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Summer Research Fellowship Programme of India's Science Academies

Phase Field Models for Microstructure Evolution

Abhishek Kumar Mishra

National Institute of Technology, Warangal, Telangana, 506004

Prof. T A Abinandanan

Indian Institute of Sciences, Bengaluru, Karnataka, 560012

Abstract

Phase Field methods are thermodynamics-based continuum approaches, which are often used for simulating phase transformations and microstructure evolution at the mesoscopic scale. Phase Field models are based on the assumption of diffuse-interface, which allows us to study the evolution of complex grain morphologies without any presumption about their shape, size or distribution in the initial stage. In phase field methods, the system is described in terms of phase field variables and order parameters which are functions of time and spatial coordinates, and are used to keep track of phases present at different locations in the system. The description of the system in terms of phase field variables and order parameters provide a unique way to incorporate the energy of the system through introduction of Free Energy functional, which is a function of phase variables, order parameters and their gradients. Free Energy functional can be suitably written in terms of phase field variables and order parameters to incorporate energies associated with strain, interfaces or external effects like electric potential, etc. The system is then evolved towards a state of equilibrium through time, as Free Energy functional is minimised by utilising the concepts of variational calculus, giving rise to defining relations between order parameters and phase variables for microstructure evolution. The equation is then numerically solved to get microstructures at different time intervals. This work investigates the microstructure evolution of a binary system undergoing spinodal decomposition utilising a phase field model based on Cahn-Hilliard equation, and further, evolution of a binary system undergoing order-disorder transformation utilising a phase field model based on Allen-Cahn Equation. Later, different types of phenomena associated with phase transformations and microstructure evolution such as precipitate coarsening, grain growth, polycrystalline spinodal decomposition, etc. are investigated utilising phase field models based on the combinations of Cahn-Hilliard equation and Allen-Cahn Equation.

Keywords: Spinodal Decomposition, Cahn-Hilliard Equation, Allen-Cahn Equation, Order-Disorder

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