Modeling Non-Equilibrium Microstructure Formation

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Technical SummaryThis award supports theoretical and computational research and education to further develop methods of phase field modeling to the atomic length scale and diffusive time scales and enable the simulation of multi-component alloys.The understanding of many non-equilibrium processes has been enhanced by the use of "phase-field" modeling methods. These methods have proven very successful in modeling many aspects of solidification phenomena and are now incorporated in commercially available software packages. More recently the PI and collaborators have introduced a second generation of phase field models that describe phenomena on atomic length and diffusive time scales. This "phase field crystal" method naturally incorporates elasticity, plasticity, anisotropy and multiple crystal orientations in addition to all the physics of traditional models of solidification and phase segregation.While the phase field crystal models developed for monatomic and binary alloys can describe many physical phenomena, including grain growth, epitaxial growth, eutectic solidification, the yield strength of polycrystalline materials, climb and glide, and grain boundary melting, there are many important phenomena that are beyond description by the current models. For example, the binary model cannot describe sublattice ordering in multi-component alloys. This is a key issue since sublattice ordering is extremely common and influences structural properties. Another limitation of current phase field crystal models is that they describe spherically symmetric particles and thus cannot describe the physics associated with extra degrees of freedom, such as rotation. A technologically important example which exploits these freedoms is elastomers; the rotation of elongated cross-linked polymers allows shear strains at almost zero energy cost. The goal of this project is to greatly extend the applicability of phase field crystal modeling to incorporate sublattice ordering and anisotropic particles. The PI also plans to extend the amplitude expansion of the monatomic phase field crystal developed by Goldenfeld and collaborators to binary systems. The amplitude approach incorporates much of the essential elastic and plastic behavior and is more amenable to analytic and numerical calculations. The resulting model will be used to examine the influence of the discrete nature of the crystalline lattice and compositional in homogeneities on morphological instabilities in strained epitaxial films.The PI has a contract with Wiley publishing to write a book on phase field modeling in materials science. Much of the text will be devoted to the phase field crystal formulations developed in this proposal and in the expired NSF grant. The text will be written as an instructional guide for engineering and physics students who wish to learn the fundamentals and technical details of phase field modeling. The PI will hire and train undergraduate students in cutting edge computational materials physics. The work will also have an impact on many areas of research since the methods developed are applicable to a wide range of phenomena such as the structural properties of multi-component alloys, the exotic elastic properties of elastomers and the formation of quantum dots in strained epitaxial growth.Non-Technical SummaryThis award supports theoretical and computational research and education to further develop a potentially powerful method for computer simulation of materials that was developed by the PI and collaborators. The research involves the extension of a modeling technique, called phase field modeling, that is computationally fast but useful on length scales of many atoms. The extension enables computer simulations to access information on much shorter length scales, atomic length scales, and longer times. Simulations of materials processing and related materials phenomena that span many length scales from single atoms to microns are promising applications of the new method.The PI will also write a book on phase field modeling and its application to modeling materials and materials related phenomena. Undergraduate students will be involved in research activities directly related to this project.