Third-order elastic constants of tin and of a tin--indium alloy

The complete set of 12 third-order elastic constants (TOEC) of white (metallic) tin and a set of 11 of the 12 TOEC of tin containing 0.3 at.% indium were determined from the hydrostatic and uniaxial stress dependence of ultrasonic velocity. The experiments were carried out on single crystals, using the two-specimen interferometric method of measuring velocity changes. In both the pure and the alloyed crystals c₃₃₃ was largest and negative, and only c₁₂₃ was positive. Some of the TOEC for the alloy were found to differ from the corresponding ones for the pure tin by as much as 20%, e.g. (in units of 10¹² dyn/cm²), $c_{112\left(tin\right)}=-5.83\pm 0.12$ and $c_{112\left(alloy\right)}=-4.82\pm 0.13$. All the second-order elastic constants were measured for both types of specimens and were found to be the same within the experimental uncertainty of ≈ 0.1%.