Phase transition
In
Types of phase transition
States of matter
Phase transitions commonly refer to when a substance transforms between one of the four states of matter to another. At the phase transition point for a substance, for instance the boiling point, the two phases involved - 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 boiling point the gaseous form is the more stable.
Common transitions between the solid, liquid, and gaseous phases of a single component, due to the effects of temperature and/or pressure are identified in the following table:
To From
|
Solid | Liquid | Gas | Plasma |
---|---|---|---|---|
Solid | Melting | Sublimation | ||
Liquid | Freezing | Vaporization | ||
Gas | Deposition | Condensation | Ionization | |
Plasma | Recombination |
For a single component, the most stable phase at different temperatures and pressures can be shown on a
Structural
Phase transitions can also occur when a solid changes to a different structure without changing its chemical makeup. In elements, this is known as
The
Magnetic
Phase transitions can also describe the change between different kinds of
Mixtures
Phase transitions involving solutions and mixtures are more complicated than transitions involving a single compound. While chemically pure compounds exhibit a single temperature melting point between solid and liquid phases, mixtures can either have a single melting point, known as congruent melting, or they have different liquidus and solidus temperatures resulting in a temperature span where solid and liquid coexist in equilibrium. This is often the case in solid solutions, where the two components are isostructural.
There are also a number of phase transitions involving three phases: a
Separation into multiple phases can occur via spinodal decomposition, in which a single phase is cooled and separates into two different compositions.
Non-equilibrium mixtures can occur, such as in supersaturation.
Other examples
Other phase changes include:
- Transition to a mesophase between solid and liquid, such as one of the "liquid crystal" phases.
- 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 metamaterial properties in artificial photonic media as their parameters are varied.[2][3]
- Quantum condensation of bosonic fluids (Bose–Einstein condensation). The superfluid transition in liquid helium is an example of this.
- The 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.[4]
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 small. Phase transitions can occur 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.
Condensed matter physics |
---|
Classifications
Ehrenfest classification
Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables.[5] 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.[6] 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.[6] 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. For example, the Gross–Witten–Wadia phase transition in 2-d lattice quantum chromodynamics is a third-order phase transition.[7][8] The Curie points of many ferromagnetics is also a third-order transition, as shown by their specific heat having a sudden change in slope.[9][10]
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 first example of a phase transition which did not fit into the Ehrenfest classification was the exact solution of the Ising model, discovered in 1944 by Lars Onsager. The exact specific heat differed from the earlier mean-field approximations, which had predicted that it has a simple discontinuity at critical temperature. Instead, the exact specific heat had a logarithmic divergence at the critical temperature.[11] In the following decades, the Ehrenfest classification was replaced by a simplified classification scheme that is able to incorporate such transitions.
Modern classifications
In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:[5]
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.[12][13]
Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into
Second-order phase transitions are also called "continuous phase transitions". They are characterized by a divergent susceptibility, an infinite
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. They are continuous but break no
The
Characteristic properties
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.[20] This slowing down happens below a glass-formation temperature Tg, which may depend on the applied pressure.[17][21] 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,[22] such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials,[23][24] magnetocaloric materials,[25] magnetic shape memory materials,[26] and other materials.[27] 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
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).
Symmetry
Phase transitions often involve a
Order parameters
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.[29] At the critical point, the order parameter susceptibility will usually diverge.
An example of an order parameter is the net
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
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.[citation needed]
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
Symmetry-breaking phase transitions play an important role in
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[30] and David Layzer.[31]
See also
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. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.
Continuous phase transitions can be characterized by parameters known as
The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59[32] A similar behavior, but with the exponent ν instead of α, applies for the correlation length.
The exponent ν is positive. This is different with α. Its actual value depends on the type of phase transition we are considering.
The critical exponents are not necessarily the same above and below the critical temperature. When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as , the exponent of the susceptibility) are not identical.[33]
For −1 < α < 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the
For 0 < α < 1, the heat capacity diverges at the transition temperature (though, since α < 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional Ising model for uniaxial magnets, detailed theoretical studies have yielded the exponent α ≈ +0.110.
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. 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
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 impressively, but understandably 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. Again, the divergence of the correlation length is the essential point.
Critical phenomena
There are also other critical phenomena; e.g., besides static functions there is also critical dynamics. As a consequence, at a phase transition one may observe critical slowing down or speeding up. Connected to the previous phenomenon is also the phenomenon of enhanced fluctuations before the phase transition, as a consequence of lower degree of stability of the initial phase of the system. The large static universality classes of a continuous phase transition split into smaller dynamic universality classes. 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.[citation needed]
Phase transitions in biological systems
Phase transitions play many important roles in biological systems. Examples include the
In biological membranes, gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by chloroplast thylakoid membranes which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of linolenic acid, 18-carbon chain with 3-double bonds.
It has been proposed that some biological systems might lie near critical points. Examples include neural networks in the salamander retina,[39] bird flocks[40] gene expression networks in Drosophila,[41] and protein folding.[42] However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality.[43] It has also been suggested that biological organisms share two key properties of phase transitions: the change of macroscopic behavior and the coherence of a system at a critical point.[44] Phase transitions are prominent feature of motor behavior in biological systems.[45] Spontaneous gait transitions,[46] as well as fatigue-induced motor task disengagements,[47] show typical critical behavior as an intimation of the sudden qualitative change of the previously stable motor behavioral pattern.
