Elastic Constants ofα-Phase Cu-Al Alloys

Abstract

The three independent adiabatic elastic constants and their temperature derivatives have been measured near room temperature for single-crystal $\ensuremath{\alpha}$-phase Cu-Al alloys for compositions to 13 at.% Al using an ultrasonic pulse-superposition technique. The elastic shear constant ${C}_{44}$ increases linearly over this entire composition range. The elastic shear coefficient ${C}^{\ensuremath{'}}=\frac{1}{2}({C}_{11}\ensuremath{-}{C}_{12})$ decreases linearly with increasing Al content to approximately 7 at.% Al. For higher Al concentrations ${C}^{\ensuremath{'}}$ decreases at a greater rate. The measured bulk modulus $B=\frac{1}{3}({C}_{11}+2{C}_{12})$ decreases in a linear manner with increasing Al concentration. The temperature derivatives of the elastic constants are only weakly dependent upon alloy composition. The change in the Debye temperature ${\ensuremath{\Theta}}_{0}$ calculated from the elastic data is positive and in agreement with that determined calorimetrically. The changes in the elastic constants upon alloying have been corrected for the effects of lattice expansion. The corrected change in the bulk modulus $B$ upon alloying is positive. The corrected changes in the elastic shear coefficients extrapolated to 0 \ifmmode^\circ\else\textdegree\fi{}K have been analyzed in terms of a generalized Fuchs theory of homogeneous deformation. It is concluded that a conduction-electron term must be considered in calculating the shear coefficients of copper along with the original electrostatic and ioncore repulsion terms, and that changes in this conduction-electron term with increasing Al content make a significant contribution to the changes in the elastic shear coefficients upon alloying. The results indicate an increase in conduction-electron density with increasing Al concentration.