Phase boundary solid-vapour

The strict definition of a phase is any homogeneous and physically distinct region that is separated from another such region by a distinct boundary . For example a glass of water with some ice in it contains one component (the water) exhibiting three phases liquid, solid, and gaseous (the water vapour). The most relevant phases in the oil industry are liquids (water and oil), gases (or vapours), and to a lesser extent, solids. 

Similar results, to the Fe-Zn system were obtained in the Ti,j,-Al(,) and Ti(j)-Al, ) system where, in the solid-liquid couples some of the expected surface layer phases were not formed, whereas in the solid-vapour system it was possible to obtain all the phases and predict from the AG -concen-tration curves the compositions at the different layer phase boundaries. 

The theoretical treatment which has been developed in Sections 10.2-10.4 relates to mass transfer within a single phase in which no discontinuities exist. In many important applications of mass transfer, however, material is transferred across a phase boundary. Thus, in distillation a vapour and liquid are brought into contact in the fractionating column and the more volatile material is transferred from the liquid to the vapour while the less volatile constituent is transferred in the opposite direction this is an example of equimolecular counterdiffusion. In gas absorption, the soluble gas diffuses to the surface, dissolves in the liquid, and then passes into the bulk of the liquid, and the carrier gas is not transferred. In both of these examples, one phase is a liquid and the other a gas. In liquid -liquid extraction however, a solute is transferred from one liquid solvent to another across a phase boundary, and in the dissolution of a crystal the solute is transferred from a solid to a liquid. 

An alternative explanation concerns the existence of two equilibria. As the vapour/liquid equilibrium is disturbed by the passage of air, the concentration of dissolved compounds in the liquid phase falls, disturbing the solid /liquid equilibrium. The kinetics of transfer across this latter phase boundary are much slower than for the liquid/vapour transfer, so that the extraction of odour becomes limited by the rate of diffusion into the liquid phase. 

Using this equation AHV can be estimated with a knowledge of the equilibrium vapour pressure of a liquid at two different temperatures. For the solid-vapour phase boundary (sublimation), an analogous equation is obtained by replacing AHv with the heat of sublimation AHs. 

A phase is a part of a system that is chemically uniform and has a boundary around it. Phases can be solids, liquids and gases, and, on passing from one phase to another, it is necessary to cross a phase boundary. Liquid water, water vapour and ice are the three phases found in the water system. In a mixture of water and ice it is necessary to pass a boundary on going from one phase, say ice, to the other, water. 

The outer boundary of liquid water (of any liquid phase in general), which is in contact with its vapour or the air, is called the surface. The surface forming a boundary between two or more separate phases (phase boundary), such as liquid-gas, liquid-solid, gas-solid, or, for immiscible materials, Hquid-liquid or solid-solid, is called the interface. The surface or interface can be planar or curved. Thermodynamic properties of systems with planar and curved phase interfaces are different. 

If any component is absent from a particular phase (for example, the vapour phase, or a solid phase), there is one variable the less, but also one boundary condition the less, for migration of that component cannot occur with respect to the phase considered. Equation a) is therefore still true. 

Bivariant Systems.—If we examine Figs. 3 and 4, we see that the curves OA, OB, OC, which represent diagrammatically the conditions under which the systems, solid and vapour, liquid and vapour, solid and liquid, are in equilibrium, form the boundaries of three fields or areas. These areas give the conditions of temperature and pressure under which the single phases, solid, liquid and vapour, are capable of stable existence. These different areas are the regions of stability of the phase common to the two curves by which the area is enclosed. Thus, the phase common to the two systems represented by OA (solid and vapour) and OB (liquid and vapour) is the vapour phase and the area enclosed by the curves AO and OB is therefore the area of the vapour phase. Similarly, the area AOC is the area of the solid phase, and BOC the area of the liquid phase. 

The occurrence of all those interfaces which have been mentioned depends upon the conditions of preparation of the solid - as, for example, upon the method of solidification or of deposition from the vapour phase, or upon rolling, drawing, bending, etc. - and upon the subsequent annealing process by means of which transformation, recrystallization, or relaxation (i. e. the formation of low-angle grain boundaries at the expense of randomly distributed dislocations) can proceed [7]. 

Eqs. (4) - (7) are solved simultaneously at a given time. Gas, liquid and solid phases have their own simulation domains interconnected with each other via corresponding boundary conditions. In the present study the equation for heat transfer (7) is connected to the vapour diffusion equation (4) by calculating the saturated vapour concentration at the liquid-gas interface as a function of local temperature. 

In Fig. 8.11, which we have adapted from Cahn and from Teletzke er al., we show the temperature (T) vs composition (x) coexistence curve for the equilibrium of the phases B and y (two liquids, say), while these are also in equilibrium widi a third phase, a, which is not shown in the diagram (a vapour phase, say, or a solid boundary). The By critical point is at C. The points marked y and B tmd shown connected by a tieline are a general pair of equilibrium y and B phases. The tieline labelled P marks the Cahn transition in the three-phase (apy) region, and corresponds to P in Hg. 8.10. In the three-phase region above P, that is, dcmr to the critical point C, the ay interface is wetted by B, below P it is not. 

Figure 3.16 contains results for the drying of a porous stmcture consisting of spatially fixed solids. The small dots denote the gas phase with the colour coding corresponding to the partial vapour pressure. The simulations have been carried out two-dimensionally for a flat geometry (initially 4(X) pm x 300 pm water and a gas layer of 100 pm height) with periodic boundary cmiditions in x-direction. The vapour pressru e at the top of the porous system was kept constant at 0 Pa. The gas vapour diffusion coefficient was set to 2.5-10" m /s and the liquid temperature was 80 °C. 

Within the scope of the stochastic approach, there is no strict boundary between homogeneous and inhomogeneous broadening. The boundary depends on the timescale of the experiment. This approach is convenient for considering the line broadening problem in vapour or liquid phases. However, stochastic theory cannot explain the optical band shape in solids. Therefore, we shall only use a dynamical approach to the line broadening problem. 

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