The transitions of a substance from one phase to another when the state of the system changes are called phase transformations. Phase - a set of bodily objects that have a certain chemical composition and thermodynamic properties, separated from other phases by the interface. Or in other words: a phase is a homogeneous part of an inhomogeneous system, which can be separated from the system in any mechanical way. There is, as a rule, one gas phase (with the exception of rare cases of stratification of gas mixtures at very high pressures). The number of liquid and especially solid phases can be quite large.

The main characteristic of phase transformations is the temperature at which the phases are in a state of thermodynamic equilibrium, the phase transition point. In 1933, P. Ehrenfest, a professor at the University of Leiden in the Netherlands, proposed a classification of phase transitions. According to this classification, for phase transitions of the first kind, it is characteristic that at the point of the phase transition, heat is released or absorbed ($q$) and the volume changes ($Δv$). Phase transitions of the first kind include, for example, the transformation of a solid into a liquid (melting) and the reverse process (crystallization), a liquid into vapor (evaporation, boiling), one crystalline modification into another (polymorphic transformations), etc. During phase transitions There are no thermal and volumetric effects of the second kind, but at the transition point, a change in the heat capacity, volumetric coefficient of thermal expansion, and compressibility is observed. Phase transitions of the second kind include, for example, the transition of a normal conductor to a superconducting state (see Superconductivity), helium I to superfluid helium II (see Superfluidity), a ferromagnet to a paramagnet (see Magnetism), etc.

The state of phase equilibrium is characterized by a certain relationship between the phase transformation temperature and pressure. So, the melting or boiling point depends on the external pressure, and the pressure saturated steam has a definite value at a given temperature. Numerically, this dependence for phase transitions of the first kind is given by the Clausius-Clapeyron equation, according to which $Δp/ΔT=q/TΔv.$ >0$), then the melting temperature, as a rule, increases with increasing pressure. The exception is cases when the volume increases during solidification (bismuth, gallium, water, cast iron). The effect is usually small, on the order of $((10)^(−2))$ K/atm. Saturated vapor pressure always increases with temperature.

Phase equilibrium is conveniently depicted using diagrams. For the simplest one-component system consisting of one substance, such as water, such a diagram is shown in Fig. 1. Below the lines $OA$ and $OC$, i.e. at low pressures and high temperatures, there is a region corresponding to the stability of the vapor, between the lines $OB$ and $OC$ - liquid and between the lines $OA$ and $OB$ - solid ice. Inside each of these regions, two parameters can be arbitrarily and independently changed - temperature $T$ and pressure $p$, while remaining in the stability region of one of the phases.

The states of the system described by the lines $OA,$ $OB$ and $OC,$ correspond to the equilibrium between two phases, for example $OC$ - to the equilibrium between water and steam.

At the point of intersection of all three curves, the so-called triple point, three phases (ice, water, steam) are in equilibrium. At the triple point, the temperature and pressure are strictly specified (for example, $0.0078°C$ and $4.579$ mm Hg for water).

The dotted line $OE$ in fig. 1, which is a continuation of the $OC$ line, shows the dependence of the vapor pressure of supercooled water on temperature. It is obviously always higher than the vapor pressure of ice. Such a phase is unstable (metastable) in the presence of a more stable phase. The possibility of the existence of metastable phases (overheating and supercooling) is a characteristic feature of first-order phase transitions. Superheating and supercooling are associated with the need to expend energy on the formation of nuclei of a new phase (ice crystals, liquid droplets, vapor bubbles). If you have to resort to various tricks to transfer vapor and liquid to another phase (for example, vapor bubbles are easily formed on dust particles, then superheated water must be extremely pure), then for crystals the possibility of a long, stable existence in unstable phases is almost a rule. So, diamond is quite stable, which at room temperature and atmospheric pressure should be graphite. White tin should turn into gray tin powder (tin plague) at $18°C.$ However, it is known to easily withstand $20$–$30$ supercooling. And yet, in a harsh winter, the transformation of tin occurs. Ignorance of this was one of the reasons for the death of R. Scott's expedition on South Pole in 1912. The liquid fuel supplies of the expedition were in vessels sealed with tin. In severe cold, the vessels broke open, and the fuel leaked out.

At the interface separating one phase from another, the properties usually change abruptly. For example, the density of water vapor is much less than the density of water. But if the temperature is increased, they approach each other (Fig. 2) and become equal at some critical temperature. The critical temperature is the temperature at which the difference in physical properties ah between liquid and saturated steam. The corresponding pressure is called the critical pressure. At temperatures below the critical, there are two easily distinguishable states of water - a vapor liquid. At temperatures above critical, the substance is in a homogeneous vapor state. If the volume occupied by this vapor decreases, then the pressure increases, but the vapor does not turn into a liquid. Two states with a sharp boundary cannot be obtained at any pressure (as happens below the critical temperature due to vapor condensation). Therefore, for so long M. Faraday failed to condense oxygen and hydrogen by increasing the pressure; they had to be cooled below a critical temperature.

