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Chemistry 360
Fall 2014
Dr. Jean M. Standard
November 12, 2014
Binary Solid-Liquid Phase Diagrams
Introduction
Previously, we have explored the P-x and T-x liquid-vapor phase diagrams of binary systems. A typical T-x solidliquid phase diagram of a binary system is illustrated in Figure 1. Note that P-x phase diagrams are not
particularly useful for solid-liquid phase diagrams due to the low vapor pressure of most solids. For the solid-liquid
binary system illustrated in Figure 1, it has been assumed that the liquid phase is completely miscible, while the
solid phase is completely immiscible (a common situation). Also note that though the position of the point labeled
"eutectic" is shown at a mole fraction of approximately 0.5 in this figure, the eutectic composition may be larger or
smaller than this for specific systems.
T*fus,A
L
T*fus,B
Eutectic
L+SA
L + SB
T
SA + SB
0
1
xA
Figure 1. Typical solid-liquid T-x phase diagram of a binary system.
At high temperatures, the phase diagram indicates the presence of a single liquid phase, consisting of a mixture of
the two components. At low temperatures, below the point labeled "eutectic" on the diagram, the system consists of
two separate solid phases: the solid phase of pure component A and the solid phase of pure component B. In
between the high and low temperature regimes, the phase diagram indicates that the system consists of a single
liquid phase in equilibrium with either pure component A or pure component B in the solid phase.
The Eutectic Point
The eutectic temperature corresponds to the lowest freezing temperature of the system. For temperatures lower than
the eutectic temperature, the system consists of pure A and pure B in solid form. The eutectic composition
corresponds to the only point at which both A and B freeze at the same time. For all other compositions, either
component A or component B freezes first.
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Cooling the System: To the Left of the Eutectic Point
To the left of the eutectic point, a tie line drawn in the region of liquid-solid equilibrium indicates the compositions
of the liquid and solid phases at temperature T1 for compositions that are low in component A, as shown in Figure 2.
In this region, the solid phase consists of pure component B and the liquid phase is a mixture of A and B.
As the system is cooled from the liquid phase with a composition to the left of the eutectic point, the phase diagram
shows that pure B freezes out of solution; thus, as the temperature is lowered, the liquid phase becomes enriched in
component A. Once the system is cooled to the eutectic temperature, component A also freezes.
Tie Line
L
T1
L+SA
L + SB
SA + SB
0
1
xA
Composition of solid phase
Composition of liquid phase
Figure 2.
Tie line indicating composition of solid and liquid phases at temperature T1 for a system
rich in component B.
Cooling the System: To the Right of the Eutectic Point
To the right of the eutectic point, a tie line drawn in the region of liquid-solid equilibrium indicates the compositions
of the liquid and solid phases at temperature T1 for compositions that are rich in component A, as shown in Figure 3.
In this region, the solid phase consists of pure component A and the liquid phase is a mixture of A and B.
As the system is cooled from the liquid phase with a composition to the right of the eutectic point, the phase
diagram shows that pure A freezes out of solution; therefore, in this case as the temperature is lowered, the liquid
phase becomes enriched in component B. Finally, once the system is cooled to the eutectic temperature, component
B also freezes.
Tie Line
L
T1
L + SB
L+SA
SA + SB
0
1
xA
Composition of liquid phase
Composition of solid phase
Figure 3.
Tie line indicating composition of solid and liquid phases at temperature T1 for a system
rich in component A.
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Binary Solid-Liquid Phase Diagram Example: Water/NaCl
The phase diagram shown in Figure 4 is a real example of a binary solid-liquid phase diagram for NaCl and H2O.
Much of the data for the phase diagram was published in1855 by a scientist named Matthew Maury in The Physical
Geography of the Sea and its Meteorology. In the book, Maury quoted sea water temperatures from around the
world. The coldest temperatures for NaCl/H2O mixtures recorded in Maury’s book were from the arctic region,
where the system consisted of brine (salty sea water) in equilibrium with icebergs. The freezing temperature of the
particular brine solution found in the arctic region was determined to be 27.2ºF.
Note that the phase diagram in Figure 4 is cut off on the right side (that is, it should extend to 100 wt% NaCl) so that
the regions of interest with respect to sea water temperatures are more easily visible. The eutectic temperature is –
6ºF.
Figure 4. Solid-liquid T-x phase diagram of NaCl and H2O.