Thermodynamics of internal strain in perfect crystals

The thermodynamic theory of solids is generalized to take explicit account of internal strains in perfect non-Bravais crystals. Treating external and internal strains as independent leads to the definition of generalized thermodynamic properties, namely elastic constants, heat capacities, thermal expansion coefficients and Gruneisen parameters. Expressions are obtained relating these to the usual bulk properties, thus facilitating the calculation of the bulk properties from theoretical models and also providing a method of analysing experimental results obtainable from the direct measurement of internal strain. The theory can be applied both to the complete set of internal and external strains and to restricted sets appropriate to particular experimental conditions (eg those that preserve symmetry). By way of illustration, the theory is applied to the trigonal structure of selenium and tellurium, and a simple force constant model with this structure is used for the calculation of elastic stiffnesses for symmetry preserving strains. The limitations and advantages of the present theory are discussed and contrasted with those of methods previously used in treating internal strain.