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), c₁₁₂₍ₜᵢₙ₎=-5.83±0.12 and c112(alloy)=-4.82±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%.