(488g) Analysis of Temperature Gradient Zone Melting and Annealing for Mitigation of Second-Phase Particles in Single Crystals

Interfacial transport plays a predominant role in the temperature gradient zone melting (TGZM) technique, whereby small, second-phase particles embedded within a crystalline matrix can be induced to migrate by heating to slightly above the eutectic temperature and applying a temperature gradient across the sample. Under such conditions, the now-liquid particle dissolves on the hot side and re-solidifies on the cool side, with a net effect of the particle migrating toward the hotter region. Historically, the discovery of these effects was motivated by the experience of arctic explorers, who found that newly formed sea ice was not potable due to brine inclusions. However, after 2-3 years of exposure to sunlight, this sea ice could be used for drinking water. In the aging process, brine inclusions migrate to the surface by diurnal heating, thus purifying the ice.

In a more modern application, TGZM has been applied to crystals of cadmium zinc telluride (CZT) grown from liquid phases. This material typically exhibits significant populations of large (10 micron and above) tellurium-rich particles that are deleterious to the performance of semiconductor radiation detectors. While the specific formation mechanisms of these particles are not well understood, their presence is unavoidable due to the supersaturation of tellurium controlled by near-equilibrium thermodynamics during growth.

In this presentation, we present the formulation of a mathematical model for particle migration via TGZM that represents solute transport across interfaces defined by conditions of local thermodynamic eqilibrium. We demonstrate that an approximate analytical solution to this model in one spatial dimension well describes the general behavior of particle migration. The analytical solution shows that steady-state migration is not possible, and that, under a constant thermal gradient, the particle velocity and size increase continually with time. We demonstrate that this analytical solution provides good estimates for the overall outcomes of TGZM experiments.

We also describe the implementation of a moving-boundary, finite-element method that solves for particle position and shape, with no simplifying assumptions about mechanistic interactions. We account for the Gibbs-Thompson effect, whereby equilibrium melting temperature is affected by local curvature of the solid-liquid interface. By varying the Gibbs-Thompson parameter, we are able to gauge its role in maintaining the particle’s interface stability during migration. We observe evolution of particle velocity, size, and shape over time and compare model results with experimental observations of tellurium-rich particles in CZT. We also consider how annealing under a cadmium-rich atmosphere can reduce the size of second-phase particles. Finally, we consider the combined strategy of TGZM and cadmium-overpressure annealing.

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This work has been supported in part by U.S. Department of Homeland Security, 2012-DN-077-ARI066-06, and no official endorsement should be inferred.