Real systems and phase transitions. Phase transitions main types of phase transitions (physical classification) Table pressure during phase transition of various substances

2. Phase transitions of the first and second kind………………………..4

3. Ideal gas………………………………………………………….7

4. Real gas………………………………………………………....8

5. Molecular - kinetic theory critical events….….9

6. Superfluidity………………………………………………………..11

7. Superconductivity………………………………………………..13

7.1 Discovery of superconductivity………………….…...13

7.2 Electron - phonon interaction……………..14

7.3 Superconductors of the first and second kind………...16

7.4 Recipe for making a superconductor…………….17

7.5 Safety precautions………………………………….18

7.6 The Meisner Effect…………………………………………………………………………20

8. Conclusion………………………….……………………….22

9. References…………………………………………….25

1. Introduction.

Phases are called homogeneous different parts of physico-chemical systems. A substance is homogeneous when all the parameters of the state of the substance are the same in all its volumes, the dimensions of which are large compared to the interatomic states. Mixtures of different gases always form one phase if they are in the same concentration throughout the volume.

The same substance, depending on external conditions, can be in one of three states of aggregation - liquid, solid or gaseous. Depending on external conditions, it can be in one phase, or in several phases at once. In the nature around us, we especially often observe phase transitions of water. For example: evaporation, condensation. There are pressure and temperature conditions under which the substance is in equilibrium in different phases. For example, when liquefying a gas in a state of phase equilibrium, the volume can be anything, and the transition temperature is related to the saturation vapor pressure. The temperatures at which transitions from one phase to another occur are called transition temperatures. They depend on pressure, although to varying degrees: the melting point is weaker, the temperature of vaporization and sublimation is stronger. At normal and constant pressure, the transition occurs at a certain temperature, and here melting, boiling and sublimation (or sublimation.) take place. Sublimation is the transition of a substance from a solid to a gaseous state, which can be observed, for example, in the shells of cometary tails. When a comet is far from the sun, almost all of its mass is concentrated in its nucleus, which measures 10-12 kilometers. The nucleus, surrounded by a small shell of gas, is the so-called head of a comet. When approaching the Sun, the nucleus and shells of the comet begin to heat up, the probability of sublimation increases, and desublimation decreases. The gases escaping from the nucleus of the comet entrain solid particles, the head of the comet increases in volume and becomes gas and dust in composition.

2. Phase transitions of the first and second kind.

Phase transitions are of several kinds. Changes in the aggregate states of a substance are called first-order phase transitions if:

1) The temperature is constant during the entire transition.

2) The volume of the system is changing.

3) The entropy of the system changes.

For such a phase transition to occur, it is necessary for a given mass of substance to sheathe a certain amount of heat corresponding to the latent heat of transformation. Indeed, when a condensed phase passes into a phase with a lower density, a certain amount of energy must be imparted in the form of heat, which will go to destroy the crystal lattice (during melting) or to remove liquid molecules from each other (during vaporization). During the transformation, latent heat will go to the transformation of cohesive forces, the intensity of thermal motion will not change, as a result, the temperature will remain constant. With such a transition, the degree of disorder, and hence the entropy, increases. If the process goes in the opposite direction, then latent heat is released. Phase transitions of the first kind include: the transformation of a solid into a liquid (melting) and the reverse process (crystallization), liquid into vapor (evaporation, boiling). One crystalline modification - to another (polymorphic transformations). Phase transitions of the second kind include: the transition of a normal conductor to a superconducting state, helium-1 to superfluid helium-2, a ferromagnet to a paramagnet. Metals such as iron, cobalt, nickel and gadolinium stand out for their ability to be highly magnetized and to maintain a state of magnetization for a long time. They are called ferromagnets. Most metals (alkali and alkaline earth metals and a significant part of transition metals) are weakly magnetized and do not retain this state outside magnetic field are paramagnetic. Phase transitions of the second, third, and so on kind are associated with the order of those derivatives of the thermodynamic potential ∂f that experience finite measurements at the transition point. Such a classification of phase transformations is associated with the work of the theoretical physicist Paul Ernest (1880 -1933). So, in the case of a second-order phase transition, the second-order derivatives experience jumps at the transition point: heat capacity at constant pressure Cp \u003d -T (∂f 2 / ∂T 2), compressibility β \u003d - (1 / V 0) (∂ 2 f / ∂p 2), coefficient thermal expansionα=(1/V 0)(∂ 2 f/∂Tp), while the first derivatives remain continuous. This means that there is no release (absorption) of heat and no change in specific volume (φ - thermodynamic potential).

