- Phase diagram
physical chemistry, mineralogy, and materials science, a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases. In mathematicsand physics, a phase diagram also has an alternative meaning, as a synonym for a phase space.
ingle-component phase diagrams
Two-dimensional (2D) phase diagrams
The simplest phase diagrams are pressure-temperature diagrams of a single simple substance, such as water. The
axescorrespond to the pressureand 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 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 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 critical point. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable [P. Papon, J. Leblond, and P.H.E. Meijer, "The Physics of Phase Transition - Concepts and Applications" Springer 1999.] , in what is known as a
supercritical fluid. In water, the critical point occurs at around convert|647|K|R and convert|22.064|MPa|psi.Fact|date=August 2008
The existence of the liquid-gas critical point reveals a slight ambiguity in the 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, the liquid and gaseous phases can blend continuously into each other. However, the solid-liquid phase boundary can only end in a critical point this way if the solid and liquid phases have the same
symmetry groupFact|date=January 2008.
Noteworthy is that the solid-liquid phase boundary in the phase diagram of most substances has a positive
slope. This is due to the solid phase having a higher densitythan the liquidFact|date=August 2008, so that increasing the pressure increases the melting point; the temperature at which a substance melts. In some parts of the phase diagram for water the solid-liquid phase boundary has a negative slope (especially the portion corresponding to standard pressure). This reflects the fact that ice has a lower density than water, which is an unusual property for a material.
Other thermodynamic properties
In addition to just temperature or pressure, other thermodynamic properties may be graphed in phase diagrams. Examples of such thermodynamic properties include
specific volume, specific enthalpy, or specific entropy. For example, single-component graphs of Temperature vs. specific entropy (T vs. s) for water/ steamor for a refrigerantare commonly used to illustrate thermodynamic cycles such as a Carnot cycle, Rankine cycle, or vapor-compression refrigerationcycle.
two-dimensional graph, two of the thermodynamic quantities may be shown on the horizontal and vertical axes. Additional thermodymic quantities may each be illustrated in increments as a series of lines - curved, straight, or a combination of curved and straight. Each of these iso-lines represents the thermodynamic quantity at a certain constant value.
Three-dimensional (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
orthographic projectionof 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
concentrationbecomes 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 a
mixturecalled 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. A textbook example of a eutectic phase diagram is that of the olivine( forsteriteand fayalite) system.
Another type of binary phase diagram is a boiling point diagram for a mixture of two components, i. e.
chemical compounds.For two particular volatilecomponents at a certain pressure such as atmospheric 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.
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 Equilibriumfor 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- carbonsystem for less than 7% carbon (see steel).
The x-axis of such a diagram represents the
concentrationvariable of the mixture. As the mixtures are typically far from dilute and their density as a function of temperature usually unknown the preferred concentration measure is mole fraction. A volume based measure like molaritywould be unadvisable.
Common components of a phase diagram
Lines of equilibrium or phase boundaries refer to the lines that demarcate where phase transitions occur.
triple pointis, in a pressure-temperature phase diagram, the unique intersection of the lines of equilibrium between three states of matter, usually solid, liquid, and gas.
The solidus is the temperature below which the substance is stable in the solid state. The
liquidusis 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").
olid and liquid crystal phase diagrams
liquid crystalphysics, phase diagrams are used in the case of mixing of nematogeniccompounds to distinguish between the isotropicliquid phase, the nematicliquid phase.
Congruent meltingand incongruent melting
Gibbs phase rule
* [http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/kimcon.html Iron-Iron Carbide Phase Diagram Example]
* [http://www.soton.ac.uk/~pasr1/build.htm How to build a phase diagram]
* [http://www.chm.davidson.edu/ChemistryApplets/PhaseChanges/PhaseDiagram1.html Phase Changes: Phase Diagrams: Part 1]
* [http://www.matter.org.uk/steelmatter/metallurgy/6_1_3_1.html Equilibrium Fe-C phase diagram]
* [http://mtdata.software.googlepages.com/periodictableSolders.htm Phase diagrams for lead free solders]
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