ELASTIC PROPERTIES OF MINERALS AND THE INFLUENCE OF PHASE TRANSITIONS

Almost any change in structure of a crystal is typically accompanied by a change in lattice parameters. If there is a change strain state, there is inevitably also a change in elastic properties. However, strain and elasticity differ by being determined by first and second derivatives, respectively, of the free energy of the crystal. As a consequence, while changes in strain accompanying cation ordering or displacive phase transitions are typically on a scale of ~0.1 – 2 %, the elastic constants can vary by tens of percent. This has implications both for how effectively the elastic properties of minerals can be extrapolated from laboratory conditions to pressure/temperature conditions relevant for the earth’s crust or mantle, and for the extent to which patterns of elastic constants reveal the mechanisms of underlying structural changes.

It is well known that phase transitions which are accompanied by a strain conform closely to the precepts of Landau theory. The long interaction length of strains causes the order parameter to evolve in an effectively mean field manner. The overall approach is to use a free energy expansion in the order parameter and include terms in strain and elasticity terms explicitly, according to symmetry rules. The variations of individual elastic constants can then be expressed in terms of strain/order parameter coupling coefficients, the order parameter and the order parameter susceptibility. Bulk and shear moduli are given by Voigt or Reuss averages. Examples for which this approach has been developed quantitatively are the co-elastic transition at ~573 ºC in quartz and the pseudo-proper ferroelastic transition at ~50 GPa in stishovite. The same approach is also proving to be illuminating for understanding new data for improper ferroelastic transitions in (Ca,Sr)TiO3 perovskites, which are analogous to possible transitions in (Mg,Fe)SiO3 perovskite. Cation ordering can also produce diverse patterns of elastic constant evolution, as illustrated by lawsonite and plagioclase feldspars.