The state of phase equilibrium is characterized by a certain relationship between the phase transformation temperature and pressure. Numerically, this dependence for phase transitions is given by the Clausius-Clapeyron equation: Dp/DT=q/TDV. Research at low temperatures is a very important branch of physics. The fact is that in this way it is possible to get rid of interference associated with chaotic thermal motion and study phenomena in a “pure” form. This is especially important in the study of quantum regularities. Usually, due to chaotic thermal motion, a physical quantity is averaged over a large number of its different values, and quantum jumps are “smeared out”.

Low temperatures (cryogenic temperatures), in physics and cryogenic technology, the temperature range is below 120°K (0°C=273°K); the work of Carnot (he worked on a heat engine) and Clausius laid the foundation for research on the properties of gases and vapors, or technical thermodynamics. In 1850, Clausius noticed that saturated water vapor partially condenses during expansion and becomes superheated during compression. Renu made a special contribution to the development of this scientific discipline. The intrinsic volume of gas molecules at room temperature is approximately one thousandth of the volume occupied by the gas. In addition, molecules are attracted to each other at distances greater than those from which their repulsion begins.

Equal to the specific values ​​of the entropy, taken with the opposite sign, and the volume: (4.30) If at points that satisfy the phase equilibrium: , the first derivatives of the chemical potential for different phases experience a discontinuity: , (4.31) they say that the thermodynamic system experiences a phase transition of the 1st kind. Phase transitions of the first kind are characterized by the presence of latent heat of the phase transition, ...

Against overlifts, zero and maximum protection. - provide for stopping the vessels at intermediate points of the trunk. light signaling about the operating modes of the lifting unit in the building of the lifting machine, from the operator of the loading device, from the dispatcher. Modern adjustable DC electric drives for automated lifting installations are based on DC motors ...

44.5 cm, c = 12 cm, a = 20 cm, l = 8 cm. The force action of the magnetic system was estimated by a value equal to the product of the field modulus H and its gradient. It was found that the distribution of the field modulus H of the magnetic system under consideration is characterized by a pronounced angular dependence. Therefore, the calculation of the field modulus H was carried out with a step of 1° for points located on two different arcs for all...

The system consists in obtaining its “phase portrait” (Volkenshtein, 1978). It makes it possible to reveal the stationary states of the system and the nature of its dynamics when deviating from them. The phase portrait method is used in engineering to analyze and predict the behavior of physical systems of varying complexity and in mathematical ecology to analyze population dynamics (Volkenshtein, 1978; Svirezhev...

PHASE TRANSITION, phase transformation, in a broad sense - the transition of a substance from one phases to another when external conditions change - temperature, pressure, magnetic and electric. fields, etc.; in the narrow sense - an abrupt change in physical. properties with a continuous change in external parameters. The difference between the two interpretations of the term "F. p." seen from the following example. In a narrow sense, the transition of a substance from the gas phase to the plasma one (cf. Plasma) is not a F. p., since ionization gas occurs gradually, but in a broad sense it is F. p. In this article, the term "F. p." considered in a narrow sense.

The value of temperature, pressure or k.-l. another physical The quantities at which a phase transition occurs are called the transition point.

