Phase transition. Phase transformations

We have considered transitions from liquid and gaseous state into 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 latent heat the corresponding transition (heat of fusion, heat of vaporization, 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 The first kind is characterized by an abrupt, i.e., occurring in a very narrow temperature range, change in the properties of substances. 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. relative position 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 crystal structure, but at which the state also changes simultaneously in 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 the electrical resistance. 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. Fluctuations play the main role in phase transformations physical quantities. We have already met with them when discussing the question of the cause brownian motion 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 second-order phase transition 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 everything more of people begins 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 - 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.

The transition of matter from one state to another is a very common occurrence in nature. Boiling water in a kettle, freezing of rivers in winter, melting of metal, liquefaction of gases, demagnetization of ferrites when heated, etc. relate precisely to such phenomena, called phase transitions. Phase transitions are detected by a sharp change in the properties and features (anomalies) of the characteristics of a substance at the time of the phase transition: by the release or absorption of latent heat; jump in volume or jump in heat capacity and coefficient of thermal expansion; change in electrical resistance; the appearance of magnetic, ferroelectric, piezomagnetic properties, changes in the X-ray diffraction pattern, etc. Which of the phases of a substance is stable under certain conditions is determined by one of the thermodynamic potentials. At a given temperature and volume in a thermostat, this is the Helmholtz free energy, at a given temperature and pressure, the Gibbs potential.

Let me remind you that the Helmholtz potential F (free energy) is the difference between the internal energy of a substance E and its entropy S, multiplied by absolute temperature T:

Both energy and entropy in (1) are functions external conditions(pressure p and temperature T), and the phase, which is realized under certain external conditions, has the smallest Gibbs potential of all possible phases. In terms of thermodynamics, this is a principle. When external conditions change, it may turn out that the free energy of the other phase has become smaller. The change in external conditions always occurs continuously, and therefore it can be described by some dependence of the volume of the system on temperature. Given this agreement in the values of T and V, we can say that the change in phase stability and the transition of a substance from one phase to another occur at a certain temperature along the thermodynamic path, and the values for both phases are functions of the temperature near this point. Let us consider in more detail how the change occurs sign. Close addiction for one and for another phase can be approximated by some polynomials that depend on :

The difference between the free energies of two phases takes the form

As long as the difference is small enough, we can restrict ourselves to only the first term and state that if , then phase I is stable at low temperatures, at high temperatures- phase II. At the transition point itself, the first derivative of the free energy with respect to temperature naturally undergoes a jump: at , and at . As we know, there is, in fact, the entropy of things. Consequently, during a phase transition, the entropy experiences a jump, determining the latent heat of transition , since . The described transitions are called transitions of the first kind, and they are widely known and studied at school. We all know about the latent heat of vaporization or melting. That's what it is .

Describing the transition in the framework of the above thermodynamic considerations, we did not consider only one, at first glance, unlikely possibility: it may happen that not only free energies are equal, but also their derivatives with respect to temperature, that is, . It follows from (2) that such a temperature, at least from the point of view of the equilibrium properties of the substance, should not be singled out. Indeed, at and in the first approximation with respect to we have

and, at least at this point, no phase transition should occur: the Gibbs potential, which was smaller at , will also be smaller at .

In nature, of course, not everything is so simple. Sometimes there are deep reasons for the two equalities and to hold at the same time. Moreover, phase I becomes absolutely unstable with respect to arbitrarily small fluctuations of the internal degrees of freedom at , and phase II - at . In this case, those transitions occur which, according to the well-known classification of Ehrenfest, are called transitions of the second kind. This name is due to the fact that during second-order transitions, only the second derivative of the Gibbs potential with respect to temperature jumps. As we know, the second derivative of free energy with respect to temperature determines the heat capacity of a substance

Thus, during transitions of the second kind, a jump in the heat capacity of the substance should be observed, but there should be no latent heat. Since at , phase II is absolutely unstable with respect to small fluctuations, and the same applies to phase I at , neither overheating nor overcooling should be observed during second-order transitions, that is, there is no temperature hysteresis of the phase transition point. There are other remarkable features that characterize these transitions.

What are the underlying causes of the thermodynamically necessary conditions for a second-order transition? The fact is that the same substance exists both at and at. The interactions between the elements that make it up do not change abruptly, this is the physical nature of what thermodynamic potentials for both phases cannot be completely independent. How the relationship between and , and etc. arises can be traced on simple models of phase transitions by calculating the thermodynamic potentials under different external conditions using the methods of statistical mechanics. The easiest to calculate free energy.

