fig. 15), consistent with the metal solubility data of Borisov et al. (1994) and Laurenz et al. (2010). By this analysis, the partition coefficients are expected to change markedly for the fO2 interval within which both species are abundant, then level off to constant values at more reduced, or oxidized conditions, in which a single species dominates. Given the evidence for changes in valence state of the HSEs described in Solid Metal–Liquid Metal Partitioning, it seems clear that characterizing partition coefficients over a range of fO2 is essential to capture the behavior likely for natural magmas.
In addition to the role of ionic radius and charge, changes in the crystallographic site occupancy as a function of composition is an additional factor that may influence the HSE incorporation into spinels. The structural formula for spinel can be written as
in which A and B are di- and trivalent cations (so-called 2,3 spinel) or di- and tetravalent cations (so-called 2,4 spinel) in IV-fold (curved brackets) or VI-fold (square brackets) coordination, and x is the inversion parameter. The inversion parameter ranges from 0, corresponding to fully “normal” spinel, to 1, or fully “inverted” spinel, in which half of the octahedral sites are occupied by divalent cations. Hence, the availability of sites for di- and trivalent cations stabilized by VI-fold coordination will vary according to the degree of inversion. As demonstrated by Brenan et al. (2012), this effect may become evident when considering the partitioning involving spinels in which the chromite component is replaced by magnetite with increasing fO2, which is an important exchange in spinels from mafic and ultramafic magmas. Chromite (FeCr2O4) is a normal spinel, with all Cr in VI-fold coordination owing to the very high octahedral site preference energy (OSPE) of Cr3+ (d 3 valence electron configuration; McClure 1957; Dunitz and Orgel 1957). In contrast, magnetite (Fe3O4) is an inverse spinel at room temperature, but can show a decrease in the amount of divalent octahedral substitution at high temperature (e.g., Wißmann et al. 1998). A general formula for magnetite–chromite solid solutions takes the form:
where z = Cr3+/(Fe3+ + Cr3+). Site occupancies across the chromite–magnetite join, calculated after the method of Kurepin (2005), are displayed in Figure 16. For end-member chromite, the octahedral site is completely filled by trivalent cations (Cr3+), thereby restricting the uptake of divalent cations which prefer VI-fold coordination. As the magnetite component increases, however, there is a rise in the divalent cation occupancy of the octahedral site. In terms of HSE partitioning, Rh and Ir are likely to be dissolved as divalent species in oxide solutions at the fO2 of terrestrial magmas (Borisov and Palme 1995; O’Neill et al. 1995; Ertel et al. 1999; Brenan et al. 2005), with a d 7 valence electron configuration and in the low spin state (e.g., Zhang et al. 2010). There is, however, evidence for Ir3+ in the CMAS system at 1500 ºC (Fonseca et al. 2011). Based on trends in cation size with charge in VI-fold coordination, Rh2+ and Ir2+ are estimated to have ionic radii of ~ 72 and 74 pm (1 pm = 10−12 m), respectively, similar to Fe2+ and Mg2+ (78 and 72 pm, respectively; Shannon 1976). Both HSE cations are therefore expected to have a high affinity for octahedral sites in the chromite structure, and owing to their divalent charge, incorporation of Rh and Ir into chromite is predicted to be sensitive to the degree of inversion, as influenced principally by the magnetite component. As described above, results of metal solubility measurements suggest that Ru is dissolved as a 3+ or 4+ cation in oxide solutions at moderate to high fO2 (Borisov and Nachtweyh 1998; Laurenz et al. 2013). Results of mineral–melt partitioning experiments seem to be most consistent with a 3+ oxidation state, which has a d 5 electron configuration, in low spin state (Geschwind and Remeika 1962), suggesting a strong affinity for octahedral coordination. Based on trends in cation size with charge in VI-fold coordination, Ru3+ is estimated to have an ionic radius of ~ 68 pm, similar to Fe3+ and Cr3+ (64.5 and 61.5 pm, respectively; Shannon 1976). These considerations are consistent with the overall compatibility of the IPGEs in chromium-rich spinels, and with larger partition coefficients as the magnetite component increases, owing to a higher abundance of divalent octahedral sites (Righter et al. 2004; Brenan et al. 2012). Brenan et al. (2012) developed a model for partitioning of di- and trivalent cations into chromium-spinel taking into account the variation in site occupancy with magnetite component, which provides reasonable agreement to the existing experimental data, as well as empirical estimates from natural samples (i.e., Puchtel and Humayun 2001; Locmelis et al. 2011; Pagé et al. 2012).
In terms of the HSEs that are highly incompatible in olivine and spinel (Au, Pd, and Pt) either ionic radius or steric effects account for this behavior. At the conditions of the partitioning experiments, Au and Pd solubility systematics indicate the predominance of Au1+ and Pd1+ (Borisov et al. 1994; Borisov and Palme 1996), which in VI-fold coordination have ionic radii of 150 pm and 100 pm, respectively (estimated from Shannon 1976). These are considerably larger than either Mg2+ (72 pm) or Fe2+ (78 pm), so the low D values are consistent with a large mismatch in ionic radius compared to the dominant substituent cations in these phases. Metal solubility experiments have shown that Pt2+ is the likely oxidation state at the fO2 of past partitioning experiments (Ertel et al. 1999), although Pt4+ has been inferred spectroscopically, but only under highly oxidizing conditions (Farges et al. 1999). Pt2+ has a d 8 electronic configuration, and an ionic radius of 80 pm in VI-fold coordination (Shannon 1976), similar to Mg2+ and Fe2+, predicting a strong preference for octahedral sites in the olivine and spinel structures. The relatively low values for DPt would therefore seem anomalous. Documented occurrences of VI-fold complexes containing Pt2+ are rare, however, with the square planar coordination being most common, stabilized by the enhanced bond strength overwhelming the pairing energy required for this configuration (Cotton and Wilkinson 1988). Although square planar sites are unavailable in chromite and olivine, it may be that Pt2+ forms such complexes in the coexisting silicate melt, accounting for the low value for DPt.
Local PGM saturation during chromite growth
Both empirical observations and recent experiments suggest that the HSE may not always be fractionated by forming a homogeneous solution in a mineral or melt phase. For example, the occurrence of PGM inclusions in chromite is well-documented, with the most common association involving minerals of the laurite–erlichmanite series (RuS2–OsS2), as well as Pt–Fe and Os–Ir–Ru-bearing alloy (Legendre and Augé 1986; Talkington and Lipin 1986; Garuti et al. 1999; Merkle 1992; Cabri et al. 1996; Gervilla and Kojonen 2002; Zaccarini et al. 2002). Phase equilibrium experiments confirm these PGMs are stable at chromian spinel liquidus temperatures over some range of fS2, provided the system is undersaturated with sulfide liquid, indicating that such inclusions can be interpreted as a primary magmatic texture (Brenan and Andrews 2001; Andrews and Brenan 2002; Bockrath et al. 2004). The origin of these inclusions has been somewhat enigmatic, but may in part account for the association between chromite and enrichment of certain HSE. In the course of experiments designed to measure chromite–silicate melt partitioning of the HSE, which involved re-equilibration or growth of chromite in molten silicate, Finnigan et al. (2008) documented the occurrence of PGMs (including metal alloys and laurite) at the crystal–liquid interface. The mechanism of formation proposed by these authors involves the development of a redox gradient, owing to local reduction within the mineral–melt interfacial region, occurring as a consequence of the selective uptake of trivalent Cr and Fe from the melt, relative to the divalent species. Recalling that at conditions more oxidizing than the IW buffer, the solubility of the HSE increases with fO2, hence local reduction provides a driving force for precipitation of the PGMs in magmas that are not too far from metal saturation. Finnigan et al. (2008) modeled the processes of growth, as well as crystal–melt re-equilibration by Cr–Al exchange, to show that sufficient reduction occurs such that metal solubilities will decrease by several percent in the silicate melt at the melt–crystal interface. Once a sufficient degree of oversaturation occurs, the PGMs nucleate and continue to grow until either the redox gradient dissipates, or they become entrapped within the adjacent chromite crystal. Inclusion of such PGMs, then subsequent accumulation of chromite, constitutes a mechanism to fractionate the HSEs via mechanical means, rather than as a dissolved component in a major crystallizing phase. González-Jimenez et al. (2009) argue that the occurrence of zoned laurite–erlichmanite grains entrapped in chromite from different ophiolite localities arise from the redox gradients induced by chromite growth, providing support for the Finnigan et al. (2008) model.
MAGMATIC SULFIDE AND ASSOCIATED PHASES
During melting or solidification, sulfur-bearing silicate magmas can reach saturation in a sulfide phase, typically rich in Fe, with lesser amounts of Ni and Cu. Phase equilibrium experiments on typical magmatic sulfide compositions predict an immiscible sulfide liquid to form crystalline Fe-rich monosulfide solid solution (MSS; [Fe,Ni]1−xS), which at 0.1 MPa occurs at Tmax of 1190 ºC, corresponding to Fe0.917S (Jensen 1942). The exact liquidus will depend on pressure, Ni and Cu content and fS2/fO2 (Naldrett 1969; Fleet and Pan 1994; Ebel and Naldrett 1996; Bockrath et al. 2004). With cooling, MSS is followed at T of ≤ 900 ºC by a Cu-rich Intermediate Solid Solution ([Cu,Fe]1−xS; ISS; Dutrizac 1976), and magnetite, with the MSS–ISS assemblage undergoing subsolidus crystallization to mostly pyrrhotite (Fe1−xS), pentlandite ((Fe,Ni)9S8) and chalcopyrite (CuFeS2). In the crustal environment, there is evidence for efficient magmatic sulfide differentiation associated with relatively large igneous bodies, as documented in the world-class Ni–Cu–PGE deposits of the Sudbury (Canada) and Norilsk-Talnakh (Russia) Districts, for example, with separation of ores rich in Fe and Ni, interpreted as MSS cumulates, from those which are Cu-rich, representing mixtures of evolved sulfide liquid and cumulate ISS (e.g., Naldrett et al. 1992, 1996; Li and Naldrett 1992; Zientek et al. 1994; Ballhaus et al. 2001; see also Barnes and Ripley 2016, this volume). This process has resulted in a significant separation of the HSE, with the IPGE and Re concentrated in the MSS cumulates, and the PPGE and Au following the evolved liquid. Past studies of sulfide in upper mantle peridotites and diamonds have also identified both trapped sulfide liquid and residual MSS, albeit on a much smaller scale (Szabó and Bodnar 1995; Guo et al. 1999; Alard et al. 2000; Lorand and Alard 2001; Luguet et al. 2001, 2004). In that context, a distinction is made between so-called Type 1 and Type 2 sulfides, using criteria and nomenclature from Luguet et al. (2001). Type 1 sulfides are characterized by high Ni relative to Cu abundances, and primitive upper mantle (PUM)-normalized depletions in Rh and Pd relative to Ir (as well as Ru and Os), and interpreted to be residual MSS. Type 2 sulfides have variable Ni/Cu, and similar PUM-normalized abundances of Ir (Ru, Os), Rh, and Pd, considered to be consistent with trapped immiscible sulfide liquid. Although sulfur has long been implicated as an important ligand in the concentration of the HSE in magmatic sulfide systems, field evidence suggests that As, and the other chalcogens Se, Te, and Bi could be important in some cases. For example, Gervilla et al. (1996, 1998), Hanley (2007) and Godel et al. (2012) have reported a close textural relationship between relatively PGE–(Au)-depleted base-metal sulfide and coexisting PGE–(Au)-rich arsenide phases (NiAs, nickeline; Ni11As8, maucherite; NiAsS, gersdorffite) in the magmatic sulfide segregations within the Ronda and Beni Besoura peridotite bodies, the Kylmakoski (Finland) Ni–Cu deposit and komatiite-hosted base-metal sulfide mineralization (Dundonald Beach South, Ontario; Rosie Ni Prospect, Western Australia), implying the presence of an immiscible arsenide melt at the magmatic stage. Recent work on samples from Creighton Mine, Sudbury (Dare et al. 2010) have shown that the base-metal sulfides are not the dominant hosts for some PGE, and that Ir, Rh, Pt occur as chalcogen-rich discrete platinum-group minerals (PGMs; i.e., irarsite–hollingsworthite, IrAsS–RhAsS; sperrylite, PtAs2), possibly crystallizing before or with MSS. Chalcogen-bearing phases are also associated with late-stage low sulfur precious metal haloes around massive sulfide bodies, as has been documented at various locations around Sudbury, Ontario (Farrow and Watkinson 1997). There is also evidence for remobilized chalcogen-rich melts associated with high grade metamorphism of base-metal deposits (Frost et al. 2002; Tomkins et al. 2007). Thus the chalgogens may affect the distribution of HSE within a magmatic sulfide system in several ways, including early sequestration as immiscible semi-metal-rich liquids or discrete PGMs at the magmatic stage, ligands to maintain the PGEs in solution during ore solidification, and agents of remobilization during subsequent metamorphism.
In this section, we focus primarily on the results of experiments to measure the partitioning between base-metal sulfide phases (MSS, sulfide melt) and silicate melt, but also include the limited (but likely to grow) body of results available for the chalcogens. Past experimental studies to measure partitioning amongst MSS–sulfide melt–arsenide melt–silicate melt are listed in Tables A3 and A4 in the Appendix.
