(551f) Thermal-Capillary Analysis of the Micro-Pull-Down Process for Oxide Scintillator Crystals

The micro-pull-down crystal growth technique is becoming increasingly popular to grow small-diameter, fiber crystals.  Recently, it is also being developed for quick screening of promising scintillator crystals for radiation detectors in the crystal growth facility of E.D. Bourret-Courchesne at Lawrence Berkeley National Laboratory (LBNL).  In this use, time delays are often associated with establishing suitable growth conditions for micro-pull-down experiments for new materials that have never been grown before. 

The goal of our research is to develop computational models that can address the determination of suitable growth conditions in the micro-pull-down systems using a minimal amount of information.  The overall model will couple an outer, heat transfer model to compute furnace heat transfer with an inner, thermal-capillary model to describe the detailed interactions between growth, transport, and capillary effects in the micro-pull-down method.  Except for one prior modeling effort [1] for the micro-pull-down process, applied to the growth of germanium-silicon fiber crystals, theoretical analysis of this growth process is rather limited. 

In this presentation, we focus on the inner process model and present a finite-element, thermal-capillary model for the micro-pull-down technique.  We choose sapphire as a model system and show results for the growth of fibers of this material.  A quasi steady-state, Galerkin finite element method is employed to solve a system of coupled equations governing flow, heat transfer, and capillary mechanics to determine the melt-solid interface and its shape, the melt meniscus, and the radius of the growing crystal. While internal radiation and heat conduction are accounted for in the crystalline phase, convection and conduction are assumed to dominate the transport through the melt.  We validate the model by comparing to experimental results from the LBNL group and carry out parametric sensitivity studies to probe the underlying physics of the growth system.  Of particular interest are instabilities that can limit the window of possible growth conditions.

[1] C. W. Lan, S. Uda, T. Fukuda, "Theoretical analysis of the micro-pulling-down process for GexSi(1-x) fiber crystal growth", J. Crystal Growth, Vol. 193, Issue 4, Pages 552-562 (1998).

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This work has been supported in part by the Department of Energy, National Nuclear Security Administration, under Award Numbers DE-FG52-06NA27498 and DE-FG52-08NA28768, the content of which does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred.