3D numerical investigation of the factors affecting the thermal stresses and the wavy external shape of Li2MoO4 crystals grown by the Czochralski method

Abstract

Three-dimensional (3D) modeling was applied to investigate heat transfer, convection and thermal stresses in Czochralski growth of Li₂MoO₄ (LMO) crystals used to build the core of heat-scintillation cryogenic bolometers (HSCBs). Several crystals of $4cm$ and $5cm$ in diameter were grown in two different Czochralski configurations. The largest ingot ($4cm$-diameter and $6cm$-length) grown in a furnace based on coupling the inductive coil and a platinum crucible, has cracked as the bottom part of the crystal was cut. Another crystal ($5cm$-diameter and $15cm$-length) was grown in a furnace based on inductive heating of a susceptor, which was previously optimized by numerical modeling in order to reduce the thermal stresses in LMO crystals. The external surface of this ingot shows a slightly wavy shape. This irregular shape was investigated by considering 3D convective effects at the free surface of the melt, which can affect the liquid meniscus shape, and generate slight instabilities of the growth process. It is concluded that this wavy shape can be avoided by changing the sensitivity of the automatic crystal shape control. The thermal stress computations, conducted for the ingot of $4cm$ in diameter, show that the normal stress in the longitudinal section has a maximum which highly exceeds the critical value of the tensile stress in a region located at the bottom part of the ingot. That explains the fracture observed during the cutting of the ingot’s tail. The computations performed in the case of $5cm$-diameter ingot, grown in an optimized configuration, show that the crystal exhibits low thermal stress, except for a thin region of $2mm$ located at the ingot periphery, where the stress slightly exceeds the critical value. Thermal stresses can be reduced by a factor of 2 by growing the ingots parallel to the c-axis.