The Debye-Waller factors of K_xRb_(1-x)I and NaCl_xBr_(1-x) mixed crystals have been determined from X-ray diffraction intensities. The mean Debye-Waller factor is found to vary nonlinearly with the composition with positive deviations from linearity. The Debye temperatures (calculated from the Debye-Waller factors) are found to vary slightly non-linearly with composition with negative deviations from linearity. The Debye temperatures of seven alkali halide mixed crystal systems are critically compared with values predicted from six laws for composition variation. Using the estimated standard deviation as the criterion for the goodness of the fit, it is shown that the inverse cube (Kopp-Neumann) law provides the best description for the composition dependence of Debye temperatures of mixed crystals.

During the period 1949–1961 Szigeti published four seminal papers on the dielectric behaviour of crystals. Szigeti's theory is applicable to isotropic and anisotropic, ionic and covalent crystals with different structures. Szigeti's theory connects dielectric, spectroscopic and elastic properties. An important outcome of Szigeti's theory is the concept of the effective ionic charge (𝑠). It is pointed out that 𝑠 correlates with a number of physical properties and is a measure of ionicity of the interatomic bond. Since Szigeti's work, several theoretical models have been proposed to account for the fact that $s < 1$. These models provide an insight into the complex polarization mechanisms in solids. This review summarizes Szigeti's work and the work that followed; the implications and applications of Szigeti's theory are discussed. Some new results are also included.