Crystal-vapor interfaces

MOTION OF CRYSTAL/VAPOR AND CRYSTAL/LIQUID INTERFACES... 

Another type of motion of crystal/vapor interfaces occurs when a supersaturation of vacancies anneals out by diffusing to the surface where they are destroyed. In this process, the surface acts as a sink for the incoming vacancy flux and the surface moves inward toward the crystal as the vacancies are destroyed. This may be regarded as a form of crystal dissolution, and the kinetics again depend upon the type of surface that is involved. 

Under these conditions, the growth velocity is simply proportional to the undercooling, and the situation resembles crystal growth at a rough crystal/vapor interface where the growth rate is proportional to the excess vapor pressure (Fig. 12.4).5... 

Crystal/crystal interfaces possess more degrees of freedom than vapor/crystal or liquid/crystal interfaces. They may also contain line defects in the form of interfacial dislocations, dislocation-ledges, and pure ledges. Therefore, the structures and motions of crystal/crystal interfaces are potentially more complex than those of vapor/crystal and liquid/crystal interfaces. Crystal/crystal interfaces experience many different types of pressures and move by a wide variety of atomic mechanisms, ranging from rapid glissile motion to slower thermally activated motion. An overview of crystal/crystal interface structure is given in Appendix B. 

Interfaces may be sharp or diffuse. A sharp interface possesses a relatively narrow core structure with a width close to an atomic nearest-neighbor separation distance. Examples of sharp crystal/vapor and crystal/crystal interfaces are shown in Figs. B.l and B.2. 

Interfaces may also be classified broadly into homophase interfaces and heterophase interfaces. A homophase interface separates two regions of the same phase, whereas a heterophase interface separates two dissimilar phases. Crystal/vapor and crys-tal/liquid interfaces are heterophase interfaces. Crystal/crystal interfaces can be either homophase or heterophase. Examples of crystal/crystal homophase interfaces are illustrated in Figs. B.2, B.4, and B.5. Examples of heterophase crystal/crystal interfaces are shown in Figs. B.6 and B.7. Figure B.6o shows an interface between f.c.c. and h.c.p. crystals where the small mismatch between close-packed lll fcc... 

Reactions in rigid environments and application to reactions in crystals or at crystal-vapor interfaces... 

Figure 18.55 shows the predicted steady-state temperature and meridional flow streamlines for (a) no melt convection and stationary crystal, (b) no crystal rotation with buoyancy-induced melt flow, (c) modest rotation and mixed melt convection, and (d) high rotation rates with mixed melt convection [213], The emissivity of the crystal-vapor interface of the system was specified to be 0.3, while the melt-crystal interface emissivity was set to 0.9 for the GGG crystal of refractive index 1.8. Additional property values and geometric details are listed elsewhere [215]. The crucible diameter is 200 mm, the crystal diameter is 100 mm, and thermocapillary convection was not included in the analysis. 

To reduce the free energy contributed by the surface tension term, the molecules at the liquid crystal/vapor interface favor a layer structure. In the smectic phase, the outermost layers favor a better molecular packing than exists in the interior. The enhanced surface order has been reported for various liquid crystal phases, for example the surface SmA order on the bulk isotropic or nematic sample [50] the surface SmI order on a SmA film [47] the surface SmB gx order on a SmA film [45,48] the surface SmI on a SmC film [17,93] the surface B on a SmA film [49] the surface crystal E order on a SmBhex film [100]. Realizing the importance of the surface tension in characterizing the liquid crystal free-standing films, we... 

Early theories of crystal-liquid interfaces were based on phenomenological models of interface structure that were extensions of models for liquid-vapor or crystal-vapor interfaces. At one end are models, such as that due to Jackson, that view the interface as being relatively sharp with a clear distinction between liquid and crystal particles even at the interface. At the other are theories of diffuse structureless interfaces that, while useful for liquid-vapor interfaces, are not ideal for the highly structured crystal-liquid case. 

As we already know, the work done in creating unit surface area in the vapor phase equals the specific surface free energy at the crystal/vapor interface boundary ob = y/x/lcf [1.21]. Therefore, since the work gained in solvating unit surface area and creating the electrical double layer thereon in the electrolyte is A iE) then the specific free surface energy at the crystal/solution interface is defined as ... 

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

Molecular dynamics calculations have been made on atomic crystals using a Lennard-Jones potential. These have to be done near the melting point in order for the iterations not to be too lengthy and have yielded density functioi). as one passes through the solid-vapor interface (see Ref. 45). The calculations showed considerable mobility in the surface region, amounting to the presence of a... 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Zone refining is one of a class of techniques known as fractional solidification in which a separation is brought about by crystallization of a melt without solvent being added (see also Crystallization) (1 8). SoHd—Hquid phase equiUbria are utilized, but the phenomena are much more complex than in separation processes utilizing vapor—Hquid equiHbria. In most of the fractional-solidification techniques described in the article on crystallization, small separate crystals are formed rapidly in a relatively isothermal melt. In zone refining, on the other hand, a massive soHd is formed slowly and a sizable temperature gradient is imposed at the soHd—Hquid interface. 

A difiiculty with this mechanism is the small nucleation rate predicted (1). Surfaces of a crystal with low vapor pressure have very few clusters and two-dimensional nucleation is almost impossible. Indeed, dislocation-free crystals can often remain in a metastable equilibrium with a supersaturated vapor for long periods of time. Nucleation can be induced by resorting to a vapor with a very large supersaturation, but this often has undesirable side effects. Instabilities in the interface shape result in a degradation of the quality and uniformity of crystalline material. 

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