Corresponding author: Vladimir S. Berdnikov (berdnikov@itp.nsc.ru)

This work is a brief overview of experimental study results for hydrodynamics and convective heat exchange in thermal gravity capillary convection modes for the classic Czochralski technique setup obtained at the Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences. The experiments have been carried out at test benches which simulated the physics of the Czochralski technique for 80 and 295 mm diameter crucibles. Melt simulating fluids with Prandtl numbers Pr = 0.05, 16, 45.6 and 2700 have been used. Experiments with transparent fluids have been used for comparing the evolution of flow structure from laminar mode to well-developed turbulent mode. Advanced visualization and measurement methods have been used. The regularities of local and integral convective heat exchange in the crucible/melt/crystal system have been studied. The experiments have shown that there are threshold Grashof and Marangoni numbers at which the structure of the thermal gravity capillary flow undergoes qualitative changes and hence the regularities of heat exchange in the melt change. The effect of melt hydrodynamics on the crystallization front shape has been studied for Pr = 45.6. Crystallization front shapes have been determined for the 1 × 10^{5} to 1.9 × 10^{5} range of Grashof numbers. We show that the crystallization front shape depends largely on the spatial flow pattern and the temperature distribution in the melt.

Solving the practical task to improve the quality of crystals and hence optimize single crystal melt growth process modes requires fundamental studies of melt hydrodynamics and complex conjugate heat and mass transfer in growth units of general type [

Below we will present the first part of this four-part overview of experimental and numerical results for convection in various fluids simulating various setups of the Czochralski technique obtained at the Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences. By now the most complete hydrodynamic and convective heat exchange simulation data have been obtained for the classic fixed crucible setup of the Czochralski technique. The aim of the present series of studies is to simulate the crystal growth conditions at different process stages and develop a fundamental basis for improving the methods of controlling the melt hydrodynamics and the heat exchange conditions. When designing the benches for the simulation of physical models of various directional crystallization techniques, we used proprietary methods for the visualization and parameter measurement of velocity and temperature fields developed at the IT SB RAS for the fundamental investigations of near-wall turbulence [42]. The experiments dealt with laminar-turbulent transition

Under real process conditions, melt hydrodynamics are determined by the cooperative action of a set of bulk forces (buoyancy, centrifugal, Coriolis, shear and electromagnetic forces) and surface forces (thermo- and concentration-capillary, Laplacian and friction forces). If the effect of the buoyancy forces is significant, the temperature and velocity fields are self-consistent. The presence of the thermocapillary effect further increases the hydrodynamics/heat exchange feedback. The development of hydrodynamic control methods requires understanding of the specific influence mechanisms (or the specific expression regularities) and the relative contributions of each of the forces in question to the formation of the melt flow structure and analysis of the results of their nonlinear interaction. This problem cannot be solved using solely experimental tools since the buoyancy forces which are inevitable in Earth conditions and other bulk forces act jointly with surface forces. Controlling their relative contributions or separately studying their individual action under the conditions of a physical experiment is an extremely complex or even impossible task. Therefore there is a need for combined complementary experimental and numerical investigations. Results of numerical investigations into free convection flow modes will be presented in the second part of this overview, and experimental and numerical results for the effect of the abovementioned forces on the convective processes in the melt during crystal and crucible rotation will be discussed in the third and the fourth parts.

Natural convection was experimentally studied at different stages from laminar mode to well-developed turbulent flow mode [

Below we present the results of studies conducted using two physical models of the classic Czhochralski technique. These models had almost similar designs of the working zones, but the crucibles differed considerably in size: the crucible diameter was _{c} = 80 mm for the first section and _{c} = 295 mm for the second section. The working media were gallium/indium/tin melt (Prandtl number Pr = 0.05), ethyl alcohol (96 %, Pr = 16), PES-5 siloxane fluid (Pr = 2700), and saturated hydrocarbons, i.e., hexadecane and heptadecane (Pr = 45.6). The two latter fluids have the solidification points at 18 and 22 °C, respectively, and allow studying crystallization processes for a transparent fluid. Transparent fluids were visualized using specially selected fraction of scale-shaped aluminum particles 10 to 15 µm in size. Fluid movement was observed in the central section (the

Thermal gravity convection caused by the temperature difference between the ^{2})Δ_{sc}^{3} or the Rayleigh number Ra = GrPr = (β_{sc}^{3}, where _{p} is the thermal diffusivity coefficient, λ is the thermal conductivity coefficient, _{p} is the constant pressure heat capacity and _{sc} is the crystal radius. The Prandtl number Pr = ν/_{sc}/

Thermal gravity capillary convection

For free convection which always has a gravity capillary origin in a physical experiment, the flow arrangement is as follows. In the center (Fig.

Figure _{c} ≤ 1.5 range) and the ratio of the model crystal radii (in the 7.0 ≤ _{c}/_{sc} ≤ 1.3 range) have a negligible effect on the qualitative aspect of the spatial pattern of the flow. This mode occurs in media with medium Pr numbers.

Spatial flow pattern in buoyancy and thermocapillary driven convection mode for Pr = 16: (_{c} = 1.5, _{c}/_{sc} = 6.68, Gr = 1.05 × 10^{4}; (_{c} = 1.5, _{c}/_{sc} = 1.29, Gr = 2.05 × 10^{6}; (_{c} = 0.9, _{c}/_{sc} = 2.75, Gr = 1.35 × 10^{6}. _{c} is the crucible radius.

