Temperature and pressure derivatives of elastic constants in single crystal Au-47.5 at.% Cd near martensitic phase transformation

Abstract

The behavior of the elastic properties and their pressure derivatives near the martensitic transformation β→ β′ was determined from sound velocity measurements at a frequency of 10 MHz, on a single crystal of Au-47.5 at.% Cd. The transformation of the β phase to the martensitic β' phase was obtained from the anisotropic elastic constants c 11, c 44 and c′, and their pressure derivatives. The behaviour of c 11 and c 44 is normal as a function of temperature, while the variation of c′ is positive with temperature. Before the β→ β′ phase change the value of c′ is very small and exhibits high elastic anisotropy. The small value of c′ and the anisotropy were explained according to the crystallographic mechanism of the martensitic transformation and the Zener theory of instability of the b.c.c. structure. The pressure derivatives of c′ are negative and the variation of dc 44 dP with temperature is anomalous. This behavior can be explained by the influence of pressure on the transformation temperature, and by the instability of the β phase. It was found that the elastic constants c′ determine the mechanism of the transformation. From the pressure derivatives of c 11, c 44 and c′ the Grüneisen parameters for different modes of vibration were calculated. For the c′ mode the values are negative, for the c 44 mode the variation of the parameter with temperature is negative. This anomalous behavior can be explained as due to the anisotropic softening of the atom bonding on the (110) planes of the cubic structure, as a consequence of the phase transformation mechanism.