Phase-Field Model of Dendritic Sidebranching with Thermal Noise

TL;DR

This paper uses a phase-field model with thermal noise to simulate dendritic sidebranching, validating the model against theoretical spectra and comparing sidebranching features with linear noise amplification theory.

Contribution

It introduces a phase-field simulation incorporating microscopic thermal noise to study dendritic sidebranching, providing quantitative validation and comparison with existing theories.

Findings

Simulation spectrum matches exact sharp-interface spectrum

Sidebranching characteristics agree with linear WKB theory

Model captures thermal noise effects in dendritic growth

Abstract

We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show that the simulated fluctuation spectrum of a one-dimensional interface in thermal equilibrium agrees with the exact sharp-interface spectrum up to an irrelevant short-wavelength cutoff comparable to the interface thickness. Simulations of dendritic growth are then carried out in two dimensions to compute sidebranching characteristics (root-mean-square amplitude and mean spacing between sidebranches) as a function of distance behind the tip. These quantities are found to be in good overall quantitative agreement with the predictions of the existing linear WKB theory of noise amplification. The extension of this study to three dimensions remains needed to determine the origin of noise in experiments.