Volume behavior of silicate solid solutions

TLDR: The S shape of the molar volume curve for binary silicate solid solutions is Sshaped, rather than linear or near-linear as discussed by the authors, and the region of negative deviation from linearity is always close to the small-volume end-member, with positive departures near the large volume end.

Abstract: The characteristic form of the molar volume curve for binary silicate solid solutions is Sshaped, rather than linear or near-linear. The region of negative deviation from linearity is always close to the small-volume end-member, with positive departures near the large-volume end. A Non-Equivalent Site (NS) type of volume behavior is a broad sigmoid that arises from the presence of some crystallographic sites in a structure larger than others capable of accepting the same large substituting cation(s). Initial substitution of the large-volume component into the smaller-volume end-member has only a small efect on the unit-cell volume until the large "easy" sites are saturated, which occurs at a rational mole fraction. Then a region of positive excess volumes follows more or less abruptly. Examples are (Na,K) nephelines and (Mg,Fe'?*) amphiboles. An Equivalent Sr'te (ES) volume behavior occurs in systems where, because of nearly identical sites accepting a certain substituting cation, there are no preferred "easy" sites. The fust small substitution of the larger-volume component produces only local deformations without expansion of the structure as a whole, giving rise to a sharply-curving region of negative excess volume, usually within ten mole percent of the small-volume end-member. Examples are the (Fe'?*,Ca) and (Mg,Ca) garnets, and, probably, the alkali feldspars and olivines. The volume sigmoid is less common among non-silicates. It is shown by some oxide systems, e.g. (Mg,Fe'z*) ilmenites (ES) and magnetite-ulv<ispinel (NS). Thermodynamic excess quantities such as excess entropy, enthalpy, and free energy may be closely related to the volume curves. Possible examples are excess entropy in high alkali feldspars and excess free energy in (Fe'z*,Ca) garnets.