As is the case for solid metal–liquid metal partitioning experiments, loss of volatile sulfur, and some of the HSEs, is a concern, so experiments to measure sulfide–silicate partitioning are done using gas-tight containers, or under a S-bearing vapour phase. At 0.1 MPa, this involves either encapsulation in vacuum-sealed silica ampoules, or the use of sulfur-bearing gas mixtures (i.e., SO2–CO2–CO), whereas at high pressure, experiments are done in containers made from high purity graphite or natural mineral capsules (i.e., olivine), which prevents chemical interaction between the sample and the outer noble metal capsule which is typically used to ensure a gas-tight seal. In order to assist in the efficient separation of sulfide and silicate liquids during the experiment, Brenan (2008) and Mungall and Brenan (2014) subject samples to high acceleration at high temperature using a specially-designed centrifuge furnace (Roeder and Dixon 1977).
Partitioning experiments done at 0.1 MPa with evacuated silica ampoules have employed several methods for either buffering, or monitoring of fO2 and fS2. For example, Mungall et al. (2005) used synthetic solid buffers to fix both fO2 and fS2 in their MSS–sulfide melt partitioning experiments (DMSS/SulLiq) done at 950–1050 ºC, using the combined equilibria:(61)
This was accomplished by loading the buffer powders, along with the sample, in silica cups placed within an outer silica ampoule, with the experiment physically separated below the buffers, but in communication via the gas phase. Liu and Brenan (2015) employed a similar approach in their MSS–ISS–sulfide melt partitioning experiments done at 860–926 ºC (Fig. 17), but without the Pt/PtS mixture, as it was found to readily absorb the chalcogens, As, Se, and Te for which partition coefficients were also measured, in addition to the HSE. Instead the fS2 was adjusted by the metal/sulfur ratio in the sample, and monitored using the FeS content of pyrrhotite added to the FMQ assemblage, using the calibration of Toulmin and Barton (1964). A similar approach was employed by Fleet and coworkers (Stone et al. 1990; Fleet et al. 1996, 1999) in their experiments to measure sulfide melt/silicate melt partitioning (DSulLiq/SilLiq) of PGEs and Au, with fO2 buffered at relatively reducing conditions using materials representing the following equilibria:(63) (64) (65)
or C-O gas equilibrium involving graphite, used either as a sample holder or added as a solid rod, also known as the CCO buffer, defined by the reactions:(66) (67)
Brenan (2008) and Mungall and Brenan (2014) achieved somewhat more oxidizing conditions in their sulfide melt-silicate melt partitioning in experiments done at 0.1 MPa and 1200 ºC, in which samples were encapsulated in crucibles made from natural olivine or chromite (see Figure 2 of Mungall and Brenan 2014). Sulfur fugacity was fixed using either Pt–PtS, Ru–RuS2 or Ir2S3–IrS2 buffers, the latter two involving the sulfidation reactions:(68)
Once sulfur fugacity is fixed, Brenan (2008) calculated fO2 from the heterogeneous equilibrium:(70)
whereas Mungall and Brenan (2014) used the Cr content of the silicate melt, held in a chromite crucible, to estimate fO2, as the solubility of chromite varies in response to changes in the speciation of chromium (Cr2+ and Cr3+; Berry and O’Neill 2004), hence fO2, as demonstrated by Roeder and Reynolds (1991).
Partitioning experiments done at high pressure have employed graphite caspules (in some cases in a sealed Pt outer capsule; Peach et al. 1994; Sattari et al. 2002), which fix fO2 near the CCO buffer, or techniques in which the external fH2 is controlled, allowing a range of fO2 to be investigated. One method of external fH2 control employs a double capsule configuration, in which the sample + H2O is loaded into a hydrogen permeable noble metal inner capsule, then sealed, and placed into an outer capsule containing an assemblage of H2O plus solid metal + oxides (i.e., Ni–NiO) or mineral mixtures (i.e., assemblages for Reactions (61), (63), and (64); Li and Audétat 2012). The external buffer fixes both fH2 and fO2, which is transmitted to the inner sample by H2 diffusion through the noble metal capsule. For experiments done with pressurized gas vessels, the fH2 can be buffered using water as the pressure medium, and the intrinsic fO2 of the vessel (Jugo et al. 1999; Simon et al. 2008), or by adding known amounts of H2 gas to the Ar pressure medium (Bezmen et al. 1994; Botcharnikov et al. 2011, 2013). The fS2 in the experiments in which fH2 is buffered is estimated using the FeS content of an added pyrrhotite sensor.
Control of fS2 and fO2 in these experiments is important for several reasons. First, the oxidation state of the HSE can change with fO2, as has been previously described, as well as with fS2, as documented by Fonseca et al. (2007, 2009, 2011, 2012). Also, the degree of metal deficiency (metal/sulfur) in MSS varies with fS2, with metal-deficient MSS dissolving more of the HSE (Ballhaus and Ulmer 1995). The stability of sulfide liquid in molten silicate depends on the FeO content of the silicate, as well as the fO2/fS2 ratio (e.g., O’Neill and Mavrogenes 2002) through the heterogeneous equilibrium described by Equation (70), so sulfide may be absent if inappropriate fO2 or fS2 are imposed on the system. As the partitioning of the HSEs between sulfide and silicate melt can be expressed as an exchange reaction similar to 70 (see below), then the magnitude of partition coefficients will in turn depend on the relative fO2/fS2 ratio. Some of the past experiments to measure partitioning amongst MSS-sulfide melt–silicate melt were done unbuffered, however, with the metal/sulfur of the MSS and sulfide melt varying with the bulk composition of the sample. It then becomes important, therefore, to relate the metal/sulfur to the fO2/fS2 in order to accurately apply the data to modeling natural systems. For experiments in which fO2 and fS2 can be measured or estimated, extrapolation of results to natural systems is less uncertain.
As for the case of previous solubility and partitioning experiments, analysis of run products requires careful avoidance of inclusions (metal or sulfide) which contain a significantly higher HSE concentration than the phase of interest. This problem is not so acute in experiments involving sulfide mineral-sulfide melt equilibrium, although high spatial resolution is still important to obtain single phase analyses. The majority of past experiments to measure MSS–ISS–sulfide melt partitioning were doped at the 10–100 ppm level, which is close to the natural concentration range, then analyzed by either secondary ion mass spectrometry (SIMS; Fleet et al. 1993) or LA-ICPMS (Ballhaus et al. 2001; Mungall et al. 2005; Li and Audétat 2012; Liu and Brenan 2015). As sulfides dissolve relatively high concentrations of most HSE, some MSS-sulfide melt partitioning experiments were doped up to wt% levels, with run-products measured by electron microprobe (Li et al. 1996; Brenan 2002), with the results of Li et al. (1996) reproduced using the more sensitive proton microprobe method (Barnes et al. 2001). In that case, it must be shown that Henry’s Law is valid over the concentration range investigated; this is demonstrated for Os at the ~ 2–5000 ppm levels and for Rh and Pd at the ~ 10–20,000 ppm levels, by comparison of concentrations in MSS of similar metal/sulfur ratio in the studies of Fleet et al. (1993), Li et al. (1996) and Brenan (2002). Earlier experiments to measure DSulLiq/SilLiq for the PGEs and Au were doped at the ~ 100–1000 ppm level, and analyzed by bulk methods (neutron activation; see summary in Table A3), whereas more recent determinations have been done at the > 1000 ppm doping level, with analyses by LA-ICPMS. As discussed below, extreme partitioning of the PGEs into the sulfide melt, as revealed by the in situ LA-ICPMS measurements, renders bulk measurements of quenched silicate highly susceptible to overestimation, (hence, underestimation of sulfide melt/silicate melt D-values) even if only miniscule amounts of sulfide contamination are present.
MSS–sulfide melt partitioning
A summary of MSS–sulfide melt partitioning of the HSEs is provided in Figure 18. With the exception of some data for Re, Os and Au obtained at 1–3 GPa (Brenan 2008; Li and Audétat 2012, 2013), all other past measurements are from experiments done at 0.1 MPa, using evacuated silica ampoules (buffered or not). Values of DMSS/SulLiq for Ru, Os, Ir, Re, and Rh are > 1, with Ru as the most compatible (DMSS/SulLiq for Ru as high as ~ 20; Liu and Brenan 2015), and DOsMSS/SulLiq > DReMSS/SulLiq, giving rise to significant differences in the Os isotopic evolution within magmatic ore bodies (e.g., Lambert et al. 1998). In contrast, values of DMSS/SulLiq for Pt, Pd, and Au are all < 1. Fleet et al. (1993) noted that the partition coefficients between MSS and sulfide liquid change progressively between the three chemical subgroups of PGE, being higher for the iron triad (Ru, Os) and the lower for the nickel triad (Pd, Pt). Subsequent experiments have confirmed this observation, and extended it to the copper triad (Ag, Au), representing the most incompatible transition elements in MSS. In addition to these inter-element fractionations, there are some systematic differences in partitioning behavior amongst past studies, as noted below. These observations can be rationalized in the context of ligand field theory, as well as the effect of MSS and sulfide melt composition.
Monosulfide solid solution has a NiAs-type structure, with triangular Fe clusters surrounded by distorted S octahedra, incorporating vacancies on the Fe sites and Fe3+ holes to satisfy the charge imbalance in metal deficient MSS (see review by Wang and Salveson 2005). Ballhaus and Ulmer (1995) showed that Pt and Pd (and by extension, the other PGEs, Re and Au) substitute for Fe in MSS on a one-for-one basis. Insight into the possible mineral structure control on HSE incorporation into MSS can therefore be gained by considering the relative solubilities of the PGEs in MSS compared to a fixed standard state (pure metal or pure metal sulfide). Past work has shown that the solubilities of Os, Rh, Pt, and Pd in MSS increase with decreasing metal/sulfur, M/S (Makovicky and Karup-Møller 1993, 2002; Karup-Møller and Makovicky 2002; Majzan et al. 2002; Makovicky et al. 2002), indicating a decrease in metal activity coefficients, and that PGE substitution is enhanced by the presence of Fe vacancies (Ballhaus and Ulmer 1995). With this in mind, values of DMSS/SulLiq for the PGEs and Au are portrayed as a function of the M/S in the MSS in Figure 19. Where there are data for a significant range in MSS composition (Rh, Ir, Pd, Pt), partition coefficients show a weak increase with decreasing M/S—a trend consistent with the metal solubility results. Although the overall variation in partitioning with MSS composition seems consistent with expectations, the sense of HSE fractionation by MSS-melt partitioning is not reflected in the metal solubility data. Specifically, 1) Rh is found to be more soluble than Os, 2) the solubility of Pd is significantly higher than Pt, and 3) Os and Pt have similar solubilities. These differences are inconsistent with the overall incompatibility of Pt and Pd relative to Os and Rh, and the generally similar DMSS/SulLiq for the pairs Pt–Pd and Os–Rh (Fig. 18). As proposed by Liu and Brenan (2015), the inconsistencies in this comparison imply that MSS-melt partitioning of the PGEs must also be controlled by coordination complexes formed in the sulfide melt phase. Whereas Ru, Rh, Ir, and Os and Re are in octahedral coordination in their known sulfides, both Pd and Pt are in IV-fold coordination (summarized in Raybaud et al. 1997). Notably, at the conditions of past experiments, the likely oxidation state for Pt and Pd in molten sulfide is 2+ (Fonseca et al. 2009), which has a d 8 electronic configuration, and hence stabilized by square planar coordination (cf., Cotton and Wilkinson, 1988). In the absence of such sites in the NiAs-type structure, it therefore seems reasonable that both Pt and Pd are stabilized in IV-fold coordination by the more “permissive” sulfide-liquid structure. A similar argument may also hold for Au, which, assuming a 1+ oxidation state, is stabilized in low coordination number (II-fold to IV-fold) complexes (Carvajal et al. 2004). Hence, although the PGEs may be soluble in the MSS structure, it seems that their relative preference for the melt or solid phase depends on which coordination environment is most energetically favored.
