Pseudo-transient heat transfer in vertical Bridgman crystal growth of semi-transparent materials

Abstract

The temperature distribution and the solid-liquid interface shape during semi-transparent crystal growth have been studied by modelling a vertical Bridgman technique, using a pseudo-transient approximation in an ideal configuration. The heat transfer equation and the boundary conditions have been solved by the finite-element method. It has been pointed out that the optical absorption coefficients of the liquid and solid phases have a major effect on the thermal field, especially on the shape and location of the crystallization interface.

Numerical modeling of radiative heat transfer in Bridgman solidification of semi-transparent BaF2 crystals

“…The results of this work give an explanation of this phenomenon by accounting the effect of the latent heat on the interface shape, which becomes huge when the growth rate increases and can produce the destabilization of the solidification front. This assumption is also in agreement with the experimental investigations of the BaF 2 and CaF 2 Bridgman growth [13,15] which show that the concave shape of the interface and the fast solidification process of these materials give rise to a polycrystalline ingot.…”

“…The interface has a convex shape with the deflection f ¼ 1.56 mm. This approach, used also in other numerical simulations [9,13], is inconsistent in the case of BaF 2 , because the experimental measurements [8] show a significant variation of the absorption coefficient as function of wavelength. Moreover, the crystal is transparent in the spectral interval 1À8 mm.…”

Heat transfer process during the crystallization of benzil grown by the Bridgman–Stockbarger method

“…In order to look more deeply into the transient heat transfer in the vertical Bridgman-Stockbarger crystal growth furnace, the model is now restricted to the central part of the furnace. The cylindrical ampoule, containing benzil sample, exchanges heat by radiation with an infinite surrounding medium whose axial temperature distribution T¼f(z,t)¼T b +GzÀ vGt is chosen in agreement with numerical results obtained in global modelling [18,19] and with the experimental …”

Using magnetic field gradients to control the directional solidification of alloys and the growth of single crystals

“…The ampule properties were taken from Ref. [17] and the thermophysical properties of the crystal and melt from Ref. [8].…”