Numerical Analysis of Thermal Stress in Semi-Transparent Oxide Crystals Grown by Czochralski and EFG Methods

摘要

Crystal growth of oxides is generally difficult since large curvatures of the growth interface in these systems generate high thermal stress, dislocations and crystal cracking. Three-dimensional numerical modeling is applied to investigate thermal stress distribution in sapphire and langatate La3Ta0.5Ga5.5O14 (LGT) semi-transparent crystals grown by Czochralski (Cz) and Edge-defined Film-fed Growth (EFG) techniques. The analysis of thermal stress distribution in a sapphire ingot grown in a Czochralski furnace shows high von Mises stresses distributed almost symmetrically on large areas in the crystal. Thermal stress computations for piezoelectric langatate crystals grown in a Czochralski configuration show non-symmetrical von Mises distribution with higher stress on one side of the ingot. These numerical results are in agreement with experimental results showing non-symmetrical cracking at the outer surface of the crystal. 3D modeling of multi-die EFG growth of white sapphire ribbons shows that the von Mises stress is almost constant when the number of ribbons is increased from two to ten. Two models are applied to simulate the internal radiative heat transfer in the sapphire crystals: P1 approximation and the Rosseland radiation model. Numerical results show that applying Rosseland formula introduces significant errors in temperature field calculations especially in the case of the EFG configuration.