Both Mungall et al. (2005) and Liu and Brenan (2015) report partition coefficients for the compatible HSE (Ru, Re, Os, Ir, and Rh) that are systematically higher than other studies for a given MSS composition (Fig. 19). Whereas all previous work to measure partitioning of these elements was done unbuffered, and nominally oxygen free, as noted above, both Mungall et al. (2005) and Liu and Brenan (2015) employed techniques to fix fO2 at the FMQ buffer, resulting in sulfide melt with oxygen contents at the 1–2 wt% level. Results of previous experiments have documented a sharp decrease in the solubilities of Re, Os, Ir, Ru (and Pt) in molten sulfide at an fO2 of ~ FMQ − 2 to − 3 (depending on the metal, and the fS2; Fonseca et al. 2007, 2009, 2011; Andrews and Brenan 2002), corresponding to a sharp rise in the oxygen content of the sulfide liquid from nil to ~ 1–5 wt%. The solubility decrease over this interval is ~ 10-fold, and implies a complementary increase in the activity coefficient for these metals in the melt. The effect of an increase in the activity coefficient for a metal in the melt phase would be to increase DMSS/SulLiq, which is the sense of the offset noted above. In this context, it is also worth mentioning that the addition of Cu and Ni to an Fe–S melt composition has been shown to change the solubility of Ru, Ir and Os (Fonseca et al. 2007, 2009, 2011; Andrews and Brenan 2002; Brenan 2008) with these additives acting in opposite ways. Whereas Ni increases the solubility of these metals (e.g., 0–23 wt% Ni results in ~ 2-fold increase in Os solubility), Cu results in a decrease (e.g., 0–26 wt% Cu results in a 3-fold drop in Os solubility; Fonseca et al. 2011), implying sympathetic changes in the activity coefficients for these PGEs in the melt phase. Hence, the relatively high copper content (~ 30 wt%) of the melts produced in the study of Liu and Brenan (2015) compared to previous work (~ 4 to 13 wt%) would also result in a modest increase in partition coefficients. Although the variation in D with M/S for the compatible PGEs seems consistent with known activity-composition relations in the sulfide melt, the significant differences in partitioning seen for Au, and to a lesser extent Pt and Pd, is less clear. For MSS with a similar range in M/S, values of DMSS/SulLiq for Au are found to vary by ~ 10-fold, with results from Li and Audétat (2013) and Fleet et al. (1993) recording higher values than past determinations. Unlike past experiments, in which the HSE were added at ppm to low wt% levels, experiments done by Li and Audétat (2013) were at saturation in pure Au, corresponding to 9 to ~ 15 wt% Au in the sulfide liquid. The effect of such high metal loading on partitioning is unknown, but could very well be outside the concentration limits of Henryian behavior, and are certainly beyond natural abundance levels. Hence, such anomalously high values of DMSS/SulLiq for Au could be reasonably excluded as applicable to modeling natural processes. Fleet et al. (1993) also measured elevated values of DMSS/SulLiq for Au, as well as Pt and Pd. HSE dopant levels were low, so adherence to Henry’s Law is likely not an issue, and the composition of MSS and sulfide melt are similar to previous work. The only difference in method was the use of SIMS for sample analysis, with partition coefficients for Au determined using the ratio of sulfur-normalized count rates in the MSS and sulfide melt. As documented by Fleet et al. (1993), this is a robust technique for measuring Au in sulfides. However, it is possible that the rather small spot employed (20–30 μm), and small number of analyses acquired (2) might not have fully captured the true variation in the Au content of the texturally inhomogeneous quenched sulfide melt (see Fig. 17b).
MSS–ISS–sulfide melt partitioning
Experiments to measure the partitioning of the HSE between ISS and MSS have been done by Jugo et al. (1999) at 100 MPa, 850 ºC (Au) and Liu and Brenan (2015) at 0.1 MPa and 850–875 ºC (PGEs, Re, Au). Results are summarized in Figure 20, which shows that Ru, Os, Ir, Rh, and Re are more compatible in MSS than in ISS, whereas Pd, Pt, and Au partition preferentially into ISS. Results for Au partitioning are consistent between the two studies. ISS–sulfide melt partition coefficients (DISS/SulLiq) were estimated by Liu and Brenan (2015) by combining their average values for MSS–sulfide melt, and MSS–ISS partitioning (Fig. 20). The calculated partition coefficients indicate that all the HSE should behave similarly to each other when partitioning between ISS and melt, with each weakly preferring melt relative to ISS.
Sulfide melt–silicate melt and MSS–silicate melt partitioning
Experiments to measure the sulfide melt-silicate melt partitioning of the HSEs have been of two types. Most experiments involve equilibration of both sulfide and silicate in the same sample, with the added HSE usually below the solubility limit (i.e., activity of the HSE, aHSE, < 1). Another, much smaller subset of experiments are of the “indirect” type, in which the concentration of a particular HSE in either sulfide or silicate melt is measured at (or corrected to) saturation (aHSE = 1), but in separate experiments involving a single sulfide or silicate melt phase (Andrews and Brenan 2002; Fonseca et al. 2007, 2009, 2011). In this approach, partition coefficients are calculated by the ratio of concentrations in the sulfide melt–silicate melt measured in the separate experiments, for which the metal activity is the same. The rationale for this approach is that it allows for the fO2–fS2 solubility systematics for each phase to be measured independently, and without the complication of sulfide contamination of the silicate phase.
Experiments to measure values of DSulLiq/SilLiq for rhenium have employed both of the aforementioned methods. In terms of the “indirect” approach, Fonseca et al. (2007) measured the solubility of rhenium metal in molten sulfide at 0.1 MPa, 1200–1400 ºC and fO2 of ~ FMQ − 6 to − 2 (and variable fS2, using a gas-mixing furnace) which, combined with the solubility measurements of Ertel et al. (2001) for rhenium in diopside–anorthite eutectic melt, yielded estimates of DSulLiq/SilLiq. Fonseca et al. (2007) showed that, up to an fO2 equivalent to FMQ − 2, the solubility of Re in molten sulfide is independent of fO2, but then exhibits a sharp decrease (data at higher fO2 could not be obtained). At fixed fO2 of FMQ − 4.4, Re solubility in molten sulfide shows a progressive increase with fS2, consistent with a change in speciation from Re0 (low fS2) to Re4+ (high fS2). As mentioned previously in the context of the mineral–melt partitioning of Re, Ertel et al. (2001) modeled their silicate melt solubility data in terms of contributions from both Re4+ and Re6+, with the species equivalence point at ~ FMQ−3, so the presence of Re4+ is consistent with expectations. Fonseca et al. (2007) developed a partitioning model which takes into account the combined fO2 and fS2 dependences on solubility, and showed that at the fO2–fS2 conditions of mid-ocean ridge basalt (MORB) genesis (high fS2, and reduced; FMQ − 1 to − 2), DSulLiq/SilLiq for Re is ~ 1–100, thereby exhibiting chalcophile behavior. However, at the conditions of island arc basalt (IAB) genesis (low fS2; oxidized; FMQ + 2), partition coefficients are ~ 1 × 10−4, hence Re would become strongly lithophile. Brenan (2008) measured the partitioning of Re between coexisting sulfide melt and silicate melt at 1200 ºC, 0.1 MPa and ~ FMQ − 2 to FMQ + 1, with fS2 buffered using Equilibria (62), (68), and (69). Most experiments were done by first equilibrating the two melts at static conditions, then subjecting samples to high acceleration to enhance phase separation. Similar to the results predicted from the work of Fonseca et al. (2007), DSulLiq/SilLiq for Re was found to vary over a wide range, from > 20,000 to ~ 20, depending on the fO2–fS2 conditions imposed on an experiment. Following the approach of Gaetani and Grove (1997), the origin of this variation was modeled by Brenan (2008) according to the exchange of rhenium between molten sulfide and silicate as expressed by the reaction:(71)
The extent to which the partition coefficient is sensitive to fO2and fS2 depends on the value of the stoichiometric coefficients, x, y and z4. Normalized to one cation, this reaction becomes:(72)
which has an equilibrium constant of the form:(73)
(square brackets denoting activities) and can be rearranged to yield:(74)
Assuming that the ratio of activity coefficients in the sulfide and silicate melts is constant over the fO2–fS2 range of experiments, then this value can be combined with K5–12 and the factor to convert moles to wt%, to yield a single constant, KK5–14. Then, by assuming that z = y, Equation (74) becomes:(75)
If the above conditions are satisfied, then a plot of log DSulLiq/SilLiq vs. ½ log fS2 – ½ log fO2 should yield a linear relationship, with the slope equal to the anion to cation ratio for the rhenium species. The variation in DSulLiq/SilLiq modeled in this way yielded two linear, but offset, data trends, defined by the fS2 of the experiments (Fig. 21). Treated separately, the low fS2 data define a slope of ~ 3, consistent with predominantly Re6+ in both silicate and sulfide, whereas the high fS2 data are defined by a shallower slope (2.4). A possible reason for the shallower slope in the high fS2 data set is the presence of Re–S species in the silicate melt, which has been shown to occur for Ru (Laurenz et al. 2013), Pt (Mungall and Brenan 2014), Ni (Peach and Mathez 1993; Li et al. 2003), and Cu (Ripley et al. 2002). For example, Re could be dissolving in molten silicate as a mixed Re–O–S species, by the model reaction (assuming Re6+ as the dissolved species in molten sulfide at the fO2 of experiments):(76)
which has an equilibrium constant of the form:(77)
and can be cast in a similar fashion as Equation (75) to yield:(78)
in which KK5–17 is a combination of K5–16 and a mole to wt% conversion factor. For the slope of 2.4 exhibited by the high fS2 experiments, the proportion of sulfur-bonded Re is estimated as (3 – 2.4)/3 × 100 = 20%. Also included in Figure 21 are the partition coefficients estimated empirically from sulfide and glass in oceanic basalts from Loihi and FAMOUS using data from Roy-Barman et al. (1998) and Sun et al. (2003), as well as curves calculated using the model of Fonseca et al. (2007) corrected to 1200 ºC. The model curves capture the low fS2 measurements remarkably well, although the slope of the model curve is more shallow, as it assumes Re4+ as the main sulfide species. Calculated partition coefficients are systematically higher than the high fS2 measurements, however. If the lower values of DSulLiq/SilLiq determined by Brenan (2008) result from sulfur complexing in the silicate melt, then this would not be captured in the Fonseca et al. (2007) model, as it relies on Re solubility measured for molten silicate under sulfur-free conditions. This is one aspect of the “indirect” method that may compromise the accuracy of calculated values for DSulLiq/SilLiq, given the evidence for metal-sulfur complexing.
In light of the strong dependence of DSulLiq/SilLiq for Re on ½ log fS2 – ½ log fO2, it is worth considering whether large variations in sulfide–silicate partitioning are likely in different mantle environments, as predicted by the model of Fonseca et al. (2007). Although Fonseca et al. (2007) correctly point out that differences in fO2 and fS2 likely exist between MORB and IAB sources, an important aspect not considered is the requirement that, for coexisting sulfide and silicate melts, the value of ½ log fS2 – ½ log fO2 will be fixed by the heterogeneous equilibrium between FeO in the silicate melt and FeS in the sulfide melt (described by Reaction 70), and therefore if the [FeO] and [FeS] in the melts does not vary much, neither will DSulLiq/SilLiq (see also Kiseeva and Wood 2013). Although it is not easy to predict the variation in [FeS] in different basalt sources, the range in [FeO] during melting is reasonably well constrained by the iron content of primitive magmas evolving by olivine control (Francis 1985, 1995). In this context, the range in the iron content of primary Phanerozoic magmas is rather limited, and bounded by picritic lavas from Iceland (~ 8 wt% FeO; Jakobsson et al. 1978) and Hawaii (~ 11 wt% FeO; Humayun et al. 2004). For a fixed [FeS] of ~ 0.7, which corresponds to XFeS in a sulfide liquid with 15 wt% Ni, meant to be in equilibrium with mantle olivine with 3000 ppm Ni (Bockrath et al. 2004), this range corresponds to values of ½ log fS2 – ½ log fO2 of 3.99 (11 wt% FeO) to 4.13 (8 wt% FeO) or Dsulfide/silicate of ~ 380 to ~ 820 (using the high fS2 partitioning trend, for example). It is important to note that although DSulLiq/SilLiq is not likely to vary more than ~ 2-fold for this range of FeO, the bulk partition coefficient for Re could change markedly, due to the effect of fO2 on the silicate and oxide-melt partition coefficients (Mallmann and O’Neill 2007), or by differences in modal sulfide content. For example, low Re/Os and Re abundances in lunar basalts suggest that Re becomes more compatible in the residual assemblage at the reduced fO2 of the lunar mantle (Birck and Allegre 1994; Day et al. 2007). If the lunar basalt source is sulfide saturated, Dsulfide/silicate for Re may be somewhat higher than for terrestrial MORB genesis, owing to the much lower fS2 required for sulfide saturation, making the low fS2 partitioning results most applicable. Compounding this effect is the overall increase in bulk solid–melt partition coefficients for Re, as a consequence of the higher compatibility of Re4+ in the peridotite phase assemblage (Mallmann and O’Neill 2007). For the case of highly oxidized arc environments, sulfide is likely to be destabilized in the mantle source (Mungall 2002), combined with a higher abundance of the more incompatible Re6+, resulting in very low bulk partition coefficients.
Values of DSulLiq/SilLiq and DMSS/SilLiq for gold are summarized in Figure 22. With reference to the exchange reaction described by Equation (72), past solubility experiments have shown that Au1+ is the likely dissolved species in molten silicate at conditions more oxidizing than FMQ − 4 (Borisov and Palme 1996), so partitioning data plotted in the form of Equation (75) should have a slope of one half. Consideration of the full datasets for either MSS—or sulfide liquid–silicate liquid partitioning shows considerable scatter, with no well-defined linear relation in the manner predicted. Selecting just experiments done below Au saturation (for reasons described in MSS–ISS–sulfide melt partitioning), and measured by LA-ICPMS, presents a somewhat more coherent behavior for sulfide liquid–silicate liquid partitioning, as the data show a weak, albeit scattered correlation with the abscissa parameter, defining a slope of ~ 0.4 (single low value from Li and Audétat 2012, excluded), and an inferred oxidation state of + 0.8. The significant scatter, and generally low values of DSulLiq/SilLiq obtained by bulk analytical methods likely results from the presence of small amounts of sulfide contamination in the glass separate, which is avoided by the LA-ICP-MS method. However, the much larger values of DSulLiq/SilLiq reported by Bezmen et al. (1994) suggest more extreme partitioning of Au into sulfide liquid than suggested by any other studies. Bezmen et al. (1994) noted this discrepancy and attributed such large partition coefficients to the presence of hydrogen in the sulfide melt, enhancing the uptake of Au (and PGEs) in some undefined way. This interpretation is in conflict with the results for DSulLiq/SilLiq measured by Li and Audétat (2012), which were also done under high pressure, hydrous conditions, but overlap with values measured by Mungall and Brenan (2014) done under dry conditions at 0.1 MPa.