There are F. p. of two kinds. During F. p. of the first kind, such thermodynamic conditions change abruptly. characteristics of a substance, such as density, concentration of components; in a unit of mass, a very definite amount of heat is released or absorbed, which is called. transition heat. With F. p. of the second kind of some kind of physical. a value equal to zero on one side of the transition point gradually increases (from zero) as you move away from the transition point to the other side. In this case, the density and concentrations change continuously, heat is not released or absorbed.

F. p. is a phenomenon widespread in nature. Phonic phenomena of the first kind include: evaporation and condensation, melting and solidification, sublimation and condensation into a solid phase, and certain structural transitions in solids, for example. education martensite in an iron-carbon alloy. AT antiferromagnets with one axis of magnetization of magnetic sublattices A phase transition of the first kind occurs in an external magnetic field directed along the axis. At a certain value of the field, the moments of the magnetic sublattices are rotated perpendicular to the direction of the field (sublattice "overturning" occurs). In pure superconductors, a magnetic field induces a phase transition of the first kind from the superconducting to the normal state. .

At absolute zero temperature and a fixed volume, the phase with the lowest energy value is thermodynamically equilibrium. A phase transition of the first kind in this case occurs at those values ​​of pressure and external fields at which the energies of two different phases are compared. If you fix not the volume of the body V, and the pressure R, then in a thermodynamic state. equilibrium, the minimum is the Gibbs energy F (or G), and at the transition point in phase equilibrium there are phases with the same values F .

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; structure graphite is a series of far-spaced layers of carbon atoms. At sufficiently high pressures, such loose structures correspond to big values Gibbs energy. Lower values ​​of Ф under these conditions correspond to equilibrium close-packed phases. Therefore, at high pressures, graphite transforms into diamond, and molecular crystalline. hydrogen must go into atomic (metal). quantum liquids 3 He and 4 He 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 temp-pax close to abs. zero (the so-called zero oscillations ). However, an increase in pressure (up to 20 atm at T = 0 K) leads to solidification of liquid helium. At non-zero temp-pax 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 the pressure forces and the amount of heat reported to the system are subtracted).

For F. p. I kind is characterized by the existence of a region of metastable equilibrium near the curve F. p. I kind (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, for the reason that the formation of a new phase with a lower value of F (thermodynamically more favorable) begins with the appearance of nuclei of this phase. The gain in the Φ value during the formation of a nucleus is proportional to its volume, and the loss is proportional to the surface area (to the value surface energy). The resulting small embryos increase F, and therefore, with an overwhelming probability, they will decrease and disappear. However, nuclei that have reached a certain critical size grow, and the entire substance passes into a new phase. The formation of the embryo is critical. size is a very unlikely process and occurs quite rarely. The probability of formation of nuclei is critical. size increases if the substance contains foreign macroscopic inclusions. sizes (e.g., dust particles in a liquid). close critical point the difference between the equilibrium phases and the surface energy decrease, nuclei of large sizes and bizarre shapes are easily formed, which affects the properties of the substance .

Examples of F. p. II kind - 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 appearance of superconductivity in metals and alloys, the occurrence of superfluidity in 4 He and 3 He, the ordering of alloys, the appearance of spontaneous (spontaneous) polarization of matter during the transition of paraelectric ferroelectric etc.

L. D. Landau(1937) proposed a general interpretation of all PTs of the second kind as points of change in symmetry: above the transition point, the system has a higher symmetry than below the transition point. For example, in a magnet above the transition point of the direction of elementary magnetic moments (spins) particles are randomly distributed. Therefore, the simultaneous rotation of all spins does not change the physical. system properties. Below the transition points, the backs have a preferential orientation. Their simultaneous rotation changes the direction of the magnetic moment of the system. Another example: in a two-component alloy, the atoms of which A and B located at the nodes of a simple cubic crystal lattice, the disordered state is characterized by a chaotic distribution of atoms L and B over the lattice sites, so that a shift of the lattice by one period does not change its properties. 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 or vice versa. As a result of the establishment of order in the arrangement of atoms, the symmetry of the lattice decreases.

