Simulation of global heat transfer in the Czochralski process for BGO sillenite crystals

Effect of the shouldering angle on the shape of the solid–liquid interface and temperature fields in sillenite-type crystals growth

“…The validity of the code and the two stages of calculations is discussed in detail in Ref. [13]. In the first one, all processes of heat transfer, including convection in the melt and conduction in the solid blocks of a furnace were treated accurately with the exception of radiative transfer inside the crystal, which was assumed to be opaque.…”

“…For smaller cone angle, SLI is more flattened and temperature irregularities remain practically the same. For simulations of radiative heat transfer in simple model configurations (cone and cylinder) for ''ideal conditions'' when the environment temperature is much lower than the melting one, it could be expected, considering specular reflection taking place [13], that a big variation with varying angle ought to take place during angle formation. This means that for large cone angles, the crystallization front must become flatter and irregularities of the temperature fields inside the crystal have to be diminished and the dark core angle tends to disappear.…”

Growth of Sillenite-Structure Single Crystals

“…The maximum cooling rate of bismuth silicate crystals after the growth process is 64/R 2 (°C/h) at their melting point and a factor of 2 slower near room temperature [36]. The rotational instability of bismuth-containing oxide melts in BSO and BGO crystal growth was investigated in [38,40,44,48,57,58,60]. The crystal rotation rate during pulling was shown to have a strong where R is the crystal radius, ω is the crystal rotation rate, and ν is the kinematic viscosity of the melt.…”

“…The interaction between the crystal-driven and convective flows changes the sign of the vertical gradient under the crystal and, as a consequence, increases the radial heat flow. Simulation studies of heat and mass transfer processes during CZ pulling of BSO and BGO crystals in real systems demonstrate that the axial and radial heat transfer processes have a significant effect on crystal morphology if there are changes and fluctuations of heater power [57,58,60].…”

Effect of heat shield on the shape of the solid–liquid interface and temperature field in the BGO-eulithine LTG Cz growth

“…[2], the large convexity of the SLI at the initial stage of the growth is related to the specular (Fresnel) reflection of heat radiation at the shoulder surface that leads to strongly non-uniform distribution of the radiant heat flux near the SLI. In addition, specular reflection significantly influences the temperature fields in crystals that is manifested in distortion of isotherms which can take distinct ''convex-concave'' [2] or even fusiform [3] shape. It is necessary to stress that if the crystal side surface is diffuse reflective then similar problem will not emerge because diffuse reflection leads to smoothing of radiation field inside a crystal.…”