What phase transitions do you know. Phase transitions

We have considered transitions from liquid and gaseous states to solid, i.e., crystallization, and reverse transitions - melting and sublimation. Earlier in ch. VII we got acquainted with the transition of liquid to vapor - evaporation and the reverse transition - condensation. With all these phase transitions (transformations), the body either releases or absorbs energy in the form of latent heat of the corresponding transition (melting heat, evaporation heat, etc.).

Phase transitions that are accompanied by a jump in energy or other quantities associated with energy, such as density, are called first-order phase transitions.

For phase transitions of the first kind, a jump-like, i.e., occurring in a very narrow temperature range, change in the properties of substances is characteristic. One can therefore speak of a definite transition temperature or transition point: boiling point, melting point and

The temperatures of phase transitions depend on an external parameter - the pressure at a given temperature, the equilibrium of the phases between which the transition occurs is established at a well-defined pressure. The phase equilibrium line is described by the Clausius-Clapeyron equation known to us:

where is the molar heat of transition, and are the molar volumes of both phases.

During phase transitions of the first order, a new phase does not appear immediately in the entire volume. First, nuclei of a new phase are formed, which then grow, spreading over the entire volume.

We met with the process of formation of nuclei when considering the process of liquid condensation. Condensation requires the existence of condensation centers (nuclei) in the form of dust grains, ions, etc. In the same way, solidification of a liquid requires crystallization centers. In the absence of such centers, the vapor or liquid may be in a supercooled state. It is possible, for example, to observe pure water for a long time at a temperature

There are, however, phase transitions in which the transformation occurs immediately in the entire volume as a result of a continuous change in the crystal lattice, i.e., the mutual arrangement of particles in the lattice. This can lead to the fact that at a certain temperature the symmetry of the lattice changes, for example, a lattice with a low symmetry goes over to a lattice with a higher symmetry. This temperature will be the point of the phase transition, which in this case is called the second order phase transition. The temperature at which a second-order phase transition occurs is called the Curie point, after Pierre Curie, who discovered the second-order phase transition in ferromagnets.

With such a continuous change of state at the transition point, there will be no equilibrium of two different phases, since the transition occurred immediately in the entire volume. Therefore, there is no jump in internal energy II at the transition point. Consequently, such a transition is not accompanied by the release or absorption of the latent heat of the transition. But since at temperatures above and below the transition point, the substance is in different crystalline modifications, they have different heat capacities. This means that at the phase transition point, the heat capacity changes abruptly, i.e., the derivative of the internal energy with respect to temperature

The coefficient of volumetric expansion also changes abruptly, although the volume itself at the transition point does not change.

Phase transitions of the second kind are known, in which a continuous change in state does not mean a change in the crystal structure, but in which the state also changes simultaneously throughout the entire volume. The best-known transitions of this type are the transition of a substance from a ferromagnetic state to a non-ferromagnetic state, which occurs at a temperature called the Curie point; the transition of some metals from the normal to the superconducting state, in which electrical resistance disappears. In both cases, no change in the structure of the crystal occurs at the transition point, but in both cases the state changes continuously and simultaneously throughout the entire volume. A transition of the second kind is also the transition of liquid helium from the state of He I to the state of He II. In all these cases, a jump in heat capacity is observed at the transition point. (In connection with this, the temperature of the second-order phase transition has a second name: it is called the -point, according to the nature of the curve of change in heat capacity at this point; this was already mentioned in § 118, in the text on liquid helium.)

Let us now analyze in a little more detail how phase transitions occur. The main role in phase transformations is played by fluctuations of physical quantities. We have already met with them when discussing the cause of the Brownian motion of solid particles suspended in a liquid (§ .7).

Fluctuations - random changes in energy, density and other quantities associated with them - always exist. But far from the phase transition point, they appear in very small volumes and immediately dissolve again. When the temperature and pressure in the substance are close to critical, then in the volume covered by the fluctuation, the appearance of a new phase becomes possible. The whole difference between phase transitions of the first and second order lies in the fact that fluctuations near the transition point develop differently.

