Theoretical and experimental investigations are being carried out on Cu based alloys due
to their technologically important shape memory properties and pseudo-elasticity, which are
intimately associated with the martensitic transformation. The transition between the two phases,
martensite to austenite, is of continued interest in academics and in industry. The shape memory
effect, superelastic properties and biocompatibility are being applied in a variety of fields. Cu based
SMA system has large vibrational entropy, high damping capacity and good economic viability. All
these make it a potential candidate in the field of sensors and actuators. The concurrent knowledge
of the second order elastic constants (SOEC) and third order elastic constants (TOEC) enables a
better understanding of the nonlinear elasticity exhibited by these alloys. We have used a model
based on deformation theory and Keating’s potential scheme to obtain the expressions for TOEC of
the above alloys. In this paper we have calculated the complete sets of six non-vanishing TOEC of
Cu-Al-Ni, Cu-Al-Zn, Cu-Al-Be and Cu-Al-Pd and are presented along with the available
experimental data. It is remarkable that all the third order elastic constants are negative, indicating
an increase in the vibrational frequencies under stress, giving rise to an increase in the strain-free
energy. The absolute values of the TOEC are large. This means that the bcc phase observed is
considerably anharmonic. The TOEC C144 representing the shear mode has a smaller value than
C111. Hence, the effect of pressure is much greater on longitudinal wave velocity than on the shear
wave velocity in the above Cu based SMA. The mode Grüneisen parameters of the acoustic waves
are determined based on the quasi-harmonic approximation method. The low temperature limit of
the lattice thermal expansion and the Anderson– Grüneisen parameter of these alloys are also
obtained.
Thermo-Elasticity of Materials from Quasi-Harmonic Calculations
