Heat transfer in growing Bi4Ge3O12 crystals under weak convection: I—thermophysical properties of bismuth germanate in solid and liquid state

Heat transfer in growing Bi4Ge3O12 crystals under weak convection: II—radiative–conductive heat transfer

“…[18] was used. In the model involved, heat transfer by radiation in the melt was neglected [12]; radiation in the crystal was calculated by approximating methods [12] depending on the optical thickness of the crystal t ¼ k av H (k av is absorption coefficient of the crystal averaged over the spectrum in transmission band, H is its height) and on the radiant emittance of boundaries, e:…”

“…Here l m eff is the effective thermal conductivity of the melt [12] responsible for heat transfer by both conduction and radiation, l c cond is the thermal conductivity of the crystal, V is the rate of crystal growth, J is the heat of crystallization, r m is the density of the melt, T m ; T hot ; T cool and h were described earlier.…”

“…The q rad value is determined by t; temperature and optical properties of boundaries. We assume that one of the boundaries of the crystal (cool) is in contact with the platinum disc characterized by the emissivity of e Pt : Another boundary (hot) is the interface between the liquid and solid phases, with its radiative emissivity being e i : Since BGO melt is opaque [12], the e i of this boundary can be determined due to the known Fresnel equation that gives e i E1: The temperature of the hot boundary of the crystal was assumed to be constant and equal to T m .…”

“…It should be noted that the LTG Cz method and a technique for crystal growth under conditions of the axial heat flux close to the crystallization front (AHP-Axial Heat Processing method) [11] meet the abovementioned situation. Secondly, the basic mechanism of heat transfer in the BGO crystal is thermal radiation (see Part I [12]); therefore, one can expect that because of large refractive index of the crystal (n ¼ 2:15 [10]) the thermal radiation from hot parts of crystal goes through a crystal like as in a light guide. Hence, there is no large loss of thermal radiation through the side surface of the growing crystal, and for this portion of radiation, the problem seems to be close to one-dimensional one.…”

“…Hence, there is no large loss of thermal radiation through the side surface of the growing crystal, and for this portion of radiation, the problem seems to be close to one-dimensional one. Third, RCT parameters for high temperature have been determined for BGO [12] as well as the functional dependence of growth rate on supercooling [13].…”