Symmetry itself appears and disappears abruptly. However, the value characterizing the asymmetry (order parameter) can change continuously. For a phase transition of the second kind, the order parameter is equal to zero above the transition point and at the transition point itself. In a similar way behaves, for example, the magnetic moment of a ferromagnet, electric. polarization of a ferroelectric, density of the superfluid component in liquid 4 He, probability of detecting an atom BUT in the corresponding site of the crystal. two-component alloy gratings, etc.

The absence of jumps in density, concentration, and heat of transition is characteristic of phase II of the second kind. But exactly the same picture is observed in the critical. point on the curve F. p. of the first kind . The similarity is very deep. Close to critical point, the state of matter can be characterized by a quantity that plays the role of an order parameter. For example, in the case of a critical points on the liquid-vapour equilibrium curve are the density deviation from the mean value. When moving along the critical isochore from the side of high temperatures, the gas is homogeneous, and this value is equal to zero. Below critical temperature the substance separates 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 phase II phases, it is possible to form large nuclei of one phase in another. (fluctuations), in the same way as near critical. points. Many criticisms are associated with this. phenomena during F. p. of the second kind: an infinite increase in the magnetic susceptibility of ferromagnets and the dielectric constant of ferroelectrics (an analogue is the increase in compressibility near the critical point liquid-vapor), an infinite increase in heat capacity, anomalous scattering electromagnetic waves[light in liquid and vapor , X-ray in solids], neutrons in ferromagnets. Dynamic phenomena also change significantly, which is associated with a very slow absorption of the resulting fluctuations. For example, near the critical point liquid-vapor narrows the Rayleigh line light scattering, near Curie points ferromagnets and Neel points antiferromagnets, spin diffusion slows down etc. Cf. fluctuation size (correlation radius) R increases as we approach the point of the second kind F. p. and becomes infinitely large at this point.

Modern advances in the theory of functional phenomena of the second kind and critical phenomena are based on the similarity hypothesis. It is assumed that if we accept R per unit of length, and cf. the value of the order parameter of the cell with the edge R- per unit of measurement of the order parameter, then the entire pattern of fluctuations will depend neither on the proximity to the transition point, nor on the specific substance. All thermodynamic. quantities are power functions R. The exponents are called critical dimensions (indices). They do not depend on a specific substance and are determined only by the nature of the order parameter. For example, the dimensions at the Curie point of an isotropic material, the order parameter of which is the magnetization vector, differ from the dimensions in the critical. point liquid - vapor or at the Curie point of a uniaxial magnet, where the order parameter is a scalar value.

Near the transition point equation of state has a characteristic form of law corresponding states. For example, near the critical point liquid-vapor ratio (p - p k) / (p f - p g) depends only on (p - p c) / (p f - p g) * K T(here p is the density, p k is the critical density, p f is the density of the liquid, p g is the density of the gas, R - pressure, p to - critical pressure, K T - isothermal compressibility), moreover, the type of dependence with a suitable choice of scale is the same for all liquids .

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

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 phase transitions 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. F. p. 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., Kurs general physics. Mechanics and molecular physics, 2nd ed., M., 1969; Bpayt 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. 3., 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 s-expansion, trans. from English, M., 1975 (News of Fundamental Physics, v. 5).

AT. L. Pokrovsky.

According to the materials of the BSE.

concept phase in thermodynamics are considered in a broader sense than aggregate states. According to, under phase in thermodynamics, they understand the thermodynamically equilibrium state of a substance, which differs in physical properties from other possible equilibrium states of the same substance. Sometimes a non-equilibrium metastable state of a substance is also called a phase, but metastable. The phases of a substance may differ in the nature of the movement of structural particles and the presence or absence of an ordered structure. Different crystalline phases may differ from each other in the type of crystal structure, electrical conductivity, electrical and magnetic properties etc. Liquid phases differ from each other in the concentration of components, the presence or absence of superconductivity, etc.

