Temperature Variation of the Elastic Constants of Cubic Elements. I. Copper

The ultrasonic pulse technique has been used in conjunction with a specially devised cryogenic technique to measure the velocities of 10-Mc/sec acoustic waves in copper single crystals in the range from 4.2\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K. The values and the temperature variations of the elastic constants have been determined. The room temperature elastic constants were found to agree well with those of other experimental works. Fuchs' theoretical ${c}_{44}$ at 0\ifmmode^\circ\else\textdegree\fi{}K is 10 percent larger than our observed value but his theoretical ${c}_{11}$, ${c}_{12}$, $K$ and (${c}_{11}\ensuremath{-}{c}_{12}$) agree well with the observations. The isotropy, $\frac{({c}_{11}\ensuremath{-}{c}_{12})}{2{c}_{44}}$, was observed to remain practically constant from 4.2\ifmmode^\circ\else\textdegree\fi{}K to 180\ifmmode^\circ\else\textdegree\fi{}K, then to diminish gradually at higher temperatures. Some general features of the temperature variations of elastic constants are discussed.