In some two component, solid liquid systems, a eutectic mixture forms.
Consider, now a two component system at some fixed pressure, where the temperature range treated is such as to include formation of one or more solid phases. A simple behavior is shown by systems for which the liquids are completely soluble in each other and in which the only solid phases that occur are the pure crystalline forms of the two components. Such phase behavior is shown in fig. 1 for the system benzene and naphthalene. The curved lines AE and BE show the temperatures at which solutions of various compositions are in equilibrium with pure solid benzene and pure solid naphthalene, respectively. The horizontal straight line is the temperature below which no liquid phase exists.
It is instructive to consider what happens when solutions of various concentrations are cooled. The data give the temperature of the systems as a function of time. These data are plotted as cooling curves, some of which, for concentrations indicated, it is such cooling curves, in fact, that are used to obtain the data shown in the phase diagram.
The relation between the data and the information on the phase diagram can be illustrated with one of the cooling curves, b, for example, the liquid systems cools until curve BE is reached, at point solid naphthalene is inn equilibrium with the solution and starts to freeze out. As cooling continues, more naphthalene freezes out, the solution becomes richer in benzene, and its composition and temperature move down along line BE. This stage is represented on the cooling curve by the slowing fall portion, corresponding to the freezing points of solutions of varying solutions.
Cooling and freezing out of the naphthalene proceed until point E is reached by the liquid phase, at which stage the solution becomes in equilibrium with pure solid benzene as well as with pure solid naphthalene. The solution composition and temperature remain constant until the system is entirely converted to the two solids. Point E is called the eutectic, from the Greek word meaning "easily melted" and the mixture of solids that separates out is called the eutectic mixture. Application of the phase rule to the system at its eutectic point where there are two solids phases and on liquid phase in equilibrium gives
∅ = C - p + 2 = 2 - 3 +2 = 1
Solubility: the curves can be interpreted as showing the solubility of naphthalene in benzene and, a little more awkwardly, the solubility of benzene is benzene naphthalene solutions. Consider the addition of naphthalene to a sample of benzene at 20°C. The process will correspond to the movement along a horizontal 20°C line from the pure benzene limit the solid limit at the left. The added naphthalene will dissolve until the solid naphthalene solution equilibrium line is reached. At that point, which 20°C corresponds to a naphthalene molecule fraction of about 0.26, the solution is saturated with naphthalene. Thus, curve EB shows the solubility of naphthalene in benzene.
If the curve is interpreted as the depression of the freezing point of naphthalene by the addition of benzene, it gives:
ΔHfus/R (1/Tfp - 1/T) = In xA
The species for which values of ΔHfus and Tfp must be used is naphthalene, that which forms the solid. Insertion of 80°C (353 K) for the freezing point of naphthalene and 19.29 kJ mol-1 for its enthalpy fusion gives:
In xnaph = 6.572 - 2320/T
At 20°C, for example, In xnaph = -1.35 and xnaph = 0.26 this value corresponds to that which would be read.
The curve for the freezing point of naphthalene, from B toward E, will follow the same path in all ideal solutions, or the solubility of naphthalene in any solvent that follows ideal behavior.
A variation on the formation of a simple eutectic occurs when the solids that separate out can accommodated some of the second component. The system silver-cooper is illustrated and the areas at the extreme right and left along the abscissa scale show regions in which there is a solid solution of silver in along and copper in silver, respectively. Each region is bordered by a line showing the maximum solubility of the second component in the solid of the first component. Any solution that is cooled will give rise to these solid solutions. The eutectic mixture will, of course, also be a mixture of saturated solid solutions.