The transition of a substance from one phase to another is called phase transition . Phase transitions include the phenomena of vaporization and melting, condensation and crystallization, etc. In a two-phase system, the phases are in equilibrium at the same temperature. With an increase in volume, some of the liquid turns into vapor, but at the same time, in order to maintain the temperature unchanged, it is necessary to transfer a certain amount of heat from the outside. Thus, to carry out the transition from the liquid phase to the gaseous system, it is necessary to transfer heat without changing the temperature of the system. This heat is used to change the phase state of matter and is called heat of phase transformation or latent heat of transition . With increasing temperature, the latent heat of transition of a fixed mass of matter decreases, and at the critical temperature it is equal to zero. To characterize the phase transition, the specific heat of the phase transition is used. Specific heat of phase transition is the amount of latent heat per unit mass of a substance.

Phase transitions with absorption or release of latent heat of transition are called first-order phase transitions . In this case, the internal energy and density change abruptly. When moving from a more ordered state to a less ordered state, entropy increases. The table lists first-order phase transitions and their main characteristics.

Table. Phase transitions of the first rad and their main characteristics .

phase transition	Transition direction	Latent heat of transition	Change in entropy during a phase transition
vaporization	liquid  steam	L P is the specific heat of vaporization, t- mass of liquid converted to vapor.	Entropy increases
Condensation	Steam  liquid	, where L KOH is the value of the specific heat of condensation, t- mass of vapor converted to liquid	Entropy Decreases ΔS cr< 0
Melting	Solid  liquid	, where L PL is the specific heat of fusion, t- mass of a solid body converted to liquid	Entropy increases ΔS pl > 0
Crystallization	liquid  solid	, where L KR t- the mass of a liquid converted into a solid body - a crystal	Entropy Decreases ΔS cr< 0
Sublimation (or sublimation)	Solid  Steam	, where L FROM is the specific heat of sublimation, t- mass of solid body converted to steam	Entropy increases
desublimation (Crystallization bypassing the liquid phase)	Steam  Solid (bypassing the liquid phase)	, where L KR is the value of the specific heat of crystallization, t- mass of vapor transferred to a solid body - a crystal	Entropy Decreases ΔS cr< 0

FROM there is a relationship between the pressure at which the two-phase system is in equilibrium and the temperature during first-order phase transitions. This relationship is described . Consider the derivation of this equation for closed systems. If the number of particles in the system is constant, then the change in internal energy, according to the first law of thermodynamics, is determined by the expression: . The equilibrium between the phases will come under the condition that T 1 \u003d T 2 and P 1 \u003d P 2. Consider an infinitely small reversible Carnot cycle (Fig. 6.8), whose isotherms correspond to the state of a two-phase system at temperatures T and dT. Since the state parameters in this case change infinitely little, the isotherms and adiabats in Fig. 6.8 are shown as straight lines. The pressure in such a cycle changes by dP . The work of the system per cycle is determined by the formula:
. Let us assume that the cycle is implemented for a system whose mass of matter is equal to one. The efficiency of such an elementary Carnot cycle can be determined by the formulas:
or
, where L P is the specific heat of vaporization. Equating the right parts of these equalities, and substituting the expression of work through pressure and volume, we get:
. We correlate the change in pressure with the change in temperature and get:

(6.23)

Equation (6.23) is called Clausius-Clapeyron equation . Analyzing this equation, we can conclude that with increasing temperature, the pressure increases. This follows from the fact that
, which means
.

The Clausius-Clapeyron equation is applicable not only to the liquid-vapor transition. It applies to all transitions of the first kind. In general, it can be written like this:

(6.24)

Using the Clapeyron-Clausius equation, one can represent the state diagram of the system in P,T coordinates(fig.6.9). In this diagram, curve 1 is the sublimation curve. It corresponds to the equilibrium state of two phases: solid and vapor. The points to the left of this curve characterize the single-phase solid state. The points on the right characterize the vapor state. Curve 2 is the melting curve. It corresponds to the equilibrium state of two phases: solid and liquid. The points to the left of this curve characterize the single-phase solid state. The points to the right of it up to curve 3 characterize the liquid state. Curve 3 is the vaporization curve. It corresponds to the equilibrium state of two phases: liquid and vapor. The points lying to the left of this curve characterize the single-phase liquid state. The points on the right characterize the vapor state. Curve 3, in contrast to curves 1 and 2, is bounded on both sides. On the one hand - a triple point Tr, on the other hand - the critical point K (Fig. 6.9). triple point describes the equilibrium state of three phases at once: solid, liquid and vapor.