WIKIPEDIA

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 finer classification of states than the division into aggregate states of matter, not every phase transition is accompanied by a change state of aggregation. 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 with 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 also with a change in the concentration of components (for example, the appearance of salt crystals in a solution that has reached saturation).

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 below Dynamics of phase transitions).

The most common examples phase transitions of the first kind:

melting and crystallization

evaporation and condensation

sublimation and desublimation

At phase transition of the second kind density and internal energy do not change, so naked eye such a phase transition may not be noticeable. 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 matter 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 order parameter, equal to zero in a less ordered phase and changing from zero (at the transition point) to nonzero values in a more ordered phase.

The most common examples of second-order phase transitions are:

the passage of the system through a critical point

transition paramagnet-ferromagnet or paramagnet-antiferromagnet (order parameter - magnetization)

the 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 a 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 order.

Recently wide use received the concept of a quantum phase transition, 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.

Phase transitions

PHASE TRANSITIONS (phase transformations), transitions of a substance from one phase to another, occurring when temperature, pressure or under the influence of any other external factors (for example, magnetic or electric fields). Phase transitions, accompanied by a jump-like change in the density and entropy of matter, are called phase transitions of the 1st kind; These include evaporation melting, condensation, crystallization. In the course of such phase transitions, heat phase transitions. Phase transitions of the 2nd kind density and the entropy of matter change continuously at the transition point, the athermal capacity, compressibility, and other similar quantities experience a jump. As a rule, this changes and, accordingly, symmetry phase (for example, magnetic during phase transitions from a paramagnetic to a ferromagnetic state at the Curie point).

Phasetransitionsfirstkind phase transitions, for which the first derivatives change abruptly thermodynamic potentials on intense parameters system (temperature or pressure). Transitions of the first kind are realized both during the transition of the system from one state of aggregation to another, and within the limits of one state of aggregation (in contrast to phase transitions second kind that occur within a single state of aggregation).

Examples of first-order phase transitions

during the transition of the system from one state of aggregation to another: crystallization(liquid phase transition to solid), melting(transition of the solid phase into the liquid), condensation(transition of the gaseous phase into a solid or liquid), sublimation(transition of a solid phase into a gaseous one), eutectic, peritectic imonotectic transformations.

within one state of aggregation: eutectic, peritectic and polymorphic transformations, decomposition of supersaturated solid solutions, decomposition (stratification) of liquid solutions, ordering of solid solutions.

Sometimes, first-order phase transitions are also referred to as martensitic transformations(conditionally, since at the entrance of the martensitic transformation, a transition to a stable, but non-equilibrium state is realized - metastable state).

Phasetransitionssecondkind-phase transitions, for which the first derivatives thermodynamic potentials in pressure and temperature change continuously, while their second derivatives experience a jump. It follows, in particular, that energy and the volume of a substance do not change during a second-order phase transition, but its heat capacity, compressibility, various susceptibilities, etc.

FP (Wiki)

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 also with a change in the concentration of components (for example, the appearance of 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 below Dynamics of phase transitions).

The most common examples phase transitions of the first kind:

melting and crystallization

evaporation 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.

The most common examples of second-order phase transitions are:

passage of the 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

The existence of phase transitions of more than the second order has not yet been experimentally confirmed.

Recently, the concept of a quantum phase transition has become widespread, that is, 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, when 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 heat of 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" (that is, the pressure and temperature remain constant) until the process is completed.

Many substances at low pressures crystallize into loosely packed structures. For example, crystalline hydrogen consists of molecules located at relatively large distances from each other; The structure of graphite is a series of far-spaced layers of carbon atoms. At sufficiently high pressures, such loose structures correspond to large values of the Gibbs energy. Lower values of Ф under these conditions correspond to equilibrium close-packed phases. Therefore, when high pressures graphite goes into diamond, and molecular crystalline hydrogen must go into atomic (metal). Quantum liquids 3He and 4He remain liquid at normal pressure down to the lowest temperatures reached ( T~ 0.001 K). The reason for this is the weak interaction of particles and the large amplitude of their oscillations at temperatures close to absolute zero (the so-called zero oscillations, see Uncertainty relation) . However, an increase in pressure (up to 20 atm at T "0 K) leads to solidification of liquid helium. At temperatures other than zero and given pressure and temperature, the equilibrium phase is still the phase with the minimum Gibbs energy (the minimum energy from which the work of pressure forces and the amount of heat imparted to the system are subtracted).

