Aphase diagram inphysical chemistry,engineering,mineralogy, andmaterials science is a type ofchart used to show conditions (pressure, temperature, etc.) at which thermodynamically distinctphases (such as solid, liquid or gaseous states) occur and coexist atequilibrium.
Common components of a phase diagram arelines of equilibrium orphase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.Metastable phases are not shown in phase diagrams as, despite their common occurrence, they are not equilibrium phases.
Triple points are points on phase diagrams where lines of equilibrium intersect. Triple points mark conditions at which three different phases can coexist. For example, the water phase diagram has a triple point corresponding to the single temperature and pressure at which solid, liquid, and gaseous water can coexist in a stable equilibrium (273.16 K and a partial vapor pressure of611.657 Pa). The pressure on a pressure-temperature diagram (such as the water phase diagram shown) is that of the substance in question (e.g., the environmental pressure for a condensed state and thepartial pressure for the gas state).[1]
Thesolidus is the temperature below which the substance is stable in the solid state. Theliquidus is the temperature 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 consists of a mixture of crystals and liquid (like a "slurry").[2]
Working fluids are often categorized on the basis of the shape of their phase diagram.
The simplest phase diagrams are pressure–temperature diagrams of a single simple substance, such aswater. Theaxes correspond to thepressure andtemperature. The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases ofsolid,liquid, andgas.
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 thefree energy isanalytic, correspond to single phase regions. Single phase regions are separated by lines of non-analytical behavior, wherephase transitions occur, which are calledphase boundaries.
In the diagram on the right, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called thecritical point. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable,[3] in what is known as asupercritical fluid. In water, the critical point occurs at aroundTc = 647.096 K (373.946 °C),pc = 22.064 MPa (217.75 atm) andρc = 356 kg/m3.[4]
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 samesymmetry group.[5]
For most substances, the solid–liquid phase boundary (or fusion curve) in the phase diagram has a positiveslope so that the melting point increases with pressure. This is true whenever the solid phase isdenser than the liquid phase.[6] 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'sintermolecular forces. Thus, the substance requires a higher temperature for its molecules to have enough energy to break out of the fixed pattern of the solid phase and enter the liquid phase. A similar concept applies to liquid–gas phase changes.[7]
Water is an exception which has a solid-liquid boundary with negative slope so that the melting point decreases with pressure. This occurs because ice (solid water) is less dense than liquid water, as shown by the fact that ice floats on water. At a molecular level, ice is less dense because it has a more extensive network ofhydrogen bonding which requires a greater separation of water molecules.[6] Other exceptions includeantimony andbismuth.[8][9]
At very high pressures above 50 GPa (500 000 atm),liquid nitrogen undergoes a liquid-liquid phase transition to a polymeric form and becomes denser thansolid nitrogen at the same pressure. Under these conditions therefore, solid nitrogen also floats in its liquid.[10]
The value of the slope dP/dT is given by theClausius–Clapeyron equation for fusion (melting)[11]
where ΔHfus is the heat of fusion which is always positive, and ΔVfus is the volume change for fusion. For most substances ΔVfus is positive so that the slope is positive. However for water and other exceptions, ΔVfus is negative so that the slope is negative.
In addition to temperature and pressure, other thermodynamic properties may be graphed in phase diagrams. Examples of such thermodynamic properties includespecific volume,specific enthalpy, or specificentropy. For example, single-component graphs of temperature vs. specific entropy (T vs.s) for water/steam or for arefrigerant are commonly used to illustratethermodynamic cycles such as aCarnot cycle,Rankine cycle, orvapor-compression refrigeration cycle.
Any two thermodynamic quantities may be shown on the horizontal and vertical axes of a two-dimensional diagram. Additional thermodynamic quantities may each be illustrated in increments as a series of lines—curved, straight, or a combination of curved and straight. Each of theseiso-lines represents the thermodynamic quantity at a certain constant value.
It is possible to envision three-dimensional (3D) graphs showing three thermodynamic quantities.[12][13] 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, andspecific volume (v) on a third. Such a 3D graph is sometimes called ap–v–T diagram. The equilibrium conditions are shown as curves on a curved surface in 3D 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 atriple 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.
Anorthographic projection of the 3Dp–v–T graph showing pressure and temperature as the vertical and horizontal axes collapses the 3D plot into the standard 2D pressure–temperature diagram. When this is done, 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.
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.One type of phase diagram plots temperature against the relative concentrations of two substances in abinary mixture called abinary phase diagram, as shown at right. Such amixture can be either asolid solution,eutectic orperitectic, among others. These two types of mixtures result in very different graphs. Another type of binary phase diagram is aboiling-point diagram for a mixture of two components, i. e.chemical compounds. For two particularvolatile components at a certain pressure such asatmospheric pressure, aboiling-point diagram shows whatvapor (gas) compositions are inequilibrium 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.
A two component diagram with components A and B in an "ideal" solution is shown. The construction of a liquid vapor phase diagram assumes anideal liquid solution obeyingRaoult's law and an ideal gas mixture obeyingDalton's law of partial pressure. A tie line from the liquid to the gas at constant pressure would indicate the two compositions of the liquid and gas respectively.[14]
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. SeeVapor–liquid equilibrium for more information.
In addition to the above-mentioned types of phase diagrams, there are many 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 theperitectoid, a point where two solid phases combine into one solid phase during cooling. The inverse of this, when one solid phase transforms into two solid phases during cooling, is called theeutectoid.
A complex phase diagram of great technological importance is that of theiron–carbon system for less than 7% carbon (seesteel).
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 ismole fraction. A volume-based measure likemolarity would be inadvisable.
A system with three components is called a ternary system. At constant pressure the maximum number of independent variables is three – the temperature and two concentration values. For a representation of ternary equilibria a three-dimensional phase diagram is required. Often such a diagram is drawn with the composition as a horizontal plane and the temperature on an axis perpendicular to this plane. To represent composition in a ternary system an equilateral triangle is used, called Gibbs triangle (see alsoTernary plot).
The temperature scale is plotted on the axis perpendicular to the composition triangle. Thus, the space model of a ternary phase diagram is a right-triangular prism. The prism sides represent corresponding binary systems A-B, B-C, A-C.
However, the most common methods to present phase equilibria in a ternary system are the following:1) projections on the concentration triangle ABC of the liquidus, solidus, solvus surfaces;2) isothermal sections;3) vertical sections.[15]
Polymorphic andpolyamorphic substances have multiplecrystal oramorphous phases, which can be graphed in a similar fashion to solid, liquid, and gas phases.
Some organic materials pass through intermediate states between solid and liquid; these states are calledmesophases. Attention has been directed to mesophases because they enabledisplay devices and have become commercially important through the so-calledliquid-crystal technology. Phase diagrams are used to describe the occurrence of mesophases.[17]