It has already been said above that in a first-order transition, a new phase arises in the form of nuclei inside the old phase. The reason for their appearance is random fluctuations in energy and density. As the transition point is approached, fluctuations leading to a new phase occur more and more often, and although each fluctuation covers a very small volume, together they can lead to the appearance of a macroscopic nucleus of a new phase if there is a condensation center at the place of their formation.

In the case of a transition of the second kind, the situation is much more complicated. Since the new phase appears all at once in the entire volume, ordinary microscopic fluctuations by themselves cannot lead to a phase transition. Their character changes significantly. As the critical temperature is approached, the fluctuations that "prepare" the transition to a new phase cover an increasing part of the substance and, finally, at the transition point become infinite,

i.e., they occur throughout. Below the transition point, when a new phase has already been established, they begin to decay again and gradually again become short-range and short-lived.

A phase transition of the second kind is always associated with a change in the symmetry of the system; in a new phase, either an order arises that was not in the original one (for example, the magnetic moments of individual particles are ordered upon transition to a ferromagnetic state), or an already existing order changes (during transitions with a change in the crystal structure ).

This new order is also contained in fluctuations near the phase transition point.

A clear explanation of the described transition mechanism is the well-known "staring crowd effect" (Fig. 185). Let us imagine passers-by walking along the sidewalk and looking in the most random directions. This is the "normal" state of the street crowd, in which there is no orderliness. Let now one of the passers-by for no apparent reason stare into an empty window on the second floor ("random fluctuation"). Gradually, more and more people begin to look out the same window, and in the end, all eyes are directed to one point. An "orderly" phase has emerged, although there are no external forces contributing to the establishment of order - absolutely nothing happens outside the window on the second floor

Phase transitions of the second kind are a very complex and interesting phenomenon. The processes occurring in the immediate vicinity of the transition point have not yet been fully investigated, and a complete picture of the behavior of physical quantities under conditions of infinite fluctuations is still being created.

transitions in-va from one phase to another with a change in the state parameters characterizing the thermodynamic. equilibrium. The value of t-ry, pressure or k.-l. other physical quantities at which F. p. occur in a one-component system, called. transition point. With F. p. I kind of properties, expressed by the first derivatives of the Gibbs energy G with respect to pressure R, t-re T and other parameters change abruptly with a continuous change in these parameters. In this case, the transition heat is released or absorbed. In a one-component system, the transition temperature 1 related to pressure p 1 Clausius-Clapeyron equation dp 1 /dT 1 ==QIT 1 D V, where Q is the heat of transition, DV is the volume jump. The first-class phase is characterized by hysteresis phenomena (for example, overheating or supercooling of one of the phases), which are necessary for the formation of nuclei of the other phase and for the phase flow to proceed at a finite rate. In the absence of stable nuclei, the superheated (supercooled) phase is in a state of metastable equilibrium (see Fig. the birth of a new phase). The same phase can exist (albeit metastablely) on both sides of the transition point on the state diagram (however, crystalline phases cannot be overheated above the melting or sublimation temperature). At point F. p. I kind of Gibbs energy G as a function of state parameters is continuous (see Fig. in Art. state diagram), and both phases can coexist for an arbitrarily long time, i.e., there is a so-called. phase separation (for example, the coexistence of a liquid and its vapor or a solid and a melt for a given total volume of the system).

F. p. I kind - widespread phenomena in nature. These include evaporation and condensation from the gas to the liquid phase, melting and solidification, sublimation and condensation (desublimation) from the gas to the solid phase, most polymorphic transformations, some structural transitions in solids, for example, the formation of martensite in an iron-carbon alloy. . In pure superconductors, a sufficiently strong magnet. the field induces a phase transition of the first kind from the superconducting to the normal state.