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Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_2.jpg" alt="(!LANG:>Phase transitions with a change in the state of aggregation boiling (condensation) melting (crystallization ) sublimation"> Фазовые переходы с изменением агрегатного состояния кипение (конденсация) плавление (кристаллизация) сублимация (конденсация) Все эти процессы сопровождаются резким изменением порядка атомной, молекулярной или ионной структуры вещества (в зависимости от его природы). Обычно с изменением температуры эти фазовые переходы идут по такой схеме: дальний порядок (кристаллическая твердая фаза) ближний порядок (жидкость) беспорядок (газ) Увеличение температуры Уменьшение температуры дальний порядок (кристаллическая твердая фаза) беспорядок (газ) Иногда по другой:!}

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Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_5.jpg" alt="(!LANG:>4. Magnetic phase transitions with absence"> 4. Магнитные фазовые переходы Известна группа веществ, обладающих большой спонтанной намагниченностью при отсутствии внешнего магнитного поля – это ферромагнетики. Для них возможно существование ферромагнитной и парамагнитной фаз. Ферромагнитная фаза соответствует упорядоченному состоянию элементарных магнитных моментов, парамагнитная – разупорядочению таких моментов. Элементарные магнитные моменты связаны со спиновыми магнитными моментами электронов; следовательно, упорядочение связано с электронной подсистемой вещества. Переход между этими фазами называют ферромагнитным ФП, а температуру, при которой он происходит – ферромагнитной температурой (точкой) Кюри.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_6.jpg" alt="(!LANG:>5. Ferroferromagnetic phase transitions Substances are known that at certain temperatures ordering is observed"> 5. Сегнетоферромагнитные фазовые переходы Известны вещества, у которых при определенных температурах наблюдается упорядочение как электрических, так и магнитных моментов. Такие вещества называют сегнетоферромагнетиками. Сегнетоферромагнитная фаза состоит из двух подсистем – электрической и магнитной, каждая из которых претерпевает переход при разных температурах, поэтому сегнетоферромагнитный ФП следует характеризовать двумя температурами (точками) Кюри – сегнетоэлектрической и ферромагнитной. Поэтому весь такой ФП протекает в интервале температур, определяемом разностью сегнетоэлектрической и ферромагнитной температур Кюри. Электрическую и магнитную подсистемы нельзя считать вполне независимыми, т.к. между ними существует корреляция, хотя и слабая. Поэтому на электрические свойства сегнетоферромагнетиков можно повлиять, использую те факторы, которые действуют на магнитную подсистему, например, магнитное поле, и наоборот.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_7.jpg" alt="(!LANG:>6. Transitions to the superconducting state what is electric"> 6. Переходы в сверхпроводящее состояние Сущность явления сверхпроводимости состоит в том, что электрическое сопротивление некоторых веществ в районе низких температур становится практически равным нулю. При повышении температуры это свойство исчезает, и вещество переходит в нормальную фазу. Температуру, при которой это происходит, называют критической. Температурные зависимости сопротивления нормального (N) и сверхпроводящего (S) металлов!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_8.jpg" alt="(!LANG:>Chronology of increase in superconducting transition temperature Structure of high-temperature superconductor HgBa2CuO4+δ">!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_9.jpg" alt="(!LANG:>At a temperature of 2.19 K, liquid helium separates into two phases - HeI and HeII."> При температуре 2,19 К жидкий гелий разделяется на две фазы – HeI и HeII. Сверхтекучесть, то есть способность жидкости течь без трения по очень тонким капиллярам, наблюдается для HeII. 7. Переходы в сверхтекучее состояние Аномальное течение HeII!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_10.jpg" alt="(!LANG:>As you can see from the above examples, very diverse FP."> Как видно из рассмотренных примеров, в термодинамической системе могут происходить очень разнообразные ФП. Очевидно, что для понимания сущности ФП необходимо сначала провести их классификацию, причем, эта классификация должна быть как можно более общей, не уводящей исследователя к рассмотрению множества частных случаев. Для рассмотрения !} general patterns FP, it is necessary to introduce quantities and functions that make it possible to describe both individual phases and the FP itself as a whole. The easiest way to do this is with a thermodynamic consideration of the process.

