Abstract
Modeling an electromagnetic continuum is of great interest for many disciplines of engineering sciences. This chapter discusses the thermodynamics and modeling of crystal growth from binary and ternary metallic solutions including the effects of applied magnetic fields. Detailed model and simulation equations are presented for each technique. Constitutive equations for the liquid phase as well as the solid phase are presented and then linearized about a reference state. Details of the development of the constitutive equations are presented step by step, giving emphasis on the physical significance of material coefficients in each growth crystal technique. The basic equations are the well-known Maxwell equations and thermomechanical balance laws of a continuum written for a binary liquid mixture. The associated interface and boundary conditions are presented. Finally, the application of magnetic field is discussed.
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