Under F. p. of the second kind, the quantity G itself and the first derivatives of G with respect to T, p and other state parameters change continuously, and the second derivatives (respectively, heat capacity, compressibility coefficient and thermal expansion) with a continuous change in parameters change abruptly or are singular. Heat is neither released nor absorbed, hysteresis phenomena and metastable states are absent. To F.p. II kind, observed with a change in temperature, include, for example, transitions from a paramagnetic (disordered) state to a magnetically ordered (ferro- and ferrimagnetic in curie point, antiferromagnetic at the Neel point) with the appearance of spontaneous magnetization (respectively, in the entire lattice or in each of the magnetic sublattices); transition dielectric - ferroelectric with the appearance of spontaneous polarization; the appearance of an ordered state in solids (in ordering alloys); smectic transition. liquid crystals in the nematic phase, accompanied by an abnormal increase in heat capacity, as well as transitions between decomp. smectic phases; l-transition in 4 He, accompanied by the appearance of anomalously high thermal conductivity and superfluidity (see Fig. Helium); the transition of metals to the superconducting state in the absence of magnetic. fields.

F. p. may be associated with a change in pressure. Many substances at low pressures crystallize into loosely packed structures. For example, the structure of graphite is a series of widely spaced layers of carbon atoms. At sufficiently high pressures, large values ​​of the Gibbs energy correspond to such loose structures, and equilibrium close-packed phases correspond to smaller values. Therefore, at high pressures, graphite transforms into diamond. Quantum liquids 4 He and 3 He remain liquid at normal pressure up to the lowest temperatures reached near abs. zero. The reason for this is in the weak interaction. atoms and the large amplitude of their "zero vibrations" (high probability of quantum tunneling from one fixed position to another). However, an increase in pressure causes the liquid helium to solidify; for example, 4 He at 2.5 MPa forms hexagen, a close-packed lattice.

The general interpretation of F. p. of the second kind was proposed by L. D. Landau in 1937. Above the transition point, the system, as a rule, has a higher symmetry than below the transition point, therefore F. p. The genus is treated as a point of symmetry change. For example, in a ferromagnet above the Curie point, the direction of the spin magnets. moments of particles are distributed randomly, so the simultaneous rotation of all spins around the same axis by the same angle does not change the physical. St. in the system. Below the transition points of the back have advantages. orientation, and their joint rotation in the above sense changes the direction of the magnetic. moment of the system. In a two-component alloy, the atoms of which A and B are located at the sites of a simple cubic. crystalline lattice, disordered state is characterized by chaotic. distribution of A and B over the lattice nodes, so that the lattice shift by one period does not change the r.v. Below the transition point, the alloy atoms are ordered: ...ABAB... A shift of such a lattice by a period leads to the replacement of all atoms A by B and vice versa. T. arr., the symmetry of the lattice decreases, since the sublattices formed by atoms A and B become nonequivalent.

Symmetry appears and disappears abruptly; in this case, the violation of symmetry can be characterized by physical. value, to-paradise with F. p. II kind changes continuously and is called. order parameter. For pure liquids, such a parameter is the density, for solutions - composition, for ferro- and ferrimagnets - spontaneous magnetization, for ferroelectrics - spontaneous electric. polarization, for alloys - the proportion of ordered atoms for smectic. liquid crystals - the amplitude of the density wave, etc. In all these cases, at t-rah above the point F. p. II kind, the order parameter is zero, below this point its anomalous growth begins, leading to max. value at T = O.

The absence of heat of transition, jumps in density, and concentrations, which is characteristic of F. p. II kind, is also observed in critical. point on curves of F. p. of the first kind (see critical events). The similarity is very deep. State in-va about critical. points can also be characterized by a quantity that plays the role of an order parameter. For example, in the case of equilibrium liquid - vapor, such a parameter is the deviation of the density of the island from the critical. values: when moving along a critical isochore from the side of high tr gas is homogeneous and density deviation from critical. value is zero, and below the critical. t-ry in-in is stratified into two phases, in each of which the deviation of the density from the critical one is not equal to zero.

Since the phases differ little from each other near the point of the F. p. of the second kind, the existence of fluctuations of the order parameter is possible, in the same way as near the critical. points. Critical is associated with this. phenomena at the points of F. p. of the second kind: anomalous growth of magn. susceptibility of ferromagnets and dielectric. the susceptibility of ferroelectrics (analogous is the increase in compressibility near the critical point of the liquid-vapor transition); a sharp increase in heat capacity; anomalous scattering of light waves in the liquid - vapor system (the so-called critical opalescence), X-rays in solids, neutrons in ferromagnets. Significantly change and dynamic. processes, which is associated with a very slow resorption of the resulting fluctuations. For example, near the critical point liquid - vapor narrows the line of Rayleigh scattering of light, near the Curie and Neel points, respectively. in ferromagnets and antiferromagnets, spin diffusion slows down (the propagation of excess magnetization occurring according to the laws of diffusion). The average size of the fluctuation (correlation radius) increases as it approaches the point of the second-order phase function and becomes anomalously large at this point. This means that any part of the island at the transition point "feels" the changes that have occurred in other parts. On the contrary, far from the transition point of the second kind, fluctuations are statistically independent and random changes in the state in a given part of the system do not affect the properties of its other parts.

