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 a Chemical process, chemical equilibrium is the state in which the chemical activities or Concentrations of the reactants and products have no net change The binding constant is a special case of the Equilibrium constant K In a Chemical process, chemical equilibrium is the state in which the chemical activities or Concentrations of the reactants and products have no net change Chemical stability when used in the technical sense in Chemistry, means thermodynamic stability of a chemical system In the fields of organic and Medicinal chemistry, a partition (P or distribution coefficient (D is Relative volatility is a measure comparing the Vapor pressures of the components in a liquid mixture of chemicals For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. In Biochemistry, equilibrium unfolding is the process of unfolding a protein or RNA molecule by gradually changing its solution conditions i A theoretical plate in many Separation processes is a hypothetical zone or stage in which two phases such as the Liquid and Vapor phases of a substance Liquid-liquid extraction, also known as solvent extraction and partitioning, is a method to separate compounds based on their relative solubilities in two Gibbs' phase rule, stated by Josiah Willard Gibbs in the 1870s is the fundamental rule on which Phase diagrams are based In Chemistry, reaction quotient is a quantitative measure of the extent of reaction the relative proportion of products and reactants present in the reaction mixture at some Relative volatility is a measure comparing the Vapor pressures of the components in a liquid mixture of chemicals Solubility equilibrium is any type Chemical equilibrium between solid and dissolved states of a compound at saturation. For a general Chemical reaction \alpha A +\beta B. \rightleftharpoons \sigma S+\tau T. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and A theoretical plate in many Separation processes is a hypothetical zone or stage in which two phases such as the Liquid and Vapor phases of a substance Vapor-liquid equilibrium, abbreviated as VLE by some is a condition where a Liquid and its Vapor (gas phase are in equilibrium with each other Physical chemistry, is the application of Physics to macroscopic microscopic atomic subatomic and particulate phenomena in chemical systems It is mostly defined as a large Mineralogy is an Earth Science focused around the Chemistry, Crystal structure, and physical (including optical) properties of Minerals Materials Science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of Science and In mathematics the graph of a function f is the collection of all Ordered pairs ( x, f ( x) In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and In the Physical sciences a phase is a Set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties In mathematics and physics, a phase diagram also has an alternative meaning, as a synonym for a phase space. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Mathematics and Physics, a phase space, introduced by Willard Gibbs in 1901 is a Space in which all possible states of a System

Single-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. Water ( H2[[oxygen O]] H OH) is the most abundant Molecule on Earth 's surface composing of about 70% of the Earth's surface as The axes correspond to the pressure and temperature. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater 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. A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of This page is about the physical properties of gas as a state of matter

A typical phase diagram. The dotted line gives the anomalous behaviour of water. The green lines mark the freezing point and the blue line the boiling point, showing how they vary with pressure. Freezing Point (Chinese 冰點 Bīngdiǎn is a news journal in the People's Republic of China which has been the subject of controversy over its criticism The boiling point of a liquid is the temperature at which the Vapor pressure of the liquid equals the environmental pressure surrounding the liquid

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. In Thermodynamics, the term thermodynamic free energy refers to the amount of work that can be extracted from a System, and is helpful in Engineering This article is about both real and complex analytic functions The phases are separated by lines of non-analyticity, where phase transitions occur, which are called phase boundaries. In Thermodynamics, phase transition or phase change is the transformation of a thermodynamic system from one phase to another

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. In Physical chemistry, Thermodynamics, Chemistry and Condensed matter physics, a critical point, also called a critical state This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable, in what is known as a supercritical fluid. A supercritical fluid is any substance at a Temperature and Pressure above its Thermodynamic critical point. In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic 064 MPa.

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 group. The Symmetry group of an object ( Image, signal, etc eg in 1D 2D or 3D is the group of all Isometries under which it is

Noteworthy is that the solid-liquid phase boundary in the phase diagram of most substances has a positive slope. Slope is used to describe the steepness incline gradient or grade of a straight line. This is due to the solid phase having a higher density than the liquid, so that increasing the pressure increases the melting point; the temperature at which a substance melts. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different The melting point of a solid is the temperature range at which it changes state from solid to Liquid. 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). In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made 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. Specific volume (v is the volume occupied by a unit of mass of a material In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy 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. Uses A Steam engine uses the expansion of steam in order to drive a Piston or Turbine to perform Mechanical work. A refrigerant is a compound used in a heat cycle that undergoes a Phase change from a Gas to a Liquid and back A thermodynamic cycle is a series of Thermodynamic processes which returns a system to its initial state The Carnot cycle is a particular Thermodynamic cycle, modeled on the hypothetical Carnot heat engine, proposed by Nicolas Léonard Sadi Carnot in 1824 and The Rankine cycle is a thermodynamic cycle which converts heat into work Vapor-compression refrigeration is one of the many Refrigeration cycles available for use

In a two-dimensional graph, two of the thermodynamic quantities may be shown on the horizontal and vertical axes. A two-dimensional graph is the graph of a function of one Variable f ( x) 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.

