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[[文件:固体氩快速溶解.jpg|200px|thumb|right|一小块固体氩在快速溶解，同时显示出从固体到液体以及从液体到气体的转变。]]

[[文件:固体氩快速溶解.jpg|200px|thumb|right|一小块固体氩在快速溶解，同时显示出从固体到液体以及从液体到气体的转变。]]

A small piece of rapidly melting solid [[argon simultaneously shows the transitions from solid to liquid and liquid to gas.]]

[[文件:二氧化碳（红色）和水（蓝色）的相图比较.png|thumb|upright=2|二氧化碳（红色）和水（蓝色）的相图比较，解释了它们在1个大气压下的不同相变]]

{{Condensed matter physics|expanded=States of matter}}

{{Condensed matter physics|expanded=States of matter}}

* A [[eutectic]] transformation, in which a two-component single-phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a [[eutectoid]] transformation.

* A [[eutectic]] transformation, in which a two-component single-phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a [[eutectoid]] transformation.

* A [[metastable]] to equilibrium phase transformation. A metastable polymorph which forms rapidly due to lower surface energy will transform to an equilibrium phase given sufficient thermal input to overcome an energetic barrier.

* A [[metastable]] to equilibrium phase transformation. A metastable polymorph which forms rapidly due to lower surface energy will transform to an equilibrium phase given sufficient thermal input to overcome an energetic barrier.

* A [[peritectic]] transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase.

* A [[peritectic]] transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase.

* A [[spinodal decomposition]], in which a single phase is cooled and separates into two different compositions of that same phase.

* A [[spinodal decomposition]], in which a single phase is cooled and separates into two different compositions of that same phase.

* Transition to a [[mesophase]] between solid and liquid, such as one of the "[[liquid crystal]]" phases.

* Transition to a [[mesophase]] between solid and liquid, such as one of the "[[liquid crystal]]" phases.

* The transition between the [[ferromagnetism|ferromagnetic]] and [[paramagnetism|paramagnetic]] phases of [[magnet]]ic materials at the [[Curie point]].

* The transition between the [[ferromagnetism|ferromagnetic]] and [[paramagnetism|paramagnetic]] phases of [[magnet]]ic materials at the [[Curie point]].

* The transition between differently ordered, [[ANNNI model|commensurate]] or [[commensurability (mathematics)|incommensurate]], magnetic structures, such as in cerium [[antimonide]].

* The transition between differently ordered, [[ANNNI model|commensurate]] or [[commensurability (mathematics)|incommensurate]], magnetic structures, such as in cerium [[antimonide]].

* The [[martensitic transformation]] which occurs as one of the many phase transformations in carbon steel and stands as a model for [[displacive phase transformations]].

* The [[martensitic transformation]] which occurs as one of the many phase transformations in carbon steel and stands as a model for [[displacive phase transformations]].

* Changes in the [[crystallographic]] structure such as between [[Allotropes of iron|ferrite]] and [[austenite]] of iron.

* Changes in the [[crystallographic]] structure such as between [[Allotropes of iron|ferrite]] and [[austenite]] of iron.

* Order-disorder transitions such as in alpha-[[titanium aluminide]]s.

* Order-disorder transitions such as in alpha-[[titanium aluminide]]s.

* The dependence of the [[adsorption]] geometry on coverage and temperature, such as for [[hydrogen]] on iron (110).

* The dependence of the [[adsorption]] geometry on coverage and temperature, such as for [[hydrogen]] on iron (110).

* The emergence of [[superconductivity]] in certain metals and ceramics when cooled below a critical temperature.

* The emergence of [[superconductivity]] in certain metals and ceramics when cooled below a critical temperature.

* The transition between different molecular structures ([[Polymorphism (materials science)|polymorphs]], [[allotropy|allotropes]] or [[polyamorphism|polyamorphs{{not a typo}}]]), especially of solids, such as between an [[amorphous solid|amorphous]] structure and a [[crystal]] structure, between two different crystal structures, or between two amorphous structures.

