The Czochralski crystal growth system with a periodic crystal growth rate and back-melting

1982 ◽  
Vol 379 (1777) ◽  
pp. 327-343 ◽  
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Crystal Growth ◽  
Solid Phase ◽  
Harmonic Component ◽  
Preceding Paper ◽  
Crystal Growth Rate ◽  
Czochralski Crystal Growth ◽  
Solute Boundary Layer ◽  
Growth System

This paper considers the effect upon the Czochralski crystal growth process of modulating the crystal growth rate periodically, by imposing upon a constant mean growth rate a harmonic component. The case is considered when the amplitude of the harmonic component is sufficiently large that the crystal melts during part of the periodic cycle. The model of the Czochralski system discussed in the preceding paper is adopted. The system is considered in the realistic limit of Sc → ∞, σ → 0 ∆ → 0, where Sc = v / D L is the Schmidt number, σ= v / K L is the Prandtl number, and ∆ = D S / D L is the ratio of the solute diffusivities in the liquid and solid phases, v being the kinematic viscosity of the liquid, and K L the thermal diffusivity of the liquid. When the crystal melts back, large solute gradients are formed in the solid phase. It is due to the presence of these that the diffusion of solute in the solid becomes important, being responsible for the formation of a time-dependent solute boundary layer adjacent to the interface in the crystal. Four distinct periods throughout the cycle are identified in which this boundary layer has different structures. The results of numerical calculations arising from this work are presented.

The Czochralski crystal growth system with a periodic crystal growth rate and no back-melting

1982 ◽  
Vol 379 (1777) ◽  
pp. 305-325 ◽  
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Temperature Field ◽  
Crystal Growth ◽  
Liquid Phase ◽  
Solid Phase ◽  
Crystal Growth Rate ◽  
Solute Diffusion ◽  
Czochralski Crystal Growth ◽  
Periodic Crystal

By considering the Czochralski crystal growth for a periodic crystal growth rate a solution procedure is developed for the hydrodynamic, temperature, and solute fields in the limit Sc → ∞, Re → ∞, σ → 0, ∆ → 0, where Sc is the Schmidt number, Re is the Reynolds number, σ the Prandtl number of the liquid phase and ∆ = D S / D L , D S and D L being the solute diffusivities in the solid and liquid phases respectively. With this process, solutions are developed as double perturbation series in SC -½ and ∆ , with the method of matched asymptotic expansions used to overcome any singular behaviour. The effect upon the hydrodynamic field of a periodic crystal growth rate is shown to be confined to a perturbation O ( Sc -½ ). In the liquid solute field a thin boundary layer forms within the viscous boundary layer; the structure of the solute field in this region is demonstrated. The solute field in the solid phase is also considered. For the temperature field a three-layer structure is revealed in the liquid phase, directly due to the fluctuating growth rate. The temperature field in the solid phase is also considered. This work lays the foundations for considering the role of solute diffusion in the solid when the crystal is allowed to melt back.

TEMPERATURE DEPENDENCE OF THE CRYSTAL GROWTH RATE IN POLAR GLACIERS

1987 ◽  
Vol 48 (C1) ◽  
pp. C1-661-C1-662 ◽  
Author(s):  
J. R. PETIT ◽  
P. DUVAL ◽  
C. LORIUS
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Temperature Dependence ◽  
Crystal Growth Rate

Comparison of copper sulphate pentahydrate growth rates determined by different methods

1990 ◽  
Vol 55 (7) ◽  
pp. 1691-1707 ◽  
Author(s):  
Miloslav Karel ◽  
Jiří Hostomský ◽  
Jaroslav Nývlt ◽  
Axel König
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Fluidized Bed ◽  
Growth Rates ◽  
Copper Sulphate ◽  
Crystal Growth Rate ◽  
Effect Of Temperature ◽  
Rotating Disc ◽  
Shape Factors ◽  
Data Treatment

Crystal growth rates of copper sulphate pentahydrate (CuSO4.5 H2O) determined by different authors and methods are compared. The methods included in this comparison are: (i) Measurement on a fixed crystal suspended in a streaming solution, (ii) measurement on a rotating disc, (iii) measurement in a fluidized bed, (iv) measurement in an agitated suspension. The comparison involves critical estimation of the supersaturation used in measurements, of shape factors used for data treatment and a correction for the effect of temperature. Conclusions are drawn for the choice of values to be specified when data of crystal growth rate measurements are published.