Each substance has its own critical temperature and pressure. For example, for mercury it is $1730°C$ and about $1640$ atm, for water - $374°C$ and $218.4$ atm, for carbon dioxide - $31°C$ and $73$ atm, for oxygen - $−118°C$ and $50$ atm, hydrogen - $−240°C$ and $12.8$ atm, helium - $268°C$ and $2.26$ atm. Specific heat vaporization decreases with increasing temperature and is equal to zero at the critical temperature.

The second-order phase transition temperature also depends on pressure. But, as already mentioned, the thermal and volume effects are equal to zero, and this dependence is determined by the change in the heat capacity, expansion coefficient and compressibility at the phase transition point.

Phase transitions of the second kind are associated with a change in order. This can be understood by the example of a phase transition in beta brass, an alloy of copper and zinc. The copper atoms depicted in fig. 3 light circles are located at the vertices of the cube, zinc atoms (dark circles) are in the center (or vice versa). In perfect order, each copper atom has only zinc atoms as nearest neighbors. But as the temperature rises, the probability for an atom to occupy a "foreign" site increases. As long as these probabilities ($((w)_(1))$ - the probability of occupying "own" site and $((w)_(2))$ - "alien") are different (the atoms are more "sit" in “their” “knots”), the nodes are non-equivalent, and the symmetry (two cubic lattices inserted one into the other, shifted by half the volume diagonal) does not change. This is a low-temperature ordered phase. However, at some temperature, greater than or equal to the temperature phase transition ($((T)_(c))$ - the Curie point, named after the French physicist P. Curie, who discovered, in particular, in 1895 the existence of the temperature $((T)_(c))=770 °C$, above which the ferromagnetic properties of iron disappear), becomes $((w)_(1))=((w)_(2))$. Now all nodes are equivalent, and the symmetry is increased: beta brass has a body-centered cube lattice. A high-temperature disordered phase emerged with a new, higher symmetry (Fig. 4).

You can enter the degree of order $\eta =(((w)_(1))-((w)_(2))):(((w)_(1))+((w)_(2)) ).$ In a completely ordered state, at absolute zero temperature, $((w)_(1))=1,$ $((w)_(1))=0$ (all atoms "sit" in "their" nodes) and η = 1, while in the completely disordered ($T≥((T)_(c))$)$\quad((w)_(1))=((w)_(2))=1 /2$ (all nodes are the same) and $η=0.$ For any arbitrarily small $η>0$, the symmetry is the same as that of a completely ordered phase. Others are explained in the same way. phase transitions second kind. So, iron below $((T)_(c))$ has ferromagnetic properties, and above - paramagnetic (see Magnetism). The disappearance of ferromagnetism upon heating is associated with a change in the order in the arrangement of magnetic moments - spins.

Near $((T)_(c))$, the degree of order is arbitrarily close to zero. Therefore, a second-order phase transition does not require energy expenditure: the thermal and volume effects are zero. This also explains why a disordered alloy cannot be supercooled to an ordered state.

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. Detect phase transitions by a sharp change in the properties and features (anomalies) of the characteristics of a substance at the time of the phase transition: by release or absorption 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. Considering 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, and phase II is stable at high temperatures. 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 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” (rather than 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: specific volume, amount of stored internal energy, concentration of components, etc. Let us emphasize that we mean an abrupt change in these quantities with a change 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.

©2015-2017 site
All rights belong to their authors. This site does not claim authorship, but provides free use.

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 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. 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 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 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.

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 kind 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 inclusions of macroscopic dimensions (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., Nature critical condition, per. 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 the narrow sense - a jump-like change in 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, the 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.

End of work -

This topic belongs to:

Instrumentation and informatics

Ministry of Education of the Russian Federation ... Moscow state academy... Instrumentation and informatics...

If you need additional material on this topic, or you did not find what you were looking for, we recommend using the search in our database of works:

What will we do with the received material:

If this material turned out to be useful for you, you can save it to your page on social networks:

All topics in this section:

Heat capacity
Specific heat substances - a value equal to the amount of heat required to heat 1 kg of a substance by 1 K:

Isochoric process
For him V=const. Diagram of this process (isochore)

isobaric process
For him P=const. Diagram of this process (isobar)

Isothermal process
For him T-const. For example, the processes of boiling, condensation, melting and crystallization of chemically pure substances occur when constant temperature if the external pressure is constant.

adiabatic process
This is a process in which there is no heat exchange () between the system and environment. K adiabatic