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_11.jpg" alt="(!LANG:>Ehrenfest thermodynamic classification of phase transitions">!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_12.jpg" alt="(!LANG:>First derivatives of the Gibbs energy Second derivatives of the Gibbs energy and physical quantities, s related">!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_13.jpg" alt="(!LANG:>Change in thermodynamic properties during phase transitions of the first and second kind">!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_14.jpg" alt="(!LANG:>Thermodynamic theory of phase transitions of the first kind consisting of an individual substance) heterogeneous"> Термодинамическая теория фазовых переходов I рода Рассмотрим однокомпонентную (т.е. состоящую из индивидуального вещества) гетерогенную систему, состоящую из r фаз. В однокомпонентных системах отдельные фазы представляют собой одно и то же вещество в различных !} phase states. Let the system be closed (total number of moles ∑nr=const), and the main parameters of its state are p and T. The main thermodynamic function characterizing the state of such a system is the Gibbs energy G.

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_15.jpg" alt="(!LANG:>For each of the r phases of this system, we can write down the corresponding values ​​of thermodynamic parameters"> Для каждой из r фаз этой системы мы можем записать соответствующие значения термодинамических параметров и приписать ей химический потенциал: Фаза 1 – p1, T1, V1, S1, …, μ1; Фаза 2 – p2, T2, V2, S2, …, μ2; ………………………………… Фаза r – pr, Tr, Vr, Sr, …, μr. Состоянию равновесия отвечает равенство интенсивных параметров p, T и μ во всех фазах системы: T1=T2=...=Tr (условие термического равновесия); p1=p2=...=pr (условие механического равновесия) ; μ1= μ2=...= μr (условие !} chemical equilibrium). (here r=1,2,... is equal to the number of phases in the system).

