Effect of internal radiation on thermal stress fields in CZ oxide crystals

A three-dimensional finite element analysis of thermal stress fields in oxide crystals grown by the Czochralski (CZ) method has been carried out, where the crystal is assumed to be a linear elastic material whose mechanical properties are anisotropic. The von Mises equivalent stresses in the semitransparent crystals were calculated with the temperature distributions obtained by the global heat transfer analysis in the CZ furnace, taking into account the radiative heat transfer in the crystal and/or melt. The effects of the absorption coefficients of the crystal and/or melt on the thermal stress fields in the crystal were numerically investigated in addition to the effect of the interface inversion. As a result, the following observations were made for the thermal stresses at the melt/crystal interface. The thermal stresses have a minimum value near a critical Reynolds number at which the melt/crystal interface inversion occurs. Also, there exists a maximum magnitude of the thermal stresses for some optical thickness, when the Reynolds number is relatively small, and the dependence of the stresses on the optical thickness for an opaque melt is larger than that for a semitransparent melt. While, the thermal stresses in a crystal, except near the melt/crystal interface, decrease as the optical thickness decreases.