**phase diagram**(rus. фазовая диаграмма

*otherwise*диаграмма состояния) — Pictorial representation of phase composition of the system in the space of the basic parameters of state such as temperature T, pressure p and composition x.

### Description

Phase diagrams show what phase (i.e., homogeneous subsystem differing in structure and/or properties from the other ones) or phases must be present in the system of a given composition under given conditions. For complex systems consisting of many phases and components, phase diagrams derived from experimental data and thermodynamic modeling provide an essential way to predict the behaviour of the system in the course of various processes. The analysis of relative positions of the areas of given phase composition of the system, surfaces and lines of phase equilibrium that separate said areas (phase boundaries), as well as their intersections, provide a transparent way to define the phase equilibrium conditions, conditions for the formation of new phases and chemical compounds in the system, formation and decomposition of liquid and solid solutions, etc.

Phase diagrams are used in material science, metallurgy, oil refining, chemical engineering (particularly, in developing material separation techniques), electronics and microelectronics technology, etc. They help to select conditions for industrial chemical synthesis, determine the direction of phase transitions, select thermal treatment regimes, establish the optimal phase compositions, etc.

A phase diagram of a single simple substance is a planar graph in p-T coordinates. It shows the areas of stability of each particular phase (gas, liquid, various solid modifications) separated by the phase boundaries where different phases can coexist. Three different phases can coexist in equilibrium in the triple points where phase boundaries intersect. Three is the maximum number of phases that can coexist in equilibrium in a single simple substance.

The number of phases in a specific point of a phase diagram is governed by the Gibbs’ phase rule and is n + 2 - f, where n is the number of components, i.e. the substances whose quantities in the system can be varied independently from each other and fully determine the quantities of the remaining substances, “2” corresponds to pressure and temperature (thus, n + 2 is the number of parameters that define the state of the system), and f is the number of degrees of freedom, i.e. the number of generalised forces (pressure, temperature, chemical potentials of the components) that can be independently varied within certain limits without changing the equilibrium phase composition.

For example, within the areas of a phase diagram of a single simple substance where only one phase is present, pressure and temperature can be varied independently (f=2) while the triple point is the so-called invariant point of equilibrium (f=0).

In addition, a phase diagram of a single simple substance can include metastable phases, i.e., non-equilibrium phases that can remain kinetically stable in a certain range of parameters for a considerable amount of time, as well as the critical point, a point in the liquid-gas phase boundary that terminates the domain where these two fluid phases are distinguishable. Beyond the critical point (i.e. at higher temperatures/pressures) the concept of liquid-gas transition is no longer valid.

Along with temperature and pressure, there can be other relevant parameters of state such as magnetic field (H) for those substances that are able to form magnetic phases. Then the phase diagram becomes multi-dimensional and its various cross-sections are to be analysed, such as H-T, and number 2 in the Gibbs’ rule must be replaced with the corresponding number of the generalised forces.

Phase diagrams of multicomponent systems are also multidimensional. It is convenient to study their 2D sections, such as temperature-composition and pressure-composition. The isothermal-isobaric sections of three-component phase diagrams, which describe the phase composition versus the ratio of the components, the so-called Gibbs’ triangles are used.

The general considerations discussed above are applicable to multicomponent phase diagrams too. See Figure for an example of an isobaric (T-x) cross-section of a binary phase diagram that is commonly used in materials science. The spaces in those diagrams can correspond to one or two coexisting phases, including melts, solid phases of pure components or their binary compounds, and solid solutions.

The quantities of the phases inside a two phase space of a diagram can be determined via the lever rule as inversely proportional to the ratio of distances to the corresponding phase boundaries along the horizontal line, its intersection with the phase boundaries reflecting the component composition of coexisting phases.

Other important elements of the T-x cross-sections of binary phase diagrams are: the liquidus, above which there is only a liquid phase; the solidus, below which there are only solid phases, the eutectic points (the congruent melting points) at the solidus-liquidus intersection (where the liquidus line has derivative discontinuity), and the peritectic points (incongruent melting points, i.e. melting with partial decomposition of the solid phase) on the liquidus curve, where the liquid phase and two solid phases can coexist, as well as the respective horizontal boundaries of the respective eutectic and peritectic transformations.