* The transition between different molecular structures ([[Polymorphism (materials science)|polymorphs]], [[allotropy|allotropes]] or [[polyamorphism|polyamorphs{{not a typo}}]]), especially of solids, such as between an [[amorphous solid|amorphous]] structure and a [[crystal]] structure, between two different crystal structures, or between two amorphous structures.

* Quantum condensation of [[boson]]ic fluids ([[Bose–Einstein condensate|Bose–Einstein condensation]]). The [[superfluidity|superfluid]] transition in liquid [[helium]] is an example of this.

* Quantum condensation of [[boson]]ic fluids ([[Bose–Einstein condensate|Bose–Einstein condensation]]). The [[superfluidity|superfluid]] transition in liquid [[helium]] is an example of this.

* The [[Symmetry breaking|breaking of symmetries]] in the laws of physics during the early history of the universe as its temperature cooled.

* The [[Symmetry breaking|breaking of symmetries]] in the laws of physics during the early history of the universe as its temperature cooled.

* [[Isotope fractionation]] occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When [[water vapor]] condenses (an [[equilibrium fractionation]]), the heavier water isotopes (18O and 2H) become enriched in the liquid phase while the lighter isotopes (16O and 1H) tend toward the vapor phase.<ref>{{Cite web

* [[Isotope fractionation]] occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When [[water vapor]] condenses (an [[equilibrium fractionation]]), the heavier water isotopes (18O and 2H) become enriched in the liquid phase while the lighter isotopes (16O and 1H) tend toward the vapor phase.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks.

Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks.

At the phase transition point (for instance, boiling point) the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred.

At the phase transition point (for instance, boiling point) the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred.

It is sometimes possible to change the state of a system diabatically (as opposed to adiabatically) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is metastable, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in superheating, supercooling, and supersaturation, for example.

It is sometimes possible to change the state of a system diabatically (as opposed to adiabatically) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is metastable, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in superheating, supercooling, and supersaturation, for example.

 

 

 

 

 

 

 

 

 

 

[[Paul Ehrenfest]] classified phase transitions based on the behavior of the [[thermodynamic free energy]] as a function of other thermodynamic variables.<ref name="ReferenceA">{{cite journal|last1=Jaeger|first1=Gregg|title=The Ehrenfest Classification of Phase Transitions: Introduction and Evolution|journal=Archive for History of Exact Sciences|date=1 May 1998|volume=53|issue=1|pages=51–81|doi=10.1007/s004070050021}}</ref> Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. ''First-order phase transitions'' exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable.<ref name = Blundell>{{Cite book | last = Blundell | first = Stephen J. |author2=Katherine M. Blundell | title = Concepts in Thermal Physics | publisher = Oxford University Press | year = 2008 | isbn = 978-0-19-856770-7}}</ref> The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. ''Second-order phase transitions'' are continuous in the first derivative (the [[Phase transition#order parameters|order parameter]], which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy.<ref name = Blundell/> These include the ferromagnetic phase transition in materials such as iron, where the [[magnetization]], which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the [[Curie temperature]]. The [[magnetic susceptibility]], the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.

[[Paul Ehrenfest]] classified phase transitions based on the behavior of the [[thermodynamic free energy]] as a function of other thermodynamic variables.<ref name="ReferenceA">{{cite journal|last1=Jaeger|first1=Gregg|title=The Ehrenfest Classification of Phase Transitions: Introduction and Evolution|journal=Archive for History of Exact Sciences|date=1 May 1998|volume=53|issue=1|pages=51–81|doi=10.1007/s004070050021}}</ref> Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. ''First-order phase transitions'' exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable.<ref name = Blundell>{{Cite book | last = Blundell | first = Stephen J. |author2=Katherine M. Blundell | title = Concepts in Thermal Physics | publisher = Oxford University Press | year = 2008 | isbn = 978-0-19-856770-7}}</ref> The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. ''Second-order phase transitions'' are continuous in the first derivative (the [[Phase transition#order parameters|order parameter]], which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy.<ref name = Blundell/> These include the ferromagnetic phase transition in materials such as iron, where the [[magnetization]], which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the [[Curie temperature]]. The [[magnetic susceptibility]], the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.

Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. Second-order phase transitions are continuous in the first derivative (the order parameter, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the magnetization, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature. The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.

Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. Second-order phase transitions are continuous in the first derivative (the order parameter, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the magnetization, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature. The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.

根据热力学自由能的行为，Paul Ehrenfest 将相变分类为其他热力学变量的函数。在这种方案下，相变被标记为自由能的最低导数，在相变处是不连续的。自由能对一些热力学变量的一阶导数表现出不连续性。不同的固体 / 液体 / 气体跃迁被归类为一级跃迁，因为它们涉及到密度的不连续变化，而密度变化是自由能对压强的一阶导数的倒数。二阶相变在一阶导数中是连续的(阶参数是自由能对外场的一阶导数，在二阶导数中是连续的) ，但在自由能的二阶导数中表现出不连续性。这些现象包括铁等材料中的铁磁相变，其中的磁化强度是自由能相对于外加磁场强度的一阶导数，当温度降到居里点以下时，磁化强度从零开始不断增加。磁化率，自由能与场的二阶导数，不连续地变化。在 Ehrenfest 分类方案下，原则上可能存在第三、第四和更高阶的相变。

保罗·埃伦费斯特Paul Ehrenfest根据热力学自由能与其他热力学变量的函数关系对相变进行了分类。根据他的方法，可以将相变按照转变时的不连续自由能的最低导数标记。一阶相变相对于某些热力学变量，表现出自由能的一阶导数不连续。各种固/液/气的转变都归为一阶转变，因为它们都涉及到密度的不连续变化，这是自由能相对于压力的一阶导数（一阶导数的逆函数）。而二阶相变在一阶导数中是连续的（有序参数，即自由能相对于外部场的一阶导数，在整个转变过程中是连续的），但在自由能的二阶导数中表现出不连续性。比如包括铁等材料中的铁磁相变，其中磁化强度是自由能相对于施加磁场强度的一阶导数，随着温度降低到居里温度以下，磁化强度将从零开始连续增加。而磁化率，是自由能相对于磁场的二阶导数，它的变化则是不连续的。以此类推，按照埃伦费斯特的分类方法，原则上可以存在第三，第四和更高阶的相变。

 

 

The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the supercritical liquid–gas boundaries.

The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the supercritical liquid–gas boundaries.

 

 

 

In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:<ref name="ReferenceA"/>

In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:<ref name="ReferenceA"/>

In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:

In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:

 

 