Silicate melt composition may also affect HSE partitioning in sulfide-bearing systems, as Zajacz et al. (2013) has documented ~ 10-fold decrease in DMSS/SilLiq for melt compositions varying from rhyolite to basalt. The enhanced levels of Au (and therefore lower DMSS/SulLiq) in melts with lower silica content reflect a similar decrease in the activity coefficient for the dissolved HSE species as implied by the metal solubility data (see Role of silicate melt composition). The much lower values of DMSS/SulLiq measured for a rhyolite composition by Jugo et al. (1999) could reflect small amounts of trapped sulfide in the glass, as samples were analyzed by bulk methods. This does not seem surprising, since the more viscous rhyolite could trap small emulsified sulfide droplets easily. Simon et al. (2008) also report low values of DMSS/SilLiq involving a rhyolite composition, but with glasses measured by LA-ICPMS. Reported glass compositions are not homogeneous, however, with Au concentrations varying from < 0.2–6 ppm, suggesting either chemical equilibrium was not obtained, or the higher glass values are contaminated by ablated sulfide. Glasses produced in the study of Zajacz et al. (2013) are reported to contain Au metal contamination, which was minimized by accepting only the lowest portion of the time-resolved signal for quantitation. Accepting the lower glass values reported by Simon et al. (2008) would result in high values of DMSS/SilLiq, in line with the measurements of Zajacz et al. (2013). Hence, the Au-scavenging potential by early MSS crystallization in felsic systems may have been significantly underestimated by Simon et al. (2008).
Perhaps the most notable aspect of the Au partitioning dataset is the systematically smaller values of DMSS/SilLiq than DSulLiq/SilLiq, which is especially well-defined when considering only those studies in which run-products were measured in situ by LA-ICPMS (e.g., Jugo et al. 1999; Li and Audétat 2012, 2013; Botcharnikov et al. 2011, 2013; Mungall and Brenan 2014) and involving similar melt compositions. The average value of DSulLiq/SilLiq measured from the in situ analytical studies on basaltic melts is ~ 4400. This contrasts with DMSS/SilLiq of ~ 170 measured in previous studies on the same composition (Li and Audétat 2012; Botcharnikov et al. 2011, 2013; Zajacz et al. 2013), yielding DSulLiq/SilLiq/DMSS/SilLiq of ~ 30, similar to the value of ~ 20 measured by Li and Audétat (2012), in which MSS, sulfide and silicate liquids coexist in the same experiment. Clearly, the identity of the residual sulfide phase will have a significant impact on the efficiency of gold partitioning into the silicate melt during mantle melting, and therefore the crust-to-mantle transfer of this element. As shown by Bockrath et al. (2004), residual MSS can coexist with silicate melt, in the absence of sulfide liquid, along the low temperature, hydrous peridotite solidus. One may therefore expect that relatively low temperature mantle-derived melts, such as hydrous, alkalic compositions, produced in the presence of MSS, would contain a higher inventory of gold than dryer, high temperature magmas which leave behind residual sulfide liquid. This behavior was modeled in detail by Botcharnikov et al. (2013) and Li and Audétat (2013), who also emphasized the strong control of fO2 on the efficiency of mantle-to-crust transfer of gold, favouring environments in which residual sulfide is either eliminated by oxidation (Mungall 2002) or rapidly dissolved into the silicate melt under oxidizing conditions (Jugo 2009).
Platinum-Group Elements (PGEs)
A summary of sulfide–silicate melt partition coefficients for PGEs is shown in Figure 23, which includes the results from both laboratory measurements and values from natural samples. Most past measurements of DSulLiq/SilLiq have used bulk analytical methods to measure the metal content of glass and sulfide. The exceptions to this are the studies of Brenan (2008), and Mungall and Brenan (2014) in which analyses were done by LA-ICPMS. Also included in this comparison are the “indirect” estimates of sulfide-silicate partitioning done by Andrews and Brenan (2002) and Fonseca et al. (2009, 2012), which are based on the solubility of the metal in sulfide and silicate, measured in separate experiments involving only one melt phase. As is clear from the figure, nearly all of the previous measurements involving bulk analysis of the quenched silicate melt yield partition coefficients which are significantly lower than values determined either by in situ analysis of coexisting phases, or by the “indirect” method. Mungall and Brenan (2014) provide evidence to suggest the presence of micro-inclusions of sulfide melt in the silicate glass produced in their experiments, which would likely result in an overestimation of the intrinsic PGE content of the silicate melt, if measured by bulk methods. First, the time-resolved spectrum for the PGEs in run-product glasses was found to be inhomogeneous, with intensity peaks and troughs (similar to Fig. 4), with count-rates on all the PGEs added to a given experiment oscillating in unison. This is in contrast to the uniform signal observed for lithophile elements, like Ca, monitored at the same time. Second, both static and centrifuge partitioning experiments were done on Pt-doped experiments, and it was found that the Pt content of run-product glasses was always lower (by 24–70%) in the sample subject to high acceleration (~ 500 g). This suggests the high acceleration step had a cleansing effect on the silicate melt, removing some of the sulfide contamination owing to enhanced settling. In light of these observations, Mungall and Brenan (2014) concluded that past work, in which glasses were analysed by bulk methods, provided minimum values of DSulLiq/SilLiq. They also suggested that glass concentrations measured by LA-ICPMS could also be susceptible to trace sulfide contamination, even if low count-rate domains of the time-resolved spectra are selected, and so-derived values of DSulLiq/SilLiq from their study should also be regarded as minimum. Accepting this interpretation therefore indicates that minimum partition coefficients for the PGEs are > 105, with some values for Ir and Pt documented by Mungall and Brenan (2014) exceeding 106. Calculated results of the “indirect” method to measure DSulLiq/SilLiq yield values for Os, Ir, Ru, and Pt of ~ 105, ~ 107, ~ 108 and ~ 109, respectively (Andrews and Brenan 2002; Fonseca et al. 2009, 2012), determined at FMQ − 1 and log fS2 of −1.44, which is sufficient for sulfide saturation of a silicate melt with 15 mol% FeO. It is currently unknown if the “true” partition coefficients could be as high as some of the values estimated from metal solubility experiments. As mentioned in the section Gold, there is now experimental evidence to suggest that metal–sulfur complexing could enhance the solubility of certain transition metals in molten silicate, so partition coefficients calculated using metal solubility in sulfur-free experiments could be overestimated in some cases. In the current context, Laurenz et al., (2012) have shown that the solubility of Ru in molten silicate is enhanced ~ 30-fold in sulfur-bearing (but not FeS-saturated) experiments, relative to sulfur-free compositions at the same fO2. This effect would reduce the Andrews and Brenan (2002) estimate for sulfide-silicate partitioning of Ru from ~ 108 to ~ 106, in closer agreement with the minimum values estimated by Mungall and Brenan (2014). In terms of the effect on Pt, Mungall and Brenan (2014) report enhanced solubility of this metal by ~ 100-fold in molten silicate in their sulfide-saturated partitioning experiments. This would translate to a ~ 100-fold reduction in the calculated value of DSulLiq/SilLiq for Pt to ~ 1 × 107, which is still higher, but in closer agreement to the direct measurements. The DSulLiq/SilLiq of ~ 105 estimated for Os by Fonseca et al. (2011) seems unusually low in the context of results for the other PGEs determined by the same method. One possible source of inaccuracy in that determination is the data for Os metal solubility in molten silicate. The source of solubility data is from Fortenfant et al. (2006), whose measurements were done by bulk methods, so there was no control on glass contamination by undissolved metal particles. Brenan et al. (2005) provide a maximum bound on Os solubility of 10 ppb, in demonstrably particle-free glasses produced at FMQ + 0.6, as measured by LA-ICPMS. At the same oxygen fugacity, Fortenfant et al. (2006) estimate the Os solubility to be ~ 1100 ppb. Selecting the lower solubility of Brenan et al. (2005) would yield DSulLiq/SilLiq for Os of ~ 106, which is more in line with the other PGEs estimated by the indirect method, and also for the minimum values for DSulLiq/SilLiq determined by Brenan (2008) for coexisting sulfide and silicate melts (Table A3, Fig. 23).
The large values of DSulLiq/SilLiq implied by both the in situ measurements and indirect method have two important implications, in terms of alloy saturation during mantle melting, and the generation of extraordinarily PGE-rich sulfide deposits. Each is discussed in detail by Fonseca et al. (2009, 2012) and Mungall and Brenan (2014), and explored briefly below.
Formation of PGE alloys during mantle melting
Os–Ir–Ru-rich alloy grains constitute an important accessory phase in upper mantle peridotites, accounting for a significant fraction of the PGE in some samples (e.g., Luguet et al. 2001; Kogiso et al 2008). Such phases also appear to be remarkably refractory, and are likely responsible for the preservation of ancient (> 1 Ga) melt depletion events in much younger peridotite host rocks (e.g., Parkinson et al. 1998; Brandon et al. 2000). The presence of stable alloy grains is also an important consideration to models of PGE extraction from the mantle to the crust (Rehkämper et al. 1999; Mungall and Brenan 2014). Luguet et al. (2001) have proposed that the PGEs are initially concentrated into base-metal sulfide, and that alloys precipitate following the loss of sulfur during partial melting. In that context, Fonseca et al. (2012) have shown that saturation of a sulfide liquid in Os–Ir–Ru alloy is limited by the Os content of the liquid, as that is the least soluble component. Their results predict alloy saturation when the sulfide liquid concentration reaches ~ 40 ppm Os, assuming the availability of sufficient Ru and Ir. For mantle rocks with between 100–250 ppm sulfur, mass balance dictates that the base-metal sulfide which forms will be undersaturated in Os–Ir–Ru alloy for a typical undepleted upper mantle Os concentration of ~ 4 ppb (Becker et al. 2006). The key to alloy precipitation, therefore, is sufficient retention of Os (as well as Ir and Ru) in the sulfide phase, such that concentrations increase rapidly enough (due to the decrease in sulfide mass) to reach saturation before sulfide removal. Simple batch melting calculations which assume quantitative retention of the Os in sulfide result in alloy precipitation after 6–20% melting, depending on the total sulfur content of the source (Fig. 24; Fonseca et al. 2012). The occurence of alloy within this melting interval was also regarded by Fonseca et al. (2011) as necessary to reproduce the observed range in Re/Os in MORB, as the difference in DSulLiq/SilLiq for Re and Os was found to be too small. Mungall and Brenan (2014) showed that Pt metal saturation would occur during the sulfide-saturated melting interval, close to the point of sulfide exhaustion, for the same reasons described for Os. Importantly, they showed that use of the sulfur-free Pt solubility data to model the composition of mantle-derived magmas resulted in large, negative, Pt anomalies in model liquids, which are not observed in natural magmas. Instead, models in which solubilities are enhanced by Pt–S complexing provide the best fit to the data. Whereas Os was not included in their model, Mungall and Brenan (2014) did show that Ir and Ru alloy would also form in the restite just after complete exhaustion of sulfide liquid, in response to lowering fS2 and diminished metal–sulfide complexation in the silicate melt. Such results support a scenario in which alloys form as a result of the partial melting process, which is consistent with their occurence in sulfur-poor refractory mantle rocks, such as harzburgites of the Lherz massif (Luguet et al. 2007), depleted abyssal peridotites (Luguet et al. 2001), or in placer deposits likely derived from ophiolites (Nakagawa and Franco 1997; Meibom and Frei 2002; Pearson et al. 2007; Coggon et al. 2011), most of which are the residues of melting within a back-arc basin environment.
