Editing Phase diagram (section)

== 3-dimensional diagrams ==
[[File:PVT 3D diagram-en.svg|class=skin-invert-image|thumb|''p''–''v''–''T'' 3D diagram for fixed amount of pure material]]
It is possible to envision three-dimensional (3D) graphs showing three thermodynamic quantities.<ref>{{cite book |last1=Zemansky |first1=Mark W. |last2=Dittman |first2=Richard H. |year=1981 |title=Heat and Thermodynamics |edition=6th |at=Figs. 2-3, 2-4, 2-5, 10-10, P10-1 |publisher=[[McGraw-Hill]] |isbn=978-0-07-072808-0}}</ref><ref>Web applet: [http://biomodel.uah.es/Jmol/plots/phase-diagrams/ 3D Phase Diagrams for Water, Carbon Dioxide and Ammonia]. Described in {{cite journal |last1=Glasser |first1=Leslie |last2=Herráez |first2=Angel |last3=Hanson |first3=Robert M. |year=2009 |title=Interactive 3D Phase Diagrams Using Jmol |journal=[[Journal of Chemical Education]] |volume=86 |issue=5 |pages=566 |doi=10.1021/ed086p566|bibcode=2009JChEd..86..566G |doi-access=free |hdl=20.500.11937/11329 |hdl-access=free }}</ref> 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 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 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 projection]] of the 3D ''p''–''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.

===Binary mixtures===
[[Image:Eutektikum new.svg|class=skin-invert-image|thumb|right|250px|A phase diagram for a binary system displaying a [[eutectic point]].]]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 a [[wikt:binary|binary]] mixture called a ''binary phase diagram'', as shown at right. Such a [[mixture]] can be either a [[solid solution]], [[eutectic point|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 compound]]s. For two particular [[volatility (chemistry)|volatile]] components at a certain pressure such as [[atmospheric pressure]], a [[boiling point|boiling-point]] diagram shows what [[vapor]] (gas) compositions are in [[Vapor–liquid equilibrium|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.[[Image:Binary Boiling Point Diagram new.svg|class=skin-invert-image|thumb|250px|right|Boiling-point diagram]]

A two component diagram with components A and B in an "ideal" solution is shown. The construction of a liquid vapor phase diagram assumes an [[ideal solution|ideal liquid solution]] obeying [[Raoult's law]] and an ideal gas mixture obeying [[Dalton'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.<ref>{{cite journal |last1=David |first1=Carl W. |title=The phase diagram of a non-ideal mixture's p − v − x 2-component gas=liquid representation, including azeotropes |url=https://opencommons.uconn.edu/chem_educ/107/ |journal=Chemistry Education Materials |publisher=University of Connecticut |access-date=9 April 2022 |date=2022}}</ref>

A simple example diagram with hypothetical components 1 and 2 in a non-[[Azeotrope|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#Boiling-point diagrams|Vapor–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 the [[peritectoid]], 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 the [[eutectoid]].

A complex phase diagram of great technological importance is that of the [[iron]]–[[carbon]] system for less than 7% carbon (see [[steel]]).

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 inadvisable.

===Ternary phase diagrams===
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 also [[Ternary plot]]). 
<gallery mode="packed" class="skin-invert-image" heights="200">
File:Gibbs triangle-ternary plot.jpg|Gibbs triangle
File:Space diagram of a three-component system.jpg|alt=Space diagram of a three-component system|Space phase diagram of a ternary system
</gallery>
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.<ref>Alan Prince, "Alloy Phase Equilibria", Elsevier, 290 pp (1966) ISBN 978-0444404626</ref>

===Crystals===
[[Polymorphism (materials science)|Polymorphic]] and [[Polyamorphism|polyamorphic]] substances have multiple [[crystal]] or [[amorphous]] phases, which can be graphed in a similar fashion to solid, liquid, and gas phases.

[[Image:Phase diagram of water.svg|class=skin-invert-image|thumb|700px|centre|[[Semi-log plot|Log-lin]] pressure–temperature phase diagram of water. The [[Roman numeral]]s indicate various [[Phases of ice|ice phases]].<ref>A similar diagram may be found on the site Water structure and science. [http://www1.lsbu.ac.uk/water/water_phase_diagram.html Water structure and science] Site by Martin Chaplin, accessed 2 July 2015.</ref>]]

===Mesophases===
Some organic materials pass through intermediate states between solid and liquid; these states are called [[mesophase]]s. Attention has been directed to mesophases because they enable [[display device]]s and have become commercially important through the so-called [[liquid crystal|liquid-crystal]] technology. Phase diagrams are used to describe the occurrence of mesophases.<ref>{{cite book |last1=Chandrasekhar |first1=Sivaramakrishna  |author-link= Sivaramakrishna Chandrasekhar |year=1992 |title=Liquid Crystals |edition=2nd |pages=27–29, 356 |publisher=[[Cambridge University Press]] |isbn=978-0-521-41747-1}}</ref>