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In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point.
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:
For a single component, the most stable phase at different temperatures and pressures can be shown on a phase diagram. Such a diagram usually depicts states in equilibrium. A phase transition usually occurs when the pressure or temperature changes and the system crosses from one region to another, like water turning from liquid to solid as soon as the temperature drops below the freezing point. In exception to the usual case, it is sometimes possible to change the state of a system Adiabatic (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 and supercooling, for example. Metastable states do not appear on usual phase diagrams.
The martensitic transformation occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Order-disorder transitions such as in alpha-titanium aluminides. As with states of matter, there is also a metastable to equilibrium phase transformation for structural phase transitions. 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.
There are also a number of phase transitions involving three phases: 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 peritectic transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase. A peritectoid reaction is a peritectoid reaction, except involving only solid phases. A monotectic reaction consists of change from a liquid and to a combination of a solid and a second liquid, where the two liquids display a miscibility gap. (1996). 9780412539107, Chapman & Hall. ISBN 9780412539107
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.
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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.
In practice, only the first- and second-order phase transitions are typically observed. The second-order phase transition was for a while controversial, as it seems to require two sheets of the Gibbs free energy to osculate exactly, which is so unlikely as to never occur in practice. Cornelis Gorter replied the criticism by pointing out that the Gibbs free energy surface might have two sheets on one side, but only one sheet on the other side, creating a forked appearance. ( pp. 146--150)
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. In the following decades, the Ehrenfest classification was replaced by a simplified classification scheme that is able to incorporate such transitions.
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.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
Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into water vapor, but forms a turbulence mixture of liquid water and vapor bubbles). Yoseph Imry and Michael 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.
s 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 Ferromagnetism 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 Landau 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.
Several transitions are known as 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. Many quantum phase transitions, e.g., in two-dimensional electron gases, belong to this class.
The glass transition is observed in many polymers and other liquids that can be supercooling 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.Gotze, Wolfgang. "Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory." No direct experimental evidence supports the existence of these transitions.
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.
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.
There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as Quantum vortex- or defect lines.
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.David Layzer, Cosmogenesis, The Development of Order in the Universe, Oxford Univ. Press, 1991
See also relational order theories and order and disorder.
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 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 behavior:
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 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.
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 = −0.013 ± 0.003. At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample. This experimental value of α agrees with theoretical predictions based on variational perturbation theory.
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 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 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.
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. Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence, spin label electron paramagnetic resonance and NMR by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.
It has been proposed that some biological systems might lie near critical points. Examples include neural networks in the salamander retina, bird flocks gene expression networks in Drosophila, and protein folding. However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality. 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. Phase transitions are prominent feature of motor behavior in biological systems. Spontaneous gait transitions, as well as fatigue-induced motor task disengagements, 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 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. 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.
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