Some Combinations of Third-Order Elastic Constants for Strontium Titanate Single Crystals

Abstract

Three linear combinations of the six adiabatic third‐order elastic constants in cubic crystals can be determined by use of the ultrasonic second‐harmonic generation technique. The combinations which are obtained are designated K₃[100], K₃[110], and K₃[111]. In the work reported here, room‐temperature values of the K₃'s have been measured for strontium titanate single crystals. The reported values are (in units of 10¹² dyn/cm²): $$\begin{array}{c}{K}_3{\text{[100]=C}}_{111}\text{=−49.6±4.3}\\ K_3\text{[110]=}\frac{1}{4}{\mathrm{(C}}_{111}{\text{+3C}}_{112}{\text{+12C}}_{166}\text{=−27.3±3.2}\\ K_3\text{[111]=}\frac{1}{9}{\mathrm{(C}}_{111}{\text{+6C}}_{112}{\text{+12C}}_{144}{\text{+24C}}_{166}{\text{+2C}}_{123}{\text{+16C}}_{456}\text{=−27.9±2.6.}\end{array}$$ The data have been compared with the theoretical values of K₃ for the alkali halide crystals, and it has been observed that the ratio of | C₁₁₁ |/C₁₁ for strontium titanate agrees with the corresponding ratio for many of the NaCl type crystals. In order to estimate the six third‐order elastic constants of strontium titanate, it has been assumed that the Cauchy relations extended to third‐order elastic constants hold.