In the context of a discussion of the saturation of PGE-bearing alloy at the magmatic stage, it is also important to note the evidence for saturation following the ascent and emplacement of mantle-derived magmas. In all cases, the alloy composition is inferred to be either Pt- or Ir-(±Os±Ru)-rich (Peck et al. 1992; Barnes and Fiorentini 2008; Song et al. 2009; Ireland et al. 2009; Pitcher et al. 2009; Park et al. 2013). Evidence for saturation comes from either direct observation of alloy “phenocrysts”, in some cases with chromian spinel, olivine, and pyroxene included within metal grains (Heazlewood River Complex; Peck et al. 1992), or by the covariation of the PGE with other indices of differentiation, (e.g., Barnes and Fiorentini 2008; Ireland et al. 2009; Pitcher et al. 2009; Song et al. 2009; Park et al. 2013). As described in HSE Solubility Experiments: Implications for Metal–Silicate Partitioning, the solubility of the HSE under conditions more oxidizing than FMQ − 4 shows a general decrease with decreasing fO2, with the magnitude proportional to the formal oxidation state of the metal in molten silicate. There is a secondary, but less strong decrease in HSE solubility with decreasing temperature. As pointed out by Mungall and Brenan (2014), although the intrinsic temperature dependence on solubility is not strong, the absolute fO2 of a magma which is cooling along a buffer decreases markedly; at FMQ, the log fO2 changes from −5.4 at 1500 ºC to − 8.4 at 1200 ºC (O’Neill 1987). This magnitude of fO2 variation corresponds to a change in Pt solubility from 22 ppb to 0.7 ppb (Ertel et al. 1999); a compounding effect for FeO-bearing magmas is that the concentration level in the melt required for saturation will be below that for the pure metal owing to alloying with Fe (Borisov and Palme 2000), with higher Fe concentrations in the alloy at lower fO2. Hence, magmas that approach or reach alloy saturation during the melting process will tend to achieve and then continuously remain at alloy saturation as they cool during their ascent to the surface. Given their likely small size, the Stokes settling velocity of such alloy grains will be low, although attachment to larger grains, such as chromite or olivine, would likely enhance the segregation process (Hiemstra 1979; Ballhaus et al. 2006; Finnigan et al. 2008).
Concentration of PGEs by R-factor processes
Previous work to understand the concentration mechanisms for the PGEs has emphasized the scavenging role of immiscible sulfide liquid at the magmatic stage, and the importance of the silicate to sulfide mass ratio, or R-factor (e.g., Campbell and Naldrett 1979). The R-factor, derived from mass balance considerations, is defined by the relation:(79)
In which Di is the ratio of the element concentration in the sulfide (Csulf) to the initial concentration in the silicate melt (Ci,silicate). Figure 25 depicts the relation between R and DSulLiq/SilLiq for different values of Di. The exceptionally-rich concentrations of PGE in sulfide horizons from the Stillwater and Bushveld complexes yield values of Di of > 105 (Campbell and Barnes 1984). Examination of Figure 25 indicates that it is not possible to achieve such high values of Di by an R-factor-like process if DSulLiq/SilLiq is in the range of 103–104, as determined by most previous partitioning studies involving bulk analytical techniques. This is because Di reaches a limiting minimum value equal to DSulLiq/SilLiq when R ≥ 10 × Di; in other words, DSulLiq/SilLiq must be at least as large as Di to produce the necessary R-factor enrichments. Campbell and Barnes (1984) argued that DSulLiq/SilLiq must be at least 105 for the PGEs, a value which is borne out by minimum partition coefficients documented by Brenan (2008) and Mungall and Brenan (2014), and by combining PGE solubility determinations in sulfide and silicate melts (Andrews and Brenan 2002; Fonseca et al. 2009, 2011). In this context, Mungall and Brenan (2014) present a first order model to explain the high Pt concentrations in the sulfides of the Merensky Reef by mixing between primitive and fractionated B1 magmas, in which the fractionated composition is Pt and sulfur-free due to earlier sulfide removal. The Pt content of the primitive B1 magma is taken to be the same as the Bushveld marginal rocks of the Lower and lower Critical zones, which is 15–25 ppb, and only slightly higher than values in most primitive mafic magmas (Barnes et al. 2010). The observed ore concentrations are reproduced with a 50:50 mix of primitive and evolved B1 compositions, and a resulting R-factor of ~ 28,500, which is certainly permissible in the context of current minimum estimates of DSulLiq/SilLiq for Pt. Thus, very high PGE tenors can be achieved at the magmatic stage, obviating the necessity of either enrichment by orthomagmatic fluids (e.g., Meurer and Boudreau 1998) or the involvement of magmas with unusually high PGE concentrations (Naldrett et al. 2009).
Role of the chalcogens (Se, Te, As, Bi, Sb)
The relevant phase equilibria for melting and solidification of chalcogen-bearing compositions is reviewed in detail by Frost et al. (2002), Makovicky (2002) and Tomkins et al. (2007), and not repeated here. In terms of the role of chalcogens in affecting the HSE budget of magmatic sulfide systems, key parameters are the identity of the crystallizing phases, their timing of formation and the relative partitioning of elements between chalcogen and base-metal sulfide phases. The existence of S-bearing but arsenic-rich liquids is described by Skinner et al. (1976) who measured an extensive two-liquid field in the system Pd–As–S at 1000 ºC and 0.1 MPa. Helmy et al. (2013b) showed that similar phase relations extend into systems with Fe and Ni, with Pd-As-rich liquids stable to 770 ºC (and possibly below) at 0.1 MPa, with a strong preference of Ni over Fe relative to coexisting sulfide melt. Experiments on the Pt–As–S system (Skinner et al. 1976; Mackovicky et al. 1990, 1992) document extensive solid solution between As–S melts, and that sperrylite is a possible early-formed phase, although the minimum As content of the As–S liquid coexisting with sperrylite at 1000 ºC is quite high (several wt%). Helmy et al. (2013b) showed that the addition of Fe (and Ni) to this system significantly reduces the solubility of sperrylite in the sulfide melt to values ranging from 9400 ppm at 1150 ºC to 6200 ppm at 770 ºC. Similarly, Helmy et al. (2013b) determined that the arsenic content of sulfide melt coexisting with Pd–Ni-rich arsenide melts varies from 37800 ppm at 1150ºC to ~ 400 ppm at 770 ºC. Wood (2003) provided preliminary measurements of the solubility of molten Fe-As-S in basalt melt at 1200ºC and 1 GPa (fO2 ≤ than FMQ buffer), reporting values of 1100 and 3300 ppm, for silicate melts with ~ 19 and ~ 13 wt% FeO, respectively. These values are likely to change with fO2, however, as arsenic is dissolved as a cation in molten silicate (As3+ and As5+; Chen and Jahaanshi 2010; Borisova et al. 2010). In any case, such high As solubility in molten sulfide and silicate would suggest that sperrylite or Pd–Ni–As-bearing melt is not likely to form early in the magmatic sulfide crystallization sequence unless the system has acquired unusually high As levels, likely due to assimilation of sulfidic sediments enriched in organic matter, as proposed by Godel et al. (2012). Alternatively, arsenic levels can become elevated in residual sulfide melts by extensive crystallization of MSS, in which As is sparingly soluble (DMSS/SulfLiq for As varies from 0.4 to 0.01; Liu and Brenan 2015 and Helmy et al. 2010). This, combined with the decrease in arsenic solubility with falling temperature, would promote the formation of Pd–Ni–As melts at a late stage. Gervilla et al. (1994) measured phase equilibria in the system As–Pd–Ni at 790 and 450 ºC, relevant to the Ni-rich assemblages associated with what are interpreted to be natural immiscible arsenide melts. High solubilities of Pd in both nickeline and maucherite are demonstrated in that work, which at 450 ºC is ~ 5 and 9 wt%, respectively, consistent with very high concentrations of Pd (and Pt) reported for these minerals from natural occurrences (Cabri and Laflamme 1976; Cabri 1992; Watkinson and Ohnenstetter 1992). Such high solubilities would indicate these minerals can retain at least a portion of the elevated PGE content of any precursor arsenide liquid.
Insight into the solubility and phase relations for the Ir- and Rh-bearing sulfarsenides of the irarsite–hollingsworthite series can be gained by considering the results of dynamic crystallization experiments performed by Sinyakova and Kosyakov (2012). In that work, crystallization of a representative Noril’sk massive sulfide ore composition, doped with PGEs, Au, Ag, and As at the ~ 1000 ppm level of each, was simulated at 0.1 MPa and 1061–821 ºC. The sample was encapsulated in an evacuated silica tube, then completely melted, followed by cooling by moving the bottom of the sample from the hot to the cold zone of the furnace over several hours. This time–temperature history resulted in compositional and mineralogical zonation across the sample, from a MSS-rich portion, crystallized initially, to an ISS-rich portion, formed from the residual melt. Various arsenic-bearing phases were also produced over the length of the sample, including euhedral irarsite–hollingsworthite solid solution present as inclusions in early-formed MSS, as well as sperrylite, formed along the MSS–ISS cotectic, then Pt-, Pd- and As-rich segregations with a droplet-like morphology, interpreted to represent immiscible arsenide melts. The relative timing of PGM formation is remarkably similar to that proposed by Dare et al. (2010), in which crystals of irarsite–hollingsworthite, and sparse sperrylite, occur in what was early-formed MSS in contact ore at the Creighton Mine, Sudbury. The euhedral irarsite–hollingworthite inclusions produced in the crystallization experiments were suggested to form by local enrichment of components near the growing MSS crystals. The large MSS–sulfide melt partition coefficients which have been measured for Rh and Ir (see MSS–ISS-sulfide melt partitioning) would cause a depletion of these elements near growing MSS, although DMSS/SulfLiq < 1 for As would suggest that As enrichment is possible. The relatively high levels of As added to experiments, combined with the likely enrichment of this element in the melt during MSS crystallization, suggest that unusually elevated levels of this element are required for irarsite–hollingsworthite saturation in natural sulfide liquids.
There is a rather limited database for measurements of the relative partitioning of the HSE between sulfide and arsenide melts, with results from both experiments (Wood 2003; Helmy et al. 2013a) and empirical observations (Hanley 2007; Pina et al. 2013) that indicate preferential uptake by the arsenide phase. Partition coefficients, expressed as the ratio of concentration in the arsenide/sulfide liquids (DAsLiq/SulfLiq) are summarized in Table A3. Pina et al. (2013) provide the most comprehensive dataset, which includes all the HSEs, as measured by reconstructing sulfide and arsenide liquid compositions in samples from the Beni Bousera magmatic Cr–Ni mineralization (Morocco). Values of DAsLiq/SulfLiq estimated in this way are ~ 100 for the PGEs and Au, and 6 for Re. Hanley (2007) estimated relative arsenide–sulfide partitioning by comparing concentrations (on a 100% sulfide basis) between an As-rich high grade lens, with lower grade As-poor segregations, occurring in a series of mineralized komatiite flows. The arsenic-rich high grade lens was found to be enriched by ~ 7–60 × for Pt and Pd, and 2–30 × for Au. The magnitude of DAsLiq/SulfLiq measured in laboratory experiments is similar, with a value for Pd > 34 reported by Wood (2003), and 41 for Pt at 1230 ºC (Helmy et al. 2013b). The partitioning of Pd measured by Helmy was found to be strongly dependent on temperature, increasing from 18 at 1150 ºC to ~ 3500 at 770 ºC.
Helmy et al. (2013b) measured the effect of As on the partitioning of Pt between MSS and sulfide melt at the fS2 imposed by the Fe–FeS buffer at 950 ºC and 0.1 MPa. Their results showed a ~ 10-fold decrease in DMSS/SulLiq as the As content of the melt increased from 0 to 40 ppm. The decrease in DMSS/SulLiq was attributed to the formation of Pt–As nanoclusters in the sulfide liquid, as evidenced by the presence of various combinations of nm-sized crystalline PtAs2, and amorphous Pt–As phases, present as inclusions trapped in run-product MSS crystals. Importantly, experiments in which these phases were found were done at arsenic concentrations well below macroscopic saturation in immiscible Pt-arsenide melt or sperrylite. Helmy et al. (2013b) use these results to argue that the behavior of the HSEs in the presence of such ligands as As (and possibly other chalcogens) could be controlled by the surface properties of pre-crystalline nanoclusters. For comparison, Fleet et al. (1993) measured MSS–sulfide melt partitioning in experiments doped with up to 3500 ppm As, 4600 ppm Bi and 3300 ppm Te, compared to 40–50 ppm of the PGEs, in which DMSS/SulLiq was found to be identical to equivalent chalcogen-free experiments. A similar result was found by Liu and Brenan (2015) who measured DMSS/SulLiq involving sulfide melt with < 0.1 ppm to 150 ppm As (and approximately similar contents of other chalcogens) with no apparent effect on Pt or other HSE partitioning. A notable difference between studies is sulfur fugacity; whereas Fleet et al. (1993) used sulfur-excess starting materials, as did Liu and Brenan (2015), who performed experiments at log fS2 in the range of −2 to −2.6 (i.e., near values for natural silicate magmas), the fS2 of experiments done by Helmy et al. (2013b) was buffered at much lower values near Fe–FeS (approximate log fS2 of −7). Assuming both As- and S-related Pt species in the sulfide liquid, whose relative abundances are expressed as a homogeneous exchange reaction of the form:(80)
indicates that an increase in the sulfur fugacity will shift the equilibrium to the right, promoting the formation of the Pt–S species. Therefore, it seems plausible that the general lack of any effect of arsenic on Pt (or other HSE) partitioning observed at high fS2 indicates that the Pt–As species existing at low fS2 has been consumed by Reaction (80). Results would therefore suggest that arsenic is not an important complexing agent at the much higher fS2 required to stabilize sulfide liquid in an FeO-bearing silicate magma, due to the effect of fS2 on As speciation.
