The influence of Marangoni convection and of the external temperature gradient on the temperature fluctuations in a Czochralski solar silicon process

2020 ◽  
Author(s):  
Andreea Cojocaru ◽  
Oana Mares ◽  
Dragos Tatomirescu ◽  
Alexandra Popescu
Keyword(s):  
Temperature Gradient ◽  
Marangoni Convection ◽  
Temperature Fluctuations ◽  
External Temperature ◽  
Solar Silicon

scholarly journals Vapor flux and recrystallization during dry snow metamorphism under a steady temperature gradient as observed by time-lapse micro-tomography

2012 ◽  
Vol 6 (5) ◽  
pp. 1141-1155 ◽  
Author(s):  
B. R. Pinzer ◽  
M. Schneebeli ◽  
T. U. Kaempfer
Keyword(s):  
Temperature Gradient ◽  
Physical Properties ◽  
Time Lapse ◽  
Phase Changes ◽  
External Temperature ◽  
Vapor Flux ◽  
Snow Metamorphism ◽  
Diffusion Enhancement ◽  
Micro Tomography ◽  
Snow Microstructure

Abstract. Dry snow metamorphism under an external temperature gradient is the most common type of recrystallization of snow on the ground. The changes in snow microstructure modify the physical properties of snow, and therefore an understanding of this process is essential for many disciplines, from modeling the effects of snow on climate to assessing avalanche risk. We directly imaged the microstructural changes in snow during temperature gradient metamorphism (TGM) under a constant gradient of 50 K m−1, using in situ time-lapse X-ray micro-tomography. This novel and non-destructive technique directly reveals the amount of ice that sublimates and is deposited during metamorphism, in addition to the exact locations of these phase changes. We calculated the average time that an ice volume stayed in place before it sublimated and found a characteristic residence time of 2–3 days. This means that most of the ice changes its phase from solid to vapor and back many times in a seasonal snowpack where similar temperature conditions can be found. Consistent with such a short timescale, we observed a mass turnover of up to 60% of the total ice mass per day. The concept of hand-to-hand transport for the water vapor flux describes the observed changes very well. However, we did not find evidence for a macroscopic vapor diffusion enhancement. The picture of {temperature gradient metamorphism} produced by directly observing the changing microstructure sheds light on the micro-physical processes and could help to improve models that predict the physical properties of snow.

Surface Deformation and Thermal Convection in Electrostatically-Positioned Droplets Under Microgravity

1999 ◽  
Author(s):  
Suping Song ◽  
Ben Q. Li
Keyword(s):  
Surface Tension ◽  
Temperature Gradient ◽  
Laser Heating ◽  
Surface Deformation ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Energy Balance Equation ◽  
Droplet Surface ◽  
Fundamental Study ◽  
Recirculating Flow

Abstract Electrostatically positioned droplets are very useful for the fundamental study of solidification phenomena and the measurement of thermal physical properties. This paper descries a numerical analysis of surface deformation and surface tension driven flows in electrostatically positioned droplets in microgravity. The analysis is based on a fully coupled boundary element and finite element solution of the Maxwell equations, the Navier-Stokes equations and the energy balance equation. Results show that an applied electrostatic field results in a nonuniform electric stress distribution along the droplet surface, which, combined with surface tension, causes the droplet to deform into an ellipsoidal shape in microgravity. Laser heating induces a non-uniform temperature distribution in the droplet, which in turn produces Marangoni convection in the droplet. It is found that the viscous stress contribution to the deformation is small for a majority of cases. Also, a higher temperature gradient produces a stronger Marangoni convection in droplets with higher melting points that require more laser power. The internal recirculating flow may be reduced by more uniform laser heating. During the undercooling of the droplet, both temperature and fluid flow fields evolve in time such that the temperature gradient and the tangential velocities along the droplet surface subside in magnitude and reverse their directions.

