Toward an Effective Interaction Potential Model for the Shape Memory Alloy AuCd
by
Venkata Suresh Guthikonda and Ryan S. Elliott
in
AEM Report Number 2008-1
Keywords: Shape Memory Alloys, Martensitic Transformations, Morse Potential, Material Stability, Effective Interaction Potentials, AuCd
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Abstract:
The unusual properties of Shape Memory Alloys (SMAs) result from a lattice level Martensitic Transformation (MT) corresponding to an instability of the SMAs crystal structure. Currently, there exists a shortage of material models that can capture the details of lattice level MTs occurring in SMAs and that can be used for efficient computational investigations of the interaction between MTs and larger-scale features found in typical materials. These larger-scale features could include precipitates, dislocation networks, voids, and even cracks. In this paper, one such model is developed for the SMA AuCd. The model is based on Effective Interaction Potentials (EIPs). That is, atomic interaction potentials that are explicit functions of temperature. In particular, the Morse pair potential is used and its adjustable coefficients are taken to be temperature dependent. A fitting procedure is developed for the EIPs that matches, at a suitable reference temperature, the lattice parameters, instantaneous bulk moduli, thermal expansion coefficients, and heat capacities of FCC Au, HCP Cd, and the B2 cubic austenite phase of the Au-47.5at%Cd alloy. The resulting model is explored using branch-following and bifurcation techniques. A hysteretic temperature-induced MT between the B2 cubic and B19 orthorhombic crystal structures is predicted. The predicted MT is found to have characteristics that compare quite well with the experimentally observed behavior of AuCd SMAs. Unfortunately, the model exhibits an unphysical negative thermal expansion at high temperatures.
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