Phase field model for ferromagnetic domain evolution during martensitic transformation of Heusler alloys

Abstract

As the energy consumed by cooling systems is expected to increase over the next decades, magnetocaloric cooling systems are of high interest as a promising more energy efficient alternative to conventional vapor compression refrigerators.1–3 Heusler alloys show large magnetocaloric effects (MCE) and are therefore of high interest for possible application in magnetocaloric cooling devices.4,5 They exhibit a magnetostructural transition resulting in larger entropy changes ΔS, thus in larger adiabatic temperature changes ΔTad. We propose a phase field model based on Landau theory to simulate the magnetic domain evolution during the martensite formation, e.g. in Heusler alloys. With our model, we are able to simulate field- and pressure-induced phase transitions, including the martensite and magnetic domain evolution. This is of high interest for a multicaloric cooling cycle as proposed by Gottschall et al.6 In the model, the three order parameters η1, η2, and η3, represent the three martensite variants in a cubic to tetragonal phase transition. The energy of the martensite transformation is described by a Landau-type formulation after Cui et al.7 and is coupled with micromagnetic formulations to take magnetism into account. The 3D finite-element (FE) implementation has been performed within the MOOSE framework.8 The model is capable of reproducing the formation and evolution of domains in magnetic materials under external magnetic field (Fig. 1) or mechanical loading. Modeling field- and pressure-induced tansformation aims at investigating pressures and fields used in a multicaloric cooling cycle. The FE implementation further allows to investigate the influence of microstructure on the MCE. The authors acknowledge the support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No 743116, project CoolInnov).