Circular processes (cycles)
The process by which the system, after going through a series of states, returns to its original state is called circular process or cycle. On the process diagram, the cycle is depicted as a closed curve

Carnot cycle
In 1824, the French physicist and engineer N. Carnot (1796-1832) published the only work in which he theoretically analyzed the reversible most economical cycle, consisting of two isotherms and d

Entropy
4.10.1. Entropy in thermodynamics

The second law of thermodynamics (BNT)
Expressing the universal law of conservation and transformation of energy, the first law of thermodynamics (PNT) does not allow determining the direction of the processes. Indeed, the process of spontaneous transmission

Forces and potential energy of intermolecular interactions
In lectures 1-2, ideal gases were studied, the molecules of which have a negligibly small intrinsic volume and do not interact with each other at a distance. Properties of real gases at high pressures and

Van der Waals equation (VdW)
AT scientific literature there are more than 150 equations of state of a real gas that differ from each other. None of them is really true and universal. Let's stop at the equation

Van der Waals isotherms
For fixed values ​​of P and T, equation (2) is an equation of the third degree with respect to the gas volume V and, therefore, it can have either three real roots (V

Phase diagrams. triple point
Different phases of the same substance can be in equilibrium, in contact with each other. Such an equilibrium is observed only in a limited temperature range, and each temperature value

Crystal cell. Types of bonds between lattice particles
The main feature of crystals that distinguish them from liquids and amorphous solids, is the periodicity of the spatial arrangement of the particles (atoms, molecules, or ions) that make up the cry

Elements of quantum statistics
Dualism (duality) of waves and particles is one of the fundamental concepts of modern physics. There are many fields in crystals that exhibit both of these aspects - both wave and corpuscle.

Fermions and bosons. Fermi-Dirac and Bose-Einstein distribution
According to modern quantum theory, all elementary and complex particles, as well as quasiparticles, are divided into two classes - fermions and bosons. Fermions include electrons, proto

The concept of degeneration of a system of particles
A system of particles is called degenerate if its properties differ from the properties of classical systems due to quantum effects. Let us find the degeneracy criteria for particles. Fermi-Dirac and Bose-Hey distributions

The concept of the quantum theory of electrical conductivity of metals
According to quantum theory, an electron in a metal does not have an exact trajectory; it can be represented as a wave packet with a group velocity equal to the electron velocity. Quantum theory takes into account movement

Elements of the band theory of crystals
Reviewed last semester energy levels electron in a hydrogen atom [see. lecture notes, part III, formula (11. 14)]. It was shown there that the energy values ​​that can and

The division of crystals into dielectrics, metals and semiconductors
All crystals are divided into dielectrics, metals and semiconductors. Consideration

Intrinsic conductivity of semiconductors
The electrical conductivity of a chemically pure semiconductor (for example, pure Ge or pure Si

Impurity semiconductors
9.6.1. Donor impurity, n-type semiconductors The introduction of impurities into a semiconductor greatly affects its electrical properties. Let us consider, for example, what happens if in the lattice

P-n junction
In many areas modern electronics an important role is played by the contact of two semiconductors with n- and p-types

The structure of atomic nuclei
The nucleus is the central part of the atom, in which almost all the mass of the atom and its positive charge. The size of an atom is units of angstroms (1А=10-10m), and the nucleus is ~ 10

Mass defect and nuclear binding energy
When a nucleus is formed, its mass decreases: the mass of the nucleus Mn is less than the sum of the masses of its constituent nucleons by Dm - the nuclear mass defect: Dm=Zmp

Nuclear forces and their properties
The composition of the nucleus, in addition to neutrons, includes positively charged protons and they should repel each other, i.e. the nucleus of an atom should be destroyed, but it does not happen. It turns out that on small

Radioactivity
Radioactivity is a spontaneous change in the composition of the nucleus, which occurs over a time much longer than the characteristic nuclear time (10-22 s). We agreed to consider that

Law of radioactive decay
Radioactive decay is a statistical phenomenon, so all predictions are probabilistic. Spontaneous decay a large number atomic nuclei obey the law of radioactive decay

Nuclear reactions
Nuclear reactions are called transformation processes atomic nuclei caused by their interaction with each other or with elementary particles. As a rule, in nuclear reactions two cores involved

Lecture 12. Elementary particles and the modern physical picture of the world
When introducing the concept elementary particles it was originally assumed that there are primary, then indivisible particles that make up all matter. Until the beginning of the 20th century, with

Interconvertibility of particles
characteristic feature elementary particles is their ability to mutual transformations. In total, together with antiparticles, more than 350 elementary particles have been discovered, and their number continues to grow. Big

antiparticles
In the microcosm, each particle corresponds to an antiparticle. For example, the first antiparticle - the positron (antielectron) was discovered in 1935, its charge is + e. In a vacuum, the positron is just as