In Physical, a transition from phase is a transformation of the studied system caused by the variation of a particular external parameter (Température, Magnetic field…).

This transition takes place when the parameter reached a value threshold (floor or ceiling according to the direction of variation). The transformation is a change of the properties of the system; that can be:

• the transformation of a Thermodynamic system of a phase to another: fusion, boiling, sublimation…

• magnetic behavioral change of a metal or ceramic part:
• a ferromagnetic metal passes from a paramagnetic behavior to diamagnetic to the Point of Curie;
• certain ceramics becomes superconductive in lower part of a critical temperature,
• the quantum condensation of fluids bosonic in Condensat of Bump-Einstein;
• the disappearance of symmetry in the laws of the physique at the beginning of the History of the universe when its temperature cools.

The transitions from phases take place when the free energy of a system is not a analytical Fonction (for example not continues or not derivable) for certain thermodynamic variables. This not-analyticity comes owing to the fact that an extremely large number of particles interact; this does not appear when the systems are too small.

Types of transition from phase currents

Here the name of the transitions from the most current phases which utilize the following states of the matter: solid, liquid, gas:

• of solid with liquid: fusion
• of solid to gas: sublimation
• of liquid with solid: Solidification
• of liquid to gas: evaporation or boiling or Vaporization
• the gas one with solid: Deposition or Condensation
• the gas one with liquid: Condensation or Liquefaction.

Classification of the transitions from phase

Classification of Ehrenfest

Paul Ehrenfest tried the first to classify the transitions from phase, while being based on the degree of not-analyticity. Although useful, this classification is only empirical and does not represent the reality of the mechanisms of transition.

This classification is based on the study of the continuity of derived from the free energy:

The first order transitions are those for which the derivative first according to one of the thermodynamic variables of the free energy is discontinuous (presence of a " saut" in this derivative). For example, the transitions solid/liquid/gases are of first order: the derivative of the free energy according to volume gives the pressure, and this one changes in a discontinuous way at the time of the transitions.

The second-order transitions are those for which the derivative second according to one of the thermodynamic variables of the free energy is not continuous. They include/understand the ferromagnetic transition in matters like the Fer: the derivative first of the free energy according to the magnetic field applied is magnetization, the derivative second is the magnetic Susceptibilité and this one changes in a discontinuous way at the temperature known as “of Curie” (or Point of Curie).

Current classification of the transitions from phase

The classification of Ehrenfest was abandoned because it did not envisage the possibility of divergence - and not only of discontinuity - of a derivative of the free energy. However, of many models, within the thermodynamic limit, envisage such a divergence. Thus, for example, the ferromagnetic transition is characterized by a divergence from the heat-storage capacity (derivative second of the free energy).

Classification used currently also distinguishes from the transitions from first and second order, but the definition is different.

The transitions from first order are those which imply a Latent heat. During these transitions, the system absorbs or emits a fixed quantity of energy (and in general large). As energy cannot be transferred instantaneously between the system and its environment, the transitions from first order take place in extended phases in which all the parts do not undergo the transition to the same moment; these systems are heterogeneous. It is what one notes at the time of the boiling of a pan of Eau: water is not transformed instantaneously into gas but form a turbulent mixture water and bubbles of Steam. The heterogeneous wide systems are difficult to study because their dynamic is violent and not very controllable. It is the case of many systems, and in particular of the transitions solid/liquid/gases.

The transitions from second order are transitions known as “from phase continuous”; there is no associated latent heat. It is the case for example of the ferromagnetic transition, the superfluid transition and the condensation of Bump-Einstein.

There also exists of the transitions from phase of an infinite nature. They are continuous but do not break any symmetry (see below). The most famous example is the Transition Berezinsky-Kosterlitz-Thouless in the Modèle XY to two dimensions. This model makes it possible to describe many quantum transitions from phase in a gas of electrons two dimensions.

Properties of the transitions from phase

Critical points

In the case of the transition between the phases liquid and gas, there exist conditions of pressure and temperature for which the transition between the liquid and gas becomes of the second order. Close to this critical point, the fluid is sufficiently hot and compressed so that one cannot distinguish the liquid and gas phases.

The system has a milky appearance because of the fluctuations of the density of the medium, which disturbs the light on all the visible spectrum. This phenomenon is called Opalescence criticizes.

One also finds this type of transition in the magnetic systems.

Symmetry

The phases before and after transition have often, but not systematically, of different symmetries.

