Interface motion

In figure A3.3.9 the early-time results of the interface fonnation are shown for = 0.48. The classical spinodal corresponds to 0.58. Interface motion can be simply monitored by defining the domain boundary as the location where i = 0. Surface tension smooths the domain boundaries as time increases. Large interconnected clusters begin to break apart into small circular droplets around t = 160. This is because the quadratic nonlinearity eventually outpaces the cubic one when off-criticality is large, as is the case here. 

Due to the conservation law, the diffiision field 5 j/ relaxes in a time much shorter than tlie time taken by significant interface motion. If the domain size is R(x), the difhision field relaxes over a time scale R Flowever a typical interface velocity is shown below to be R. Thus in time Tq, interfaces move a distanc of about one, much smaller compared to R. This implies that the difhision field 6vj is essentially always in equilibrium with tlie interfaces and, thus, obeys Laplace s equation... 

Flere [ ] denotes the discontinuity in across tlie interface. Equation (A3.3.71). equation (A3.3.74), equation (A3.3.76) and equation (A3.3.77) together detemiine the interface motion. 

Direction of interface motion Figure 3-25 Crystal growth in a melt. 

In a foregoing section, we mentioned that field forces (e,g., of the electric or elastic field) can cause an interface to move. If they are large enough so that inherent counterforces (such as interface tension or friction) do not bring the boundary to a stop, the interface motion would continue and eventually become uniform. In this section, however, we are primarily concerned with boundary motions caused by chemical potential changes. From irreversible thermodynamics, we know that the dissipated Gibbs energy of the discontinuous system is T-ab, where crb here is the entropy production (see Section 4.2). Since dG/dV = dG/dV = crb- T/ A < ), we have with Eqn. (4.8) at the boundary b... 

Figure 11-17. a) Phase diagram of the quasi-binary system AX-BX with an extended miscibility gap. b) Schematic electrolysis cell A/AX/BX/B. Cation vacancy drift and the mechanism of interface motion are indicated. 

Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. 

Figure 3.5 Interface motion and cavitation during interdiffusion in fluids, (a) Initial...

A vast number of engineering materials are used in solid form, but during processing may be found in vapor or liquid phases. The vapor— solid (condensation) and liquid—>solid (solidification) transformations take place at a distinct interface whose motion determines the rate of formation of the solid. In this chapter we consider some of the factors that influence the kinetics of vapor/solid and liquid/solid interface motion. Because vapor and liquid phases lack long-range structural order, the primary structural features that may influence the motion of these interfaces are those at the solid surface. 

The conditions and kinetic equations for phase transformations are treated in Chapters 17 and 20 and involve local changes in free-energy density. The quantification of thermodynamic sources for kinetically active interface motion is approximate for at least two reasons. First, the system is out of equilibrium (the transformations are not reversible). Second, because differences in normal component of mechanical stresses (pressures, in the hydrostatic case) can exist and because the thermal con-... 

J.W. Cahn. Theory of crystal interface motion in crystalline materials. Acta Metall., 8(8) 554—562, 1960. 

The motion of a crystal/crystal interface is either conservative or nonconservative. As in the case of conservative dislocation glide, conservative interface motion occurs in the absence of a diffusion flux of any component of the system to or from the... 

The basic mechanisms by which various types of interfaces are able to move non-conservatively are now considered, followed by discussion of whether an interface that is moving nonconservatively is able to operate rapidly enough as a source to maintain all species essentially in local equilibrium at the interface. When local equilibrium is achieved, the kinetics of the interface motion is determined by the rate at which the atoms diffuse to or from the interface and not by the rate at which the flux is accommodated at the interface. The kinetics is then diffusion-limited. When the rate is limited by the rate of interface accommodation, it is source-limited. Note that the same concepts were applied in Section 11.4.1 to the ability of dislocations to act as sources during climb. 

Analysis is simplified if 7 is isotropic—i.e., independent of geometrical attributes such as interfacial inclination n and, for internal interfaces in crystalline materials, the crystallographic misorientation across the interface. All interfacial energy reduction then results from a reduction of interfacial area through interface motion. The rate of interfacial area reduction per volume transferred across the interface is the local geometric mean curvature. Thus, local driving forces derived from variations in mean curvature allow tractable models for the capillarity-induced morphological evolution of isotropic interfaces. 

Solid/vapor interface motion can be produced by evaporation—the atoms that compose the solid phase are removed from the surface via the vapor phase reverse motion can be produced by condensation where a vapor-phase flux is directed onto the solid phase. Figure 14.2 illustrates how simultaneous evaporation and condensation can result in surface smoothing. 

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