High-temperature elastic constants of gold single-crystals

Non-linear deviations of Young's modulus (modulus defects) have been observed in many polycrystalline metals at elevated temperatures ($>$0.7 $T\sb m$). As the quasi-harmonic theory of interatomic crystalline forces predicts a linear temperature dependence of elastic constants up to $T\sb m$, the observed modulus defect is thought to result from grain boundary effects. Comparison of polycrystalline modulus defects with single-crystal elastic constants at elevated temperatures should indicate if grain boundaries are involved in the modulus defect phenomenon. Young's modulus measurements were made from 300 $\leq T \leq$ 1275 K on high purity polycrystalline gold wires using the thin-line ultrasonic pulse-echo method. The adiabatic elastic constants $c\sbsp{\rm ij}{\rm S}$ ($c\sb{11}$, $c\sb{12}$, $c\sb{44}$) were measured on two, high purity, gold single-crystals: (100) and (110) orientations. A modulus defect was observed for each of the $c\sbsp{\rm ij}{\rm S}$ at elevated temperatures. The $c\sbsp{\rm ij}{\rm S}$ were averaged according to Hill's arithmatic and geometric methods and the results compared to the measured polycrystalline Young's modulus. The modulus defect of the polycrystalline specimen was essentially identical to the averaged $c\sbsp{\rm ij}{\rm S}$ at elevated temperatures, indicating that the large modulus defect of gold is not due to grain boundary effects. A modified quasi-harmonic model is proposed to account for the non-linear temperature dependence of the gold $c\sbsp{\rm ij}{\rm S}$ at elevated temperatures. The temperature dependence of the strictly harmonic terms due to thermal expansion are approximated using a Born-Mayer interatomic potential function and the temperature dependence of the atomic vibrational frequencies are included in the model by use of Gruneisen's approximation. The model suggested provides satisfactory agreement with measured $c\sbsp{\rm ij}{\rm S}$ at elevated temperatures