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This diagram shows the nomenclature for the different phase transitions.
This diagram shows the nomenclature for the different phase transitions.

In thermodynamics, phase transition or phase change is the transformation of a thermodynamic system from one phase to another. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " 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 The distinguishing characteristic of a phase transition is an abrupt change in one or more physical properties, in particular the heat capacity, with a small change in a thermodynamic variable such as the temperature. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity 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

In the English vernacular, the term is most commonly used to describe transitions between solid, liquid and gaseous states of matter, in rare cases including plasma. 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 state of matter (or physical state, or form of matter) has physical properties which are qualitatively different from other states of matter In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound

Contents

Types of phase transition

A typical phase diagram. The dotted line gives the anomalous behaviour of water
A typical phase diagram. The dotted line gives the anomalous behaviour of water
A small piece of rapidly melting argon ice simultaneously shows the transitions from solid to liquid to gas.
A small piece of rapidly melting argon ice simultaneously shows the transitions from solid to liquid to gas.

Examples of phase transitions include:

To
From Solid Liquid Gas Plasma
Solid Solid-Solid Transformation Melting Sublimation -
Liquid Freezing N/A Boiling/Evaporation -
Gas Deposition Condensation N/A Ionization
Plasma - - Recombination/Deionization N/A

Phase transitions happen when the free energy of a system is non-analytic for some choice of thermodynamic variables - see 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 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 This non-analyticity generally stems from the interactions of an extremely large number of particles in a system, and does not appear in systems that are too small.

It is sometimes possible to change the state of a system non-adiabatically in such a way that it can be brought past a phase transition without undergoing a phase transition. The resulting state is metastable i. Metastability is a general scientific concept which describes states of delicate equilibrium e. not theoretically stable, but quasistable. See superheating, supercooling and supersaturation. See Superheater for the device used in Steam engines In Physics, superheating (sometimes referred to as boiling retardation The term supersaturation refers to a Solution that contains more of the dissolved material than could be dissolved by the Solvent under normal circumstances

Headline text

Often also magnetic phases are used as the basis of a theory, and for introductory motivation. However, usually these are similar to the well-known liquid (\hat = ferromagnetic) or gaseous (\hat = paramagnetic) phases, as can be seen by the two equivalent interpretations, the magnetic one ("up" or "down" spins) or the lattice-gas interpretation ("occupied" or "unoccupied" sites) of a prominent binary model, the Ising model. The Ising model, named after the physicist Ernst Ising, is a mathematical model in Statistical mechanics.

Therefore we can adhere to the above table of examples.

Classification of phase transitions

Ehrenfest classification

The first attempt at classifying phase transitions was the Ehrenfest classification scheme, which grouped phase transitions based on the degree of non-analyticity involved. Paul Ehrenfest ( January 18, 1880 – September 25, 1933) was an Austrian Physicist and Mathematician, who Though useful, Ehrenfest's classification is flawed, as will be discussed in the next section.

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 a thermodynamic variable. 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 The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density (which is the first derivative of the free energy with respect to chemical potential. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical ) Second-order phase transitions have a 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 the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 Magnetization is defined as the quantity of Magnetic moment per unit volume The Curie point ( Tc) or Curie temperature, is a term in Physics and Materials science, named after Pierre Curie (1859-1906 The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. In Electromagnetism the magnetic susceptibility ( Latin: susceptibilis “receptiveness” is the degree of Magnetization of a material in response Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.

Modern classification of phase transitions

The Ehrenfest scheme is an inaccurate method of classifying phase transitions, for it does not take into account the case where a derivative of free energy diverges (which is only possible in the thermodynamic limit). In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change 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 For instance, in the ferromagnetic transition, the heat capacity diverges to infinity. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness

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

The first-order phase transitions are those that involve a latent heat. In Thermochemistry, latent heat is the amount of Energy in the form of Heat released or absorbed by a substance during a change of phase During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy. During this process, the temperature of the system will stay constant as heat is added.

