Editing Phase diagram

{{Use dmy dates|date=September 2023}}
{{short description|Chart used to show conditions at which physical phases of a substance occur}}
{{for multi|the use of this term in mathematics and physics|Phase portrait|and|Phase space}}

[[File:Phase diagram of water simplified.svg|class=skin-invert-image|thumb|upright=1.35|Simplified temperature/pressure phase change diagram for water. The pressure on a pressure-temperature diagram (such as the water phase diagram shown above) is the [[partial pressure]] of the substance in question.]]
A '''phase diagram''' in [[physical chemistry]], [[engineering]], [[mineralogy]], and [[materials science]] is a type of [[chart]] used to show conditions (pressure, temperature,  etc.) at which thermodynamically distinct [[phase (matter)|phases]] (such as solid, liquid or gaseous states) occur and coexist at [[thermodynamic equilibrium|equilibrium]].

== Overview ==
Common components of a phase diagram are ''lines of equilibrium'' or ''phase 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 point]]s 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 ({{val|273.16|ul=K}} and a partial vapor pressure of {{val|611.657|ul=Pa}}). The pressure on a pressure-temperature diagram (such as the water phase diagram shown) is the [[partial pressure]] of the substance in question.<ref>{{Cite web |url=http://ch302.cm.utexas.edu/physEQ/physical/selector.php?name=phase-diag |title=Phase Diagrams |access-date=2023-07-14 |website=ch302.cm.utexas.edu}}</ref> 

The [[solidus (chemistry)|solidus]] is the temperature below which the substance is stable in the solid state. The [[liquidus]] 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]]").<ref>{{cite book |last1=Predel |first1=Bruno |last2=Hoch |first2=Michael J. R. |last3=Pool |first3=Monte |year=2004 |title=Phase Diagrams and Heterogeneous Equilibria: A Practical Introduction |publisher=[[Springer (publisher)|Springer]] |isbn=978-3-540-14011-5}}<!-- Reference 1 covers most of the article.--></ref>

[[Working fluids]] are often categorized on the basis of the shape of their phase diagram.

== Types ==

=== 2-dimensional diagrams ===
====Pressure vs temperature====
[[Image:Phase-diag2.svg|class=skin-invert-image|thumb|310x310px|A typical phase diagram. The solid green line shows the behaviour of the [[melting point]] for most substances; the dotted green line shows [[Water (molecule)#Density of water and ice|the anomalous behavior of water]].  The red lines show the [[Sublimation (phase transition)|sublimation temperature]] and the blue line the [[boiling point]], showing how they vary with pressure.]] The simplest phase diagrams are pressure–temperature diagrams of a single simple substance, such as [[water (molecule)|water]]. The [[Cartesian coordinate system|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 [[Thermodynamic free energy|free energy]] is [[analytic function|analytic]], correspond to single phase regions. Single phase regions are separated by lines of non-analytical behavior, where [[phase transition]]s occur, which are called '''phase 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 the [[critical point (thermodynamics)|critical point]]. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable,<ref>{{cite book |first1=P. |last1=Papon |first2=J. |last2=Leblond |first3=P. H. E. |last3=Meijer |title=The Physics of Phase Transition : Concepts and Applications |location=Berlin |publisher=Springer |year=2002 |isbn=978-3-540-43236-4 }}</ref> in what is known as a [[supercritical fluid]]. In water, the critical point occurs at around ''T''<sub>c</sub> = {{convert|647.096|K|C}}, ''p''<sub>c</sub> = {{convert|22.064|MPa|atm|abbr=on}} and ''ρ''<sub>c</sub> = 356&nbsp;kg/m<sup>3</sup>.<ref>The International Association for the Properties of Water and Steam [http://www.iapws.org/relguide/fundam.pdf "Guideline on the Use of Fundamental Physical Constants and Basic Constants of Water"], 2001, p. 5</ref>

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]].<ref>{{cite book
 |author-first1=Lev D. |author-last1=Landau |author-link1=Lev Landau
 |author-first2=Evgeny M. |author-last2=Lifshitz |author-link2=Evgeny Lifshitz
 |date=1980
 |title=Statistical Physics
 |edition=3rd |volume=5
 |publisher=[[Butterworth-Heinemann]]
 |isbn=978-0-7506-3372-7
}}</ref>

For most substances, the solid–liquid phase boundary (or fusion curve) in the phase diagram has a positive [[slope]] so that the melting point increases with pressure. This is true whenever the solid phase is [[Density|denser]] than the liquid phase.<ref name=Whitten>{{cite book |last1=Whitten |first1=Kenneth W. |last2=Galley |first2=Kenneth D.  |last3=Davis |first3=Raymond E. |date=1992 |title=General Chemistry. |url=https://archive.org/details/generalchemistry00whit_0 |url-access=registration |edition=4th |page=[https://archive.org/details/generalchemistry00whit_0/page/477 477] |publisher=Saunders College Publishing|isbn=9780030751561 }}</ref> 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 [[intermolecular 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.<ref name=Dorin>{{cite book |title=Chemistry : The Study of Matter Prentice |last1=Dorin |first1=Henry |last2=Demmin |first2=Peter E. |last3=Gabel |first3=Dorothy L. |edition=Fourth |pages=[https://archive.org/details/prenticehallchem00henr/page/266 266–273] |isbn=978-0-13-127333-7 |publisher=[[Prentice Hall]] |url-access=registration |url=https://archive.org/details/prenticehallchem00henr/page/266 |year=1992 }}</ref>

