Controlling Grain Boundaries by Magnetic Fields

Abstract

The ability to use external magnetic fields to influence the microstructure in polycrystalline materials has potential applications in microstructural engineering. To explore this potential and to understand the complex interactions between electromagnetic fields and solid-state matter transport we consider a phase-field-crystal (PFC) model. Together with efficient and scalable numerical algorithms this allows the examination of the role that external magnetic fields play on the evolution of defect structures and grain boundaries, on diffusive time scales. Examples for planar and circular grain boundaries explain the essential atomistic processes and large scale simulations in 2D are used to obtain statistical data on grain growth under the influence of external fields.It is well known that material properties of polycrystalline materials are strongly influenced by the average grain size. For example, in some compounds the magnetic coercivity can increase by orders of magnitude as the grain size changes from nano to micron scales [1][2][3][4]. In metals the yield strength can not only change dramatically with grain size (the so-called Hall-Petch effect [5-10]) but it is also influenced by details of the grain size distribution [11]. Each of the cases highlights the importance of the grain structure and the technological need to understand and control its formation. The use of external magnetic fields offers additional degrees of freedom to synthesize materials and to tailor the grain structure and thus material properties. Although evidence for the interactions between external magnetic fields, diffusion and irreversible deformation mechanisms have been gathered over the years, see the review [12], a global yet detailed understanding of the interactions between magnetic fields and solid-state matter transport is far from being reached. In this Letter we analyze the properties of a theoretical model, which allows the description of the basic physics of magnetocrystalline interactions in a multiscale approach, combining the dynamics of defects, dislocation networks and grain boundaries with experimentally accessible microstructure evolution on diffusive time scales. The basic mechanisms of this interaction can be understood on thermodynamic arguments. In magnetic materials the magnetic moments are aligned with a sufficiently strong external magnetic field. If the magnetic properties of the material are anisotropic, the bulk free energy differs for differently oriented grains and the energy difference can influence grain boundary (GB) movement. Assuming setups of two differently oriented grains in a strong magnetic field, see Fig 1, the total energy of the system reads E = γl + ∆f A 0 + f 1 (A 0 + A 1 ), where l is the length of GB and A i , f i the size and the energy density of the i-th grain, ∆f = f 0 − f 1 and γ the energy of the GB. The dynamics of the GB can be described by Mullins-type models [13] v = −M (γκ − ∆f ) (1) FIG. 1. Two grains with size A0 and A1 separated by a GB with size l, which moves locally w...

Magnetically induced/enhanced coarsening in thin films

“…However, in the limit of strong external magnetic fields, B ext , the magnetization, m, can assumed to be homogeneous in the crystal. As shown in [18] the magnetization becomes perfectly aligned with the external magnetic field and independent on the relative orientation of the crystal. For paramagnetic or ferromagnetic materials near the Curie temperature, the magnitude of the magnetization m = |m| dependents on the magnitude of the external magnetic field B ext .…”

“…The model in [16][17][18] combines the rescaled number density ϕ of the original PFC model [2,3] with a mean field approximation for the averaged magnetization m. The total energy,…”

“…where m is considered as a parameter. Increasing m leads to increasing anisotropy and magnetostriction [18]. The external magnetic field B ext and thus m is assumed to be parallel to the thin film.…”

“…External magnetic fields during processing influence grain growth and as such have been proposed as an additional degree of freedom to control the grain structure, see [14,15] for reviews. The PFC model has been extended to include magnetic interactions in [16,17] and was used in [18] to explain the complex interactions between magnetic fields and solid-state matter transport. An applied magnetic field influences the texture during coarsening due to the anisotropic magnetic properties of the single grains.…”

A comparison of different approaches to enforce lattice symmetry in two‐dimensional crystals

“…These models, maybe with exception of the last, due to its increased complexity, have been intensively used to analyse the influence of lattice symmetry on both the structure and dynamics of crystalline and defected systems in 2D materials, see e.g. [15][16][17][18]. The dynamics is thereby based on the assumption of overdamped conservative dynamics, which read…”