A free energy model for magneto-mechanically coupled NiMnGa single crystals

摘要

This paper presents a one-dimensional magneto-mechanical model for NiMnGa. Following a modeling approach developed by the authors for conventional shape memory behavior and ferroelectricity, a constitutive Helmholtz free energy landscape with strain and magnetization as order parameters is constructed for a representative meso-scale lattice element. The landscape includes three paraboloidal energy wells representing the two easy-axis and one hard-axis martensite variants distinguishable in the chosen coordinate system. The resulting stress- and magnetic-field-dependent Gibbs free energy expressions are then used within the theory of thermally activated processes to derive a series of phase-fraction evolution equations. The phase fractions subsequently determine the macroscopic strain and magnetization of a sample of NiMnGa by a standard averaging procedure. Results from the model are compared to experimental data and demonstrate the model's ability to reproduce constitutive behaviors of the material. Future work includes an extension to a full thermo-magneto-mechanical model accounting for the occurrence of austenite and inhomogeneity effects and configured to function within the tensile-stress regime.