Single-Crystal Elastic Properties of Tungsten from 24° to 1800°C

Abstract

The velocities of ultrasonic shear and compressional waves in tungsten crystals have been measured in several directions and as functions of temperature to 1800°C. Adiabatic crystal elastic stiffnesses have been calculated from these velocities as follows: $$\begin{array}{c}{C}_{11}{\text{=5.2349×10}}^{12}{\text{−4.5967×10}}^8{\text{T−5.467×10}}^4{T}^2\text{±0.25\%\hspace{0.17em}}\mathrm{dyn}·{\mathrm{cm}}^{\text{−2}}\\ C_{44}{\text{=1.6028×10}}^{12}{\text{−1.0320×10}}^8{\text{T−2.054×10}}^4{T}^2\text{±0.25\%\hspace{0.17em}}\mathrm{dyn}·{\mathrm{cm}}^{\text{−2}}\\ C_N{\text{=5.2480×10}}^{12}{\text{−3.5005×10}}^8{\text{T−3.163×10}}^4{T}^2\text{±0.25\%\hspace{0.17em}}\mathrm{dyn}·{\mathrm{cm}}^{\text{−2}}\\ C_{12}{\text{=2.0445×10}}^{12}{\text{−0.3403×10}}^8{\text{T+3.249×10}}^4{T}^2\text{±2.3\%\hspace{0.17em}}\mathrm{dyn}·{\mathrm{cm}}^{\text{−2}}\\ {\text{C′=1.5952×10}}^2{\text{\hspace{0.17em}−2.1282×10}}^8{\text{T−4.358×10}}^4{T}^2\text{±1.8\%\hspace{0.17em}}\mathrm{dyn}·{\mathrm{cm}}^{\text{−2}}.\end{array}$$ Values for the elastic constants of random, polycrystalline tungsten were calculated from these crystal stiffnesses. They agree well with values determined on polycrystalline tungsten as functions of temperature.