The division of phase transitions into two kinds is somewhat arbitrary, since there are phase transitions of the first kind with small jumps in the order parameter and low heats of transition with strongly developed fluctuations. it Naib, typical for transitions between liquid crystals. phases. Most often these are F. p. of the first kind, very close to F. p. P of the genus. Therefore, they are usually accompanied by criticism. phenomena. The nature of many F. p. in liquid crystals is determined by the interaction. several order parameters associated with dec. symmetry types. In some org. conn. so-called. return liquid crystal phases that appear upon cooling below the existence temperature of primary nematic, cholesteric. and smectic. phases.

A singular point on the phase diagram at which the line of transitions of the first kind turns into a line of transitions of the second kind, called. tricritical dot. Tricritical dots were found on the lines of F. p. in the superfluid state in p-rax 4 He - 3 He, on the lines of orientational transitions in ammonium halides, on the lines of transitions of the nematic. liquid crystal - smectic. liquid crystal and in other systems.

Lit.: Braut R., Phase transitions, trans. from English, M., 1967; Landau L.D., Lifshits E.M., Statistical physics, part 1, 3rd ed., M., 1976; Pikin S. A., Structural transformations in liquid crystals, M., 1981; Patashinsky A. 3., Pokrovsky V. L., Fluctuation theory of phase transitions, 2nd ed., M., 1982; Anisimov M. A., Critical phenomena in liquids and liquid crystals, M., 1987. M. A. Anisimov.

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From the book Slavic Karmic Numerology. Improve your destiny matrix author Maslova Natalia Nikolaevna

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Phase transition (phase transformation) in thermodynamics- the transition of a substance from one thermodynamic phase to another when external conditions change. From the point of view of the movement of a system along a phase diagram with a change in its intensive parameters (temperature, pressure, etc.), a phase transition occurs when the system crosses the line separating two phases. Since different thermodynamic phases are described by different equations of state, it is always possible to find a quantity that changes abruptly during a phase transition.

Since the division into thermodynamic phases is a smaller classification of states than the division into aggregate states of a substance, not every phase transition is accompanied by a change in the aggregate state. However, any change in the state of aggregation is a phase transition.

The most frequently considered phase transitions are those with a change in temperature, but at a constant pressure (usually equal to 1 atmosphere). That is why the terms “point” (and not line) of a phase transition, melting point, etc. are often used. Of course, a phase transition can occur both with a change in pressure and at constant temperature and pressure, but with a change in the concentration of components (for example, the appearance salt crystals in a solution that has reached saturation).

Classification of phase transitions

At first-order phase transition the most important, primary extensive parameters change abruptly: the specific volume, the amount of stored internal energy, the concentration of components, etc. We emphasize: we mean the abrupt change in these quantities with changes in temperature, pressure, etc., and not an abrupt change in time (for the latter, see the section Dynamics of phase transitions below).

The most common examples phase transitions of the first kind:

  • melting and solidification
  • boiling and condensation
  • sublimation and desublimation

At phase transition of the second kind density and internal energy do not change, so such a phase transition may not be visible to the naked eye. The jump is experienced by their derivatives with respect to temperature and pressure: heat capacity, coefficient of thermal expansion, various susceptibilities, etc.

Phase transitions of the second kind occur in those cases when the symmetry of the structure of a substance changes (symmetry can completely disappear or decrease). The description of a second-order phase transition as a consequence of a change in symmetry is given by Landau's theory. At present, it is customary to talk not about a change in symmetry, but about the appearance at the transition point of the order parameter, which is equal to zero in a less ordered phase and varies from zero (at the transition point) to nonzero values ​​in a more ordered phase.

The most common examples of second-order phase transitions: the passage of a system through a critical point

  • paramagnet-ferromagnet or paramagnet-antiferromagnet transition (order parameter - magnetization)
  • transition of metals and alloys to the state of superconductivity (the order parameter is the density of the superconducting condensate)
  • transition of liquid helium to the superfluid state (pp - density of the superfluid component)
  • transition of amorphous materials to a glassy state

Modern physics also investigates systems that have phase transitions of the third or higher kind.

Recently, the concept of a quantum phase transition has become widespread, i.e. a phase transition controlled not by classical thermal fluctuations, but by quantum ones, which exist even at absolute zero temperatures, where a classical phase transition cannot be realized due to the Nernst theorem.

Dynamics of phase transitions

As mentioned above, a jump in the properties of a substance means a jump with a change in temperature and pressure. In reality, by acting on the system, we do not change these quantities, but its volume and its total internal energy. This change always occurs at some finite rate, which means that in order to "cover" the entire gap in density or specific internal energy, we need some finite time. During this time, the phase transition does not occur immediately in the entire volume of the substance, but gradually. In this case, in the case of a first-order phase transition, a certain amount of energy is released (or taken away), which is called the heat of the phase transition. In order for the phase transition not to stop, it is necessary to continuously remove (or supply) this heat, or compensate for it by doing work on the system.

As a result, during this time, the point on the phase diagram describing the system “freezes” (i.e., pressure and temperature remain constant) until the process is completed.

Literature

  • Bazarov I.P. Thermodynamics. - M.: Higher School, 1991, 376 p.
  • Bazarov IP Delusions and errors in thermodynamics. Ed. 2nd rev. - M.: Editorial URSS, 2003. 120 p.
  • Kvasnikov IA Thermodynamics and statistical physics. V.1: Theory of equilibrium systems: Thermodynamics. - Vol.1. Ed. 2, rev. and additional - M.: URSS, 2002. 240 p.
  • Stanley. D. Phase transitions and critical phenomena. - M.: Mir, 1973.
  • Patashinsky AZ, Pokrovskiy VL Fluctuation theory of phase transitions. - M.: Nauka, 1981.
  • Gufan Yu. M. Thermodynamic theory of phase transitions. - Rostov n / a: Publishing house of the Rostov University, 1982. - 172 p.

An important branch of thermodynamics is the study of transformations between different phases of a substance, since these processes occur in practice and are of fundamental importance for predicting the behavior of a system under certain conditions. These transformations are called phase transitions, to which the article is dedicated.

The concept of a phase and a system component

Before proceeding to the consideration of phase transitions in physics, it is necessary to define the concept of the phase itself. As is known from the course of general physics, there are three states of matter: gaseous, solid and liquid. In a special section of science - in thermodynamics - the laws are formulated for the phases of matter, and not for their states of aggregation. A phase is understood as a certain volume of matter that has a homogeneous structure, is characterized by specific physical and chemical properties and is separated from the rest of the matter by boundaries, which are called interphase.

Thus, the concept of "phase" carries much more practically significant information about the properties of matter than its state of aggregation. For example, the solid state of a metal such as iron may be in the following phases: low temperature magnetic body centered cubic (BCC), low temperature nonmagnetic bcc, face centered cubic (fcc), and high temperature nonmagnetic bcc.

In addition to the concept of "phase", the laws of thermodynamics also use the term "components", which means the number of chemical elements that make up a particular system. This means that the phase can be both monocomponent (1 chemical element) and multicomponent (several chemical elements).

Gibbs' theorem and equilibrium between phases of a system

To understand phase transitions, it is necessary to know the equilibrium conditions between them. These conditions can be mathematically obtained by solving the system of Gibbs equations for each of them, assuming that the equilibrium state is reached when the total Gibbs energy of the system isolated from external influence ceases to change.

As a result of solving this system of equations, conditions are obtained for the existence of equilibrium between several phases: an isolated system will cease to evolve only when the pressures, chemical potentials of each component and temperatures in all phases are equal to each other.

