Quantitative Assessment of Cracking in Oxide Bulk Single Crystals during Czochralski Growth (1st Report, Development of Computer Program for Thermal Stress Analysis)

A three-dimensional finite element computer program for thermal stress analysis was developed for the cracking of trigonal class 3 m oxide bulk single crystals such as lithium niobate (LN) and lithium tantalate (LT) during Czochralski growth. A tensor transformation technique was used to obtain the elastic constant matrix and the thermal expansion coefficient vector corresponding to an arbitrary pulling direction. The anisotropy of the elastic constants and the thermal expansion coefficients as well as their temperature dependence was considered in the program. Using this program, we analyzed thermal stress in LN bulk single crystals with three types of temperature profiles or crystal-melt interface shapes. The analyses were carried out for the pulling directions of both the a-axis [100] and the c-axis [001]. The results show that thermal stress is very sensitive to the crystal-melt interface shape, and that thermal stress is lower in the c-axis pulling than in the a-axis pulling. The relation between thermal stress and the cracking and quality of a bulk single crystal is also discussed.