晶体相场模拟微观组织生长的讲义

Figure 2: Examples of dislocation glide during shear and crack growth using the PFC method7,1
However there are situations where atomic length and time scales are needed and therefore MD might be better suited. An example of this is the effect of grain boundaries on ion bombardment. The benefit here is that PFC method has generated a blurred atomic picture but to some degree can be used to represent the atomic positions. The resulting microstructures from PFC can be used by MD simulations, this is a rare example where information across scales occurs in reverse. An example of a 3D generated polycrystalline BCC sample using PFC is shown in 3.
More recently the PFC method has shown promise in addressing the short-comings of PF. The primary difference between PFC and PF is that the order parameter is refashioned as a temporally coarse but spatially described by an atomic probability density (APD)5. This is done by choosing
∗stefanb@emergy functional which is minimized by an APD that is spatially periodic for crystalline solids and constant for liquids. It so happens that such description incorporates the necessary physics to describe things like surface tension, elasticity, anisotropy, dislocations etc. Additionally diffusive behaviour can be studied as a consequence of the time scale. In Fig. 1 an example from Provatas and Elder 6 is showing the ADP field of a partially solidified simulation. Many aspects such as orientation, liquid/solid interface, and dislocations are highlighted.
Growing Microstructures using Phase-Field Crystal
Stefan Bringuier∗1
1University of Arizona, Department of Materials Science and Engineering
December 16, 2013
1 Overview
The phase-field (PF) and phase-field-crystal (PFC) methods are relatively new approaches to modelling materials based on the variational principles of minimizing the free energy of a given system. More specifically, PFC is concerned with minimizing the free-energy functional by considering density fields that have periodic spatial variation1. Thus for crystalline solids this inherently captures the periodic description. Furthermore such model naturally incorporates elastic/plastic deformations and captures varying grain boundary orientations.
2
experimental or other computational methods. Phase-field-crystal may provide some value insight since it is possible
to grow microstructures and interfaces.These structures can then be subjected to external fields or non-equilibrium events to extract properties7. For example in Fig. 2 the dislocation glide velocity and crack propagation behaviours have been study.
Figure 1: PFC simulation showing ADP field and the various micro structure properties captured.6
2 Proposed Research
The importance of structural information such as grain boundary (GB) interfaces is crucial to understand the properties of a given material. For this reason computational methods such as molecular dynamics (MD) and first principle calculations are utilized to subject these interfaces to varies conditions. However, due to constraints from time and spatial scales it is computational difficult to grow crystals/polycrystals and furthermore interfaces using MD or first principle calculations. In some cases the use of mathematical geometric constructions make ease in building GB, an example of such approach are the coincident-site lattice model and Voronoi tessellation method. Although very useful, such methods are limiting and do not necessarily provide agreement with experimental microstructures. In addition even after considerable annealing and equilibration cycles the resulting interfaces might still reside in local minima. Thus determining the most suitable initial configuration requires some prior knowledge from
Computational investigation of microstructure evolution using PF to date has been well studied2–4. The PF method makes use of field variables such as impurity concentration and temperature to evolve the system microstructure. This has been extensively used to study dendritic growth in metals and alloys as well as spinodal decomposition. The dynamics of the system are driven by the dissipative minimization of a phenomenological determined free-energy functional. One of the limitations concerning phase field modelling is that the formulation requires uniform fields that are in equilibrium. As a result of this properties such as elasticity, anisotropy, and grain orientations are not inherent in the physical description. Although this has been addressed via different methods, PF has yet been unable to handle diffusive phase transformations and anisotropic surface energy to name a few 1,5.