Binary phase rule

While the phase rule requires tliree components for an unsymmetrical tricritical point, theory can reduce this requirement to two components with a continuous variation of the interaction parameters. Lindli et al (1984) calculated a phase diagram from the van der Waals equation for binary mixtures and found (in accord with figure A2.5.13 that a tricritical point occurred at sufficiently large values of the parameter (a measure of the difference between the two components). 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

We will be looking at first-order phase transitions in a mixture so that the Clapeyron equation, as well as the Gibbs phase rule, apply. We will describe mostly binary systems so that C = 2 and the phase rule becomes... 

In the case of a unary or one-component system, only temperature and pressure may be varied, so the coordinates of unary phase diagrams are pressure and temperature. In a typical unary diagram, as shown in Figure 3.11, the temperature is chosen as the horizontal axis by convention, although in binary diagrams temperature is chosen as the vertical axis. However, for a one-component system, the phase rule becomes F=l-P+2 = 3-P. This means that the maximum number of phases in equilibrium is three when F equals zero. This is illustrated in Figure 3.11 which has three areas, i.e., solid, liquid, and vapour In any... 

Binary phase diagrams from thermodynamics Gibbs phase rule... 

For a binary system at constant pressure the phase rule gives F=3-Ph and we need only two independent variables to express the stability fields of the phases. It is most often convenient and common to choose the temperature and composition, given for... 

In the preceding paragraphs we have seen a few examples of phase equilibria occurring in binary systems represented by means of 2D diagrams built, at constant pressure (isobaric), on temperature/composition axes for which the phase rule... 

A schematic illustration of the method, and of the correlation between binary phase diagram and the one-phase layers formed in a diffusion couple, is shown in Fig. 2.42 adapted from Rhines (1956). The one-phase layers are separated by parallel straight interfaces, with fixed composition gaps, in a sequence dictated by the phase diagram. The absence, in a binary diffusion couple, of two-phase layers follows directly from the phase rule. In a ternary system, on the other hand (preparing for instance a diffusion couple between a block of a binary alloy and a piece of a third... 

Identify the number of components present, the number of phases present, the composition of each phase, and the quantity of each phase from unary, binary, and ternary phase diagrams—that is, apply the Gibbs Phase Rule. 

Apply the Lever Rule to a two-phase field in a binary phase diagram. 

Application of the phase rule to the binary (M-O) and ternary oxide system (M1-M2-O) in a closed system ... 

The metal-H or alloy-H system can be regarded as a binary or pseudobinary system, i.e. c = 2 in the phase rule. Figure 3.17 shows schematically the relation between H2 and solid phase composition H/M for various values of T, assuming two solid phases a and p. These phases correspond to the... 

To explore the ramifications of the phase rule (7.6), we shall first consider the phase equilibria of pure chemical substances (c = 1). Subsequent sections will examine the more complex behavior of binary (c = 2) and ternary (c = 3) multiphase systems. 

For a binary fluid with c = 2, p = 2, the phase rule gives / = 2 degrees of freedom. Under these conditions, we know from the Jacobi cyclic identity (1.14b) that... 

In Figure 2.2-8 the critical endpoint temperatures for the family 0f CO2 + n-alkanes systems are plotted as a function of the carbon number n. If in a particular binary system the three-phase curve hhg is followed to low temperature then at a certain temperature a solid phase is formed (solid n-alkane or solid C02 at low carbon numbers). This occurs at one unique temperature because we now have four phases in equilibrium in a binary system, so according to the phase rule F= 0. Below this so-called quadruple point temperature the hhg curve is metastable. 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

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