In terms of the effect of other chalcogens on HSE behavior, Helmy et al. (2007) measured the high temperature phase equilibria and partitioning in the Fe–Cu–Ni–Pd–Pt–Te–S system. These experiments tracked phase compositions from 1150 to 370 ºC at 0.1 MPa, in both metal rich and Te-rich compositions. Experiments show that a Te-rich immiscible melt forms at 920–700 ºC, which highly concentrates Pd and Pt; moncheite (PtTe2) is the high-temperature PGM in this system, initially crystallizing at 920 ºC. These results are relevant to the behavior of Te in orogenic and ophiolitic peridotites, in which Te resides not only in base-metal sulfides, but also in trace amounts of an accessory Pt–Pd–Te–Bi phase (moncheite–merenskyite, PtTe2–PdTe2; e.g., Lorand et al. 2010; König et al. 2014). Notably, Te levels in natural peridotite-hosted sulfides are well below the concentration levels of ~ 3000 ppm required for PtTe2 saturation, as reported by Helmy et al. (2007). Hence, it seems that the observed PtTe2 is likely a subsolidus phase, exsolved from the Te-bearing base-metal sulfide during the protracted cooling history of the peridotite body (Lorand et al. 2010).
SILICATE MELT–AQUEOUS LIQUID–VAPOR PARTITIONING
Silicate melts generally reach saturation in a volatile phase due to decompression and crystallization during their ascent and storage in crustal reservoirs. This process is particularly significant at convergent plate margins where volatile elements such as H, C, Cl, and S may be recycled from the subducting slab into the mantle wedge, thus the generated magmas are enriched in volatile components. The exsolving magmatic volatile phase (MVP) is known to extract significant amounts of metals and may contribute to the formation of magmatic–hydrothermal ore deposits (Hedenquist and Lowenstern 1994; Williams-Jones and Heinrich 2005; Richards 2011). The most notable HSE mobilized by the MVP is gold. Gold commonly occurs in porphyry-type ore deposits along with Cu, as well as in both high- and low-sulfidation epithermal environments (Muller and Groves 1993; Richards and Kerrich 1993; Sillitoe 2002, 2008; Heinrich et al. 2004). The gold budget of most of these deposits is thought to be dominantly derived from underlying upper crustal magma reservoirs. Palladium and Pt are also enriched in some porphyry-type deposits (Eliopoulos and Economoueliopoulos 1991; Tarkian and Stribrny 1999; Berzina and Korobeinikov 2007). Their concentration shows a positive correlation with that of Au with several notable exceptions. The presence of these metals in porphyry ores, however, indicates their partitioning into the MVP at certain conditions, which may be similar to those preferential for gold extraction. In addition, there is evidence from some occurrences that Pd and Pt have been re-mobilized by late magmatic brines in compacting cumulates or by hydrothermal systems associated with magmatic-sulfide ore deposits (Boudreau et al. 1986; Boudreau and McCallum 1992; Molnar et al. 1997; Hanley et al. 2005a, 2008). Porphyry molybdenum deposits are the primary resource of rhenium, which commonly occurs as a substituting cation in molybdenite (Berzina et al. 2005; Berzina and Korobeinikov 2007; Grabezhev 2013). It is likely that Re is extracted along with molybdenum by the MVP from underlying magma reservoirs at certain physical–chemical conditions and the two metals are later co-precipitated as a sulfide phase. Gold, Pd, Pt, Ir, Os, and Re have also been found in significant concentrations in high-temperature magmatic gases sampled from vents on the surface, further signifying the mobility of these metals in the MVP (Naughton et al. 1976; Zoller et al. 1983; Toutain and Meyer 1989; Crocket 2000; Williams-Jones and Heinrich 2005; Yudovskaya et al. 2008). To our knowledge, elements within the IPGE group do not show notable enrichment in magmatic-hydrothermal ore deposits.
Metals are commonly dissolved in the MVP associated with various ligands, most notably Cl−, HS−, OH−, H2So, HClo and potentially SO42− (Candela and Piccoli 1995; Barnes 1997; Williams-Jones and Heinrich 2005). Therefore, the concentration of these ligands in the MVP significantly impacts their volatile/melt partition coefficients. The affinities of cation–ligand pairs are highly variable. A simple way to predict relative complex stabilities is the application of the Hard Soft Acid Base (HSAB) theory (Pearson 1968). The HSAB theory distinguishes Lewis acids (electron acceptors, usually metal cations) and Lewis bases (electron donors, “ligands”). Hard acids and bases have high electronegativity, low polarizability and generally high valence state, whereas soft acids and soft bases have low electronegativity, high polarizability and low valence state. Therefore, cations with small ionic radii and high positive charge behave as hard acids, whereas cations with large ionic radii and low positive charge are typically soft acids. Similar statements stand for bases except the charge is negative. Out of those occuring in significant concentrations in the MVP: OH−, Cl− and SO42− are hard, whereas HS− and H2So are soft bases. Considering HSE, Au and PPGE metals form ions that behave as soft acids (i.e., Au+, Pt2+ and Pd2+) whereas even the lowest oxidation states of IPGE ions (i.e., Ru2+, Os2+, Rh2+, Ir2+) are harder and classified as borderline acids (Pearson 1968; Parr and Pearson 1983). As hard acids prefer to bind to hard bases and soft acids prefer to bind to soft bases, a general tendency in the volatile/melt partitioning of HSE can be foreseen simply by applying the HSAB principle. Accordingly, Au, Pt, and Pd are most likely to strongly partition into reduced sulfur-bearing volatiles, whereas other HSE may prefer chloride-rich brines. As O2− can be considered as a hard base and metals in the silicate melt are generally coordinated by oxygen, one may speculate that IPGE and Re will also show less tendency to partition into the volatile phase in general.
Although Cl and S may partitioning strongly into magmatic vapor, the concentrations of these elements in natural silicate melts may still remain relatively high, reaching levels of up to a few thousands of ppm (Wallace 2005). The concentrations of reduced S and Cl has been shown to significantly affect the solubility of Au and PGE in silicate melts (Botcharnikov et al. 2010; Jego and Pichavant 2012; Zajacz et al. 2012b; Mungall and Brenan 2014), and must therefore be incorporated in parameterizations attempting to model their partitioning. The volatile/melt partition coefficients of Cl and S depend on P, T and melt composition,further adding to the complexity of predicting volatile/melt partition coefficients for HSE in P–T–X space (Webster and De Vivo 2002; Lesne et al. 2011; Zajacz et al. 2013).
An additional important variable that may affect the volatile/melt partitioning of HSE is the density of the MVP. Metal complexes are stabilized in solution by the formation of hydration shells around them, and the extent of hydration shell formation and associated drop in the Gibbs free energy of the system is primarily controlled by the dielectric constant of water (Helgeson et al. 1981; Barnes 1997), which in turn positively correlates with the density of the MVP (Pitzer 1983). Therefore, the volatile/melt partition coefficients of most metals can be expected to positively correlate with the density of the MVP provided that the activity of various ligands is kept constant. This is manifested in the much higher metal concentrations determined in high-T fluid inclusions (FI) in magmatic–hydrothermal quartz veins formed under confining pressure at upper crustal depths (Ulrich et al. 1999; Klemm et al. 2007; Audétat et al. 2008; Zajacz et al. 2008; Landtwing et al. 2010), than those typically measured in high-T volcanic gases (Taran et al. 1995; Williams-Jones and Heinrich 2005; Wardell et al. 2008; Yudovskaya et al. 2008).
As the above discussion illustrates, the construction of a thermodynamic model to predict the volatile/silicate melt partition coefficients of HSE requires complicated thermodynamic modeling relying on a wealth of experimental data, which is still missing for most HSE. In the following sections we discuss the most important experimental data produced in the past on Divolatile/SilLiq for these elements.
Most volatile/melt partitioning experiments on HSE were conducted in externally heated cold-seal pressure vessel apparatus (CSPV), which is capable to reproduce the P–T conditions of magma reservoirs in the upper crust. Such studies commonly used Ni-based superalloy vessels (e.g,. Rene 41) which limit the maximum experimental temperatures to ~ 800 ºC (Frank et al. 2002; Hanley et al. 2005b; Simon et al. 2007). Some of the later work has employed Titanium Zirconium Molybdenum (TZM) or Molybdenum–Hafnium Carbide (MHC) alloy vessels, allowing experiment temperatures up to 1000 ºC (Zajacz et al. 2010, 2012b).
A typical starting phase assemblage for volatile/melt partitioning experiments consists of a silicate glass, an aqueous solution containing various ligands and sometimes a mineral assemblage to buffer important intensive variables such as pH, fO2, and fS2. Additional salts or sulfur may be added as solids. The starting phase assemblage is sealed into a noble-metal capsule that is inert with respect to the capsule load and ductile enough to transmit pressure. Most typically, the capsule itself is the source of the HSE in the experiment to avoid problems with alloying between the capsule and the metal under study. Similar to methods described in the section Experimental approach, the control of fO2 is usually achieved by external buffering, as the often used Au, Pt, and AuPd alloys are permeable to hydrogen at magmatic temperatures (Chou 1987), and the experimental charge is generally at high water activity (aH2O) due to the presence of an aqueous volatile phase. Oxygen fugacity is therefore controlled through the dissociation of water in the capsule. Hydrogen fugacities are either established using a double capsule technique with a redox buffer assemblage in the external capsule (e.g., Ni–NiO, Re–ReO2) or by establishing a constant hydrogen fugacity in the pressure medium itself. This is conveniently done in Ni-based superalloy vessels by using water as pressure medium, as hydrogen fugacity is buffered by the reaction:(81)
The activity of Ni in these alloys is somewhat below one, therefore fH2 is slightly lower than that corresponding to the equilibrium constant of Equation (81). Due to the ease of fO2 control and the widespread availability of superalloy CSPV facilities, many of the previous volatile/melt partitioning experiments were conducted in such apparatus. Tattitch et al. (2014) determined that Rene 41 vessels impose fH2 corresponding to fO2 of about NNO + 0.1 (FMQ + 0.8) at aH2O = 1 and T = 800 ºC by using the CoPd alloy–CoO redox sensor (Taylor et al. 1992). Others imposed fH2 by mixing H2 into the Ar pressure medium in Mo-based alloy vessels (TZM and MHC), and determined that fH2 decreases only 0.3–0.4 log units in the vessel in 24 h at 1000 ºC due to diffusive loss of H2 through the vessel walls (Zajacz et al. 2010, 2012b, 2013). Note that this value is very much dependent on the pressurized gas volume/heated vessel surface area, therefore, the relative change in fH2 will be much faster when filler rods are used (Shea and Hammer 2013).
The HCl/total chloride ratio is another important variable that significantly affects the solubilities of metals in the volatile phase, and therefore their volatile/melt partitioning. The concentration of HCl has been determined by mass balance (Frank et al. 2002), pH measurement in the quench fluids (Simon et al. 2005), or by using the formula of Williams et al. (1997) to calculate it based on the aluminium saturation index (ASI) of the silicate melt in equilibrium with the volatile phase (Simon et al. 2005; Simon and Pettke 2009). Hanley et al. (2005b) used an albite–andalusite–quartz assemblage to buffer fHCl, via the reaction:(82)
Similar to a method employed to determine DSulLiq/SilLiq (see the section Sulfide-melt/silicate melt and MSS–silicate melt partitioning), Zajacz et al. (2010a, 2012a,b) conducted metal solubility experiments in the volatile phase and the silicate melt separately at T = 1000 ºC to be able to model volatile/melt partition coefficients for Au and Cu in mafic–intermediate systems. In the absence of a silicate melt phase, the HCl concentrations in the volatile phase could be directly imposed by the starting fluid composition because no cation exchange reactions could occur during the run that could consume or produce HCl. The exception are FeCl2 bearing experiments, where Fe diffusion into the Au capsule produces HCl; however, as all metal concentrations were measured by LA-ICPMS in the synthetic fluid inclusions, the equilibrium HCl concentrations could be calculated even in those experiments (Zajacz et al. 2011).
In S-bearing experiments, it is of critical importance to understand the concentration, oxidation state and speciation of S in the volatile phase and the silicate melt, as various sulfur species can have contrasting properties in terms of metal complexation (e.g., HS− is a soft base, whereas SO42− is a hard base). Simon et al. (2007) added S in the form of arsenopyrite and determined the concentration of S in the volatile phase using the measured S concentrations in the silicate glass and the solubility model of Clemente et al. (2004). Zajacz et al. (2010, 2011, 2012a,b) loaded elemental S into the capsules and used mass-balance constraints to determine S concentrations in the volatile phase in multiphase experiments. Most commonly H2S and SO2 are assumed to be the most dominant S-species in magmatic volatiles, due to the reduced tendency of neutral molecular species to dissociate because of the low dielectric constant of water at these P-T conditions. The H2S/SO2 ratios are often predicted using gas phase standard state thermochemical data to calculate the equilibrium constant of the following reaction:(83)
However, Binder and Keppler (2011) and Ni and Keppler (2012) have shown that H2SO4 species may also be stabilized in relatively high-density magmatic fluids at fO2 ≥ Re–ReO2 (FMQ + 2.6). Furthermore, Jacquemet et al. (2014) suggested that trisulfur ions (S3−) may be present in moderately S-rich (~ 3 wt% S) aqueous fluids at magmatic temperatures based on extrapolation of in situ Raman spectroscopic data obtained at 25–500 ºC. The oxidation state of S in the silicate melt may be inferred from the value of fO2 using previous calibrations (Jugo et al. 2010; Klimm et al. 2012a), or directly determined using the S-Kα line wavelength shift measured by EPMA or by monitoring changes in S K pre-edge spectral features by XANES (Wallace and Carmichael 1994; Klimm et al. 2012b).
