3D phase diagrams

It is possible to envision three-dimensional (3D) graphs showing three thermodynamic quantities For example for a single component, a 3D Cartesian coordinate type graph can show temperature (T) on one axis, pressure (P) on a second axis, and specific volume (v) on a third. Such a 3D graph is sometimes called a P-v-T diagram. The equilibrium conditions would be shown as a 3D curved surface with areas for solid, liquid, and vapor phases and areas where solid and liquid, solid and vapor, or liquid and vapor coexist in equilibrium. A line on the surface called a triple line is where solid, liquid and vapor can all coexist in equilibrium. The critical point remains a point on the surface even on a 3D phase diagram. An othografi projection of the 3D P-v-T graph showing pressure and temperature as the vertical and horizontal axes effectively collapses the 3D plot into a 2D pressure-temperature diagram. When this happens, the solid-vapor, solid-liquid, and liquid-vapor surfaces collapse into three corresponding curved lines meeting at the triple point, which is the collapsed orthographic projection of the triple line.

Binary phase diagrams

Other much more complex types of phase diagrams can be constructed, particularly when more than one pure component is present. In that case concentration becomes an important variable. 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. Phase diagrams can use other variables in addition to or in place of temperature, pressure and composition, for example the strength of an applied electrical or magnetic field and they can also involve substances that take on more than just three states of matter.

The iron–iron carbide (Fe–Fe₃C) phase diagram. The percentage of carbon present and the temperature define the phase of the iron carbon alloy and therefore its physical characteristics and mechanical properties. The percentage of carbon determines the type of the ferrous alloy: iron, steel or cast iron

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

One type of phase diagram plots temperature against the relative concentrations of two substances in a binary mixture called a binary phase diagram, as shown at right. Such a mixture can be either a solid solution, eutectic or peritectic, among others. These two types of mixtures result in very different graphs. Another type of binary phase diagram is a boiling point diagram for a mixture of two components, i. e. chemical compounds. For two particular valotile components at a certain pressure such as atmospheeric pressure. a boiling point diagram shows what vapor (gas) compositions are in equilibrium with given liquid compositions depending on temperature. In a typical binary boiling point diagram, temperature is plotted on a vertical axis and mixture composition on a horizontal axis.

Boiling point diagram

A simple example diagram with hypothetical components 1 and 2 in a non-azeotropic mixture is shown at right. The fact that there are two separate curved lines joining the boiling points of the pure components means that the vapor composition is usually not the same as the liquid composition the vapor is in equilibrium with. See Vapor-Liquid Equilibrium for a fuller discussion.

In addition to the above mentioned types of phase diagrams, there are thousands of other possible combinations. Some of the major features of phase diagrams include congruent points, where a solid phase transforms directly into a liquid. There is also the peritectoid, a point where two solid phases combine into one solid phase during heating. The inverse of this, when one solid phase transforms into two solid phases during heating, is called the eutectoid.

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

The x-axis of such a diagram represents the concentration variable of the mixture. As the mixtures are typically far from dilute and their density as a function of temperature is usually unknown, the preferred concentration measure is mole fraction. A volume based measure like molarity would be unadvisable.

2D phase diagrams

A typical phase diagram. The dotted line gives
the anomalous behavior of water.
The green lines mark the freezing point and the blue line
the boilling point, showing how they vary with pressure.

2D phase diagrams

The simplest phase diagrams are pressure-temperature diagrams of a single simple substance, such as water. The axes correspond 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.

The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and pressure in this example) change discontinuously (abruptly). For example, the heat capacity of a container filled with ice will change abruptly as the container is heated past the melting point. The open spaces, where the free energy is analytic, correspond to single phase regions. Single phase regions are separated by lines of non-analytical, where phase transitions occur, which are called phase boundaries.

In the diagram on the left, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called the crtical point. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable, in what is known as a supercritical Fluids In water, the critical point occurs at around T_c=647.096 K (1,164.773 °R), p_c=22.064 MPa (3,200.1 psi) and ρ_c=356 kg/m³.

The existence of the liquid-gas critical point reveals a slight ambiguity in labelling the single phase regions. 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, the liquid and gaseous phases can blend continuously into each other. The solid-liquid phase boundary can only end in a critical point if the solid and liquid phases have the same symmetry group.

The solid-liquid phase boundary in the phase diagram of most substances has a positive slope ; the greater the pressure on a given substance, the closer together the molecules of the substance are brought to each other, which increases the effect of the substance's intermocular forces. Thus, the substance requires a higher temperature for its molecules to have enough energy to break out the fixed pattern of the solid phase and enter the liquid phase. A similar concept applies to liquid-gas phase changes. Water, because of its particular properties, is one of the several exceptions to the rule.