Speaker: Jeff Derby, Distinguished McKnight University Professor of Chemical Engineering & Materials Science
Title: Understanding multi-scale phenomena in bulk crystal growth processes via computational modeling: Pushing the continuum from the top down
Abstract: From a modeling and simulation perspective, crystal growth processes represent some of the most complex and challenging systems ever analyzed, requiring a multidisciplinary and multi-scale approach and drawing on a wide range of scientific and engineering expertise. This lecture will describe continuum transport processes at play during crystal growth from a mathematical and computational modeling perspective.
Recent results from research studies will be used to illustrate these modeling concepts. In particular, we will focus on modeling the interactions of solid particles with a solidification interface, focusing on silicon carbide (SiC) particles in multi-crystalline silicon. We present a continuum model that allows for a rigorous representation of forces across disparate length scales, ranging from van der Waals interactions arising from atomistic effects to drag forces arising from fluid flow. We demonstrate how this model is able to represent large deformations of the melt-solid interface during the process of engulfing a solid particle that is on the order of 1-10 microns in size. Of particular interest is the inclusion of a physically motivated, pre-melted liquid layer in the problem formulation. Our finite-element representation permits nanometer-scale resolution of this layer, which, importantly, circumvents the use of arbitrary cut-off values for determining minimum gap thickness prior to particle engulfment. We address the critical factors that determine the transition from the stable pushing of a particle by a solid-melt interface to conditions where engulfment is inevitable. Of particular interest and relevance is the discovery that oscillating solidification fronts, as would arise due to turbulent fluctuations in large-scale silicon melts, can drive engulfment of silicon carbide particles at average growth rates far below those predicted by prior steady-state analyses. We also address system behavior due to carbon segregation at the solidification front and reaction at the particle surface, which can dramatically alter engulfment behavior.