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 of [[hydrogen bond]]ing which requires a greater separation of water molecules.<ref name=Whitten/> Other exceptions include [[antimony]] and [[bismuth]].<ref>{{cite book |last1=Averill |first1=Bruce A. |last2=Eldredge |first2=Patricia |date=2012 |title=Principles of General Chemistry |chapter=11.7 Phase Diagrams |chapter-url=https://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s15-07-phase-diagrams.html |publisher=Creative Commons}}</ref><ref>{{cite book |last1=Petrucci |first1=Ralph H. |last2=Harwood |first2=William S.  |last3=Herring |first3=F. Geoffrey |date=2002 |title=General Chemistry. Principles and Modern Applications |edition=8th |page=495 |publisher=Prentice Hall |isbn=0-13-014329-4}}</ref> 

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 than [[solid nitrogen]] at the same pressure. Under these conditions therefore, solid nitrogen also floats in its liquid.<ref name=Muk007>{{cite journal|last1=Mukherjee|first1=Goutam Dev|last2=Boehler|first2=Reinhard|title=High-Pressure Melting Curve of Nitrogen and the Liquid-Liquid Phase Transition|journal=Physical Review Letters|date=30 November 2007|volume=99|issue=22|pages=225701|doi=10.1103/PhysRevLett.99.225701|pmid=18233298|bibcode=2007PhRvL..99v5701M}}</ref>

The value of the slope d''P''/d''T'' is given by the [[Clausius–Clapeyron relation|Clausius–Clapeyron equation]] for fusion (melting)<ref>{{cite book |last1=Laidler |first1=Keith J. |last2=Meiser |first2=John H. |date=1982 |title=Physical Chemistry |pages=173–74 |publisher=Benjamin/Cummings}}</ref>

:<math>\frac{\mathrm{d}P}{\mathrm{d}T} = \frac{\Delta H_\text{fus}}{T\,\Delta V_\text{fus}}, </math>

where Δ''H''<sub>fus</sub> is the heat of fusion which is always positive, and Δ''V''<sub>fus</sub> is the volume change for fusion. For most substances Δ''V''<sub>fus</sub> is positive so that the slope is positive. However for water and other exceptions, Δ''V''<sub>fus</sub> is negative so that the slope is negative.

====Other thermodynamic properties====
In addition to temperature and 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/[[steam]] or for a [[refrigerant]] are commonly used to illustrate [[thermodynamic cycle]]s such as a [[Carnot cycle]], [[Rankine cycle]], or [[vapor-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 these '''iso-'''lines represents the thermodynamic quantity at a certain constant value.

<gallery mode="packed" heights="250" caption="Chart in U.S. units" class="skin-invert-image">
File:Mollier enthalpy entropy chart for steam - US units.svg|enthalpy–entropy (''h''–''s'') diagram for steam
File:Pressure-enthalpy chart for steam, in US units.svg|pressure–enthalpy (''p''–''h'') diagram for steam
File:Temperature-entropy chart for steam, imperial units.svg|temperature–entropy (''T''–''s'') diagram for steam 
</gallery>

== 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>

== See also ==
{{Div col|small=yes}}
* [[CALPHAD (method)]]
* [[Computational thermodynamics]]
* [[Congruent melting]] and [[incongruent melting]]
* [[Gibbs phase rule]]
* [[Glass databases]]
* [[Hamiltonian mechanics]]
* [[Phase separation]]
* [[Saturation dome]]
* [[Schreinemaker's analysis]]
* [https://www.linkedin.com/pulse/how-do-you-trace-hydrocarbon-phase-envelope-using-alzate-buitrago/?trackingId=vBD1%2F4UHQXKL%2B1MUEMvsCQ%3D%3D Simple phase envelope algorithm]

{{Div col end}}

== References ==
<!-- Reference 1 covers most of the article.-->
{{reflist}}

== External links ==
{{Commons|Phase diagram}}
* [https://web.archive.org/web/20080216023642/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] {{Webarchive|url=https://web.archive.org/web/20090516212458/http://www.chm.davidson.edu/ChemistryApplets/PhaseChanges/PhaseDiagram1.html |date=16 May 2009 }}
* [https://web.archive.org/web/20060427102513/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] {{Webarchive|url=https://web.archive.org/web/20090727100926/http://mtdata.software.googlepages.com/periodictableSolders.htm |date=27 July 2009 }}
* [http://www.doitpoms.ac.uk/miclib/phase_diagrams.php DoITPoMS Phase Diagram Library]
* [http://www.doitpoms.ac.uk/tlplib/phase-diagrams/index.php DoITPoMS Teaching and Learning Package – "Phase Diagrams and Solidification"]
* [https://rd.springer.com/article/10.1007/s11669-014-0343-5 Phase Diagrams: The Beginning of Wisdom – Open Access Journal Article]
* [https://av.tib.eu/media/34658?pag=1 Binodal curves, tie-lines, lever rule and invariant points – How to read phase diagrams] (Video by SciFox on TIB AV-Portal)
* [http://www.apdic.info/ The Alloy Phase Diagram International Commission (APDIC)]
* [http://simon.ayrinhac.free.fr/Publis/Poster_phase_diagrams.pdf Periodic table of phase diagrams of the elements] (pdf poster)
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