Final Report Summary - MESOPHYSDEF (Mesoscopic framework for modeling physical processes in multiphase materials with defects)
Increasing the performance of novel functional materials such as shape memory alloys, multiferroics, nanocomposites or heteroepitaxial films depends crucially on our ability to understand multiscale aspects of the physical processes occurring in these materials. The inherent sensitivity of their physical properties to lattice distortions opens a possibility of engineering novel materials with optimal properties that are achieved by the application of strain. In order to perform this strain engineering systematically, one has to gain a deep theoretical insight into the interplay between the imposed field (for example, strain) and the response of the material (phase stability, microstructure, spontaneous polarization or magnetization). Unfortunately, many of these phenomena occur at the length and time scales that fall within the so-called "micron gap" and thus they are out of the reach of the currently available computational schemes.
The main objective of this research project has been to bridge this micron gap in modeling materials by developing a solid theoretical framework that is rooted at the mesoscale. The main advantage of this model is its universality for a class of materials that share the same reference crystal structure (more specifically, the same space group symmetry) and exhibit the same behavior (e.g. a cubic to tetragonal phase transition). Secondly, the model is parameterized by the data obtained from smaller length scales (e.g. first principles or atomistic calculations) and, at the same time, predicts a macroscopic response of the material. Unlike finite element calculations, the model retains the relevant details associated with the discrete nature of the lattice. By including the interactions between the microstructure and order parameters associated with physical observables, the model developed here is capable of studying the structure-property relationships in crystalline materials. In particular, it can be used to provide answers to these challenging questions:
How to describe the elastic response of a crystalline material to an arbitrary distribution of defects?
How these defects self-organize in the microstructure?
How they alter the physical properties of the material?
The starting point of virtually all available mesoscopic models is that the action of the lattice defect at every point of the simulated volume is known. While this is an easy thing to do in isotropic materials, it may be prohibitively difficult in materials of low symmetry and/or whenever the density of defects increases during simulations. Moreover, many of these models are lattice-free and thus an extra care must be exercised to keep the dislocation network permissible, i.e. to restrict the dislocations to emanate from free surfaces or from other dislocations. Within the model, we take a completely different viewpoint. The crystal lattice is regarded as an elastic template whose long-range distortions are due to localized fields of defects. In order to insert a dislocation or a point defect into the crystal, one specifies the position of the defect in the discretized volume and its character. The latter is accomplished by giving a rank-2 tensor at the position of the defect that characterizes its coupling to the lattice. The deformation of the lattice is described by the free energy that is minimized subject to a set of conditions that ensure a continuity of the body, i.e. the surrounding lattice responds to the localized defects by just stretching or compressing atomic bonds without creating cracks or other defects.
This model is not only conceptually simple and based on correct physics, but it is also completely general in that it can be used to study the response of the lattice to an arbitrary dislocation network. These can be either generated in computer (for example, to study the effect of some important dislocation junctions on physical properties). However, they can also be measured by electron tomography, in which case the framework provides a systematic tool to understand the mechanism by which a particular distribution of dislocations gives rise to changes in physical properties of materials. For example, a straightforward extension of this model would provide a tool that would shed light onto the mechanism by which the misfit of lattice parameters in heteroepitaxial films leads to depolarization or demagnetization of the thin film grown on the top.
The aim of this research project was to lay down the foundations that are needed to demonstrate the applicability of this approach for a range of problems that cannot be studied by other means. There are three main avenues in which this project is now evolving: (i) implementation of algorithms that describe the evolution of the dislocation networks and point defects, (ii) coupling of lattice distortions with other order parameters, such as polarization or magnetization, (iii) formulation of a mesoscopic framework based on finite deformations that will will describe the response of the material to shock loading (including plasticity, heat transfer, and phase transitions). Some of these applications have been already outlined in the literature. A comprehensive summary of all achievements and future work is available online at http://mesophysdef.ipm.cz.