- © The Mineralogical Society Of America
Almost any change in the structure of a crystal, due to small atomic displacements, atomic ordering, magnetisation, etc., is usually accompanied by changes in lattice parameters. If suitable reference states are defined, such lattice parameter variations can be described quantitatively as a combination of linear and shear strains. What was originally a geometrical description then becomes a thermodynamic description if the relationships of the strains to the elastic constants are also defined. For a phase transition in which the parent and product phases are related by symmetry, only very specific combinations of strain will be consistent with the symmetry change, and the magnitudes of each strain will depend directly on the extent of transformation. In other words, such strains provide information on the evolution of the order parameter and the thermodynamic character of a phase transition. Spontaneous strains due to phase transitions in silicate minerals can be as large as a few percent, and, with modern high resolution diffractometry using neutron or X-ray sources, variations as small as ~0.1‰ can be detected routinely. This level of resolution is illustrated by the lattice parameter and strain variations through a cubic → tetragonal → orthorhombic sequence for the perovskite NaTaO3, for example (Fig. 1⇓).
Conversion from a purely geometrical description, in terms of lattice parameters, to a …