Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals
Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals (in Phase transitions in minerals; strain and elasticity, Anonymous)
European Journal of Mineralogy (August 1998) 10 (4): 621-691
The variations in lattice parameters of a crystal at phase transitions can be formalized for thermodynamic analysis using the concept of spontaneous strain. As with many other physical properties, spontaneous strains consist of up to six independent components forming a symmetric second-rank tensor, and are subject to the constraints of symmetry. Technical aspects of reference states, principal strains, scalar strains, volume strains, etc. are summarized in this review, and sets of equations defining the individual strain components in terms of lattice parameters for different changes in crystal system are also listed. The authors' purpose in this review is to bridge the gap between physics and earth science literature in relation to particular aspects of phase transitions, strain and elasticity. The background concepts are outlined, and the principles of strain analysis are illustrated for phase transitions in a selection of minerals and model systems, including albite, tridymite, anorthite, leucite, calcite, quartz, cristobalite and staurolite. The same overall approach applies whether the transitions occur in response to changing P or T; it can also be successful when lattice-parameter data for minerals displaying cation order/disorder phenomena are collected at room T (and P), rather than in situ at high T (or P). When atomic ordering does not lead to a symmetry change (non-convergent ordering), the spontaneous strains are expected to vary as e V (sub s) Q; Landau theory provides a convenient theoretical framework for the quantitative thermodynamic analysis of all these materials.