'''First-order phase transitions''' are those that involve a [[latent heat]]. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not.<ref>Faghri, A., and Zhang, Y., [https://books.google.com/books?id=bxndY2KSuQsC&printsec=frontcover&dq=Transport+Phenomena+in+Multiphase+Systems&hl=en&ei=JJdqTIikDZLdngfY4fjxAQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC8Q6AEwAA#v=onepage&q&f=false ''Transport Phenomena in Multiphase Systems''], Elsevier, Burlington, MA, 2006,</ref><ref>Faghri, A., and Zhang, Y., [https://www.springer.com/gp/book/9783030221362 ''Fundamentals of Multiphase Heat Transfer and Flow''], Springer, New York, NY, 2020</ref> Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into [[water vapor|vapor]], but forms a [[turbulence|turbulent]] mixture of liquid water and vapor bubbles). [[Yoseph Imry|Imry]] and Wortis showed that [[quenched disorder]] can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.<ref>{{cite journal | last1 = Imry | first1 = Y. | last2 = Wortis | first2 = M. | year = 1979 | title =  Influence of quenched impurities on first-order phase transitions| url = | journal = Phys. Rev. B | volume = 19 | issue = 7| pages = 3580–3585 | doi=10.1103/physrevb.19.3580|bibcode = 1979PhRvB..19.3580I }}</ref><ref name="KumarPramanik2006">{{cite journal|last1=Kumar|first1=Kranti|last2=Pramanik|first2=A. K.|last3=Banerjee|first3=A.|last4=Chaddah|first4=P.|last5=Roy|first5=S. B.|last6=Park|first6=S.|last7=Zhang|first7=C. L.|last8=Cheong|first8=S.-W.|title=Relating supercooling and glass-like arrest of kinetics for phase separated systems: DopedCeFe2and(La,Pr,Ca)MnO3|journal=Physical Review B|volume=73|issue=18|pages=184435|year=2006|issn=1098-0121|doi=10.1103/PhysRevB.73.184435|arxiv = cond-mat/0602627 |bibcode = 2006PhRvB..73r4435K }}</ref><ref name="PasquiniDaroca2008">{{cite journal|last1=Pasquini|first1=G.|last2=Daroca|first2=D. Pérez|last3=Chiliotte|first3=C.|last4=Lozano|first4=G. S.|last5=Bekeris|first5=V.|title=Ordered, Disordered, and Coexistent Stable Vortex Lattices inNbSe2Single Crystals|journal=Physical Review Letters|volume=100|issue=24|pages=247003|year=2008|issn=0031-9007|doi=10.1103/PhysRevLett.100.247003|pmid=18643617|bibcode=2008PhRvL.100x7003P|arxiv=0803.0307}}</ref>

'''First-order phase transitions''' are those that involve a [[latent heat]]. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into [[water vapor|vapor]], but forms a [[turbulence|turbulent]] mixture of liquid water and vapor bubbles). [[Yoseph Imry|Imry]] and Wortis showed that [[quenched disorder]] can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.

First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into vapor, but forms a turbulent mixture of liquid water and vapor bubbles). Imry and Wortis showed that quenched disorder can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.

First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into vapor, but forms a turbulent mixture of liquid water and vapor bubbles). Imry and Wortis showed that quenched disorder can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.

 

 

'''Second-order phase transitions''' are also called ''"continuous phase transitions"''. They are characterized by a divergent susceptibility, an infinite [[Correlation function (statistical mechanics)|correlation length]], and a [[power law]] decay of correlations near [[Critical point (thermodynamics)|criticality]]. Examples of second-order phase transitions are the [[Ferromagnetism|ferromagnetic]] transition, superconducting transition (for a [[Type-I superconductor]] the phase transition is second-order at zero external field and for a [[Type-II superconductor]] the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the [[superfluid]] transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature<ref name="J. Non-Cryst 2013">{{cite journal | last1 = Ojovan | first1 = M.I. | year = 2013 | title = Ordering and structural changes at the glass-liquid transition | url = | journal = J. Non-Cryst. Solids | volume = 382 | issue = | pages = 79–86 | doi = 10.1016/j.jnoncrysol.2013.10.016 |bibcode = 2013JNCS..382...79O }}</ref> which enables accurate detection using [[differential scanning calorimetry]] measurements.  [[Lev Landau]] gave a [[Phenomenology (particle physics)|phenomenological]] [[Landau theory|theory]] of second-order phase transitions.

'''Second-order phase transitions''' are also called ''"continuous phase transitions"''. They are characterized by a divergent susceptibility, an infinite [[Correlation function (statistical mechanics)|correlation length]], and a [[power law]] decay of correlations near [[Critical point (thermodynamics)|criticality]]. Examples of second-order phase transitions are the [[Ferromagnetism|ferromagnetic]] transition, superconducting transition (for a [[Type-I superconductor]] the phase transition is second-order at zero external field and for a [[Type-II superconductor]] the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the [[superfluid]] transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using [[differential scanning calorimetry]] measurements.  [[Lev Landau]] gave a [[Phenomenology (particle physics)|phenomenological]] [[Landau theory|theory]] of second-order phase transitions.

