Phase Field Crystal Simulations of Polycrystalline Grain Growth and Defects Evolution Under the Effect of Atomic Density and Undercooling

Using a previously developed phase field modeling method, where interface energies are described by spherical gaussians that allow the modeling of complex anisotropies, a new phase field model was developed to model 5-D anisotropy in polycrystalline grain growth. We present the use of quaternions, assigned to individual grains as orientations and misorientations for grain boundaries, as a means of simulating the ongoing mesoscale changes during anisotropic polycrystalline grain growth. The full 5-D landscape is scanned in MATLAB, and the grain boundary (GB) energy of each grain boundary is calculated from the continuous function developed by Bulatov et al. MATLAB is then used to find all local minima in the GB energy which are stored for use in the phase field model. The methodology of including these minima in the phase field model involves using 2-D gaussian switches, which match the misorientation between grains with misorientations for the GB energy minima. Within a threshold range of the minima misorientation, the switch activates a spherical Gaussian to set the GB energy to the desired value creating in combination a full 5D GB energy space. This creates a GB energy that morphs in real time and space as the GB plane or grain orientations change. Implementation methods of the model are outlined for the Multiphysics Object Oriented Simulation Environment (MOOSE), where reduced order parameters still retain individual grain identification useful for individually assigned quaternions.

In this paper, a numerical study of the convection effect on polycrystalline grain growth is performed. The coupled two-dimensional polycrystalline phase field model, energy equation and Navier-Stokes equations are solved, which is based on the discontinuous Galerkin finite element method. The numerical algorithm is validated, and the effect of the external convection flow is examined for growth of grains with different orientation. Results show that the forced convection flow affects the phase and orientation field distribution by changing the temperature gradient in the solid/liquid interface.

Analytical and numerical techniques are used to study the solidification of 1/2π and 3/2π wedges of liquid which are initially at their fusion temperature. An enthalpy method is used to obtain numerical solutions to these problems and the results are compared with asymptotic solutions for large and small Stefan numbers (the Stefan number being defined as the ratio of latent to sensible heats). The new solutions for small Stefan number are shown to provide surprisingly good approximations, especially for the 3/2π wedge. New results for heat transfer in a wedge (in the absence of a change of phase) are derived and applied in the asymptotic analysis, as are new conservation laws for the Stefan problem.

Two‐dimensional computer simulations using a multiphase field theory were carried out to study polycrystalline grain growth in the presence of second phase mobile particles.

In this paper, a numerical study of the convection effect on polycrystalline grain growth is performed. The coupled two-dimensional polycrystalline phase field model, energy equation and Navier-Stokes equations are solved, which is based on the discontinuous Galerkin finite element method. The numerical algorithm is validated, and the effect of the external convection flow is examined for growth of grains with different orientation.

The evolution of void defects in metallic films based on a nonlocal phase field model

Numerical study of solid-liquid phase change by phase field method

Effects of crystal plane orientation on blistering kinetics and defect evolution in silicon implanted by hydrogen molecular ions

The grain size is a key characteristic to strongly affect the mechanical properties and performance, and the presence of additional phases plays an important role in affecting the microstructure evolution. In this work, a phase field model was adopted for immobile second-phase particles distributed at grain boundaries and analysed its pinning effect on polycrystalline grain growth. According to the size and distribution characteristics of second-phase particles in extruded AZ80 magnesium alloy, the effects of the particle morphology, particle size and volume fraction on the grain growth were investigated. The results showed that small-sized rod high-dispersion particles exhibit a stronger pinning effect on grain boundary migration. In addition, the generalised Zener relation of R lim = 2.49r sp/f sp −0.322 was obtained for the particles located at grain boundaries.

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

GrainNN: A neighbor-aware long short-term memory network for predicting microstructure evolution during polycrystalline grain formation

Modeling length scale effects on strain induced grain boundary migration via bridging phase field and crystal plasticity methods

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

We develop a step‐flow model for the heteroepitaxy of a generic, strained, substitutional, binary alloy. The underlying theory is based on the fundamental principles of modern continuum thermodynamics. In order to resolve the inherent disparity in the spatial scales—continuous in the lateral directions vs. atomistically discrete along the epitaxial axis—we represent the film as a layered structure, with the layer height equal to the lattice parameter along the growth direction, thus extending the classical BCF framework [W. K. Burton, N. Cabrera, and F. C. Frank, Philos. Trans. Roy. Soc. London Ser. A, 243 (1951), pp. 299–358] to growth situations in which the bulk behavior impacts the surface evolution. Our discrete‐continuum model takes the form of a free‐boundary problem for the evolution of monoatomic steps on a vicinal surface, in which interfacial effects on the terraces and along the step edges couple to their bulk counterparts (i.e., within both film and, indirectly, substrate). In particular, the proposed constitutive theory is such that the film layers are endowed with (generalized) Ginzburg–Landau free energies that account for phase segregation and, concomitantly, competition between gradient‐driven coarsening and elastic refining of the separated domains. Importantly, the bulk and terrace effects are intertwined with the step dynamics via novel boundary conditions at the step edges derived from separate balance laws for configurational and microforces. Specifically, the former forces are associated with the evolution of defects (in the present setting, the steps), whereas the latter forces accompany micro‐ and nanoscopic changes in an order parameter (for a binary alloy subject to diffusion‐mediated phase separation, the atomic density of one of its components or, equivalently, the relative atomic density), and the postulated balances should be viewed as generalizations to a dynamic, dissipative setting—such as epitaxial growth, a far‐from‐equilibrium process—of more standard variational calculations.

Applications of phase field fracture in modelling hydrogen assisted failures