Ultrasonic Measurements of the Elastic Constants and their Temperature Dependence for Nearly Perfect Single Crystals of Potassium Tetrachlorozincate (K₂ZnCl₄)

Ultrasonic and thermal expansivity measurements have been used to calculate the elastic properties of nearly perfect single crystals of potassium tetrachlorozincate. Determination of the nine components of the elastic tensor indicates that this material has lower elastic constants than comparable tetrahedral compounds containing sulfate anions [von Hausshül (1965). Acta Cryst. 18, 841-845]. The largest elastic constant is along the crystallographic a axis, along which are aligned the pseudo-equivalent tetrachlorozincate anions associated with the structural modulation. Conversely, the b axis exhibits the smallest of the three principal elastic constants and the highest thermal-expansion coefficient. Measurements of the temperature dependence of the elastic constants as the incommensurate phase transition is approached show similar behaviour for most of the components with the exception of the off-diagonal component C₁₃, where a significantly different temperature sensitivity is observed. Comparison of the calculated elastic constant values with those for other A₂BX₄ systems indicates that the introduction of the ZnCl₄ grouping has a significant effect in lowering the C₄₄ constant. A reduction in these constants is a reflection of the effects that this grouping has on the overall lattice energy, leading eventually to the formation of incommensurate phase behaviour. The unusual temperature dependence of the C₁₃ component is indicative of soft-mode generation, which may play a role in the onset of the ferroelectric-to-incommensurate phase transformation.