Microscopic strain, macroscopic strain and the thermodynamics of phase transitions in minerals
Almost any change in the local structure of a crystal, such as replacement of one cation by another of different size, reordering of cations between neighbouring crystallographic sites, ordering of magnetic dipoles, Jahn–Teller distortions etc., will give rise to two types of strain. Firstly, there will be a unit cell scale strain which will decay in magnitude as it extends away from the point where the structural change has occurred. Secondly there will be a net strain at a much longer length scale such as might be detected in the average lattice parameters of hundreds to thousands of unit cells. Both will be associated with a change in elastic energy. If the microscopic strain fields remain isolated or overlap in an uncorrelated way, the increase in elastic energy would be associated predominantly with local elastic strain heterogeneity. If the local strain fields interact in a correlated or collective manner, the change in elastic energy could be understood in terms of macroscopic distortions of a homogeneous material. The former might provide an appropriate model for solid solution formation, while the latter describes more or less what happens in a phase transition.
For a complete description of solid state processes in minerals, it is necessary to understand the length scales over which such strain fields operate for a given type of structural change. In the limit of local strain fields only extending to first and second nearest neighbours, say, a model based on only a few unit cells might be sufficient to account