Vapor transport mechanism

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. 

To optimize the applicability of the electrothermal vaporization technique, the most critical requirement is the design of the sample transport mechanism. The sample must be fully vaporized without any decomposition, after desolvation and matrix degradation, and transferred into the plasma. Condensation on the vessel walls or tubing must be avoided and the flow must be slow enough for elements to be atomized efficiently in the plasma itself. A commercial electrothermal vaporizer should provide flexibility and allow the necessary sample pretreatment to introduce a clean sample into the plasma. Several commercial systems are now available, primarily for the newer technique of inductively coupled plasma mass spectroscopy. These are often extremely expensive, so home built or cheaper systems may initially seem attractive. However, the cost of any software and hardware interfacing to couple to the existing instrument should not be underestimated. 

Once molecules reach the surface, whether from a buried source as in the foregoing discussion or by some other transport mechanism from a nonburied source, they tend to sorb onto the surface particles. Some will be in the vapor state and some in solution, but as any water evaporates, they must revert to vapor state or sorb to surface particles. 

The rate and characteristics of surface evolution depend on the particular transport mechanisms that accomplish the necessary surface motion. These can include surface diffusion, diffusion through the bulk, or vapor transport. Kinetic models of capillarity-induced interface evolution were developed primarily by W.W. Mullins [1-4]. The models involving surface diffusion, which relate interface velocity to fourth-order spatial derivatives of the interface, and vapor transport, which relate velocity to second-order spatial derivatives, derive from Mullins s pioneering theoretical work. 

Equation 14.17 can be used to model grain-boundary grooving kinetics when vapor transport is the dominant mechanism. The normal velocity dh/dt is related... 

Different growth-law exponents are obtained for other dominant transport mechanisms. Coblenz et al. present corresponding neck-growth laws for the vapor transport, grain-boundary diffusion, and crystal-diffusion mechanisms [10]. 

The preparation of single crystals. The need for fundamental studies of the mechanical, electrical, and surface properties of carbides and nitrides have necessitated the preparation of single crystals.27 Carbide single crystals are prepared by the Vernouil technique, the floating zone technique, and methods involving precipitation from liquid metals. Nitride single crystals are prepared by vapor transport processes. 

Nevertheless efforts to understand, treat and model sintering/thermal-deactivation phenomena are easily justified. Indeed deactivation considerations greatly influence research development, design and operation of commercial processes. While catalyst deactivation by sintering is inevitable for many processes, some of its immediate drastic consequences may be avoided or postponed. If sintering rates and mechanisms are known even approximately, it may be possible to find conditions or catalyst formulations that minimize thermal deactivation. Moreover it may be possible under selected circumstances to reverse the sintering process through redispersion (the increase in catalytic surface area due to crystallite division or vapor transport followed by redeposition). 

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