Single-component systems phase diagrams

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

A sublimation process is controlled primarily by the conditions under which phase equilibria occur in a single-component system, and the phase diagram of a simple one-component system is shown in Figure 15.30 where the sublimation curve is dependent on the vapour pressure of the solid, the vaporisation curve on the vapour pressure of the liquid, and the fusion curve on the effect of pressure on the melting point. The slopes of these three curves can be expressed quantitatively by the Clapeyron equation ... 

Figure 15.30. Phase diagram for a single-component system...

In the three-dimensional diagram, the curve formed by the intersection of the two surfaces represents all of the equilibrium points of the two-phase system. Such a curve is obtained for each type of a two-phase equilibrium existing in a single-component system. At any triple point of the system three such curves meet at a point, giving the temperature and pressure of the triple point. 

Fig. 11. A typical pressure-temperature phase diagram for a single-component system, e.g., xenon, showing the supercritical region, which can he accessed from either the liquid or gas phase without crossing a phase boundary.

For better understanding of the CVD phase diagrams, examples based on single component system such as tungsten carbide coating and multi-component system such as mullite coating are discussed below for various process conditions. 

Figure 1 Phase diagrams of single-component systems...

The factors that determine the crystal structure of particles formed in aerosol reactors have not been studied systematically. In this section, we identify key theoretical concepts and review relevant experimental observations. Consideration is limited to single-component systems. Panicle crystal structure depends on a combination of thermodynamic (equilibrium) factors and rate processes. The equilibrium shape of a particle is detennined by the surface energies of its crystal face.s according to the Wulff construction (Chapter 8). Another factor that inay enter into the process is the excess pressure inside small particles according to the Laplace formula (Chapter 9). Thus the equilibrium form may vary with panicle size depending on the phase diagram,... 

Based on this, we can now construct phase diagrams just as we did in the case of single-component systems (Chap. 11). This will be discussed extensively in the next chapter. 

Fig. 8.2 Illustration of basic phase diagrams of gas, liquid and solid of the single component system separately according to temperature versus pressure (/ ) and temperature versus density (right)...

Figure 7.1 shows the phase diagram for a single-component system. The phase diagrams for systems with two and three components are more complex. In this section we shall consider examples of two- and three-component systems. 

Phase diagrams of single-component systems are useful in illustrating a simple idea that answers a common question How many variables must be specified in order to determine the phase(s) of the system when it s at equilibrium These variables are called degrees of freedom. What we need to know is how many degrees of freedom we need to specify in order to characterize the state of the system. This information is more useful than one might think. Because the position of phase transitions (especially transitions that involve the gas phase) can change quickly... 

Single-component systems are useful for illustrating some of the concepts of equilibrium. Using the concept that the chemical potential of two phases of the same component must be the same if they are to be in equilibrium in the same system, we were able to use thermodynamics to determine first the Clapeyron and then the Clausius-Clapeyron equation. Plots of the pressure and temperature conditions for phase equilibria are the most common form of phase diagram. We use the Gibbs phase rule to determine how many conditions we need to know in order to specify the exact state of our system. 

Equations of state (ES) may be divided between those that are analytic and those that are not. Analytic equations of the form P(p,T,[Zi]) cannot provide an accurate description of thermodynamic properties in the critical region whether for the pure components or their mixtures. Scaled ES are non-analytlc in the usual P (p,T) coordinates but assume analyticlty in y(p,T) for pure components. The choice of variables for a scaled ES for a mixture is not well-defined although Leung and Griffiths (1 ) have used P(T,[uil) with success on the 3He- He system. Phase diagrams are simplier in such coordinates as the bubble-point surface and dew-point surface collapse into a single sheet. 

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