Introduction to Phase-field Method of Ferroic Domain Structures 

Long-Qing Chen
Department of Materials Science and Engineering and Materials Research Institute, Penn State University, University Park, PA 16802, USA

Materials research is largely concerned with the study and manipulation of the spatial and temporal evolution of structural, magnetic, electric polarization, charge, and chemical domains in a material as well as their responses to changes in environmental conditions during processing and in service. This tutorial will give a brief introduction to the phase-field method for modeling and predicting hierarchical materials microstructures and properties and their evolution under different mechanical and electric stimuli with a particular emphasis on ferroic domain structures. Phase-field method describes a mesoscale microstructure through a set of continuum fields such as the spatial distributions of atomic density, chemical composition, long-range atomic order, crystallinity, ferroic order, defects, etc. It can handle complex microstructures and takes into account the interfacial and defect energies as well as the long-range electrostatic, magnetic, and elastic interactions within a mesoscale microstructure. It has been successfully applied to modeling and predicting mesoscale microstructure evolution during ferroic phase transitions and domain formation, solidification, grain growth, particle coarsening, electrochemical processes, and plastic deformation. A number of examples from our recent applications of phase-field method to ferroelectric domain structures will be presented to illustrate the applications of the phase-field method to help interpreting experimental observations as well as to provide guidance to achieve desirable mesoscale microstructures and thus properties of materials. The presentation will also give a brief introduction to the phase-field software package mu-PRO and its applications to ferroic materials.  I will demonstrate how one can learn and start to use phase-field simulations to understand domain structure evolution and to compute effective properties of inhomogeneous microstructures without becoming an expert in the phase-field method.

Chen is the Donald W. Hamer Professor of Materials Science and Engineering, Professor of Engineering Science and Mechanics, and Professor of Mathematics at Penn State.  He received his Ph.D. from MIT in Materials Science and Engineering in 1990 and joined the faculty at Penn State in 1992. He has published over 600 papers in the area of computational microstructure evolution and multiscale modeling of structural metallic alloys, functional oxides, and energy materials. For his research accomplishments, he has received numerous awards including the 2014 Materials Research Society (MRS) Materials Theory Award, a Guggenheim Fellowship, a Humboldt Research Award, the 2011 The Minerals, Metals and Materials Society (TMS) EMPMD Distinguished Scientist Award, and ASM International Silver Medal. He is a Fellow of TMS, MRS, American Physical Society (APS), The American Association for the Advancement of Science (AAAS), American Ceramic Society (ACerS), and ASM International (ASM). He is a Clarivate Analytics Highly Cited Researcher and the Editor-in-Chief for npj Computational Materials published by Springer-Nature.