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Composition Variation and Phase Fractions

We now consider a very important system that has internal degrees of freedom: a system composed of variable chemical elements and various phases. In other words, the internal degrees of freedom are the compositions of the various regions that compose our system.

This topic often confuses students, so I will go over the terms very carefully, first a few definitions:

phase: A part of a system that can be indentified as ``different'' from another part of the system. A phase is always separated from another phase by an identifiable interface. Examples of phases are a solution of iron and carbon in an FCC structure and a solution of iron and carbon in a BCC structure.
composition: The fractions of the various chemical components that comprise a system.
phase fraction of $\alpha$: The fraction of a system that is the $\alpha$ -phase.
composition of phase $\alpha$: The composition of the subsystem composed of $\alpha$ -phase alone.

**Figure 18-4:** A system in equilibrium with its surroundings and composed of two phases $\alpha$ and $\beta$ , each having a different chemical composition. This illustration is for two phases and two independent components but it may be extrapolated to to as many phases and components as required. Later, a relation between the number of phases and the number of components that can exist at equilibrium will be derived.
$\begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/NBNW.eps}} \end{figure}$

$\bgroup\color{blue}$ \ensuremath{N_{B}}$\egroup$ and $\bgroup\color{blue}$ \ensuremath{N_{W}}$\egroup$ represent numbers of $\bgroup\color{blue}$ B$\egroup$ - and $\bgroup\color{blue}$ W-$\egroup$ type molecules. The number of moles in phases $\bgroup\color{blue}$ \alpha$\egroup$ and in phase $\bgroup\color{blue}$ \beta$\egroup$ can be varied.

The following notation should be studied carefully.

$\begin{center}\vbox{\input{tables/notation} }\end{center}$

Therefore the total numbers of $\bgroup\color{blue}$ B$\egroup$ molecules (or atoms) and $\bgroup\color{blue}$ W$\egroup$ molecules in the system are: