Elastic and Plastic Deformation in Binary Alloy Crystallization

Oakland University, Rochester MI

Investigators

Abstract

This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. A phase field crystal (PFC) model has been developed to study elastic behavior in the crystallization of pure materials. This was achieved by modeling the mass density on diffusive time and atomic length scales. The PFC approach naturally incorporates elastic and plastic deformations, multiple crystal orientations and free surfaces and was used to study grain boundary energy, liquid phase epitaxial growth and the yield strength of nano-crystalline solids. One ingredient not included in the original work was concentration which is particularly important since most materials contain at least two elements and the relative concentration of the elements can significantly impact the non-equilibrium processes and resulting microstructures. In addition, since all elements have different lattice structures and sizes, elastic and plastic deformations are strongly influenced by concentration. The goal of the proposed research is to develop a computationally efficient model of microstructure formation and stability in binary alloy crystallization phenomena and to use this model to study technologically important applications such as dendritic growth, eutectic crystallization and liquid phase epitaxial growth in binary alloys. The model will be developed by introducing a density field for each element, constructing an appropriate free energy functional F of these fields and assuming the dynamics are dissipative and driven to minimize F. The PI has extensive experience in constructing such models and has developed, in collaboration with others, models of eutectic solidification, driven charge density waves, polymorphic crystallization and imbibition. For the purposes of this research the PI has developed a preliminary model of binary alloy crystallization that includes elastic and plastic deformation. This model combines the PFC approach with a model of eutectic solidification. Initial calculations indicate that this preliminary model incorporates the generic features of a eutectic phase diagram and many of the typical patterns observed in non-equilibrium phenomena such as dendrites and eutectic crystallites with lamellar structures. In addition to these standard features the model includes all the elastic behavior incorporated in the original PFC model discussed above and was designed so that the concentration dependence of the lattice and elastic constants can be easily adjusted. While this preliminary model may need to be fine tuned, these initial calculations indicate a high likelihood that the PI will accomplish the primary goals of this project. The research will have broad impact on both fundamental and applied science. Undergraduate students will be involved in the projects. %%% This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. A new model has been developed to describe microstructural evolution of binary alloys that also includes their elastic and plastic behavior as a function of their relative concentration. The research will have broad impact on both fundamental and applied science. Undergraduate students will be involved in the projects. ***