Because energy cannot be instantaneously transferred between the system and its environment, first-order transitions are associated with "mixed-phase regimes" in which some parts of the system have completed the transition and others have not. This phenomenon is familiar to anyone who has boiled a pot of water: the water does not instantly turn into gas, but forms a turbulent mixture of water and water vapor bubbles. Water is a common Chemical substance that is essential for the survival of all known forms of Life. In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes General properties of water vapor Evaporation/sublimation Whenever a water molecule leaves a surface it is said to have evaporated Mixed-phase systems are difficult to study, because their dynamics are violent and hard to control. However, many important phase transitions fall in this category, including the solid/liquid/gas transitions and Bose-Einstein condensation. A Bose–Einstein condensate (BEC is a State of matter of Bosons confined in an external Potential and cooled to Temperatures very near to

The second class of phase transitions are the continuous phase transitions, also called second-order phase transitions. These have no associated latent heat. Examples of second-order phase transitions are the ferromagnetic transition and the superfluid transition. Superfluidity is a phase of matter or description of Heat capacity in which unusual effects are observed when Liquids, typically of Helium-4

Several transitions are known as the infinite-order phase transitions. They are continuous but break no symmetries. The most famous example is the Kosterlitz-Thouless transition in the two-dimensional XY model. The Kosterlitz–Thouless transition, or Berezinsky–Kosterlitz–Thouless transition, is a special transition seen in the XY model for interacting spin Like the famous Ising and Heisenberg models the XY model is one of the many highly simplified models in Statistical mechanics. Many quantum phase transitions in two-dimensional electron gases belong to this class. In Physics, a quantum phase transition ( QPT) is a Phase transition between different Quantum phases ( phases of matter at zero In Solid-state physics, the free electron model is a simple model for the behaviour of Valence electrons in a Crystal structure of a Metallic

Properties of phase transitions

Critical points

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. In Physical chemistry, Thermodynamics, Chemistry and Condensed matter physics, a critical point, also called a critical state 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). Critical opalescence is a phenomenon which arises in the region of a continuous or second-order Phase transition.

Symmetry

Phase transitions often (but not always) take place between phases with different symmetry. Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or Consider, for example, the transition between a fluid (i. e. liquid or gas) and a crystalline solid. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating A fluid, which is composed of atoms arranged in a disordered but homogeneous manner, possesses continuous translational symmetry: each point inside the fluid has the same properties as any other point. A crystalline solid, on the other hand, is made up of atoms arranged in a regular lattice. In Mineralogy and Crystallography, a crystal structure is a unique arrangement of Atoms in a Crystal. Each point in the solid is not similar to other points, unless those points are displaced by an amount equal to some lattice spacing.

Generally, we may speak of one phase in a phase transition as being more symmetrical than the other. The transition from the more symmetrical phase to the less symmetrical one is a symmetry-breaking process. In the fluid-solid transition, for example, we say that continuous translation symmetry is broken.

The ferromagnetic transition is another example of a symmetry-breaking transition, in this case the symmetry under reversal of the direction of electric currents and magnetic field lines. This symmetry is referred to as "up-down symmetry" or "time-reversal symmetry". It is broken in the ferromagnetic phase due to the formation of magnetic domains containing aligned magnetic moments. Inside each domain, there is a magnetic field pointing in a fixed direction chosen spontaneously during the phase transition. The name "time-reversal symmetry" comes from the fact that electric currents reverse direction when the time coordinate is reversed.

The presence of symmetry-breaking (or nonbreaking) is important to the behavior of phase transitions. It was pointed out by Landau that, given any state of a system, one may unequivocally say whether or not it possesses a given symmetry. Lev Davidovich Landau ( Russian language: Ле́в Дави́дович Ланда́у ( January 22, 1908 &ndash April 1, 1968 Therefore, it cannot be possible to analytically deform a state in one phase into a phase possessing a different symmetry. This means, for example, that it is impossible for the solid-liquid phase boundary to end in a critical point like the liquid-gas boundary. However, symmetry-breaking transitions can still be either first- or second-order.

