Solid-vapour transitions

The best-known examples of phase transition are the liquid-vapour transition (evaporation), the solid-liquid transition (melting) and the solid-vapour transition (sublimation). The relationships between the phases, expressed as a function of P, V and T consitute an equation of state that may be represented graphically in the form of a phase diagram. An idealized example, shown in figure 1, is based on the phase relationships of argon [126]. 

We discuss classical non-ideal liquids before treating solids. The strongly interacting fluid systems of interest are hard spheres characterized by their harsh repulsions, atoms and molecules with dispersion interactions responsible for the liquid-vapour transitions of the rare gases, ionic systems including strong and weak electrolytes, simple and not quite so simple polar fluids like water. The solid phase systems discussed are ferroniagnets and alloys. 

Accurate enthalpies of solid-solid transitions and solid-liquid transitions (fiision) are usually detennined in an adiabatic heat capacity calorimeter. Measurements of lower precision can be made with a differential scaiming calorimeter (see later). Enthalpies of vaporization are usually detennined by the measurement of the amount of energy required to vaporize a known mass of sample. The various measurement methods have been critically reviewed by Majer and Svoboda [9]. The actual teclmique used depends on the vapour pressure of the material. Methods based on... 

This hypothesis of a compressional force of great magnitude on the surface of charcoal effecting a marked contraction in a relatively thick skin of liquid is open to serious criticism. We have noted already that in the case of vapours on solid surfaces the first unimolecular layer may be held very tenaciously whilst the subsequent layers when formed are held but loosely. Again, all available evidence seems to indicate that the surface of a film but a few hundred molecules thick at the most, would possess all the properties ot a surface of the bulk liquid. It is unlikely that any serious change in the properties of the interface would occur in a transition from a solid-vapour to a solid-liquid system. 

Vora, K.L. Buckton, G. Clapham, D., The use of dynamic vapour sorption and near infrared spectroscopy (DVS-NIR) to study the crystal transitions of theophylline and the report of a new solid-state transition Eur. J. Pharm. Sci. 2004, 22, 97-105. 

Concomitant crystallization is by no means limited to crystallization from solution, nor to preservation of constant molecular conformation. As noted in Section 2.2.5 the classic pressure vs temperature phase diagram for two solid phases (Fig. 2.6) of one material exhibits two lines corresponding to the solid/vapour equilibrium for each of two polymorphs. At any one temperature one would expect the two polymorphs to have different vapour pressures. This, in fact, is the basis for purification of solids by sublimation. Nevertheless there are examples where the two have nearly equal vapour pressures at a particular temperature and thus cosublime. This could be near the transition temperature or simply because the two curves are similar over a large range of temperatures or in close proximity at the temperature at which the sublimation is carried out. For instance, the compounds 3-VI and 3-Vn both yield two phases upon... 

Bulk Fluids. - Here we focus on liquid-vapour transitions and liquid-solid transitions, and briefly mention some recent deposition studies. 

Schwarz and Knoetze [24] found that for their VLE data an approximately linear relationship exists between temperature and the phase transition pressure at constant composition. This relationship has a positive gradient and indicates a higher solubility at lower temperatures, converse to that of the solid-vapour equilibrium (SVE) phase behaviour. This positive gradient was also found through the entire mass fraction range studied and the authors did not find any indications of temperature inversions in this system. 

The electrodeposition of conducting polymer from a solution phase is a transformation reaction. The usual cooperative processes (solid -o- liquid, liquid <-> vapour, solid vapour) which possess a latent heat of transition and present a discontinuous volumic modification are called first-order transitions. The absence of any latent heat and density variations and the presence of a discontinuity in the heat capacity-temperature curve are of second-order transitions. 

In the case of solid-vapour and liquid-vapour transitions equation (6 10) may be used as an approximation. Substituting (6 10) in the last term of (6 13)... 

Nichita et al calculated the wax precipitation from hydrocarbon mixtures using a cubic equation of state (see Chapter 4) to describe the vapour and the liquid lumping into pseudo-components to simplify the phase equilibrium calculation. However, the information lost in this procedure effected the location of the predicted solid phase transition. This issue was avoided by an inverse lumping procedure, in which the equilibrium constants of the original system are related to some quantities evaluated from lumped fluid flash results. The method was tested for two synthetic and one real mixture yielding good agreement between calculated and experimental results. 

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present hr the interatomic potential (e.g. atoms interacting tlirough a Leimard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of tire critical isothemr in the P - Vplane. 

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

Another application is in tire oxidation of vapour mixtures in a chemical vapour transport reaction, the attempt being to coat materials with a tlrin layer of solid electrolyte. For example, a gas phase mixture consisting of the iodides of zirconium and yttrium is oxidized to form a thin layer of ytnia-stabilized zirconia on the surface of an electrode such as one of the lanthanum-snontium doped transition metal perovskites Lai j.Srj.M03 7, which can transmit oxygen as ions and electrons from an isolated volume of oxygen gas. 

The variation of enthalpy for binary mixtures is conveniently represented on a diagram. An example is shown in Figure 3.3. The diagram shows the enthalpy of mixtures of ammonia and water versus concentration with pressure and temperature as parameters. It covers the phase changes from solid to liquid to vapour, and the enthalpy values given include the latent heats for the phase transitions. 

Not all of them are equally suitable as fixed points for thermometry. In (b) and (c), the points are characterized by a high equilibrium pressure and may be better considered as pressure fixed points (see, for example, ref. [9]). Types (d) and (e) are not generally referred to as triple points, but as solid-solid and liquid-liquid transitions, respectively. At low temperature, the last solid-liquid-vapour triple point is that of hydrogen (para 99.996%) at 13.8033 K. 

Most of the generated vapour is condensed in spray condensers which are equipped with circulation pumps and an EG cooler. The vapour that is still uncondensed is withdrawn from the gas phase with the help of a vapour jet which is located down-stream behind the spray condenser and generates the necessary vacuum in the reaction zone. The most critical part of the spray condenser system is the end of the pipe leading the vapour from the prepolycondensation reactors and the finishers into the spray condenser. The transition from a hot to a cold environment causes deposition of solid material onto the cold walls which has to be removed manually or by means of a mechanical scraper. 

Point B At this point a changes to b. It is known as transition temperature. Thus there are three phases [Two solids (a b) and one vapour)... 

The vapour deposition method is widely used to obtain amorphous solids. In this technique, atoms, molecules or ions of the substance (in dilute vapour phase) are deposited on to a substrate maintained at a low temperature. Most vapour-deposited amorphous materials crystallize on heating, but some of them exhibit an intervening second-order transition (akin to the glass transition). Amorphous solid water and methanol show such transitions. The structural features of vapour-deposited amorphous solids are comparable to those of glasses of the same materials prepared by melt-quenching. 

Belertser et al (1988) have observed that the electrical resistivity of amorphous chromium films at liquid-helium temperatures jumps from a value (10 3 O cm) characteristic of a poor metal by a factor 103, when the hydrogen content is increased sufficiently to increase the lattice constant by 10%. The transition is not abrupt, and is thought by these authors to be of Anderson type. They claim that it is the first time such a transition has been observed in a solid, and that it is similar to that in expanded mercury vapour (Section 4). 

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