Second-order phase transitions are also called "continuous phase transitions". They are characterized by a divergent susceptibility, an infinite correlation length, and a power law decay of correlations near criticality. Examples of second-order phase transitions are the ferromagnetic transition, superconducting transition (for a Type-I superconductor the phase transition is second-order at zero external field and for a Type-II superconductor the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the superfluid transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using differential scanning calorimetry measurements.  Lev Landau gave a phenomenological theory of second-order phase transitions.

Second-order phase transitions are also called "continuous phase transitions". They are characterized by a divergent susceptibility, an infinite correlation length, and a power law decay of correlations near criticality. Examples of second-order phase transitions are the ferromagnetic transition, superconducting transition (for a Type-I superconductor the phase transition is second-order at zero external field and for a Type-II superconductor the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the superfluid transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using differential scanning calorimetry measurements.  Lev Landau gave a phenomenological theory of second-order phase transitions.

 

 

Apart from isolated, simple phase transitions, there exist transition lines as well as multicritical points, when varying external parameters like the magnetic field or composition.

Apart from isolated, simple phase transitions, there exist transition lines as well as multicritical points, when varying external parameters like the magnetic field or composition.

Several transitions are known as ''infinite-order phase transitions''.

另外还存在其他相变类型例如无序相变。无序相变是连续的但并不破坏对称性。最著名的例子是二维XY模型中的Kosterlitz-Thouless相变。除此之外二维电子气中的量子相变也都属于此类。

The [[glass transition|liquid–glass transition]] is observed in many [[polymers]] and other liquids that can be [[supercooling|supercooled]] far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a ''[[quenched disorder]]'' state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions.

 

 

 

 

 

 

 

The [[glass transition|liquid–glass transition]] is observed in many [[polymers]] and other liquids that can be [[supercooling|supercooled]] far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a ''[[quenched disorder]]'' state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times.<ref>Gotze, Wolfgang. "Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory."</ref><ref>{{cite journal | last1 = Lubchenko | first1 = V. Wolynes | last2 = Wolynes | first2 = Peter G. | year = 2007 | title = Theory of Structural Glasses and Supercooled Liquids | url = | journal = Annual Review of Physical Chemistry | volume = 58 | issue = | pages = 235–266 | doi=10.1146/annurev.physchem.58.032806.104653| pmid = 17067282 |arxiv = cond-mat/0607349 |bibcode = 2007ARPC...58..235L }}</ref> No direct experimental evidence supports the existence of these transitions.

The liquid–glass transition is observed in many polymers and other liquids that can be supercooled far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a quenched disorder state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions.

The liquid–glass transition is observed in many polymers and other liquids that can be supercooled far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a quenched disorder state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions.

在许多聚合物和其他液体中可以观察到液-玻转变，这些聚合物和液体可以被过冷到远低于结晶相的熔点。这在几个方面是非典型的。它不是热力学基态之间的过渡: 人们普遍认为真正的基态总是晶态的。玻璃是一种淬火无序态，其熵、密度等都依赖于热历史。因此，玻璃化转变主要是一种动态现象: 在冷却液体时，内部自由度相继失去平衡。一些理论方法预测了在无限长弛豫时间的假设极限下的潜在相变。没有直接的实验证据支持这些跃迁的存在。

在过度冷却至远低于结晶相熔点的聚合物和其他液体中，观察到了液体-玻璃转变。该现象仓多个方面考虑均属于非典型的相变过程。它不是热力学基态之间的转变：人们普遍认为，真正的基态始终是晶体。玻璃是淬火无序状态，其熵，密度等取决于热历史。因此，玻璃相变主要是一种动态现象：冷却液体时，内部自由度会逐渐失去平衡。一些理论方法预测其潜在相变发生在无限长时间的假象极限内。但是目前并不存在直接的实验证据来支持这些相变的存在。

===Phase coexistence===

A disorder-broadened  first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions. This slowing down happens below a glass-formation temperature Tg, which may depend on the applied pressure. If the first-order freezing transition occurs over a range of temperatures, and Tg falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition, such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials, magnetocaloric materials, magnetic shape memory materials, and other materials.The interesting feature of these observations of Tg falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between Tg and Tc in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses.

