Growth of crystals

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

Purely physical laws mainly control the behaviour of very large particles. Further down the particle size range, however, specific surface area, i.e. surface area per unit mass, increases rapidly. Chemical effects then become important, as in the nucleation and growth of crystals. Thus, a study of particulate systems within this size range of interest has become very much within the ambit of chemical engineering, physical chemistry and materials science. 

Burton, W.K., Cabrera, N. and Frank, F.C., 1951. The growth of crystals and the equilibrium structure of their surfaces. Philosophical Transactions, A243, 299-358. 

Nielsen, A.E., 1969. Nucleatioii and growth of crystals at high supersaturation. Kristall tind Technik, 4, 17-38. 

The growth of crystals—or more generally the solidification of a sohd from a fluid phase—is definitely not an equilibrium problem. Why, therefore, should we discuss here equihbrium thermodynamics, instead of treating directly, for example the coagulation of two atoms and then simply following the growth of the cluster by adding more particles with time ... 

W. Burton, N. Cabrera, F. Frank. The growth of crystals and the equiUbrium structure of their surfaces. Phil Trans Roy Soc London A 243 299, 1951. 

L. M. Martiouchev, V. D. Seleznev, S. A. Skopinov. Computer simulation of nonequilibrium growth of crystals in a two-dimensional medium with a phase-separating impurity. J Stat Phys 90 1413, 1998. 

D. Maynes, J. Klewicki, P. McMurty, H. Robey. Hydrodynamic scalings in the rapid growth of crystals from solution. J Cryst Growth 178 545, 1997. 

Brice, J., "The Growth of Crystals from Liquids , pp. 4-5. North-Holland Publ., Amsterdam, 1973. 

The next most importtmt parameters in Czochralski growth of crystals are the heat flow and heat losses in the system. Actually, aU of the parameters (with the possible exception of 2 and 9) are strongly ciffected by the heat flow within the crystal-pulling system. A tj pical heat-flow pattern in a Czochralski sjretem involves both the crucible and the melt. The pattern of heat-flow is important but we will not expemd upon this topic here. Let it suffice to point out that heat-flow is set up in the melt by the direction of rotation of the cr5rstal being pulled. It is also ctffected by the upper surface of the melt and how well it is thermally insulated from its surroundings. The circular heat flow pattern causes the surface to radiate heat. The crystal also absorbs heat and re-radiates it... 

Operating Parameters for Vatxjr Phase Growth of Crystals... 

The growth of crystals proceeds in two subsequent-parallel stages (1) diffusion and (2) integration. 

A novel technique of producing waveguiding structures by growth of crystals in glass capillaries is presented. This method of crystal growth is simple and is particularly suited to organic materials. 

Trentler, T. J. Hickman, K. M. Goel, S. C. Viano, A. M. Gibbons, P. C. Buhro, W. M. 1995. Solution-liquid-solid growth of crystalling III-V semiconductors—an analogy to vapor-liquid-solid growth. Science 270 1791-1794. 

Table 9.7 shows the results of the calculations of average parameters of PBU/P for isotropic DRP, fulfilled by Serra [134] and Meijering [152], Serra used VD-method while Meijering used the Johnson-Mehl s (JM) statistical model [150] of simultaneous growth of crystals until the total filling of the whole free space was accomplished. The parameter Nv in the table is the number of PBUs in a unit of system volume, thus Nv 1 is the mean volume of a single PBU, which is related to the relative density of the packing (1—e) with an interrelation... 

Wagner in 1906 investigated the use of slow agitation similar to that practiced in the cane sugar industry. The conditions of temperature, concentration, and type and proportion of seed crystals used were the same as those described previously by Behr. Simultaneous growth of crystals of the anhydrous and monohydrate types gave products which were difficult to separate. 

It is interesting to note that many crystal poisons not only interfer with nucleation and the growth of crystals but may also retard their dissolution. As we have seen (Chapter 6), precipitation and dissolution of solids proceed by the attachment or detachment of ions most favorably at kink sites of the crystalline surface. Solutes such as organic substances, or phosphates may upon adsorption immobilize kinks and thus retard dissolution. 

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