Solid-vapor boundary

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

Answer Solid C02 is heated until it begins to sublime at the solid-vapor boundary. The temperature remains constant until all the C02 has vaporized. The vapor is then heated to 25°C. ... 

The solid-vapor boundary line extrapolates to P = 0 and T = 0. This is a consequence of the direct link between temperature and molecular energy. At T = 0 K, molecules have minimum energy, so they cannot escape from the solid lattice. At 0 K, the vapor pressure of every substance would be 0 atm. 

The critical state is evidently an invariant point (terminus of a line) in this case, because it lies at a dimensional boundary between states of / =2 (p = 1) and /= 1 (p = 2). The critical point is therefore a uniquely specified state for a pure substance, and it plays an important role (Section 2.5) as a type of origin or reference state for description of all thermodynamic properties. Note that a limiting critical terminus appears to be a universal feature of liquid-vapor coexistence lines, whereas (as shown in Fig. 7.1) solid-liquid and solid-vapor lines extend indefinitely or form closed networks with other coexistence lines. 

Figure 7.5 Phase diagram of elemental sulfur, showing the stable solid phases a-sulfur (orthorhombic red sulfur ) and /3-sulfur (monoclinic yellow sulfur ) and equilibrium phase boundaries (solid lines) as well as the metastable phase boundary (dashed line) that connects a-sulfur to liquid and vapor phases.

Vapor-pressure lowering of a solution decreases the triple-point temperature, the intersection of the liquid-vapor (vapor pressure) and solid-vapor phase boundaries. The solid-liquid phase boundary originating at the triple point is moved slightly to the left on the phase diagram (the solid-vapor boundary is unchanged). The freezing temperature of the solution is thereby lowered (the freezing-point is depressed). 

Figure 4.2 Variation of the vapor pressure, Pv, of a substance with the temperature, 7, showing the phase transition between solid, liquid and vapor phases. Two phases can coexist in equilibrium only at pressures and temperatures defined by the phase boundary lines in the phase diagram, such as liquid-vapor, solid-liquid and solid-vapor lines. The liquid-vapor phase boundary terminates at the critical point, 7C. All three phases can coexist in equilibrium only at the triple point, 73, which is the intersection of the three two-phase boundaries.

Dynamic contact angles are the angles which can be measured if the three-phase boundary (liquid/solid/vapor) is in actual motion. A Wilhelmy plate is used in dynamic contact angle measurements, and this method is also called the tensiometric contact angle method. It has been extensively applied to solid-liquid contact angle determinations in recent years. In practice, a solid substrate is cut as a thin rectangular plate, otherwise a solid material is... 

Figure 10.3 (a) Equilibrium dihedral angle between grain boundary and solid/vapor interfaces, (h) Equilibrium dihedral angle between grain boundary and liquid phase. 

A necessary condition for densification to occur is that the grain boundary energy 7gb be less than twice the solid/vapor surface energy This implies that the equilibrium dihedral angle 0 shown in Fig. 10.3 and defined as... 

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