Gibbs phase rule for equilibrium

A system consisting of several phases and components can be in equilibrium not only under certain conditions, for example, at a specific temperature and pressure. Some of the variables in the Gibbs theorem for equilibrium can be changed while maintaining both the number of phases and the number of components that are in this equilibrium. The number of variables that can be changed without disturbing the equilibrium in the system is called the number of freedoms of this system.

The number of freedoms l of a system consisting of f phases and k components is uniquely determined from the Gibbs phase rule. This rule is mathematically written as follows: l + f = k + 2. How to work with this rule? Very simple. For example, it is known that the system consists of f=3 equilibrium phases. What is the minimum number of components such a system can contain? You can answer the question by reasoning as follows: in the case of equilibrium, the most stringent conditions exist when it is realized only at certain indicators, that is, a change in any thermodynamic parameter will lead to imbalance. This means that the number of freedoms l=0. Substituting the known values ​​of l and f, we obtain k=1, that is, a system in which three phases are in equilibrium can consist of one component. A striking example is the triple point of water, when ice, liquid water and steam exist in equilibrium at specific temperatures and pressures.

Classification of phase transformations

If you begin to change some in a system that is in equilibrium, then you can observe how one phase will disappear, and another will appear. A simple example of this process is the melting of ice when it is heated.

Given that the Gibbs equation depends on only two variables (pressure and temperature), and a phase transition involves a change in these variables, then mathematically the transition between phases can be described by differentiating the Gibbs energy with respect to its variables. It was this approach that was used by the Austrian physicist Paul Ehrenfest in 1933, when he compiled a classification of all known thermodynamic processes that occur with a change in phase equilibrium.

It follows from the basics of thermodynamics that the first derivative of the Gibbs energy with respect to temperature is equal to the change in the entropy of the system. The derivative of the Gibbs energy with respect to pressure is equal to the change in volume. If, when the phases in the system change, the entropy or volume suffers a break, that is, they change sharply, then they speak of a first-order phase transition.

Further, the second derivatives of the Gibbs energy with respect to temperature and pressure are the heat capacity and the coefficient of volumetric expansion, respectively. If the transformation between phases is accompanied by a discontinuity in the values ​​of the indicated physical quantities, then one speaks of a second-order phase transition.

Examples of transformations between phases

There are a huge number of different transitions in nature. Within the framework of this classification, striking examples of transitions of the first kind are the processes of melting metals or the condensation of water vapor from air, when there is a volume jump in the system.

If we talk about transitions of the second kind, then striking examples are the transformation of iron from a magnetic to a paramagnetic state at a temperature of 768 ºC or the transformation of a metallic conductor into a superconducting state at temperatures close to absolute zero.

Equations that describe transitions of the first kind

In practice, it is often necessary to know how the temperature, pressure, and absorbed (released) energy change in a system when phase transformations occur in it. Two important equations are used for this purpose. They are obtained based on knowledge of the basics of thermodynamics:

  1. Clapeyron's formula, which establishes the relationship between pressure and temperature during transformations between different phases.
  2. The Clausius formula, which relates the absorbed (released) energy and the temperature of the system during the transformation.

The use of both equations is not only in obtaining quantitative dependences of physical quantities, but also in determining the sign of the slope of equilibrium curves in phase diagrams.

Equation for describing transitions of the second kind

Phase transitions of the 1st and 2nd kind are described by different equations, since the use of and Clausius for transitions of the second kind leads to mathematical uncertainty.

To describe the latter, the Ehrenfest equations are used, which establish a relationship between changes in pressure and temperature through knowledge of the change in heat capacity and the coefficient of volumetric expansion during the transformation process. The Ehrenfest equations are used to describe conductor-superconductor transitions in the absence of a magnetic field.

Importance of phase diagrams

Phase diagrams are a graphic representation of areas in which the corresponding phases exist in equilibrium. These areas are separated by equilibrium lines between the phases. P-T (pressure-temperature), T-V (temperature-volume) and P-V (pressure-volume) axes are often used.

The importance of phase diagrams lies in the fact that they allow you to predict what phase the system will be in when the external conditions change accordingly. This information is used in the heat treatment of various materials in order to obtain a structure with desired properties.