Paul Sonda

The feedback control of the vertical Bridgman crystal growth process by crucible rotation: two case studies

In this work, we consider the feedback control of flows within the vertical Bridgman crystal growth process. We investigate the use of crucible rotation, via feedback control algorithms, in suppressing oscillatory flows in two prototypical vertical Bridgman crystal growth configurations—a laminar flow regime driven by a time-oscillatory furnace disturbance and a time-varying regime driven by strong buoyant forces. Proportional, proportional–integral, and input–output linearizing controllers are applied to the vertical Bridgman model to attenuate the flow oscillations. Simulation results show that for the first configuration, crucible rotation is an appropriate actuation method for feedback control. In addition, nonlinear control provides superior performance to P and PI control. For the latter case, crucible rotation is less effective, due to its exacerbating effect on the inherent time-dependent flows within this system.

High-Performance Computing, Multi-Scale Models for Crystal Growth Systems

Large-scale numerical simulation carried out via high performance computing is proving to be an increasingly useful approach to understand crystal growth systems. However, increasing realism demands new approaches for describing phenomena important at several disparate length scales. Of special importance is the ability to represent three-dimensional and transient continuum transport (flows, heat and mass transfer), phase-change phenomena (thermodynamics and kinetics), and system design (such as furnace heat transfer during melt growth). A brief overview is presented of mathematical models and numerical algorithms employed to include such multi-scale effects. Sample results are presented for Bridgman crystal growth and solution crystal growth systems

Developing quantitative, multiscale models for microgravity crystal growth

Abstract:  Crystal growth conducted under microgravity conditions has had a profound impact on improving our understanding of melt crystal growth processes. Here, we present a brief history of microgravity crystal growth and discuss the development of appropriate models to interpret and optimize these growth experiments. The need for increased model realism and predictive capability demands new approaches for describing phenomena important at several disparate length scales. Of special importance is the ability to represent three‐dimensional and transient continuum transport (flows, heat, and mass transfer), phase‐change phenomena (thermodynamics and kinetics), and system design (such as furnace heat transfer during melt growth). An overview of mathematical models and numerical algorithms employed to represent such multiscale effects is presented.

Complex dynamics within the vertical Bridgman crystal growth process

Abstract This paper addresses the modeling and dynamical analysis of the vertical Bridgman process for the growth of single crystals. Specifically, a distributed parameter model comprising of balance equations for energy, mass, and momentum transport is developed. The Galerkin finite element method is employed for the numerical solution of the model equations. Numerical simulations of the system reveal that as the crystal is grown, the melt evolves from time-periodic behavior to a laminar regime. The key process variable is the Rayleigh number, a dimensionless measure of flow intensity that bears a fourth order dependence on melt height. The discovery of these rich dynamics in the vertical Bridgman model presents exciting new challenges with respect to materials processing, nonlinear dynamics, and control.