Crystal growth speed

The crystal growth speed can be controlled by the heat extraction capacity of the substrate material. During cooling, the difference in thermal expansion coefficient between substrate material and Si ribbon causes a separation of the silicon ribbon from the substrate and allows the re-use of the substrate material. 

Are there further manifestations of a polar axis in crystals Obviously, the morphology,the crystal growth speed,the form of etch figures,and the chemical reactivity of faces are properties that can express a polar symmetry. 

Figure 2-5 The temperature dependency of nucleation speed I and crystal growth speed U [(a) Vitrification occurs readily, (b) Crystals are formed readily] [Ref. 17].

We have so far assumed that the atoms deposited from the vapor phase or from dilute solution strike randomly and balHstically on the crystal surface. However, the material to be crystallized would normally be transported through another medium. Even if this is achieved by hydrodynamic convection, it must nevertheless overcome the last displacement for incorporation by a random diffusion process. Therefore, diffusion of material (as well as of heat) is the most important transport mechanism during crystal growth. An exception, to some extent, is molecular beam epitaxy (MBE) (see [3,12-14] and [15-19]) where the atoms may arrive non-thermalized at supersonic speeds on the crystal surface. But again, after their deposition, surface diffusion then comes into play. 

Both reaction types are carried out in sealed tantalum containers at temperatures around 700 °C, above the melting point of Pr2ls to speed up the reaction and to assure crystal growth upon slow cooling. 

The crystal growth rate has been found in many eases to be extremely rapid, more rapid than can be accounted for on the diffusion hypothesis thus Tammann (foe. cit.) found for benzophe-none a maximum crystallisation velocity of 2 4 mm. per minute (Walton and Judd, J. Phys. Ohem. xvni, 722,1914). Much higher values, e.g. 6840 mm. per minute for water and 60,000 mm. per minute for phosphorus (Gernez, O.R, xcv. 1278, 1882) have been recorded. In some cases the rate was found independent of the speed of rotation of the stirrer and occasionally the reaction velocity followed a bimolecular law instead of the simple unimolecular expression which holds true for solution. 

Denote boundary motion speed as u that may or may not depend on time. For crystal growth, the interface moves to the right with x = Xo>0. For crystal dissolution, the interface moves to the left with x = Xo<0. That is, u is positive during crystal growth and negative during crystal dissolution under our setup of the problem. The interface position can be found as... 

The zinc salt and BaS solutions are mixed thoroughly under controlled conditions (vessel geometry, temperature, pH, salt concentration, and stirring speed, see (a) in Fig. 20). The precipitated raw lithopone does not possess pigment properties. It is filtered off (b2) and dried (c) ca. 2 cm lumps of the material are calcined in a rotary kiln (d) directly heated with natural gas at 650-700 °C. Crystal growth is controlled by adding 1-2 wt% NaCl, 2 wt % Na2S04 and traces of Mg2 + (ca. 2000 ppm), and K+ (ca. 100-200 ppm). The temperature profile and residence time in the kiln are controlled to obtain ZnS with an optimum particle size of ca. 300 nm. 

Overview of Unit Operations. To maximize the electron or hole (carrier) mobility and thus device speed, ICs are built in single-crystal substrates. Methods of bulk crystal growth are therefore needed. The most common of these methods are the Czochralski and float-zone techniques. The Czochralski technique is a crystal-pulling or melt-growth method, whereas the float-zone technique involves localized melting of a sintered bar of the material, followed by cooling and, thus, crystallization. 

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