In the phases composed of nano-sized particles, the physical properties can depend on their size, so the dispersion diagram is sometimes added to the phase diagram.

Phase diagrams are used in material science, metallurgy, oil refining, chemical engineering (particularly, in developing material separation techniques), electronics and microelectronics technology, etc. They help to select conditions for industrial chemical synthesis, determine the direction of phase transitions, select thermal treatment regimes, establish the optimal phase compositions, etc.

A phase diagram of a single simple substance is a planar graph in p-T coordinates. It shows the areas of stability of each particular phase (gas, liquid, various solid modifications) separated by the phase boundaries where different phases can coexist. Three different phases can coexist in equilibrium in the triple points where phase boundaries intersect. Three is the maximum number of phases that can coexist in equilibrium in a single simple substance.

The number of phases in a specific point of a phase diagram is governed by the Gibbs’ phase rule and is n + 2 - f, where n is the number of components, i.e. the substances whose quantities in the system can be varied independently from each other and fully determine the quantities of the remaining substances, “2” corresponds to pressure and temperature (thus, n + 2 is the number of parameters that define the state of the system), and f is the number of degrees of freedom, i.e. the number of generalised forces (pressure, temperature, chemical potentials of the components) that can be independently varied within certain limits without changing the equilibrium phase composition.

For example, within the areas of a phase diagram of a single simple substance where only one phase is present, pressure and temperature can be varied independently (f=2) while the triple point is the so-called invariant point of equilibrium (f=0).

In addition, a phase diagram of a single simple substance can include metastable phases, i.e., non-equilibrium phases that can remain kinetically stable in a certain range of parameters for a considerable amount of time, as well as the critical point, a point in the liquid-gas phase boundary that terminates the domain where these two fluid phases are distinguishable. Beyond the critical point (i.e. at higher temperatures/pressures) the concept of liquid-gas transition is no longer valid.

Along with temperature and pressure, there can be other relevant parameters of state such as magnetic field (H) for those substances that are able to form magnetic phases. Then the phase diagram becomes multi-dimensional and its various cross-sections are to be analysed, such as H-T, and number 2 in the Gibbs’ rule must be replaced with the corresponding number of the generalised forces.

Phase diagrams of multicomponent systems are also multidimensional. It is convenient to study their 2D sections, such as temperature-composition and pressure-composition. The isothermal-isobaric sections of three-component phase diagrams, which describe the phase composition versus the ratio of the components, the so-called Gibbs’ triangles are used.

The general considerations discussed above are applicable to multicomponent phase diagrams too. See Figure for an example of an isobaric (T-x) cross-section of a binary phase diagram that is commonly used in materials science. The spaces in those diagrams can correspond to one or two coexisting phases, including melts, solid phases of pure components or their binary compounds, and solid solutions.

The quantities of the phases inside a two phase space of a diagram can be determined via the lever rule as inversely proportional to the ratio of distances to the corresponding phase boundaries along the horizontal line, its intersection with the phase boundaries reflecting the component composition of coexisting phases.

Other important elements of the T-x cross-sections of binary phase diagrams are: the liquidus, above which there is only a liquid phase; the solidus, below which there are only solid phases, the eutectic points (the congruent melting points) at the solidus-liquidus intersection (where the liquidus line has derivative discontinuity), and the peritectic points (incongruent melting points, i.e. melting with partial decomposition of the solid phase) on the liquidus curve, where the liquid phase and two solid phases can coexist, as well as the respective horizontal boundaries of the respective eutectic and peritectic transformations.

In the phases composed of nano-sized particles, the physical properties can depend on their size, so the dispersion diagram is sometimes added to the phase diagram.

### Illustrations

#### Authors

- Goldt Ilya V.
- Ioffe Ilya N.

#### Sources

- V. J. Anosov et al. Basic Principles of Physical and Chemical Analysis (in Russian). — Moscow.–Saint Petersberg.: AN USSR publishing, 1947. — 876 P.
- Chemical encyclopedia (in Russian). — Moscow: The Great Soviet Encyclopedia, 1988.