The characteristic feature of second order phase transitions is the appearance of fractals in some scale-free properties. It has long been known that protein globules are shaped by interactions with water. There are 20 amino acids that form side groups on protein peptide chains range from hydrophilic to hydrophobic, causing the former to lie near the globular surface, while the latter lie closer to the globular center. Twenty fractals were discovered in solvent associated surface areas of > 5000 protein segments.[48] The existence of these fractals proves that proteins function near critical points of second-order phase transitions.
In groups of organisms in stress (when approaching critical transitions), correlations tend to increase, while at the same time, fluctuations also increase. This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants.[49]
Experimental
A variety of methods are applied for studying the various effects. Selected examples are:
- Thermogravimetry(very common)
- X-ray diffraction
- Neutron diffraction
- Raman Spectroscopy
- SQUID (measurement of magnetic transitions)
- Hall effect (measurement of magnetic transitions)
- Mössbauer spectroscopy (simultaneous measurement of magnetic and non-magnetic transitions. Limited up to about 800–1000 °C)
- Perturbed angular correlation (simultaneous measurement of magnetic and non-magnetic transitions. No temperature limits. Over 2000 °C already performed, theoretical possible up to the highest crystal material, such as tantalum hafnium carbide 4215 °C.)
See also
- Allotropy
- Autocatalytic reactions and order creation
- Crystal growth
- Differential scanning calorimetry
- Diffusionless transformations
- Ehrenfest equations
- Ising Model
- Jamming (physics)
- Kelvin probe force microscope
- Landau theory of second order phase transitions
- Laser-heated pedestal growth
- List of states of matter
- Micro-pulling-down
- Percolation theory
- Superfluid film
- Superradiant phase transition
- Topological quantum field theory
References
- ISBN 978-0-412-53910-7.
- PMID 26626302.
- ^ Eds. Zhou, W., and Fan. S., Semiconductors and Semimetals. Vol 100. Photonic Crystal Metasurface Optoelectronics, Elsevier, 2019
- ^ Carol Kendall (2004). "Fundamentals of Stable Isotope Geochemistry". USGS. Retrieved 10 April 2014.
- ^ S2CID 121525126.
- ^ ISBN 978-0-19-856770-7.
- S2CID 119122520.
- ISBN 978-0-521-09101-5.
- ISSN 0019-7866.
- ^ Stanley, H. Eugene (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford: Clarendon Press.
- ^ Faghri, A., and Zhang, Y., Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA, 2006,
- ^ Faghri, A., and Zhang, Y., Fundamentals of Multiphase Heat Transfer and Flow, Springer, New York, NY, 2020
- .
- S2CID 117080049.
- S2CID 1568288.
- ^ .
- ^ Gotze, Wolfgang. "Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory."
- S2CID 46089564.
- S2CID 220105648.
- S2CID 4410586.
- S2CID 16851501.
- S2CID 98145553.
- S2CID 9036412.
- ISSN 1098-0121.
- S2CID 206037831.
- S2CID 119165221.
- ISBN 978-3-540-79357-1. Retrieved 12 October 2014.)
{{cite book}}
: CS1 maint: multiple names: authors list (link - S2CID 95616565.
- ISBN 978-0-674-00342-2.
- ^ David Layzer, Cosmogenesis, The Development of Order in the Universe, Oxford Univ. Press, 1991
- S2CID 96326822.
- S2CID 22181730.
- S2CID 55646571.
- S2CID 117436273.
- S2CID 23837885.
- PMID 3428918.
- PMID 2365951.
- ].
- PMID 24785504.
- PMID 24516161.
- S2CID 703231.
- PMID 25148352.
- S2CID 723820.
- ISBN 978-0-262-61131-2.
- PMID 7707029.
- PMID 20619908.
- PMID 17358197.
- S2CID 276956.
Further reading
- Perseus Publishing(1997).
- Faghri, A., and Zhang, Y., Fundamentals of Multiphase Heat Transfer and Flow, Springer Nature Switzerland AG, 2020.
- .
- Goldenfeld, N., Lectures on Phase Transitions and the Renormalization Group, Perseus Publishing (1992).
- Ivancevic, Vladimir G; Ivancevic, Tijana T (2008), Chaos, Phase Transitions, Topology Change and Path Integrals, Berlin: Springer, ISBN 978-3-540-79356-4, retrieved 14 March 2013
- M.R.Khoshbin-e-Khoshnazar, Ice Phase Transition as a sample of finite system phase transition, (Physics Education(India)Volume 32. No. 2, Apr - Jun 2016)[1]
- ISBN 9971-5-0210-0 (readable online physik.fu-berlin.de)
- ISBN 981-02-4659-5 (readable online here [2]).
- Kogut, J.; .
- Krieger, Martin H., Constitutions of matter : mathematically modelling the most everyday of physical phenomena, University of Chicago Press, 1996. Contains a detailed pedagogical discussion of Onsager's solution of the 2-D Ising Model.
- Lifshitz, E.M., Statistical Physics Part 1, vol. 5 of Course of Theoretical Physics, Pergamon Press, 3rd Ed. (1994).
- Mussardo G., "Statistical Field Theory. An Introduction to Exactly Solved Models of Statistical Physics", Oxford University Press, 2010.
- W. H. Freeman, 1991. Very well-written book in "semi-popular" style—not a textbook—aimed at an audience with some training in mathematics and the physical sciences. Explains what scaling in phase transitions is all about, among other things.
- H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford and New York 1971).
- Yeomans J. M., Statistical Mechanics of Phase Transitions, Oxford University Press, 1992.
External links
- Interactive Phase Transitions on lattices with Java applets
- Universality classes from Sklogwiki