Temperature and thermal stress evolutions in sapphire crystal during the cooling process by heat exchanger method

Transient numerical calculations were carried out to predict the evolutions of temperature and thermal stress in sapphire single crystal during the cooling process by heat exchanger method (HEM). Internal radiation in the semitransparent sapphire crystal was taken into account using the finite volume method (FVM) in the global heat transfer model. The numerical results seem to indicate that the narrow bottom region of the sapphire crystal is subjected to high thermal stress during the cooling process, which could be responsible for the seed cracking of the as-grown crystal, while the thermal stress is relatively small in the central main body of the crystal, and is less than 10 MPa during the whole cooling process. The fast decrease of the thermal stress in the bottom region of the crystal during the initial stage of cooling process is dominated by the reduction of the cooling helium gas in the heat exchanger shaft, and is not significantly affected by the heating power reduction rate.