Comparison of Measured and Predicted Bulk Moduli of Tantalum and Tungsten at High Temperatures

Abstract

The elastic constants of tantalum have been determined from room temperature to 500°C by means of a dynamic resonance method to obtain the adiabatic bulk modulus at elevated temperature. The adiabatic bulk modulus (B_s) of tantalum is found to be 1897 kbar at room temperature and it decreases almost linearly with a slope (dB_s/dT) of −0.11 kbar/°C as temperature rises. The calculation of the Grüneisen constant γ and a parameter δ, defined as − (dB_s/dT)/αB_s, from the present data shows that both parameters are almost independent of the temperature (1.57 for γ and 3.1 for δ). The constancy of γ and δ at high temperatures has also been tested for tungsten by using the recent data of Lowrie and Gonas [J. Appl. Phys. 36, 2189 (1965)]. The results indicate that both γ and δ are virtually constant at high temperature. The applicability of the following equation to estimate the bulk‐modulus‐temperature relationship for the refractory metals Ta and W has also been tested: $$B_s^T{\mathrm{=B}}_s^{25}{\mathrm{-(\delta \gamma /V)(H}}^T{\mathrm{-H}}^{25})$$ , where H is the enthalpy and the superscripts indicate values at 25° and T°C.