The existence of a region of metastable equilibrium near the curve of the first kind F. p. is characteristic of a first-class F. P. (for example, a liquid can be heated to a temperature above the boiling point or supercooled below the freezing point). Metastable states exist for quite a long time because the formation of a new phase with a lower value of Ф (thermodynamically more favorable) begins with the appearance of nuclei of this phase. The gain in the value of Ф during the formation of the nucleus is proportional to its volume, and the loss is proportional to the surface area (the value of the surface energy) . The small nuclei that have arisen increase F, and therefore they will decrease and disappear with overwhelming probability. However, nuclei that have reached a certain critical size grow, and the entire substance passes into a new phase. The formation of a nucleus of a critical size is a very improbable process and occurs quite rarely. The probability of the formation of nuclei of a critical size increases if the substance contains foreign macroscopic inclusions (for example, dust particles in a liquid). Near the critical point, the difference between the equilibrium phases and the surface energy decrease, nuclei are easily formed large sizes and bizarre shape, which affects the properties of matter (see Critical Phenomena) .

Examples of phase II phenomena are the appearance (below a certain temperature in each case) of a magnetic moment in a magnet during the transition paramagnet - ferromagnet, antiferromagnetic ordering during the transition paramagnet - antiferromagnet, the occurrence of superconductivity in metals and alloys, the occurrence of superfluidity in 3He and 4He, ordering alloys, the appearance of spontaneous (spontaneous) polarization of a substance during the paraelectric-ferroelectric transition, etc.

Great progress has been made in the theoretical calculation of critical dimensions and equations of state in good agreement with experimental data. Approximate values of critical dimensions are given in the table.

Table of critical dimensions of thermodynamic and kinetic quantities

Value

T - Tk

Heat capacity

Susceptibility*

A magnetic field

Magnetic moment

Rayleigh line width

Dimension

* Change in density with pressure, magnetization with tension magnetic field and etc. Tk- critical temperature.

The further development of the theory of FPs of the second kind is connected with the application of the methods of quantum field theory, in particular the method of the renormalization group. This method allows, in principle, to find critical indices with any required accuracy.

The division of F. p. into two kinds is somewhat arbitrary, since There are phase transitions of the first kind with small jumps in heat capacity and other quantities and small heats of transition with highly developed fluctuations. Php is a collective phenomenon that occurs at strictly defined values of temperature and other quantities only in a system that has, in the limit, an arbitrarily large number of particles.

Lit.: Landau L. D., Lifshits E. M., statistical physics, 2nd ed., M., 1964 (Theoretical Physics, vol. 5); Landau L. D., Akhiezer A. I., Lifshits E. M., Course of general physics. Mechanics and Molecular physics, 2nd ed., M., 1969; Braut R., Phase transitions, trans. from English, M., 1967; Fisher M., The nature of the critical state, trans. from English, M., 1968; Stanley G., Phase transitions and critical phenomena, trans. from English, M., 1973; Anisimov M. A., Studies of critical phenomena in liquids, "Advances in physical sciences", 1974, v. 114, c. 2; Patashinsky A. Z., Pokrovsky V. L., Fluctuation theory of phase transitions, M., 1975; Quantum theory fields and physics of phase transitions, transl. from English, M., 1975 (News of fundamental physics, issue 6); Wilson K., Kogut J., Renormalization group and e-expansion, transl., from English, M., 1975 (News of fundamental physics, v. 5).

V. L. Pokrovsky.

phase is a set of parts of the system that are identical in all physical, chemical properties and structural composition. For example, there are solid, liquid, and gaseous phases (called states of aggregation).

Phase transition (phase transformation), in a broad sense - the transition of a substance from one phase to another with a change in external conditions ( T, R, magnetic and electric fields, etc.); in a narrow sense - a stepwise change physical properties with a continuous change in external parameters. We will further consider phase transitions in the narrow sense.

There are phase transitions of the first kind and second kind. Phase transition of the first kind is a widespread phenomenon in nature. These include: evaporation and condensation, melting and solidification, sublimation or sublimation (the transition of a substance from a crystalline state directly, without melting, into a gaseous state, for example, dry ice) and condensation into a solid phase, etc. Phase transitions of the first kind are accompanied by evolution or absorption heat (heat of phase transition q), while the density, concentration of components, molar volume, etc. change abruptly.

A second-order phase transition is not accompanied by the release or absorption of heat, the density changes continuously, but abruptly changes, for example, molar heat capacity, electrical conductivity, viscosity, etc. Examples of second-order phase transitions can be the transition of a magnetic substance from a ferromagnetic state ( m>> 1) to paramagnetic ( m" 1) when heated to a certain temperature, called the Curie point; the transition of some metals and alloys at low temperatures from the normal state to the superconducting state, etc.

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