Third-Order Elastic Constants of Single-Crystal and Polycrystalline Columbium

Abstract

The second‐order and third‐order elastic constants for both single‐crystal and polycrystalline columbium were determined at 298°K using an ultrasonic phase comparison method. It is shown that any dislocation contribution to the measurements is negligible with respect to other uncertainties. The third‐order elastic constants (Brugger convention) in units of 10¹² dyn/cm² are $$\begin{array}{ccc}{c}_{111}\text{=−25.64±0.25;}& c_{144}\text{=−3.43±0.10;}& {\nu }_1\text{=−4.8±1.2;}\\ c_{112}\text{=−11.40±0.25;}& c_{166}\text{=−1.677±0.05;}& {\nu }_2\text{=−3.70±0.2;}\\ c_{123}\text{=−4.67±0.25;}& c_{456}\text{=+1.366±0.05;}& {\nu }_3\text{=+0.75±0.05.}\end{array}$$ The Grüneisen parameter calculated from these values is 1.511±0.026 for the single crystal, and 1.546±0.092 for the polycrystal, in good agreement with the value 1.52 calculated from bulk‐property measurements. The polycrystalline third‐order elastic constants are in very good agreement with those calculated from the single‐crystal values by the method of Chang.