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Continuum Mechanics and Thermodynamics

, Volume 9, Issue 2, pp 97–114 | Cite as

Numerical simulation of polyhedral crystal growth based on a mathematical model arising from non–local thermomechanics

  • Pasqua D'Ambra

In this work we present some results of the numerical simulation of the growth of a crystal from its melt, taking into account faceting. The simulation is based on a numerical solution of a three–dimensional generalized Stefan problem. That problem arises from a non–local thermomechanical theory applied to a continuous system with an interface and embodies ideas from the dislocation theory of crystal growth. In the model, the crystal surface is an isotherm and the growth velocity of a crystal face depends on the velocities of the other faces and on the whole crystal configuration as well as on the temperature gradient. A front fixing formulation of the model is considered. This is a conservative form of the Isotherm Migration Method [6, 7, 8, 9, 10, 11] in spherical coordinates. The numerical solution is based on an explicit finite difference discretization of the resulting non–linear equations. We develop a theoretical analysis of the interface equations that drive the crystal face motion. Numerical results, showing evolution of complex crystals with configuration changing during the growth, are in accord with experimental results. Furthermore, numerical experiments offer useful information on the influence of certain parameters in the model on the growth process.

Key words: Crystal growth; Non–local theory; Dislocation theory; Generalized Stefan problem; Front fixing; Isotherm Migration Method; Finite difference method 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Pasqua D'Ambra
    • 1
  1. 1. Center for Research on Parallel Computing and Supercomputers of the National Research Council (CPS–CNR), Complesso Universitario Monte S. Angelo, Via Cintia, 80126 Naples, ItalyIT

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