And the abscissa represents the composition the alloy

increase in the free energy and in a possible spontaneous change to another state whereby the free energy is lowered.

The term phase equilibrium, often used in the context of this discussion, refers to equilibrium as it applies to systems in which more than one phase may exist. Phase equilibrium is reflected by a constancy with time in the phase characteristics of a system. Perhaps an example best illustrates this concept. Suppose that a sugar–water syrup is contained in a closed vessel and the solution is in contact with solid sugar at 20�C. If the system is at equilibrium, the composition of the syrup is 65 wt% C12H22O11–35 wt% H2O (Figure 10.1), and the amounts and compositions of the syrup and solid sugar will remain constant with time. If the temperature of the system is suddenly raised—say, to 100�C—this equilibrium or balance is temporarily upset in that the solubility limit has been increased to 80 wt% C12H22O11 (Figure 10.1). Thus, some of the solid sugar will go into solution in the syrup. This will continue until the new equilibrium syrup concentration is established at the higher temperature.

Much of the information about the control of microstructure or phase structure of a particular alloy system is conveniently and concisely displayed in what is called a phase diagram, also often termed an equilibrium or constitutional diagram. Many microstructures develop from phase transformations, the changes that occur be-tween phases when the temperature is altered (ordinarily upon cooling). This may involve the transition from one phase to another, or the appearance or disappear-ance of a phase. Phase diagrams are helpful in predicting phase transformations and the resulting microstructures, which may have equilibrium or nonequilibrium character.

A couple of comments are in order regarding nomenclature. First, for metallic alloys, solid solutions are commonly designated by lowercase Greek letters (�, �,�, etc.). Furthermore, with regard to phase boundaries, the line separating the L and � � L phase fields is termed the liquidus line, as indicated in Figure 10.2a; the liquid phase is present at all temperatures and compositions above this line. The solidus line is located between the � and � � L regions, below which only the solid� phase exists. For Figure 10.2a, the solidus and liquidus lines intersect at the two composition extremities; these correspond to the melting temperatures of the pure components. For example, the melting temperatures of pure copper and nickel are 1085�C and 1453�C, respectively. Heating pure copper corresponds to moving vertically up the left-hand temperature axis. Copper remains solid until its melting tempera-ture is reached. The solid-to-liquid transformation takes place at the melting temperature, and no further heating is possible until this transformation has been completed.