Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li2MoO4 growth

Abstract

The three dimensional thermal stress field was calculated for different growth stages of a Li₂MoO₄ (LMO) crystal grown in an inductively heated Czochralski furnace using the anisotropy and temperature-dependent mechanical properties. Four pulling directions were considered, including [100], [010], [001] and [110]. The elastic and thermal expansion matrices corresponding to a, b and [110] directions are computed by a tensor transformation method from the available experimental coefficients characterizing the LMO crystal pulled along the c-direction. The crystal–melt interface convexity and the input heat power obtained numerically for the final growth stage meet the experimental values for the absorption coefficient close to 0.2 cm⁻¹. Compared to an assumed opaque case, von Mises stress increases strongly at the semitransparent LMO interface due to the internal radiative heat transfer inside the crystal which leads to a large convexity of the crystal–melt interface. The thermal stresses for the [100] and [010] pulling growth directions were the same since they present the same crystallographic axes and are larger than the c-pulling case, especially for the earlier stages where the increase rate is about 36%. Three and two-fold symmetries are shown for c and a (or b) pulling cases, respectively, in the distribution of von Mises stress at a cross section of the LMO crystal. Thermal stresses along the [110] direction were almost the same compared to the [100] and [010] pulling axes with two-fold symmetries. The gas convection and temperature dependence of the mechanical properties have an important effect on the thermal stress values and distributions and have be taken into account in accurate computation of the stress field.