Roughness interface

The effects of a solvent on growth rates have been attributed to two sets of factors (28) one has to do with the effects of solvent on mass transfer of the solute through adjustments in viscosity, density, and diffusivity the second is concerned with the stmcture of the interface between crystal and solvent. The analysis (28) concludes that a solute-solvent system that has a high solubiUty is likely to produce a rough interface and, concomitandy, large crystal growth rates. 

Figure 3.28 shows 3D-SIMS distributions of the elements Si, Al,Ti, and Cr. The Cr distribution is shown from the bottom, to illustrate the rough interface. It is apparent that the interfaces are not smooth. This is the reason for the slowly decreasing Cr signal in the depth profile. As is apparent in the 3D-distribution, the different depth profiles of Si,Ti, and A1 in the layer are a result of respective particulate inclusions. 

We will use it here in order to derive an analytical form for a crystal profile with a rough interface as an exphcit example. An order parameter

crystalline phase with 0 > 0 and the gaseous (or hquid) one with 0 < 0. 

According to the capillary wave approximation , a rough interface is characterized by a width that diverges logarithmically with its transverse dimensions ... 

A number of investigators (66. 67 have recently employed the critical Ising temperature (transition temperature from smooth to rough interface) to determine the relative importance of F faces. In general, results obtained by this method are quite similar to those obtained from attachment energy calculations. 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

Spiral growth is a mechanism that is expected only on smooth interfaces. The assistance provided by screw dislocations is not necessary in the growth of rough interfaces, where an adhesive-type growth operates. 

Crystal faces with curved or wavy surfaces, not exhibiting either striations or step patterns, are rarely encountered. In most cases, these faces appear by dissolution. Rough interfaces grow by the adhesive-type growth mechanism, their normal... 

With regard to the attachment and detachment energies, the corners of a crystal or a rough interface that is constructed by kinks alone are sites where the process proceeds most quickly, whereas the low-index crystal faces, corresponding to smooth interfaces, represent the direction with the minimum rate of normal growth and dissolution. As a result, if a single crystalline sphere is dissolved in an isotropic environmental phase, a dissolution form bounded by both flat and curved crystal faces appears. This is called the dissolution form, which is not the same as the growth form. 

Figure 6.3 illustrates schematically features seen in the growth banding patterns in respective growth sectors, in relation to the order of morphological importance of the crystal faces. A rough interface disappears as growth proceeds, but the... 

From these observations, we may conclude that, in the growth of natural diamond crystals, three faces, 111, 110, and 100, behave and show characteristics completely in agreement with the characteristics expected from PBC analysis. Therefore, we may conclude that, under the environmental conditions of natural diamond growth (principally in the silicate solution phase), 111 always behaves as a smooth interface under A/r/kT conditions, whereas the Ap,/lcT of 110, and particularly of 100, stays close to the origin under any conditions, and these faces behave exclusively as rough interfaces. 

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