Let us consider for example the transition between a fluid (liquid or gas) and a solid Cristal flax. The fluid is composed of arranged molecules in a disordered way but homogeneous, it has a continuous translationnelle symmetry: each point in the fluid has same the properties as any other point. The crystalline solid on the other hand is made atoms arranged according to a network. This network is heterogeneous and anisotropic: the properties largely vary point with another, and according to the directions considered, but are periodic.

The ferromagnetic transition is another example of a transition breaking symmetry; it acts in this case of symmetry of the electric currents and the lines of magnetic field. This symmetry is broken by the formation of magnetic fields containing of the aligned magnetic moments. Each field has a magnetic field pointing in a spontaneously selected direction fixed during the transition from phase. One speaks about “symmetry top and low”, or of “symmetry of inversion of time” because the electric currents reverse their direction when the direction of time is reversed.

The presence or the absence of a rupture of symmetry is important for the behavior of the transitions from phase. This was noted by Landau: it is not possible to find a function continuous and derivable between phases having a different symmetry. This explains why it is not possible to have a critical point for a solid transition crystalline lens-fluid. The transitions breaking a symmetry are necessarily of the first or the second order.

In general, the most symmetrical phase is the stable phase at high temperature; it is for example the case of the solid-liquid and ferromagnetic transitions. Indeed, the Hamiltonien of a system has usually all possible symmetries of the system, and some of these symmetries are absent in the basic states energy; one calls this the spontaneous Rupture of symmetry.

The rupture of symmetry requires the introduction of additional variables to describe the state of the system. For example in the ferromagnetic phase, it is necessary to describe the system to indicate the “clear magnetization” of the fields which takes place at the time of the passage under the point of Curie. These variables are of the parameters of order. Note however that the parameters of order can also be defined for transitions which do not break symmetry.

The transitions from phase which break symmetry play a big role in Cosmologie. In the theory of the Big bang, the vacuum (theory of the quantum field) initial has a great number of symmetries. During the expansion of the universe, the vacuum cools what involves a series of transitions breaking from symmetries. For example, the electro-weak transition breaks symmetry KNOWN (2) × U (1) of the électrofaible field, the electromagnetic Champ current having a symmetry U (1). This transition is important to include/understand asymmetry between the quantity of matter and Antimatière in the universe present (see électrofaible Baryogénèse).

Critical exhibitors and classes of universality

The continuous transitions from phase are easier to study than those of first order because of the absence of latent heat, and they have many interesting properties. The phenomenon associated with the transition from continuous phase is called phenomenon criticizes , because of its association with the critical points.

The continuous transitions from phase can be characterized by parameters called critical exhibitors . Although the transition is continuous (and thus is not done at constant temperature), one can define a temperature all the same criticizes T_c .

When T is close T_c , the Heat-storage capacity C follows typically one of law of power:

$C\; \backslash sim\; |T\_c\; -\; T|^\; \{-\; \backslash \; alpha\}$

The constant α is the critical exhibitor associated with the heat-storage capacity. Since the transition does not have latent heat, it is necessary necessarily that α is strictly lower than 1 (if not, the law C ( T ) is not continuous any more). The value of α depends on the type of transition from phase considered:

• for -1 < α < 0, the heat-storage capacity has a “anomaly” at the temperature of transition. It is the behavior of liquid helium to the “transition lambda” from a “normal” state towards the state Superfluide; in experiments, one finds α = -0,013±0,003 in this case.
• For 0 < α < 1, the heat-storage capacity diverges at the temperature from transition, however, the divergence is not enough important to produce a latent heat. The third dimension of the transition from the ferromagnetic phase follows such a behavior. In three-dimensional the Ising model for the uniaxial magnets, of the detailed theoretical studies determined a value of the exhibitor α ∼ 0,110.

Some systems do not follow this law of power. For example, the theory of average field predicts a discontinuity finished of the heat-storage capacity at the temperature of transition, and two-dimensional the Ising model has a divergence logarithmic curve. However, these systems are ideal models; the transitions from phase observed up to now follow a whole a law of power.

One can define several critical exhibitors - noted β, γ, δ, ν, and η - corresponding to the variations of several physical parameters around the critical point.

Remarkable fact, of the different systems often have the same whole of critical exhibitors. This phenomenon is called universality. For example, in the case of the point criticizes liquid-gas, the critical exhibitors are largely independent of the chemical composition of the fluid. More surprising, the critical exhibitors of the transition from phase ferromagnetic are exactly the same ones for all the uniaxial magnets. Such systems are known as being in same the class of universality.

The universality is a prediction of the theory of the transition from phase of the Groupe of renormalization, which indicates that the thermodynamic properties of a system close to the transition depends only on one small number of elements, like the dimensionality and symmetry, and is insensitive with the microscopic subjacent properties of the system.

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