European Journal of Applied Physics ISSN: 2684-4451 DOI: http://dx.doi.org/10.24018/ejphysics.2022.4.3.169 Vol 4 | Issue 3 | May 2022 3 Abstract — In this work, we have studied the precipitate growth behavior of a metal matrix when subjected to hydrostatic pressure. We utilized Zenner-Frank phase field kinetics with integrated free energy density functional based on volumetric strain energy. We studied the precipitate growth up to 2 GPa under varying bulk modulus of the precipitate phase. We observed that subjecting to hydrostatic pressure influences the growth kinetics by reducing the precipitate growth under time evolution. In addition, the bulk modulus of the precipitate has shown an abnormality in the growth behavior compared to general observations under hydrostatic pressure. This work contributes to the smart tailoring of novel materials to reduce detrimental impacts on holistic material properties, used in large hydrostatic pressure applications. Keywords — Free Energy Density Functionals, Phase Field Modeling, Precipitate Growth, Microstructure Evolution, Zenner-Frank Kinetics. I. INTRODUCTION 1 Phase field modeling (PFM) can be considered an important simulation tool for scientists and engineers to identify the evolution of microstructures under unique environments [1]. PFM stems from the classical solid state diffusion definition (Fick’s law) by integrating Fick’s definition to incorporate interface tracking between multiple phases. Where, PFM defines chemical potential as the driving parameter rather than the composition in classical definition [1], [2]. By incorporating chemical potential, non-classical diffusion phenomena is successfully addressed to describe experimental observations (uphill diffusion, grain growth, etc.) [1], [3]. PFM utilizes free energy of the considering system unique to a specific environment. However, general Gibbs free energy is defined only based on composition, and composition is a conserved property for any given system, therefore, non-conserved properties such as phase/microstructure are not accounted [2], [4]. To address the contributions from both composition and microstructure, in PFM, free energy is defined as a free energy functional (FF). In this approach, total free energy is embedded as a function of chemical-free energy and interfacial diffusion processes of composition and microstructures [2]. Due to this definition, FF helped tremendously in defining unique properties specific to a phase system not only based on internal or chemical contributions but under external fields (uniaxial stress, hydrostatic pressure, electric field, etc.) [2], [3], [5]–[7]. We extract a few previous works performed based on defining free energy density unique to specific external conditions. Initially, PFM to study precipitate growth at uniaxial stresses is soundly demonstrated by Mukherjee et al. [2]. They utilized Zenner-Frank (ZF) phase field kinetics under elastic strain energy contributions to FF. Secondly, precipitate kinetics under thermal energy such as isothermal aging is widely studied by Weerasekera et al. [1], [3]. They have also used ZF kinetics to address the phenomena. Ohno et al. [8] studied phase transformations in the steel welding process using Kurz-Giovanola-Trivedi (KGT) model. They used the KGT integrated FDF to define the solid-fluid multiphase transformation process. Yang et al. [5] studied phase transformation kinetics of the electron power bed fusion process [9]. They defined the FDF using a powder scale thermal fluid flow model (TFF) to address the problem. Based on all such contributions, PFM as a study tool for phase transformation problems is widely used by the modern research community [4], [6], [10]–[15]. Through this study, we are closing another research gap on precipitate growth kinetics which are at extreme hydrostatic pressures (> 0.1 GPa). Microstructure evolution at hydrostatic pressures is highly important for many engineering and commercial applications [11], [16] to observe material property Submitted on April 15, 2022. Published on May 17, 2022. S. Cao, Department of Mathematics and Statistics, Portland State University, USA. N. Weerasekera, Department of Mechanical Engineering, University of Louisville, USA. D. R. Shingdan, Department of Environmental Sciences, Nagoya University, Japan. A. I. Abdulla, Department of Mechanical Engineering, National Institute of Technology-Silchar, India. (corresponding e-mail: naveen12.weerasekera louisville.edu) @ Understanding Precipitate Growth Kinetics at Ultra-High Hydrostatic Pressures Siyua Cao, Naveen Weerasekera, Dawa Ram Shingdan, and Ahmed Ijaz Abdulla