The elastic behaviour of tetrahedral materials with vacant sites

As part of a study of defect tetrahedral structure compounds, the elastic constants of single crystal specimens of Hg₃Ga₂□Te₆ and HgIn₂□Te₄ have been measured between 77 K and room temperature using the pulse superposition technique. These compounds are included in the series HgTe, Hg₅In₂□Te₈, Hg₃In₂□Te₆ and HgIn₂□Te₄ and HgTe, Hg₅Ga₂□Te₈, Hg₃Ga₂□Te₆ where there is a progressive increase in the concentration of vacant sites. While the other compounds studied are cubic, HgIn₂□Te₄ has a tetragonal structure with a $\text{c}\text{a}$ ratio of 2.0. The components of the elastic stiffness tensor of this material at 77 K are (in units of 10¹¹ dyne cm^?2) C₁₁ = 4.31 C₁₂ = 2.54 C₄₄ = 2.14 C₃₃ = 4.47 C₁₃ = 2.18 C₆₆ = 2.41. In a cubic material C₁₁ = C₃₃, C₄₄ = C₆₆ and C₁₂ = C₁₃: the elastic behaviour of this tetragonal compound closely resembles that of a cubic material, as might be anticipated from its structure. This similarity is further illustrated by reference to the symmetry of phase velocity and Young's modulus surfaces. Examination of the elastic constants and reduced elastic constants of these compounds shows a regular trend, the elastic stiffness decreases as the number of vacant sites increases. There is an approximately linear relationship between the reduced bulk modulus and the number of sited vacancies.