Typically, the more symmetrical phase is on the high-temperature side of a phase transition, and the less symmetrical phase on the low-temperature side. This is certainly the case for the solid-fluid and ferromagnetic transitions. This happens because the Hamiltonian of a system usually exhibits all the possible symmetries of the system, whereas the low-energy states lack some of these symmetries (this phenomenon is known as spontaneous symmetry breaking). Hamiltonian mechanics is a re-formulation of Classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton. In Physics, spontaneous symmetry breaking occurs when a system that is symmetric with respect to some Symmetry group goes into a Vacuum state At low temperatures, the system tends to be confined to the low-energy states. At higher temperatures, thermal fluctuations allow the system to access states in a broader range of energy, and thus more of the symmetries of the Hamiltonian.

Order parameters

The order parameter is the quantity which is indeterminate at the critical point (the point of the phase transition). For the ferromagnetic case, it is the magnetic susceptibility. For solid/liquid or liquid/gas transitions, it is the density.

When symmetry is broken, 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. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it Magnetization is defined as the quantity of Magnetic moment per unit volume The Curie point ( Tc) or Curie temperature, is a term in Physics and Materials science, named after Pierre Curie (1859-1906 Such variables are examples of order parameters. An order parameter is a measure of the degree of order in a system; the extreme values are 0 for total disorder and 1 for complete order. [1] For example, an order parameter can indicate the degree of order in a liquid crystal. Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional Liquid, and those of a Solid However, note that order parameters can also be defined for non-symmetry-breaking transitions.

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. V erification of the O rigins of R otation in T ornadoes Ex periment or VORTEX, is a field project that seeks to understand how a

Relevance for cosmology

Symmetry-breaking phase transitions play an important role in cosmology. Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its It has been speculated that, in the hot early universe, the vacuum (i. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. e. the various quantum fields that fill space) possessed a large number of symmetries. In quantum field theory (QFT the forces between particles are mediated by other particles 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. In Particle physics, the electroweak interaction is the unified description of two of the four Fundamental interactions of nature Electromagnetism and the The electromagnetic field is a physical field produced by electrically charged objects. 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[2] and David Layzer [3]. Eric J Chaisson is an American Astrophysicist and science educator best known for his research teaching and writing on the interdisciplinary science of See also Relational order theories. A number of independent lines of research depict the universe including the social organization of living creatures which is of particular interest to humans as Systems or networks of

See also: order-disorder

Critical exponents and universality classes

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. In Quantum field theory and Statistical mechanics in the Thermodynamic limit, a system with a Global symmetry can have more than one phase 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. Critical exponents describe the behaviour of physical quantities near continuous Phase transitions. The most important one is perhaps the exponent describing the divergence of the thermal correlation length by approaching the transition. The Correlation function in Statistical mechanics is measure of the order in a system For instance, let us examine the behavior of the heat capacity near such a transition. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity We vary the temperature T of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature Tc. When T is near Tc, the heat capacity C typically has a power law behaviour:

C \propto |T_c - T|^{-\alpha}.

A similar behaviour, but with the exponent ν instead of α, applies for the correlation length. A power law is any Polynomial relationship that exhibits the property of Scale invariance.

The exponent ν is positive. This is different with α. Its actual value depends on the type of phase transition we are considering.

For -1 < α < 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the lambda transition from a normal state to the superfluid state, for which experiments have found α = -0. The λ (lambda Universality class is probably the most important group in Condensed matter physics. Superfluidity is a phase of matter or description of Heat capacity in which unusual effects are observed when Liquids, typically of Helium-4 013±0. 003. At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample (see here). This experimental value of α agrees with theoretical predictions based on variational perturbation theory (see here). In Mathematics, variational perturbation theory is a mathematical method to convert divergent Power series in a small expansion parameter say s=\sum_{n=0}^\infty

For 0 < α < 1, the heat capacity diverges at the transition temperature (though, since α < 1, the divergence is not strong enough to produce a latent heat). An example of such behavior is the 3-dimensional ferromagnetic phase transition. In the three-dimensional Ising model for uniaxial magnets, detailed theoretical studies have yielded the exponent α ∼ +0. The Ising model, named after the physicist Ernst Ising, is a mathematical model in Statistical mechanics. 110.

Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a logarithmic divergence. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior.

