Unidirectional solidification

S. Coriell, M. Cordes, W. Boettinger, R. Sekerka. Convective and interfacial instabilities during unidirectional solidification of a binary alloy. J Cryst Growth 49 13, 1980. 

Let us consider the influence of a solid-liquid interface advancing at a constant velocity on the solid-liquid fractionation of an element i. In the case of unidirectional solidification, it is convenient to consider that liquid crosses the immobile interface with an absolute constant velocity v, while a solid-liquid fractionation coefficient K is applied to the fractionation of element i. Let us assume that the interface is at x=0, the medium being solid for x<0. Liquid fills the half-space 0[Pg.442]

Coaxial intergrowth is a paragenetic relation that describes crystals of two different species growing with a common axis the misfit ratios between the two crystals in the direction of the common axis are small, without exception. The formation of coaxial intergrowth can be understood to be one crystal conjunct to the other in an epitaxial relation, where both continue to grow. If a liquid of eutectic A-B component is solidified from one side (unidirectional solidification), crystals of the two phases A and B precipitate in dotted, columnar or lamellar (with common axis) form, and show unique textures for unidirectional solidification. This is a well known phenomenon in metallurgy. 

Solute concentration fields are shown in Figure 17 for the flows in Figure 16. The diffusion-controlled profile for unidirectional solidification is un-... 

Abstract. This chapter introduces crystallization process of multicrystalline silicon by using a directional solidification method. Numerical analysis, which includes convective, conductive, and radiative heat transfers in the furnace is also introduced. Moreover, a model of impurity segregation is included in this chapter. A new model for three-dimensional (3D) global simulation of heat transfer in a unidirectional solidification furnace with square crucibles was also introduced. 

Conductive heat transfer in all solid components, radiative heat exchange between all diffusive surfaces in the unidirectional solidification furnace, and the Navier-Stokes equations for the melt flow in the crucible are coupled. 

Then, they are solved iteratively in a transient way. Time histories of heater power, fraction solidified, and growth velocity during a unidirectional solidification process are shown in Fig. 4.3 [16]. Variation of heater power as a function of time was imposed as a process parameter. 

There have been many papers concerning the computational studies of unidirectional solidification for solar cells, in which the growth system was imposed to be axisymmetric. However, the actual crystal shape is square, calculation of square-shaped crystals is necessary. When square crucibles are used, the configuration of the furnace becomes asymmetric, and heat transfer in the furnace consequently becomes three-dimensional. Three-dimensional (3D) global modeling is, therefore, necessary for the investigation of m-c interface shape with square crucibles [20],... 

There have been no works using global analysis to investigate the effect of crucible shape on m-c interface shape. The author developed a steady code with 2D and 3D global models for the unidirectional solidification process used for cylindrical and square crucibles, respectively. 

The unidirectional solidification method has both merits and demerits. Controlling the process is a key issue for achieving solidification process that can produces solar cells with high conversion efficiency. Numerical modeling is important for realizing such a process with optimization. A 3D global model and code were developed for analyzing 3D features of a unidirectional solidification process with square crucibles. A 2D/3D mixed discretization scheme... 

Fuk] Fukumoto, S., Okane, T., Umeda, T., Kurz, W., Crystallographic Relationships Between 6-Ferrite and y-Austenite During Unidirectional Solidification of Fc-Cr-Ni Alloys , ISIJInt., 40, 677-684 (2000) (Experimental, Phase Relations, 40)... 

Car] Unidirectional solidification experiments, DTA measurements, microscopic analysis 1120-1200°C / Fe rich alloys with 3.9-4.3 mass% C and mass% 0.21-2.27 Si... 

YOS] Unidirectional solidification measurements Electrical resistance Fe-l.72Si-3.91C and Fe-l.77Si-3.75C... 

Haipeng J, Jiarong L, Jing Y, et al. Study of Heat Transfer Coefficient Used in the Unidirectional Solidification Simulation Based on Orthogonal Design[J]. Rare Metal Materials and Engineering. 2010,39(5) 767-770. 

Nakahata T, Nakajima H (2004) Fabrication of lotus-type porous silicon by unidirectional solidification in hydrogen. Mater Sci Eng A 384 373... 

Molten salt electrolysis should be developed for the production of MG-Si and SOG-Si as energy-efficient and environmentally sound processes. Since the required purity and cost are different between Mg-Si and SOG-Si, a proper approach should be taken for each purpose. For SOG-Si, special attention should be paid for the impurities of boron, phosphorous, and carbon, because they are very difficult to be removed by after treatment like unidirectional solidification process. 

Kokubo T, Arioka M., and Tashiro M., "Preparation of Li2 2Si02 Ceramics with Oriented Microstructure by Unidirectional Solidification of their Melts," Bull. Inst. Chem. Res., Kyoto Univ., 57, 355-75 (1979). 

Equations (26) indicate that at a high imdercooling of above 27 K, Ra becomes larger than Rc. Therefore, the results of the constant-undercooling method are not in conflict with those of unidirectional solidification when considering the difference in undercooling. These results can qualitatively explain also the trend of the RJRc ratio as a function of the pulling rate (fig. 21b). 

Fig. 22. A brief classification of R123 crystal growth techniques on a basis of different phenomena taking place at various interfaces between solid, liquid and gaseous phases participating in the solidification process (a) possible interface boundaries and phenomena connected with the presence of such interfaces (b) different interfaces present in the self-flux method note that numbers in brackets correspond to the general scheme of classification (a) (c) a number of interfaces and phenomena of some importance for the unidirectional solidification method note that (crystal-high-temperature phase and melt-high-temperature phase) interfaces are close to each other (d) different interfaces and phenomena to be considered in the SRL-CP pulling technique of bulk crystal production note that solute transport and nudeation can be controlled in order to achieve a desired morphology of the crystal.

Fumya, K., Y. Nakamura, T. Izumi and Y. Shiohara, 1994, Effect of Ag addition on unidirectional solidification processing of YBCO superconducting oxides, in Proc. ISS 93, Hiroshima, Japan, eds T. Fujita and Y. Shiohara, Vol. VI of Advances in Superconductivity (Springer, Tokyo) pp. 795-798. 

Because the sintered pore structure form as replicas of camphene dendrites, unidirectional solidification was tried to control the growth direction of the camphene dendrites. A special... 

Figure 1. Unidirectional solidification, a Planar front with a shape fluctuation - b Solute mass density profile (k > 1) -c Temperature profile.

Under zero-gravity conditions it is necessary to take into account the time variation of T2 in Eq. 11 so as to have enough coupling between Narangoni convection and unidirectional solidification. We have thus to seek for an oscillatory marginal state. 

Consider a mushy layer that lies above a static solid region and below a semiinfinite fluid region in a binary solution of concentration Coo, and temperature Too, and unidirectional solidification from below. Both the melt/mushy and mushy/solid interfaces move upwards with a constant velocity V. The mushy layer extends form z = 0 to z = h x, y. t). The boundary conditions at the Z -> oo are. 

Chen JH, Tsai HL (1993) Inverse segregation for a unidirectional solidification of aluminum-copper alloys. Int J Heat Mass Transf 36(12) 3069-3075... 

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