Phase-field modeling of paramagnetic austenite-ferromagnetic martensite transformation coupled with mechanics and micromagnetics

A three-dimensional phase-field model is proposed for simulating the magnetic martensitic phase transformation. The model considers a paramagnetic cubic austenite to ferromagnetic tetragonal martensite transition, as it occurs in magnetic Heusler alloys like Ni2 MnGa, and is based on a Landau 2-3-4 polynomial with temperature dependent coefficients. The paramagnetic-ferromagnetic transition is recaptured by interpolating the micromagnetic energy as a function of the order parameter for the ferroelastic domains. The model is numerically implemented in real space by finite element (FE) method. FE simulations in the martensitic state show that the model is capable to correctly recapture the ferroelastic and -magnetic microstructures, as well as the influence of external stimuli. Simulation results indicate that the paramagnetic austenite to ferromagnetic martensite transition shifts towards higher temperatures when a magnetic field or compressive stress is applied. The dependence of the phase transition temperature shift on the strength of the external stimulus is uncovered as well. Simulation of the phase transition in magnetocaloric materials is of high interest for the development of energy-efficient magnetocaloric cooling devices

Stability predictions of magnetic M₂AX compounds

Based on high throughput density functional theory calculations, we evaluated systematically the stability of 580 M₂AX compounds. The thermodynamic, mechanical, and dynamical stability and the magnetic structure are calculated. We found 20 compounds fulfilling all three stability criteria, confirming Cr₂AlC, Cr₂GeC, Cr₂GaC, Cr₂GaN, and Mn₂GaC, which have been synthesized. The stability trends with respect to the M- and A-elements are discussed by analyzing the formation energies, indicating that Cr and Mn containing M₂AX compounds are more stable than Fe, Co, or Ni containing compounds. Further insights on the stability are obtained by detailed analysis of the crystal orbital Hamilton population (COHP)

Towards engineering the perfect defect in high-performing permanent magnets

Permanent magnets draw their properties from a complex interplay, across multiple length scales, of the composition and distribution of their constituting phases, that act as building blocks, each with their associated intrinsic properties 1. Gaining a fundamental understanding of these interactions is hence key to decipher the origins of their magnetic performance2 and facilitate the engineering of better-performing magnets, through unlocking the design of the “perfect defects” for ultimate pinning of magnetic domains3. Here, we deployed advanced multiscale microscopy and microanalysis on a bulk Sm2(CoFeCuZr)17 pinning-type high-performance magnet with outstanding thermal and chemical stability 4. Making use of regions with different chemical compositions, we showcase how both a change in the composition and distribution of copper, along with the atomic arrangements enforce the pinning of magnetic domains, as imaged by nanoscale magnetic induction mapping. Micromagnetic simulations bridge the scales to provide an understanding of how these peculiarities of micro- and nanostructure change the hard magnetic behaviour of Sm2(CoFeCuZr)17 magnets. Unveiling the origins of the reduced coercivity allows us to propose an atomic-scale defect and chemistry manipulation strategy to define ways toward future hard magnets

Multi-physics phase-field modeling of magnetic materials

With the fast growth of economies around the globe, especially in warmer climate regions, the demand of cooling devices is expected to increase drastically within the next decades and with it the emission of greenhouse gases. In an attempt to develop a more energy efficient and environment friendly cooling device, a multi-stimuli concept utilizing the magneto- and elastocaloric effect was proposed. The goal of this work is to build a multi-physics phase-field model for the simulation of this multi-stimuli concept. Micromagnetic simulations are firstly introduced as a tool to simulate the relation between magnetic properties and microstructure. Micromagnetic simulations are performed on Y-Co and Sm-Co structures, showing that the magnetic properties, especially the coercivity of permanent magnets, strongly depend on microstructural features. In a second step, a new methodology for the extrapolation of micromagnetic simulations to temperatures around and above TC is introduced. A combination of micromagnetic simulations and the Arrott-Noakes equation allows for the calculation of the magnetocaloric effect, taking into account the influence of microstructure and magnetocrystalline anisotropy. Applying the methodology on Co2B nanograins shows good agreement with experimental results. In order to not only consider second-order materials, a multi-physics phase-field model is presented which combines a tetragonal martensite and cubic austenite phase-field model with micromagnetism. With a finite element implementation of this three-dimensional real-space model, the structural and magnetic features observed in MSMA are simulated. In addition, it is shown that the temperature-dependent energy formulation allows for the simulation of the martensite-austenite transition, including the thermal hysteresis. As final step, the micromagnetic energy terms are modified to also take into account magnetic transitions that occur along the martensite-austenite transition. Depending on the modification of the magnetic energy terms with the phase order parameter, the model can take into account the transition between a ferromagnetic martensite and paramagnetic austenite, as well as the transition between a paramagnetic martensite and ferromagnetic austenite. While the application of uniaxial pressure shifts Tt to higher temperature, the direction of the shift with applied magnetic fields depends on the magnetic transition considered. Summarizing, after presenting the individual physics to be considered, this work presents a new multi-physics phase-field model, which is capable of capturing the martensite-austenite transition under the consideration of different magnetic transitions. With the ability to simulate the thermal hysteresis and shift of Tt with external stimuli, the presented model is capable of simulating the multi-stimuli concept

Phase-field modelling of paramagnetic austenite–ferromagnetic martensite transformation coupled with mechanics and micromagnetics

A three-dimensional phase-field model is proposed for simulating the magnetic martensitic phase transformation. The model considers a paramagnetic cubic austenite to ferromagnetic tetragonal martensite transition, as it occurs in magnetic Heusler alloys like Ni2 MnGa, and is based on a Landau 2-3-4 polynomial with temperature dependent coefficients. The paramagnetic–ferromagnetic transition is recaptured by interpolating the micromagnetic energy as a function of the order parameter for the ferroelastic domains. The model is numerically implemented in real space by finite element (FE) method. FE simulations in the martensitic state show that the model is capable to correctly recapture the ferroelastic and -magnetic microstructures, as well as the influence of external stimuli. Simulation results indicate that the paramagnetic austenite to ferromagnetic martensite transition shifts towards higher temperatures when a magnetic field or compressive stress is applied. The dependence of the phase transition temperature shift on the strength of the external stimulus is uncovered as well. Simulation of the phase transition in magnetocaloric materials is of high interest for the development of energy-efficient magnetocaloric cooling devices