Coupled microstructural-compositional evolution informed by a thermodynamic database using the hybrid Potts-phase field
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Coupled microstructural-compositional evolution informed by a thermodynamic database using the hybrid Potts-phase field model Jordan J. Cox1, Eric R. Homer1* and Veena Tikare2 1 Dept. of Mechanical Engineering, Brigham Young University, Provo, UT 84602, U.S.A. 2 Advanced Nuclear Fuels Cycle Technology Dept., Sandia National Laboratories, Albuquerque, NM 87185, U.S.A. ABSTRACT A recently introduced hybrid Potts-phase field method has demonstrated the ability to evolve microstructures in conjunction with compositional fields tied to different phases. In this approach, Monte Carlo Potts methods are used to evolve the microstructure while phase field methods are used to evolve the composition, and the two fields are coupled through free energy functionals. Recent developments of the model allow different multi-component alloy systems to be simulated by using thermodynamic databases and kinetic quantities to dictate the behavior. An example of the method using the aluminum-silicon binary system is demonstrated. INTRODUCTION Microstructural and compositional evolution represent two key phenomena influencing the processing of alloyed materials. The local microstructure is usually described in terms of the grains and grain boundaries while the composition focuses on constituent and phase distribution. These two phenomena are fundamentally linked but due to their respective complexities are frequently modeled individually [1]. Recent work by some of the authors developed a new Potts-phase field method to model the simultaneous evolution of microstructure and composition [2]. The method couples the Monte Carlo Potts and phase field methods in a way that balances computational efficiency with solution accuracy. The Monte Carlo Potts model has proved to be an efficient method to evolve large microstructures, including a variety of different phenomena [3]. In practice, the method evolves a collection of individual particles, or sites, defined on a lattice, using statistical models derived from the Monte Carlo method. Each site is assigned a spin, which can represent a feature of the microstructure, including grain membership, orientation etc. Over time, the spin at a given site is allowed an attempt to change to a different spin, thereby evolving the microstructure. Spin changes that lower the overall energy of the system are accepted while spins that raise the energy are accepted with a Boltzmann probability. Over time, the system lowers its overall energy. The phase field model has proven to be efficient for modeling phase, composition or microstructural evolution, as well as a variety of other phenomena [3]. However, the three are not typically coupled due to the complexity of generating an appropriate free energy functional. In practice, the phase field method is a continuum thermodynamic method that utilizes continuum or phase field variables to represent the state of the system at a given point. Kinetic equations, such as the Cahn-Hilliard or Ginzburg-Landau equations, govern the evolution of each
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