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Third-order elastic constants and low-temperature thermal expansion of the shape memory alloy Cu–Al–Ni

Numerous 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 austenite phase in Cu-based shape memory alloys is known for its high elastic anisotropy. The complete set of second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of Cu–Al–Ni in the β phase has been obtained. A combination of the deformation theory and finite strain elasticity theory has been employed to get the expressions for the strain energy density of the lattice. The theory is based on the Keating’s approach by taking into account the two-body as well as three-body interactions up to second nearest neighbors in the Cu–Al–Ni lattice. The elastic constants are compared with the reported experimental values. The relevant role of the comparatively large TOECs in describing the instability of the bcc structure towards the martensitic transformation is also discussed. The aggregate elastic properties, such as the adiabatic bulk modulus, shear modulus, Cauchy pressure and anisotropy factor, are calculated. The mode Gruneisen 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–Gruneisen parameter of Cu–Al–Ni are also obtained.