=== Critical points 临界点===

 

 

 

 

 

 

===Critical points===

 

In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the [[Critical point (thermodynamics)|critical point]], at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of [[critical opalescence]], a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).

In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the [[Critical point (thermodynamics)|critical point]], at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of [[critical opalescence]], a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).

In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the critical point, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of critical opalescence, a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).

In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the critical point, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of critical opalescence, a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).

 

 

 

 

对称性

=== Symmetry 对称性===

Phase transitions often involve a [[symmetry breaking]] process. For instance, the cooling of a fluid into a [[crystalline solid]] breaks continuous [[translation symmetry]]: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to [[spontaneous symmetry breaking]], with the exception of certain [[accidental symmetry|accidental symmetries]] (e.g. the formation of heavy [[virtual particles]], which only occurs at low temperatures).<ref>{{cite book|last1=Ivancevic|first1=Vladimir G.|last2=Ivancevic|first2=Tijiana, T.|title=Complex Nonlinearity|date=2008|publisher=Springer|location=Berlin|isbn=978-3-540-79357-1|pages=176–177|url=https://books.google.com/?id=wpsPgHgtxEYC&pg=PA177 |accessdate=12 October 2014}}</ref>

Phase transitions often involve a [[symmetry breaking]] process. For instance, the cooling of a fluid into a [[crystalline solid]] breaks continuous [[translation symmetry]]: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to [[spontaneous symmetry breaking]], with the exception of certain [[accidental symmetry|accidental symmetries]] (e.g. the formation of heavy [[virtual particles]], which only occurs at low temperatures).

Phase transitions often involve a symmetry breaking process. For instance, the cooling of a fluid into a crystalline solid breaks continuous translation symmetry: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to spontaneous symmetry breaking, with the exception of certain accidental symmetries (e.g. the formation of heavy virtual particles, which only occurs at low temperatures).

Phase transitions often involve a symmetry breaking process. For instance, the cooling of a fluid into a crystalline solid breaks continuous translation symmetry: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to spontaneous symmetry breaking, with the exception of certain accidental symmetries (e.g. the formation of heavy virtual particles, which only occurs at low temperatures).

 

An '''order parameter'''<!--boldface per WP:R#PLA--> is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other.<ref>{{Cite book | title = Compendium of Chemical Terminology | editor = A. D. McNaught and A. Wilkinson | isbn = 978-0-86542-684-9 | doi =  | publisher = [[IUPAC]] | url = http://goldbook.iupac.org/goldbook/O04323.html | accessdate = 2007-10-23 | year = 1997 }}{{Dead link|date=May 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> At the critical point, the order parameter [[susceptibility (disambiguation)|susceptibility]] will usually diverge.

An '''order parameter''' is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter [[susceptibility (disambiguation)|susceptibility]] will usually diverge.

 

 

An example of an order parameter is the net magnetization in a ferromagnetic system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities.

An example of an order parameter is the net magnetization in a ferromagnetic system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities.

序参数的一个例子是正在发生相变的铁磁系统的净磁化。对于液体 / 气体跃迁，序参数是密度之差。

关于序参数的一个示例是，发生相变的铁磁系统中的净磁化强度。对于液/气相变，序参数是它们的密度之差。

 

 

From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the ferromagnetic phase, one must provide the net magnetization, whose direction was spontaneously chosen when the system cooled below the Curie point. However, note that order parameters can also be defined for non-symmetry-breaking transitions.

From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the ferromagnetic phase, one must provide the net magnetization, whose direction was spontaneously chosen when the system cooled below the Curie point. However, note that order parameters can also be defined for non-symmetry-breaking transitions.

 

 

Some phase transitions, such as superconducting and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.

Some phase transitions, such as superconducting and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.

 

 

There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as vortex- or defect lines.

There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as vortex- or defect lines.

