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Phosphorus was discovered in 1669 by Hennig Brand. The word phosphorus originates from the two Greek words phôs, meaning light, and phoros, meaning bearer, due to the phosphorescent nature of white phosphorus. Phosphorus is the tenth most abundant element on Earth and tends to be concentrated in igneous rocks. It is an incompatible element in common rock-forming minerals, and hence is susceptible to concentration via fractionation in geochemical processes. It reaches its highest abundance in sedimentary rocks: the major constituents of phosphorite are the minerals of the apatite group. Phosphorus is the second most abundant inorganic element in our bodies (after Ca); it makes up about 1% of our body weight, occurring primarily in bones and teeth. Phosphorus (atomic number 15) is a non-metal in group VA of the periodic table, and has the ground-state electronic configuration 1s2 2s2 2p6 3s2 3px1 3py1 3pz1 or [Ne]3s23p3. There are three orbitals occupied with only one electron each in the third energy level (the M shell). Phosphorus participates in essentially covalent bonds; electron gain to form P3− from P requires considerable energy (on the order of 1450 kJ mol−1). Loss of electrons is also difficult due to the high ionization potentials of P (the sum of the first three ionization potentials is 60.4 eV).
Here we use bond-valence theory (Brown 1981) and its developments (Hawthorne 1985a, 1994, 1997) to consider structure topology and hierarchical classification of crystal structures, and we point out that bond-valence theory can be considered as a simple form of molecular-orbital theory (Burdett and Hawthorne 1993; Hawthorne 1994, 1997).
STEREOCHEMISTRY OF (Pϕ4) POLYHEDRA IN MINERALS
The variation of P-ϕ (ϕ: O2−, …