In highly viscous media with Pr = 2700 the thermocapillary effect has but a little effect on the spatial pattern of the laminar flow, and no superficial swirl forms. In non-transparent gallium/indium/tin melt with Pr = 0.05 the temperature distributions normal to the

In

Laminar fluid convection mode with Pr = 16 shown in Fig. _{c}/_{sc} ≥ 3 radii ratios, the cold fluid downward stream loses stability at an initial stage: low-frequency axial-symmetric single-harmonic velocity and temperature oscillations develop; then the second harmonic appears after the next threshold Δ

Rayleigh-Benard instability develops under the

Figure _{c} = 0.7 but for different crystal model radii, one can trace the following temperature oscillation regularities during an increase in the temperature difference. In Region I to the left of Curve

Regions of various space-time flow arrangements in free convection mode (Pr = 16).

_{c}/_{sc} = 6.68, Gr_{x}^{6}; (_{c}/_{sc} = 5.0, Gr_{x}^{4}; (_{c}/_{sc} = 4.0, Gr_{x}^{6}; (_{c}/_{sc} = 2.5, Gr_{x}^{6}; (_{c}/_{sc} = 1.29, Gr_{x}^{6}. Gr_{x}^{2})Δ^{3}, where

Once threshold conditions are reached (Region IIb between Curves

_{c}/_{sc} = 4.0, Gr_{x}^{6}; (_{c}/_{sc} = 3.33, Gr_{x}^{5}; (_{c}/_{sc} = 2.76, Gr_{x}^{4}; (_{c}/_{sc} = 7.43, Gr_{x}^{4}.

_{c}/_{sc} = 6.68, Gr_{x}^{6}; (_{c}/_{sc} = 2.76, Gr_{x}^{4}; (_{c}/_{sc} = 1.29, Gr_{x}^{6}.

An increase in Gr causes a shrinkage of the ordered secondary flow existence region and noise contamination of the temperature oscillation spectra. The outer edge of the boundary layer exhibits irregular outbursts of the melt cooled under the _{sc}/2, the spectra becoming increasingly noise-contaminated as one moves down the flow, i.e., their quality depends on

The temperature oscillation behavior features noted above correlate with the regularities of heat boundary layer development at the _{c} = 80 mm, _{c} = 0.7 and _{c}/_{sc} = 2.76) for an increase in the temperature difference from 0.41 to 10.3 °C and Gr from 0.62 × 10^{4} to 3.13 × 10^{5}: (_{sc} = 1 and the local minimum in the _{c}/_{sc} ranging from 1.29 to 7.0 [

Radial local heat flow distributions at ^{6}: (

For a large-scale model with a 295 mm diameter crucible the laminar-turbulent transition processes in the boundary layer at the _{c} = 0 and the _{c} ≈ 0.4 and the turbulent boundary layer region at 0.4 ≤ _{c} ≤ 1. Figure _{c} = 0.33 and _{c}/_{sc} = 3.69. Results of quite detailed investigations into the evolution of temperature oscillation spectra in radial directions with an increase in Δ

Practically important feature of free convective flow modes is that the abovementioned _{i}_{i}

Another important problem is the dependence of melt flow structure and heat exchange regularities at the

^{5}; (^{5}; (^{5}; (^{5}.

One more problem is associated with the effect of temperature boundary conditions at the crucible bottom. Figure _{b} and the crucible side wall _{w} temperatures. The experiments were carried out with independent bottom and wall heating. The left-hand photos show the flow and the right-hand ones present the main flow trajectories providing qualitative and numerical characterization of the meridian flow dimensions and direction. The general flow pattern is initially close to the one that is typical of the abovementioned flat _{b} < _{w} only increases the fluid circulation rate at the meridian flow contour. An increase in the crucible bottom temperature with small overheating relative to the crucible wall temperature produces a flow structure that is typical of Rayleigh-Benard convection. A cell forms consisting of two torus-shaped swirls with an upward flow at a certain distance from the crucible walls (see Fig.

_{c} = 0.7, _{c}/_{sc} = 2.5, Gr = 1.79 · 10^{5}): (_{b}/_{w} = 0.93; (

Buoyancy and thermocapillary driven convection was studied experimentally for melt simulating fluids in thermal hydrodynamic systems similar to the classic Czochralski technique, for laminar to well-developed turbulent flow modes, with 80 and 295 mm crucible diameter models. The experiments proved that an increase in the Grashof and Marangoni numbers induces multiple stepwise qualitative changes in the structure of the initial buoyancy and thermocapillary driven flow. Once the next threshold temperature difference (or the threshold Gr and Ma numbers) is reached the space-time flow arrangement becomes more complex (new secondary swirl flow develops against the background of the main flow or a new oscillation harmonic emerges). The heat exchange regularities change accordingly. The scale factor proved to affect the hydrodynamics, laminar-turbulent transition and heat exchange regularities, yet further studies for full-scale models are required for practical purposes.

This research was realized under the project III.18.2.5, number of state registration АААА-А17-117022850021-3.

_{4}Ge

_{3}O

_{12}crystals grown by the low-gradient Czochralski method.

_{4}Ge

_{3}O

_{12}crystals under weak convection: I—thermophysical properties of bismuth germanate in solid and liquid state.

_{4}and CdWO

_{4}single crystals from melt by the low thermal gradient Czochralski technique.

_{12}GeO

_{20}and Bi

_{12}SiO

_{20}crystals by the low-thermal gradient Czochralski technique.

_{4}Ge

_{3}O

_{12}crystals by the LTG CZ technique.