- © 2000 Mineralogical Society of America
The art and science of crystal chemistry lies in the interpretation of three-dimensional electron and nuclear density data from diffraction experiments in terms of interatomic bonding and forces. With the exception of meticulous high-resolution studies (e.g. Downs 1983, Downs et al. 1985, Zuo et al. 1999), these density data reveal little more than the possible atomic species and their distributions within the unit cell. Other parameterizations of crystal structures, including atomic radii, bond distances, packing indices, polyhedral representations, and distortion indices, are model-dependent. These secondary parameters have proven essential to understanding structural systematics, but they are all based on interpretations of the primary diffraction data.
Comparative crystal chemistry carries this interpretive process one step further, by comparing parameters of a given structure at two or more sets of conditions. In this volume we focus on structural variations with temperature or pressure, though the general principles presented here are just as easily applied to structural variations with other intensive variables, such as electromagnetic field, anisotropic stress, or composition along a continuous solid solution. Two or more topologically identical structures at different temperatures or pressures may vary slightly in unit-cell parameters and atomic positions, thus adding a variable of state to the structural analysis.
A straightforward procedure for reporting structural data at a sequence of temperatures or pressures is to tabulate the standard primary parameters (unit-cell parameters, fractional atomic coordinates and thermal vibration coefficients, along with refinement conditions) and secondary parameters (e.g. individual and mean cation-anion bond distances, bond angles, polyhedral volumes and distortion indices) for each set of conditions. Most such structural studies also include graphical illustrations of the variation of key secondary parameters with temperature or pressure. In addition, several useful comparative parameters, including bond compressibilities and thermal expansivities, polyhedral bulk moduli, and strain ellipsoids, have been devised …