One of the main challenges in volatile/melt partitioning experiments is posed by the often unquenchable nature of the volatile phase. Early studies on volatile/melt partitioning used mostly Cl-bearing, S-free fluids and focused on metals which remained in solution upon quenching. The quenched fluids were extracted from the capsule and analyzed by various bulk methods (e.g., mass spectrometry, atomic absorption spectrometry; Holland 1972; Candela and Holland 1984). The applicability of this technique is, however, questionable for the HSE, as experiments involving these elements are generally conducted in the presence of the pure metal phase, which generally is the capsule itself. As the solubility of these metals at high P–T is typically higher than at ambient conditions, one may assume that a part of the dissolved metal could precipitate on the already present metallic phase upon quenching, and therefore cannot be representatively recovered for solution-based analysis. Consequently, the fluid phase has to be sampled at the experimental P–T and analyzed later, or it has to be directly analyzed at run conditions by in situ spectroscopic methodologies. Technological developments made in recent years allow in situ determination of trace element concentrations in high P–T fluids by X-ray Absorption Spectroscopy (Testemale et al. 2005), and abundant data were obtained on Au (Pokrovski et al. 2009a,b). Nevertheless, experimental difficulties arising at magmatic temperatures have so far limited the applicability of these techniques to lower-T, hydrothermal conditions. The development of the synthetic fluid inclusion technique paralleled by the rapid evolution of more and more sensitive, high spatial resolution, in situ but non-surface analytical methodologies such as LA-ICP-MS and proton-induced X-ray emission (PIXE) opened new pathways for the investigation HSE solubilities in magmatic volatiles. The volatile phase can be trapped at the experimental run P–T in the form of synthetic fluid inclusions (SFI) in quartz (Bodnar and Sterner 1987), and the bulk composition of the SFI can subsequently be analyzed by the above analytical techniques. The first such study used PIXE to determine the concentration of Au and Pt amongst other elements (Ballhaus et al. 1994). This was followed by several others after a new methodology had been established to analyze FI in quartz by the more widely available LA-ICP-MS (Gunther et al. 1998; Heinrich et al. 2003). This technique is capable to detect HSE concentrations down to sub-ppm levels in FI as small as 20–40 μm in diameter. Frank et al. (2002) used an alternative methodology to study the partitioning of Au between a rhyolite melt and a high-salinity aqueous liquid phase (brine) taking advantage of the fact that microscopic sized (~ 0–30 μm) bubbles containing the brine phase do not physically separate from the rhyolite melt due to its high viscosity on the experimental time scale. The bulk composition of glasses containing varying mass fraction of brine inclusions was obtained by instrumental neutron activation analysis (INAA), whereas the clean glass was analyzed by in situ methods (EPMA, SIMS). The composition of the brine was then derived by mass balance. Others working on felsic systems also analyzed FI in the silicate glass by laser ablation ICP-MS in addition to, or instead of SFI in quartz (Hanley et al. 2005b; Simon et al. 2007; Simon and Pettke 2009).
Another challenging aspect of volatile/melt partitioning experiments on HSE is the likely occurrence of HSE metal nuggets in the silicate melt and in the volatile phase. Nuggets of Au and PGE commonly occur in the silicate melt and have been discussed in detail in Possible mechanisms of metal inclusion formation. Gold nuggets in the silicate glass were observed in many volatile/melt partitioning studies (Frank et al. 2002; Hanley et al. 2005b; Simon et al. 2005, 2007; Zajacz et al. 2012b). Some studies interpreted these to be quench products and integrated them into the glass composition (Frank et al. 2002; Simon et al. 2005, 2007), whereas others considered them as stable phase at run conditions and removed them from the signal (Hanley et al. 2005b; Zajacz et al. 2012b). Zajacz et al. (2012b) repeated some of the most nugget-rich experiments after adding a small amount of oxalic acid to the starting solution which secured low fO2 at the beginning of the run before equilibrium with the apparent fH2 in the pressure medium has been reached. This effectively eliminated the occurrence of Au nuggets, and the such-determined Au concentrations in the glass were equal to those obtained from the identical, but oxalic acid-free experiment by eliminating Au nuggets from the LA-signal. This observation strongly suggests that Au nuggets are indeed stable phases in hydrous silicate melts at run conditions, and should be excluded from the glass composition. This result is consistent with the model described in Possible mechanisms of metal inclusion formation, that there is a time evolution in the fO2 of metal solubility experiments—generally from high to low—so the elimination of the high fO2 portion prevents initial HSE dissolution, then subsequent precipitation of metal particles as the fO2 decreases to the equilibrium value.
Though Au nuggets in the volatile phase are likely non-existent or insignificant based on the low standard deviation of Au concentrations in SFI, the situation is less clear in the case of Pt. All previous studies found highly scattering concentrations of Pt in synthetic FI from individual experiments (Ballhaus et al. 1994; Hanley et al. 2005b; Simon and Pettke 2009). Ballhaus et al. (1994) argued that this may relate to the heterogeneous entrapment of polynuclear complexes; however, these would need to be extremely large to induce the observed variation in Pt concentrations. Simon and Pettke (2009) speculated that the erratic concentrations may relate to the re-equilibration between the fluid inclusions and the host silicate glass upon quenching. Hanley at al. (2005b) noted a positive correlation between the formation time of the FI and the measured Pt concentrations, and suggested that the range in Pt concentrations is due to premature fracture healing before equilibrium between the brine and the Pt metal has been reached. However, even for a specific entrapment time interval, about an order of magnitude scatter was observed in Pt concentrations. This may suggest the heterogeneous entrapment of nuggets. In addition, Hanley et al. (2005b) proposed that the time dependent concentrations may relate to the re-precipitation of Pt in the unhealed fractures under a temperature gradient.
The volatile/melt partitioning of Au
Due to its pronounced presence in magmatic-hydrothermal ore deposits, Au has received by far the most attention out of all HSE with respect to volatile/melt partitioning behavior. A summary of the data is provided in Table A5 and displayed in Figure 26. Most studies investigated felsic melts in equilibrium with chloride-bearing magmatic volatiles in Rene-41 vessels at fO2 = FMQ + 0.7. Only Simon et al. (2007) also added sulfur to the system. As all these studies were conducted in Au capsules, the measured concentrations in the silicate glass and the volatile phase represent the solubility of Au and are shown separately. Zajacz et al. (2010) and Zajacz et al. (2011) studied the solubility of Au in S- and Cl-bearing low-density vapors at 1000 ºC, and later combined these data with Au solubilities obtained in andesite melts and S, Cl partitioning, and Cl speciation data to develop a model to calculate DAuvolatile/SilLiq (Zajacz et al. 2012a).
In S-free systems, a common conclusion of Au solubility studies is that the concentration of Cl and HCl/total Cl ratios significantly affect the Au content of the volatile phase and therefore. Simon et al. (2005) noted a strong preferential partitioning of Au into the brine phase relative to the vapor, and Zajacz et al. (2010) also found a positive correlation between the concentration of chloride species in the vapor phase and the solubility of Au. On the other hand, Hanley et al. (2005b) observed a strong negative correlation between Au solubilities and total chloride concentration in brines and partially attributed this to the salting-out effect, wherein stronger dipole NaCl ion pairs successfully compete against weaker-dipole neutral Au chloride complexes for the limited number of water molecules to form hydration shells around them. Considering that Hanley et al. (2005b) covered the 4.3–39.9 m total-chloride concentration range, whereas vapors in Simon et al. (2005) and Zajacz et al. (2010) were characterized by mCltotal < 1.5, it may be possible that there is a maximum in Au solubility at intermediate chloride concentrations. However, this requires further experimental confirmation. It can also be noted that the Au solubility values of Hanley et al. (2005b) are typically much higher than those of Simon et al. (2005) at similar salinity and T. A possible explanation for this difference would be if the HCl/NaCl ratios in Hanley’s experiments were higher. The values reported by the authors are against this hypothesis, however, one must note that very different methodologies were used to estimate HCl concentrations in these two studies. The silicate melt present at 800 ºC in Hanley’s experiments is highly peraluminous, which would be in equilibrium with an HCl-rich fluid according to Williams et al. (1997), whereas the melt in Simon’s experiments is slightly peralkaline. The solubility values of Hanley at al. (2005b) fall into the same range with the most HCl-rich fluids of Frank et al. (2002) at identical T, further supporting this hypothesis. Considering the speciation of Au in chloride-bearing volatiles, Frank et al. (2002) proposed AuCl and HAuCl2 as the dominant species at low and high HCl concentrations, respectively, whereas Zajacz et al. (2010) argued for the dominance of AuCl and NaAuCl2 even in HCl-rich fluids.
The gold solubility data in S-free silicate melts are also somewhat controversial, which can likely be attributed to different handling of Au nuggets. Studies that integrated Au nuggets into the glass composition obtained Au solubilities for haplogranite melts with ASI of 0.9–1.1 ranging from 0.5 to 4.7 ppm (Frank et al. 2002; Simon et al. 2005, 2007). Therefore, the obtained DAuvolatile/SilLiq values are around 10–20 for vapors, in the high tens for low-HCl brines and in the hundreds to low-thousands for high-HCl brines (Table 6). Hanley et al. (2005b) and Zajacz et al. (2013) chose to exclude Au nuggets from the integrated signal, whereas Zajacz et al. (2012b) effectively eliminated nugget formation. Yet, the Au solubility determined by Hanley et al. (2005b) in strongly peraluminous haplogranite melt (ASI = 1.33–1.49) is 0.82 ppm as opposed to the 0.02 ppm reported by Zajacz et al. (2013) for less peraluminous (ASI =1.02), Cl-free granite melts. This apparent inconsistency may partially be resolved by correcting for the difference in fO2, and by noting the difference in the ASI and dissolved Cl concentrations in the silicate melts in these two studies. For example Zajacz et al. (2012b) showed positive correlation between Cl concentration and Au solubility in andesite melts, whereas Zajacz et al. (2013) showed that Cu and Ag solubilities increase rapidly with ASI in peraluminous melts, which may also apply to Au. Nevertheless, Au solubilities at T = 1000 ºC in hydrous andesite melts with 1 wt% dissolved Cl, determined on nugget-free glasses, are only about 0.2 ppm at FMQ + 0.2 (Zajacz et al. 2012b). This would scale to about 0.27 ppm at FMQ + 0.7. As the solubility of Au in metaluminous rhyolite melts at 800 ºC would likely be lower (Zajacz et al. 2013), it is probable that Au concentrations reported with inclusion of nuggets give an upper estimate for the true Au solubility in silicate melts. If this statement is valid, the reported DAuvolatile/SilLiq values in these studies are minimum estimates; however, this needs further experimental confirmation.
Considering S-bearing systems, to our knowledge, only four studies investigated the solubility of Au in S-bearing aqueous fluids at magmatic temperatures (Loucks and Mavrogenes 1999; Simon et al. 2007; Zajacz et al. 2010, 2011), and only one of these included silicate melt in the same experiment (Simon et al. 2007). Loucks and Mavrogenes (1999) determined Au solubility values of 30–1180 ppm in aqueous volatiles at 625–725 ºC and in the presence of magnetite-pyrrhotite and magnetite-pyrrhotite-pyrite assemblages constraining fO2 and fS2. Based on the relationship between the calculated fH2S and the measured Au solubility as determined over a fairly narrow range of fH2S (22–46 bars), they proposed a 4-coordinated AuHS(H2S)3 complex in the fluid. Later studies could not identify the same complex in aqueous hydrothermal solutions or magmatic volatiles (Pokrovski et al. 2009b; Williams-Jones et al. 2009; Zajacz et al. 2010). Experiments at hydrothermal conditions and those of Zajacz et al. (2010) at 1000 ºC proposed S/Au ratios of 1 to 2 in the stable Au complexes (e.g., AuHS, Au(HS)2−, AuHSH2S). In addition, Zajacz et al. (2010) observed that the addition of even small concentrations of alkali-chlorides to H2O–H2S vapors increases the solubility of gold by about an order of magnitude in low-density vapors at 1000 ºC. This effect was the most pronounced with KCl, somewhat weaker with NaCl, and minor with LiCl. Feasible explanation may be the presence of mixed alkali–gold–hydrosulfide (e.g., KAu(HS)2) or alkali–gold–chloride–hydrosulfide (NaAuClHS) complexes in such low-dielectric fluids. The stability of such complexes was later predicted by ab initio static quantum chemistry calculations and molecular dynamics simulations as well for both Au and Cu (Zajacz et al. 2011; Mei et al. 2014).
