Analysis of Coarsening and the Moving Boundary Problem for Nucleation and Growth, with Non Integer Exponents for the Power Law.

EasyChair Preprint 13884

Abstract

This paper presents a novel exploration of the relationship between coarsening annealing and the moving boundary problem approach, with a particular emphasis on diffusion, Stefan's solution, and non-integer exponents in the power law of interface versus time. The research delves into the complex dynamics of phase transformations, specifically the process of coarsening annealing, and how it can be effectively modeled using the moving boundary problem approach. The role of diffusion in these transformations is explored, elucidating how atomic mobility influences the coarsening process. A significant focus of this study is the investigation of non-integer exponents in the power law of interface versus time. This aspect challenges traditional models and provides a more nuanced understanding of phase transformations. It is demonstrated that non-integer exponents can accurately model the dynamics of the interface over time, offering new insights into the coarsening process. This research has significant applications in materials science and engineering, particularly in the design and manufacture of alloys and composite materials. Furthermore, our findings can inform the development of more efficient manufacturing processes, reduce waste and improving product quality.

Keyphrases: Cahn-Hilliard equation, Coarsening Diffusion Asymptotic, MBP, Nucleation, Phase Transformation Perturbation, Precipitation hardening, particle coarsening kinetics and size distribution, phase transformations, power law of interface versus time

@booklet{EasyChair:13884,
  author    = {Rahul Basu},
  title     = {Analysis of Coarsening and the Moving Boundary Problem for Nucleation and Growth, with Non Integer Exponents for the Power Law.},
  howpublished = {EasyChair Preprint 13884},
  year      = {EasyChair, 2024}}