Phase diagram

Phase diagram

In 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 mathematics and 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

Pressure-temperature 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 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 density than 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/steam or for a refrigerant are commonly used to illustrate thermodynamic cycles such as a Carnot cycle, Rankine cycle, or vapor-compression refrigeration cycle.

In a 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 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.

One type of phase diagram plots temperature against the relative concentrations of two substances in a 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. A textbook example of a eutectic phase diagram is that of the olivine (forsterite and 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 volatile components 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 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 (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 usually unknown the preferred concentration measure is mole fraction. A volume based measure like molarity would be unadvisable.

Common components of a phase diagram

Lines of equilibrium or phase boundaries refer to the lines that demarcate where phase transitions occur.

A triple point is, 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 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").

olid and liquid crystal phase diagrams

Polymorphic and polyamorphic substances have multiple crystal or amorphous phases, which can be graphed in a similar fashion to solid, liquid, and gas phases.

In liquid crystal physics, phase diagrams are used in the case of mixing of nematogenic compounds to distinguish between the isotropic liquid phase, the nematic liquid phase.

ee also

* CALPHAD (method)
* Congruent melting and incongruent melting
* Gibbs phase rule
* Hamiltonian mechanics
* Glass databases

References

External links

* [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]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Phase diagram — Phase diagram. См. Фазовая диаграмма. (Источник: «Металлы и сплавы. Справочник.» Под редакцией Ю.П. Солнцева; НПО Профессионал , НПО Мир и семья ; Санкт Петербург, 2003 г.) …   Словарь металлургических терминов

  • phase diagram —  Phase Diagram  Фазовая диаграмма (диаграмма состояния)   Графическое изображение соотношения между параметрами состояния термодинамически равновесной системы (температурой, давлением, составом и др.). Фазовая диаграмма позволяет определить,… …   Толковый англо-русский словарь по нанотехнологии. - М.

  • phase diagram — Chem. a graph, usually using temperature, pressure, and composition as coordinates, indicating the regions of stability of the various phases of a system. [1910 15] * * * ▪ physics  graph showing the limiting conditions for solid, liquid, and… …   Universalium

  • phase diagram — būsenos diagrama statusas T sritis chemija apibrėžtis Pusiausvirųjų fazių savybes apibūdinančių termodinaminių parametrų tarpusavio priklausomybės grafinis vaizdas. atitikmenys: angl. constitution diagram; constitutional diagram; equilibrium… …   Chemijos terminų aiškinamasis žodynas

  • phase diagram — fazių diagrama statusas T sritis chemija apibrėžtis Fizikocheminės sistemos pusiausvyros grafinis vaizdas. atitikmenys: angl. constitution(al) diagram; equilibrium diagram; phase diagram rus. диаграмма состояния; диаграмма фазового равновесия;… …   Chemijos terminų aiškinamasis žodynas

  • phase diagram — noun : a diagram composed of equilibrium curves between different phases of the same substance the phase diagram of the gold uranium system Journal of Research …   Useful english dictionary

  • phase diagram — fazių diagrama statusas T sritis fizika atitikmenys: angl. phase diagram vok. Phasendiagramm, n rus. фазовая диаграмма, f pranc. diagramme de phase, m; diagramme des phases, m …   Fizikos terminų žodynas

  • phase diagram — fazių diagrama statusas T sritis Standartizacija ir metrologija apibrėžtis Daugiafazės termodinaminės sistemos būsenų diagrama. atitikmenys: angl. phase diagram vok. Gleichgewichtsdiagramm, n; Phasendiagramm, n; Zustandsdiagramm, n;… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • phase diagram method — fazių diagramos metodas statusas T sritis fizika atitikmenys: angl. phase diagram method vok. Phasendiagrammethode, f rus. метод фазовой диаграммы, m pranc. méthode du diagramme de phase, f …   Fizikos terminų žodynas

  • phase diagram — noun a) A graph, with axes representing temperature and pressure, showing the equilibrium conditions for a given substance to be a solid, liquid or gas. b) a similar diagram for a binary …   Wiktionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”