Simulation of radial solute segregation in vertical Bridgman growth of pyridine-doped benzene, a surrogate for binary organic nonlinear optical materials

Abstract

We present steady axisymmetric computations of solute distributions and radial segregation for vertical Bridgman growth of pyridine-doped benzene, a binary aromatic system with anisotropic solid-phase thermal conductivity, that serves as a model of solute transport in crystal growth of organic nonlinear optical materials. The radial variation of solid-phase mass fraction ( C s) of pyridine, which is rejected at the growing interface, depends strongly on growth conditions. High growth velocities tend to increase C s near the centerline, the ampoule wall, or both, and low growth velocities give more nearly uniform radial distributions. The maximum ampoule-wall temperature gradient also affects radial segregation, with convex-to-the-liquid interfaces at small temperature gradients being associated with radially monotonic C s distributions, and ridged interfaces at higher gradients being associated with nonmonotonic distributions having maxima at the centerline and ampoule wall. Nonuniformity is strongly determined by both interface shape and the nature of the flow near the interface. Solute is transported down to the interface by a large toroidal vortex, and swept radially inward to the centerline by a second, flattened toroidal cell. When the interface is depressed at its junction with the ampoule wall, rejected solute accumulates in the overlying liquid, where convection is relatively weak, resulting in local solute enrichment of the solid. Computations at normal and zero gravity show that for two very similar interface shapes, a maximum in the radial solid-phase solute distribution at the ampoule wall is associated with the interface shape, while the maximum on the centerline is associated with sweeping of solute to the centerline by a vortical flow on the interface. We also show that radial solute segregation depends significantly on whether account is taken of the anisotropy of the solid-phase thermal conductivity. Finally, the computations provide guidance as to the minimum ampoule length required to produce an axially uniform solute distribution over at least part of the length of a boule.