The solubility of Au in hydrous silicate melts shows a strong positive linear correlation with the concentration of dissolved reduced sulfur and this needs to be accounted for when modeling volatile/melt partition coefficients (Botcharnikov et al. 2010; Zajacz et al. 2012b). For example, in andesite melts at fO2 = FMQ − 0.1, Au solubility increases from 0.06 ppm to 1.27 ppm when the melt composition is changed from S-free to pyrrhotite saturated with 354 ppm dissolved S (Zajacz et al. 2013). This effect is even more pronounced in the presence of dissolved Cl and in peralkaline melts, but more subtle in peraluminous rhyolites (Zajacz et al. 2012b, 2013). Interestingly, Simon et al. (2007) found the solubility of Au to decrease with the addition of S to the silicate melt, however, this may relate to artificially higher Au concentrations in S-free experiments due to more extensive nugget formation in the glass (Zajacz et al. 2012b). The Au solubilities determined for S-bearing rhyolites by Simon et al. (2007) (0.18–1.10 ppm) still exceed the value of Zajacz et al. (2013) for similar slightly peraluminous rhyolite melt at 800 ºC (0.1 ppm corrected for difference in fO2).
Zajacz et al. (2012b) modeled the partition coefficients of Au between andesite melts and magmatic volatiles using Au solubility data in both phases as well as S and Cl partition coefficients determined in the same system. The results showed DAuvolatile/SilLiq reaches values around 200 in pyrrhotite saturated systems, but are significantly lower (~ 20) in S-free systems. The lower DAuvolatile/SilLiq in S-free andesites is mainly due to the weak partitioning of Cl into the volatile phase from intermediate melts. Simon et al. (2007) determined DAuvolatile/SilLiq of 11–50 for reduced S-bearing slightly peraluminous rhyolites, which may be treated as minimum values because Au nuggets were included in the glass analysis.
All in all, we conclude that exsolving volatiles will most efficiently extract Au from mafic to felsic silicate melts if significant reduced S is present in the system (i.e., at or slightly below pyrrhotite saturation). However, even in the absence of reduced S-species, gold extraction from felsic melts can be highly efficient as the fluids derived from such evolved compositions are typically chloride-rich. This may further be promoted in peraluminous systems, as HCl/metal chloride ratios will be high, and therefore Au solubilities in the volatile phase will increase with increasing ASI of the melt.
The volatile/melt partitioning of PPGE
To our knowledge only two studies investigated directly the volatile/melt partitioning behavior of Pt and data on other PPGE are still lacking. Simon and Pettke (2009) conducted experiments at T = 800 ºC and P = 100 and 140 MPa in a rhyolite melt–vapor–brine assemblage. The reported average Pt solubility values in the vapor and brine are 0.15–1.67 ppm, and 2.33–45 ppm, respectively. The fluids were HCl-rich corresponding to the peraluminous nature of the silicate melt (ASI = 1.19–1.31). Platinum nuggets were observed in the silicate glass, but their contribution to the laser ablation signal was judged insignificant. The so-determined Pt solubilities in the melt ranged over 0.17–0.53 ppm. The corresponding vapor/melt partition coefficients were between 0.88 and 6.0, whereas the brine/melt partition coefficients were between 6.7 and 149. Hanley et al. (2005b) found a negative correlation between the total chloride concentration and the solubility of Pt in supercritical brines, with Pt solubilities dropping from ~ 1700 ppm to ~ 20 ppm as mCltotal was increased from 4.3 to 39.9. This is similar to the effect observed for Au in the same study, however, the Pt concentrations are less consistent and scatter over a range of 1–2 orders of magnitude from individual FI in the same experiments. Platinum solubilities were reported in two haplogranite melts, one with an ASI of 1.33 contained 0.115 ± 0.078 (1σ) ppm, whereas the other one with an ASI of 1.49 contained 0.035 ± 0.018 (1σ) ppm Pt. The corresponding DPtvolatile/SilLiq values are 21000 ± 14000 (1σ) and 3300 ± 5700 (1σ), respectively. These are orders of magnitude higher than those of Simon et al. (2009). As the P, T, silicate melt and fluid compositions in these two studies are rather similar; there is no simple explanation for this inconsistency. It is apparent that the fluid inclusions in Hanley et al. (2005b) are much more Pt-rich, whereas the silicate glass is lower in Pt. The latter may be due to the fact that Hanley et al. did not integrate the Pt nuggets into the laser ablation signal, whereas the more Pt-rich fluids of Hanley et al. (2005b) could be an artifact of heterogeneous entrapment of Pt nuggets in the FI or Pt re-precipitation under a temperature gradient as discussed by the authors. Similar processes may have played a role in the experiments of Ballhaus et al. (1994), who measured erratic Pt concentrations of up to several wt% in SFI sampling brines in the presence or absence of sulfides at 900 ºC and 1 GPa. These experiments did not contain silicate melt.
Unfortunately, to our knowledge there is no direct solubility or partitioning data published for other PPGE at magmatic temperatures. However, Fleet and Wu (1993, 1995) assessed the relative mobility of PGE in low-density vapors at 1000 ºC by monitoring the efficiency of metal transport along temperature gradients in vacuum-sealed silica tubes in the presence of various ligands. They found that PGE, in particular Pt and Pd were most mobile in the simultaneous presence of sulfide and NaCl species in water-free vapors, but less mobile in sulfide-bearing but chloride-free systems. This observation is consistent with that of Zajacz et al. (2010) on Au in low-density aqueous vapors at the same temperature. Fleet and Wu (1993) also pointed out that the mobility of PGE in the vapor is significantly reduced in the presence of pnictogens and chalcogens that form refractory compounds with them. For example, Pt mobility was reduced in the presence of As, due to the formation of refractory PtAs2.
In addition, numerous studies were conducted on the solubility of Pd and Pt at hydrothermal conditions, mostly in the temperature range of 100–500 ºC. The detailed discussion of these studies is beyond the scope of this review and the reader is referred to Wood (2002). However, in brief summary, these studies agreed that Pd and Pt are most likely transported in the form of chloride complexes in strongly acidic and oxidizing hydrothermal solutions, whereas bisulfide complexes dominate under slightly acidic to neutral and reducing conditions. The equilibrium constant of the dissolution reactions to produce chloride complexes is decreasing with increasing temperature, however, if the fO2 of the system is tied to one of the common geologic redox buffer assemblages a net solubility increase is expected with increasing T due to parallel increase in fO2. The stability of Pt and Pd bisulfide complexes were found to have a maximum at around 150 ºC. These characteristics are in qualitative agreement with those observed for Au at hydrothermal temperatures (Williams-Jones et al. 2009), however, the equilibrium constants of the dissolution reactions for Pt and Pd are generally much smaller than those for Au, with Pt being slightly more soluble than Pd (Wood et al. 1992; Pan and Wood 1994). The predicted solubilities at most typical geological conditions at 300 ºC are in the sub-ppb range for both metals (Wood et al. 1992, 1994; Gammons and Bloom 1993; Gammons 1995, 1996), which is several orders of magnitude smaller than the values proposed for Pt at magmatic temperatures as discussed above.
The highest temperatures were reached by Xiong and Wood (2000) and Hsu et al. (1991) using hydrothermal autoclaves to study Pd solubility. Xiong and Wood (2000) reported Pd solubilities of 40 ppb at T = 500 ºC, P = 55 MPa, a pH of ~ 5.5 and fO2 = Re–ReO2 (FMQ + 3.2) in 0.1 m KCl solution. Interestingly, Hsu et al. (1991) determined a much higher Pd solubility of 6.5 ppm, at lower fO2 (FMQ + 0.4) and slightly higher pH (6.5) and pressure (100 MPa), but otherwise identical conditions. Hsu et al. (1991) also identified retrograde Pd solubility with increasing temperature, which was still as high as 12.5 ppm at 700 ºC in 3 m NaCl solution at a pH of 6.5. The rather high solubilities determined by Hsu et al. (1991) were proposed to be an experimental artifact by Wood and Mountain (1991).
The volatile/melt partitioning of IPGE and Re
Out of all HSE, the least is known about IPGE solubilities in magmatic volatiles. To our knowledge no volatile/melt partitioning experiments were conducted on these metals. The experiments of Fleet and Wu (1993) included Os and Ir in the set of PGE investigated. These metals showed approximately identical mobility in the silica tubes, which was however, lower than that of Pt and Pd by about a factor of 40. Xiong and Wood (2000) studied the solubility of Os in KCl-bearing hydrothermal fluids at 400 and 500 ºC, 80 MPa and pH corresponding to the K-feldspar–quartz–muscovite buffer. They determined Os solubilities of up to about 1.7 ppm in 1.5 m aqueous KCl solution at 500 ºC and fO2 = Re–ReO2.
MacKenzie and Canil (2011) determined DRevolatile/SilLiq of 7.5–356 between haplobasalt melts and chloride-rich (5–30 M CaCl2 + MgCl2) aqueous fluids at T = 1300–1400 ºC and P = 1 GPa; however, no clear systematics were observed as a function of fluid composition. Amongst other elements, Johnson and Canil (2011) investigated the kinetics of the degassing of Re and Au from silicate melts at T = 1200–1430 ºC and atmospheric pressure. Gold was the most efficiently degassed element with a log diffusivity (D) of −10.7 m2/s, whereas Re was lost to the air more slowly (log D = −12.2 m2/s). Volatile/melt partition coefficients were not determined in that study.
Within the temperature regime of hydrothermal systems, Xiong and Wood (1999) and Xiong and Wood (2002) identified 4+ to be dominant oxidation state of Re in solution, and noted a steep positive correlation between Re solubility and chloride concentrations in the fluid phase. Rhenium solubilities of about 36 ppm were determined in 1 m KCl solution at T = 500 ºC, P = 55 MPa, fO2 = Re–ReO2 (FMQ + 3.2) and pH of the K-feldspar–muscovite–quartz buffer. Xiong and Wood (2002) proposed that the most stable chloride complexes of Re at 400–500 ºC are ReCl40 and ReCl3+. They also pointed out that the solubility of ReS2 is about two orders of magnitude lower than that of ReO2 at these conditions, limiting the mobility of Re in the presence of reduced S-species for these elements.
Despite considerable efforts, our understanding of the geochemistry of the HSE in magmatic systems is still rather limited. Whereas the effects of temperature and oxygen fugacity are now reasonably well documented as to their impact on metal–silicate melt partitioning, most results have been obtained in experiments done at relatively low confining pressure. At such conditions, oxygen is only sparingly soluble in the Fe melt, however, so its influence on partitioning of the HSE is poorly known. Results of very high pressure experiments (i.e., >35 GPa) have shown that oxygen can influence the activity of the moderately siderophile elements in the metallic melt (Siebert et al. 2013), so this is an area that needs further exploration for the HSE. The zeroth order conclusion that sulfide is important to concentrate the HSE has been known for several decades. However, the absolute magnitude of DSulfLiq/SilLiq for the HSE is only now being constrained accurately, with the variation in DSulfLiq/SilLiq with fO2 and fS2 reasonably well determined for Re, but results are scattered for Au, and largely unknown for the PGE. The recent discovery that alloys are important during mantle melting (and subsequent magma solidification) is still difficult to incorporate into petrogenetic models, as solubility data in both sulfide and silicate melt are incomplete. Moreover, the effect of dissolved sulfur (as well as other potential complexing agents, such as As) on HSE solubility in silicate melt is an area of considerable uncertainty, but initial results suggest this could be an important effect. With regard to low pressure degassing in magmatic systems, the majority of past experimental work has focussed only on the behavior of Au, Pt, and Pd, and in the hydrothermal regime. The capacity of low density orthomagmatic fluids to dissolve and transport the other HSE is less well known, but of importance to our understanding of the formation of magmatic ores, their possible remobilization, as well as the transfer of the HSE to the oceans and atmosphere.
The authors are grateful for the time spent by Raul Fonseca, Kate Kiseeva and Dave Walker to read and provide detailed and helpful reviews on an earlier version of this chapter. Editors James Day and Jason Harvey also provided detailed comments, and patiently nudged us along to chapter completion. Funding for Brenan’s research comes from Equipment, Discovery and Discovery Accelerator Grants from the Natural Sciences and Engineering Research Council of Canada. Bennett acknowledges post-doctoral support from the Carnegie Insitution of Washington, as well as previous graduate student funding from a Mineralogical Society of America Grant for Student Research in Mineralogy and Petrology, and a Geological Society of America Graduate Student Research Grant. Zajacz is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Special thanks to Josée Normand and Yanan Liu who helped draft figures, compile the data tables and format the final document.
↵1 In this chapter two different, but related, fO2 references are used. The first, fayalite–magnetite–quartz (FMQ) denotes relatively oxidized conditions, and is near the fO2 of most terrestrial magmas. Iron–wustite (IW) is the other reference point, corresponding to highly reduced conditions, with the conversion that IW is approximately 3.5 log units more reduced than FMQ, i.e., IW ~ FMQ – 3.5.
↵2 Note that there is a similar problem encountered in sulfide-bearing silicate systems, further described in the Section Sulfide–melt/silicate melt and MSS–silicate melt partitioning.
↵3 The carbonate anion is chosen in this case to represent the dissolved carbon species as it has previously been identified as an oxidized carbon species present in silicate melts (e.g., Mysen et al. 2011).
↵4 The reader is also referred to Kiseeva and Wood (2013) who propose an alternate approach, that makes use of an exchange reaction involving the element of interest and Fe in the sulfide or silicate, and does not have an explicit dependence on fO2 or fS2; this requires knowledge of the silicate melt FeO content, however, making it difficult to compare results with the model of Fonseca (2007).