Phase diagram

In physical chemistry and materials science, a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases. In mathematics and physics, a phase diagram also has an alternative meaning, as a synonym for a phase space.

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Pressure-temperature diagrams

The simplest phase diagrams are pressure-temperature diagrams of a single simple substance, such as water. The axes corresponds to the pressure and temperature. The phase diagram shows, in pressure-temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas.

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A typical phase diagram

The markings on the phase diagram show the points where the free energy is non-analytic. The open spaces, where the free energy is analytic, correspond to the phases. The phases are separated by lines of non-analyticity, where phase transitions occur, which are called phase boundaries.

In the diagram, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called the critical point. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable. In water, the critical point occurs at around 647 K (374°C or 705°F) and 22.064 MPa.

The existence of the liquid-gas critical point reveals a slight ambiguity in our above definitions. When going from the liquid to the gaseous phase, one usually crosses the phase boundary, but it is possible to choose a path that never crosses the boundary by going to the right of the critical point. Thus, phases can sometimes blend continuously into each other. We should note, however, that this does not always happen. For example, it is impossible for the solid-liquid phase boundary to end in a critical point in the same way as the liquid-gas boundary, because the solid and liquid phases have different symmetry.

An interesting thing to note is that the solid-liquid phase boundary in the phase diagram of most substances, such as the one shown above, has a positive slope. This is due to the solid phase having a higher density than the liquid, so that increasing the pressure increases the melting temperature. However, in the phase diagram for water the solid-liquid phase boundary has a negative slope. This reflects the fact that ice has a lower density than water, which is an unusual property for a material.

Other phase diagrams

Other, more complex types of phase diagrams can be constructed.

For example, phase diagrams can involve substances that take on more than just three states of matter. Also, phase diagrams can use other variables in place of temperature and pressure. Phase diagrams with more than two dimensions can be constructed that show the effect of more than two variables on the phase of a substance.

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A phase diagram for a binary system displaying a eutectic point.

One type of phase diagram plots temperature against the relative concentrations of two substances in a binary mixture. Such a mixture can be either a solid solution or a eutectic. These two types of mixtures result in very different graphs. A textbook example of a eutectic phase diagram is that of the olivine (forsterite and fayalite) system.

A complex phase diagram of great technological importance is that of the iron-carbon system for less than 7% carbon.

Common components of a phase diagram

Lines of equilibrium or phase boundaries refer to the lines that demarcate where phase transitions occur.

A triple point is, in a pressure-temperature phase diagram, the unique intersection of the lines of equilibrium between three states of matter, usually solid, liquid, and gas.

For a phase diagram with temperature on the vertical axis, a solidus is a line below which the substance is stable in the solid state. A liquidus is a line above which the substance is stable in a liquid state. There may be a gap between the solidus and liquidus; within the gap, the substance is not stable as either a solid or a liquid.

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