Optical resolution of N-formylphenylalanine succeeds by crystal growth rate differences of diastereomeric salts

2007 ◽  
Vol 18 (2) ◽  
pp. 260-264 ◽  
Author(s):  
Laura Bereczki ◽  
Emese Pálovics ◽  
Petra Bombicz ◽  
György Pokol ◽  
Elemér Fogassy ◽  
...  
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Optical Resolution ◽  
Crystal Growth Rate ◽  
Diastereomeric Salts

Crystal-growth kinetics of protein single crystals along capillary tubes in the gel-acupuncture technique

1999 ◽  
Vol 55 (2) ◽  
pp. 577-580 ◽  
Author(s):  
Abel Moreno ◽  
Manuel Soriano-García
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Capillary Tube ◽  
Crystal Growth Rate ◽  
Equilibrium Studies ◽  
Acta Cryst ◽  
Average Growth ◽  
X Ray Crystallography ◽  
Growing Cell ◽  
Kinetics Of

In attempts to obtain protein crystals of a sufficient size for structural studies, lack of knowledge of the physicochemical properties of protein solutions and of their crystal-growth behaviour lead to a bottleneck for drug design as well as for X-ray crystallography. Most formal investigations on crystal-growth phenomena have been focused on equilibrium studies, where the protein is soluble, and on the kinetics of crystal growth, which is related to both nucleation and crystal-growth phenomena. The aim of this work is to measure the crystal-growth rate along a capillary tube used as a growing cell. These experiments were carried out using the gel-acupuncture technique [García-Ruiz et al. (1993). Mater. Res. Bull. 28, 541–546; García-Ruiz & Moreno (1994). Acta Cryst. D50, 484–490; García-Ruiz & Moreno (1997). J. Cryst. Growth, 178, 393–401]. Crystal-growth investigations took place using lysozyme and thaumatin I as standard proteins. The maximum average growth rate obtained in the lower part of the capillary tube was about 35 Å s−1 and the minimum average growing rate in the upper part of the capillary tube was about 8 Å s−1. The crystal-growth rate as a function of the supersaturation was experimentally estimated at a constant height along the capillary tube.

Phase separation in undercooled molten Pd80Si20: Part I

1999 ◽  
Vol 14 (9) ◽  
pp. 3653-3662 ◽  
Author(s):  
K. L. Lee ◽  
H. W. Kui
Keyword(s):  
Growth Rate ◽  
Phase Separation ◽  
Crystal Growth ◽  
Grain Refinement ◽  
Crystallization Temperature ◽  
Sharp Decrease ◽  
Nucleation And Growth ◽  
Crystal Growth Rate ◽  
Large Undercooling ◽  
Kinetic Crystallization

Three different kinds of morphology are found in undercooled Pd80Si20, and they dominate at different undercooling regimens ΔT, defined as ΔT = T1 – Tk, where T1 is the liquidus of Pd80Si20 and Tk is the kinetic crystallization temperature. In the small undercooling regimen, i.e., for ΔT ≤ 190 K, the microstructures are typically dendritic precipitation with a eutecticlike background. In the intermediate undercooling regimen, i.e., for 190 ≤ ΔT ≤ 220 K, spherical morphologies, which arise from nucleation and growth, are identified. In addition, Pd particles are found throughout an entire undercooled specimen. In the large undercooling regimen, i.e., for ΔT ≥ 220 K, a connected structure composed of two subnetworks is found. A sharp decrease in the dimension of the microstructures occurs from the intermediate to the large undercooling regimen. Although the crystalline phases in the intermediate and the large undercooling regimens are the same, the crystal growth rate is too slow to bring about the occurrence of grain refinement. Combining the morphologies observed in the three undercooling regimens and their crystallization behaviors, we conclude that phase separation takes place in undercooled molten Pd80Si20.

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