Thermodynamic Properties of Solids Containing Defects

Abstract

Using thermodynamics and elasticity theory, a unified treatment of the changes in the properties of solids containing defects is given. The results are expressed in terms of temperature and pressure derivatives of the energy required to form a single defect. The procedure is most useful for defects described by elasticity theory, where it is shown that the required pressure and temperature dependence of the energy is given by the measured pressure and temperature dependence of the elastic constants appearing in the energy expression for zero pressure and temperature. Some results which would otherwise have to be obtained from lengthy and complicated finite-elasticity calculations, as well as other results not obtainable at all from elasticity theory, are given by simple derivatives of the free energy. The results are specialized to a number of particular defects by using various expressions for the defect energies. These calculations are compared with available measurements of the properties of real crystals. For dislocations, reliable expressions for the energy are most soundly based for this case. Unfortunately, there are relatively few measurements for these defects. A number of specific predictions are made, some of which are partially confirmed by the available data. On the other hand, for the discussion of the large volume of measurements available for point defects, there is no generally acceptable model for the defect energy. The extent to which the properties of crystals containing point defects can be correlated on the basis of several models for the defect energy is explored.