 

===Relevance in cosmology===

=== Relevance in cosmology 宇宙学的相关性 ===

 

Symmetry-breaking phase transitions play an important role in [[physical cosmology|cosmology]]. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the [[electroweak force|electroweak field]] into the U(1) symmetry of the present-day [[electromagnetic field]]. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see [[electroweak baryogenesis]]).

Symmetry-breaking phase transitions play an important role in [[physical cosmology|cosmology]]. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the [[electroweak force|electroweak field]] into the U(1) symmetry of the present-day [[electromagnetic field]]. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see [[electroweak baryogenesis]]).

Symmetry-breaking phase transitions play an important role in cosmology. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the electroweak field into the U(1) symmetry of the present-day electromagnetic field. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see electroweak baryogenesis).

Symmetry-breaking phase transitions play an important role in cosmology. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the electroweak field into the U(1) symmetry of the present-day electromagnetic field. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see electroweak baryogenesis).

 

 

Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of [[Eric Chaisson]]<ref>{{cite book|last = Chaisson|first = Eric J.|title =Cosmic Evolution|url = https://archive.org/details/cosmicevolutionr00chai|url-access = registration|publisher= Harvard University Press|date = 2001|isbn = 9780674003422}}</ref> and [[David Layzer]].<ref>David Layzer, ''Cosmogenesis, The Development of Order in the Universe'', Oxford Univ. Press, 1991</ref>

Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of [[Eric Chaisson]] and [[David Layzer]].

Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of Eric Chaisson and David Layzer.

Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of Eric Chaisson and David Layzer.

 

 

See also relational order theories and order and disorder.

See also relational order theories and order and disorder.

 

 

 

 

 

 

Continuous phase transitions are easier to study than first-order transitions due to the absence of [[latent heat]], and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.

Continuous phase transitions are easier to study than first-order transitions due to the absence of [[latent heat]], and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.

Continuous phase transitions are easier to study than first-order transitions due to the absence of latent heat, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.

Continuous phase transitions are easier to study than first-order transitions due to the absence of latent heat, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.

 

 

It turns out that continuous phase transitions can be characterized by parameters known as critical exponents. The most important one is perhaps the exponent describing the divergence of the thermal correlation length by approaching the transition. For instance, let us examine the behavior of the heat capacity near such a transition. We vary the temperature  of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature T_c . When  is near T_c , the heat capacity  typically has a power law behavior,

It turns out that continuous phase transitions can be characterized by parameters known as critical exponents. The most important one is perhaps the exponent describing the divergence of the thermal correlation length by approaching the transition. For instance, let us examine the behavior of the heat capacity near such a transition. We vary the temperature  of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature T_c . When  is near T_c , the heat capacity  typically has a power law behavior,

:<math> C \propto |T_c - T|^{-\alpha}.</math>

:<math> C \propto |T_c - T|^{-\alpha}.</math>

 

The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent {{mvar|ν}} instead of {{mvar|α}}, applies for the correlation length.

 

 

The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59<ref>{{cite journal |url= http://eprints.whiterose.ac.uk/1958/1/ojovanmi1_Topologically2.pdf |doi=10.1088/0953-8984/18/50/007|bibcode = 2006JPCM...1811507O |title=Topologically disordered systems at the glass transition|journal=Journal of Physics: Condensed Matter|volume=18|issue=50|pages=11507–11520|year=2006|last1=Ojovan|first1=Michael I|last2=Lee|first2=William E}}</ref> A similar behavior, but with the exponent {{mvar|ν}} instead of {{mvar|α}}, applies for the correlation length.

The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent  instead of , applies for the correlation length.

The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent  instead of , applies for the correlation length.

非晶态材料的热容在玻璃化转变温度附近具有这样的行为，在这个温度附近，通用临界指数0.59 a 具有类似的行为，但相关长度是指数而不是。

非晶体材料的热容在接近玻璃相变温度时具有这样的行为，其中通用临界指数α= 0.59。类似的行为适用于相关长度，但使用指数需要改为ν而不是α。