| When a molten binary alloy is unidirectionally solidified by pulling it through an imposed temperature gradient at a controlled velocity, the planar melt/solid interface can destabilize to form cellular patterns. The presence of crystalline anisotropy, which causes the surface properties of the alloy to vary with crystal orientation, leads to markedly different interface patterns than those arising in the absence of anisotropy. Specifically, anisotropy causes the cells to become asymmetric, and if the anisotropy is large enough, causes the interface to develop kinks which lead to facets. This thesis investigates the effects of crystalline anisotropy on the unidirectional solidification of both non-faceting and faceting materials.; The non-faceted cells of an anisotropic material appear as traveling waves, unlike the steadily growing cells of an isotropic material. A nonlinear mathematical model for the unidirectional solidification of an anisotropic material was developed and solved numerically using the Galerkin finite element method on a grid generated with an orthogonal mapping. The effects of anisotropic surface free energy, segregation coefficient, and interfacial undercooling on the melt/solid interface shape were examined. The constant amplitude traveling waves predicted by linear theory for the latter two forms of anisotropy developed amplitude oscillations almost immediately after the onset of cellular growth. When surface free energy is anisotropic, steadily growing cells existed until a transition to a homoclinic orbit occurred. The range of these calculations is limited by the onset of faceted growth.; During faceted growth, the interface is composed of atomically smooth surfaces intersecting at sharp angles. To model faceted growth, the conditions describing a kink in a quasi-equilibrium melt/solid interface were added to the non-faceted growth model. Faceted interfaces resembling experimental observations were calculated, but our method has major limitations in not being able to determine the wavelength of the faceted cell or to calculate interface shapes having asymmetric kinks.; These results demonstrate that different anisotropic surface properties have different effects on solidification and can be viewed as a first step toward understanding the solidification of anisotropic materials. |