Temperature vs. specific entropy phase diagram for water/steam. Uses A Steam engine uses the expansion of steam in order to drive a Piston or Turbine to perform Mechanical work. In the area under the red dome, liquid water and steam coexist in equilibrium. The critical point is at the top of the dome. Liquid water is to the left of the dome. Steam is to the right of the dome. The blue lines/curves are isobars showing constant pressure. The green lines/curves are isochors showing constant specific volume. The red curves show constant quality.

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. Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D 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. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance 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 and 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.

The Iron–Iron Carbide (Fe–Fe₃C) phase diagram. The percentage of carbon present and the temperature define the phase of the iron carbon alloy and therefore its physical characteristics and mechanical properties. The percentage of carbon determines the type of the ferrous alloy: iron, steel or cast iron

A phase diagram for a binary system displaying a eutectic point.

One type of phase diagram plots temperature against the relative concentrations of two substances in a binary mixture called a binary phase diagram, as shown at right. In Chemistry, a mixture is a substance made by combining two or more different materials without a chemical reaction occurring (the objects do not bond together Such a mixture can be either a solid solution, eutectic or peritectic, among others. A solid solution is a Solid - state Solution of one or more solutes in a Solvent. 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. The Mineral olivine (when gem-quality also called Peridot) is a Magnesium Iron silicate with the formula ( Mg Forsterite (Mg2SiO4 is the magnesium rich end-member of the Olivine Solid solution series Fayalite (Fe2SiO4 is the Iron rich end-member of the Olivine solid-solution series

Another type of binary phase diagram is a boiling point diagram for a mixture of two components, i. e. chemical compounds. A chemical compound is a substance consisting of two or more different elements chemically bonded together in a fixed proportion by Mass. 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. A vapor or vapour (see Spelling differences) is a substance in the Gas phase at a Temperature lower than its Critical temperature Vapor-liquid equilibrium, abbreviated as VLE by some is a condition where a Liquid and its Vapor (gas phase are in equilibrium with each other In a typical binary boiling point diagram, temperature is plotted on a vertical axis and mixture composition on a horizontal axis.

Boiling Point Diagram

A simple example diagram with hypothetical components 1 and 2 in a non-azeotropic mixture is shown at right. An azeotrope (pronounced 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. Vapor-liquid equilibrium, abbreviated as VLE by some is a condition where a Liquid and its Vapor (gas phase are in equilibrium with each other

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). Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0

The x-axis of such a diagram represents the concentration variable of the mixture. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance 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. In Chemistry, the mole fraction of a component in a Mixture is the relative proportion of molecules belonging to the component to those in the mixture A volume based measure like molarity would be unadvisable. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance

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. In Thermodynamics, the triple point of a substance is the Temperature and Pressure at which three phases (for example Gas, Liquid In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and

The solidus is the temperature below which the substance is stable in the solid state. In Chemistry, Materials science, and Physics, the solidus is a temperature (a line on a Phase diagram) below which a given substance is completely The liquidus is the temperature above which the substance is stable in a liquid state. The liquidus temperature, TL or Tliq is mostly used for Glasses and Alloys It specifies the maximum temperature at which Crystals 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").

Solid 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 Materials science polyamorphism is the ability of a substance to exist in several different Amorphous modifications In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating An amorphous solid is a Solid in which there is no Long-range order of the positions of the Atoms (Solids in which there is long-range atomic order are

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. Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional Liquid, and those of a Solid Isotropy is uniformity in all directions Precise definitions depend on the subject area Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional Liquid, and those of a Solid

See also

• Gibbs phase rule
• Hamiltonian mechanics
• Congruent melting and Incongruent melting
• Phase Equilibria Diagrams database
• CALPHAD (method)

External links

• A collection of about 150 alloy phase diagrams and some PT diagrams
• Iron-Iron Carbide Phase Diagram Example
• How to build a phase diagram
• Phase Changes: Phase Diagrams: Part 1
• Equilibrium Fe-C phase diagram