Effect of Marangoni Convection on InSb Single Crystal Growth by Horizontal Bridgman Method

2001 ◽  
Vol 692 ◽  
Author(s):  
K. Kodera ◽  
A. Kinoshita ◽  
K. Arafune ◽  
Y. Nakae ◽  
A. Hirata
Keyword(s):  
Crystal Growth ◽  
Binary System ◽  
Temperature Gradient ◽  
Single Crystal ◽  
Grown Crystal ◽  
Marangoni Convection ◽  
Single Crystal Growth ◽  
Control Technique ◽  
Growth System

AbstractIt is necessary to clarify the effect of Marangoni convection on single crystal growth from a melt in order to improve the quality of the grown crystal. Particularly, the deviation of crystalmelt (C-M) interface from a planar shape is a major problem because it may deteriorate the quality of the grown crystal. In this paper, we investigated the effect of thermal and solutal Marangoni convection on C-M interface shape in an In-Sb binary system by the horizontal Bridgman (HB) method. The C-M interface concavity strongly depends on the cooling rate and the temperature gradient under uniform concentration distribution conditions in the melt. A large concavity was observed at low cooling rates and high temperature gradient conditions. The concavity was found to be caused by thermal Marangoni convection, by taking Péclet number into account. Then, we varied the composition of the In-Sb binary system to induce solutal Marangoni convection intentionally. The C-M interface was kept planar in case solutal Marangoni convection occurred in the direction opposite to the thermal one. Therefore, we believe that the utilization of solutal Marangoni convection will be a new control technique to make the C-M interface planar for the HB system. From these results, it was clarified that Marangoni convection plays a significant role in the HB crystal growth system.

X-ray diffraction method for determination of interplanar spacing and temperature distribution in crystals under an external temperature gradient

2015 ◽  
Vol 48 (3) ◽  
pp. 853-856 ◽  
Author(s):  
V. R. Kocharyan ◽  
A. S. Gogolev ◽  
A. E. Movsisyan ◽  
A. H. Beybutyan ◽  
S. G. Khlopuzyan ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Temperature Gradient ◽  
Single Crystal ◽  
Interplanar Spacing ◽  
Diffraction Method ◽  
X Ray Diffraction ◽  
External Temperature ◽  
X Ray ◽  
Spacing Distribution

An X-ray diffraction method is developed for the determination of the distribution of temperature and interplanar spacing in a single-crystal plate. In particular, the temperature and the interplanar spacing differences in two different parts of a quartz single crystal of X-cut are experimentally determined depending on the value of the temperature gradient applied perpendicularly to the reflecting atomic planes (10\bar 11). The temperature distribution along the direction perpendicular to the reflecting atomic planes (10\bar 11) and the interplanar spacing distribution of atomic planes (10\bar 11) are determined as well.

On the thermocapillary motion of partially engulfed compound drops

2009 ◽  
Vol 626 ◽  
pp. 263-289 ◽  
Author(s):  
L. ROSENFELD ◽  
O. M. LAVRENTEVA ◽  
A. NIR
Keyword(s):  
Temperature Gradient ◽  
Volume Ratio ◽  
Thermal Conductivity Ratio ◽  
External Temperature ◽  
Interfacial Tensions ◽  
Thermocapillary Motion ◽  
Physical Conditions ◽  
Thermal Fields ◽  
Induced Motion ◽  
Compound Drops

In this work the thermocapillary-induced motion of partially engulfed compound drops is considered. This phenomenon occurs in many natural and technological processes in which heat is exchanged between such hybrid drops and the medium around them through the interfaces. Two types of thermal fields and the resulting motions are studied; flow induced by an external temperature gradient and spontaneous thermocapillary motion. For the first flow type, it was found that, in general, the motion is induced in the direction of the temperature gradient. However, under certain physical conditions and drops' configuration a motion against the temperature gradient may be observed. In the second case, spontaneous thermocapillary motion, the compound drop moves due to surface tension gradients which result from the geometric non-uniformity of the system. Results are presented for several parameters such as configuration of the compound drop, viscosity, thermal conductivity ratio, the dependence of the various interfacial tensions on temperature and the volume ratio of the phases within the drop.

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