Several other critical exponents - β, γ, δ, ν, and η - are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations such as β = γ / (δ − 1), ν = γ / (2 − η). It can be shown that there are only two independent exponents, e. g. ν and η.

It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid-gas critical point have been found to be independent of the chemical composition of the fluid. More amazingly, but understandable from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. In Theoretical physics, renormalization group (RG refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views Again, the divergency of the correlation length is the essential point.

Critical slowing down and other phenomena

There are also other critical phenoma; e. g. , besides static functions usually there is also the critical dynamics . As a consequence, at a phase transition one may observe critical slowing down or speeding up, respectively. As a consequence, the large static universality classes of a continuous phase transition split into smaller dynamic universality classes. Furthermore, in addition to the critical exponents there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.

Phase-change data storage

Several data-storage technologies use chalcogenide glass, which can be "switched" between two states, crystalline or amorphous, with the application of heat. A chalcogenide is a chemical compound consisting of at least one Chalcogen ion and at least one more Electropositive element

Phase change and optical disc technology

Phase change technology is also used to write to optical discs, such as CD-RW or DVD-RW discs. Compact Disc ReWritable (CD-RW is a rewritable Optical disc format A DVD-RW disc is a rewritable Optical disc with equal storage capacity to a DVD-R, typically 4 This is accomplished by including both a read laser and a more powerful write laser inside the drive. The discs contain a layer of a crystalline material that, when hit by a pulse of laser light from the write laser, changes to an amorphous state, thus changing its reflectivity. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission. 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 photometry and Heat transfer, reflectivity is the fraction of incident radiation reflected by a surface A different pulse level will reverse the changes, thus erasing the recorded information. The read laser is not powerful enough to induce a phase change, but can be used by the drive to tell whether a bit is "on" or "off" based on an area of the disc's reflectivity. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication

History of phase change optical disc technology

Phase-change memory

Main article: phase-change memory

Phase-change memory (PRAM) is a kind of non-volatile computer memory. Phase-change memory (also known as PCM, PRAM, PCRAM, Ovonic Unified Memory, Chalcogenide RAM and C-RAM) is a type Phase-change memory (also known as PCM, PRAM, PCRAM, Ovonic Unified Memory, Chalcogenide RAM and C-RAM) is a type Non-volatile Random access memory ( NVRAM) is the general name used to describe any type of random access memory which does not lose its information Prototype PRAM devices have demonstrated higher density and faster write times than flash memory.

PRAM uses chalcogenide glass, the same material utilized in re-writable optical media (such as CD-RW and DVD-RW). A chalcogenide is a chemical compound consisting of at least one Chalcogen ion and at least one more Electropositive element The amorphous, high resistance state is used to represent a binary 1, and the crystalline, low resistance state represents a 0.

Samsung, Intel, and STMicroelectronics demonstrated prototype PRAM devices in 2006, and announced plans for commercial productions.

See also

References

  1. ^ in A. Differential scanning calorimetry or DSC is a thermoanalytical technique in which the difference in the amount of Heat required to increase the Temperature The λ (lambda Universality class is probably the most important group in Condensed matter physics. Superfluidity and superconductivity are of inherent interest because they are Macroscopic manifestations of quantum mechanics. Autocatalytic reactions are Chemical reactions in which at least one of the products is also a Reactant. D. McNaught and A. Wilkinson: Compendium of Chemical Terminology (commonly called The Gold Book). Compendium of Chemical Terminology (ISBN 0-86542-684-8 is a book published by IUPAC containing internationally accepted definitions for terms in Chemistry. IUPAC. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization ISBN 0-86542-684-8. Retrieved on 2007-10-23. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 4004 BC - Creation of the world begins according to the calculations of Archbishop James Ussher 42 BC -  
  2. ^ Chaisson, “Cosmic Evolution”, Harvard, 2001
  3. ^ David Layzer, Cosmogenesis, The Development of Order in the Universe", Oxford Univ. Press, 1991

General references

External links

Dictionary

phase transition

-noun

  1. (physics) The transition between thermodynamic phases of a physical system, especially one between the solid, liquid, and gaseous phases of a substance.
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