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_16.jpg" alt="(!LANG:>Let's assume for simplicity that only 2 phases."> Примем для упрощения, что в нашей однокомпонентной гетерогенной системе сосуществуют только 2 фазы. Условия равновесия для двухфазной системы: T1=T2; p1=p2; μ1= μ2. μ1(p,T)=μ2(p,T). Из определения химического потенциала, поэтому Давление и температура фазового перехода не являются независимыми переменными и должны быть связаны уравнением.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_17.jpg" alt="(!LANG:>Let's get an explicit expression for this dependency. Let's take into account that in single component systems"> Получим явное выражение для этой зависимости. Примем во внимание, что в однокомпонентных системах, состоящих из чистого вещества i, химический потенциал равен энергии Гибсса одного моля этого вещества: μi=Gi. При T, p = const условие равновесия: G1=G2. В общем случае выражения для G=G(p,T) в интегральной форме не могут быть найдены. Поскольку G – это функция состояния системы, то ее дифференциал – это полный дифференциал. Мы можем получить уравнение в дифференциальной форме.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_18.jpg" alt="(!LANG:>Based on the expression G=U+pV-TS, after differentiation we get: dG=dU+pdV+Vdp-TdS-SdT Let's take into account the expression"> Исходя из выражения G=U+pV-TS, после дифференцирования получим: dG=dU+pdV+Vdp-TdS-SdT. Примем во внимание выражение для объединенного I и II начала термодинамики dU=TdS-δA и соотношение δA=pdV; произведем замену: dG=TdS-pdV+pdV+Vdp-TdS-SdT. Мы получили выражение для полного дифференциала энергии Гиббса: dG=Vdp -SdT!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_19.jpg" alt="(!LANG:>Phase transformation occurs at T,p=const and is accompanied by a volume change V1 to V2."> Фазовое превращение происходит при T,p=const и сопровождается изменением объема от V1 до V2. Пусть оно происходит для 1 моля индивидуального вещества, тогда V1 до V2 – это молярные объемы первой и второй фазы. Для изобарно-изотермических потенциалов в двух равновесных фазах 1 и 2: dG1=V1dp-S1dT dG2=V2dp-S2dT Вычитая верхнее уравнение из нижнего, получим: dG2 - dG1 =(V2 - V1) dp – (S2 - S1)dT. Изменения T и p здесь не являются независимыми; они такие, при которых сохраняется равновесие между фазами 1 и 2.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_20.jpg" alt="(!LANG:>Thus, between T and p, the functional relationship corresponding to the phase equilibrium, so if"> Таким образом, между T и p сохраняется функциональная связь, соответствующая фазовому равновесию. Поэтому, если G1=G2 (равновесие при T и p), то G1+dG1=G2+dG2 (равновесие при T+dT и p+dp). Тогда dG1=dG2, или dG1-dG2 =0. Следовательно, (V2 - V1) dp – (S2 - S1)dT=0 или. Примем во внимание, что. Qф.п - теплота фазового превращения, поглощаемая при переходе 1 моля вещества из фазы 1 в фазу 2; ΔHф.п. – молярная энтальпия фазового перехода.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_21.jpg" alt="(!LANG:>Combining the last two equations and denoting V2 -V1=ΔV (difference molar volumes of two phases),"> Комбинируя два последних уравнения и обозначив V2 -V1=ΔV (разность молярных объемов двух фаз), получим: Здесь T - температура фазового перехода (кипения, плавления, полиморфного превращения и т.д.). Это уравнение называется уравнением Клаузиуса-Клапейрона и является общим термодинамическим уравнением, приложимым ко всем фазовым переходам !} pure substances. It shows how the phase transition temperature changes with pressure.

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_22.jpg" alt="(!LANG:>Transition between condensed phases For melting (crystalline phase - liquid transition)"> Переход между конденсированными фазами Для плавления (перехода кристаллическая фаза – жидкость) удобнее переписать уравнение Клаузиуса-Клапейрона в виде: , – изменение температуры плавления при изменении давления. где Если Vж>Vкр и ΔV>0, то с увеличением давления температура плавления повышается (большинства веществ). Если ΔV!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_23.jpg" alt="(!LANG:>Liquid-vapor transition (evaporation) If phase transition conditions (p ,T) are far enough from the critical"> Переход жидкость – пар (испарение) Если условия фазового перехода (p,T) достаточно далеки от критической точки, то Vпар>>Vж, и тогда ΔV= Vпар-Vж≈ Vпар. Для 1 моля идеального газа. Тогда (ΔHисп – молярная энтальпия испарения), откуда Поскольку ΔHисп, R и T всегда положительны, то >0. C ростом T давление насыщенного пара над жидкостью всегда увеличивается.!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_24.jpg" alt="(!LANG:>Transition crystalline phase - vapor (sublimation) The Clausius-Clapeyron equation has the same look but"> Переход кристаллическая фаза – пар (сублимация) Уравнение Клаузиуса-Клапейрона имеет тот же вид, но вместо ΔHисп – энтальпия сублимации ΔHсуб:!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_25.jpg" alt="(!LANG:>Sometimes the Clausius-Clapeyron equation for the transition from a condensed phase to a gaseous one is written in integral form:"> Иногда уравнение Клаузиуса-Клапейрона для перехода из конденсированной фазы в газообразную записывается в интегральном виде: Эта форма уравнения справедлива только для узкого интервала температур, в котором ΔH испарения или сублимации можно приближенно считать постоянной величиной. Строго говоря, это не так: зависимость Qp=ΔH изобарного процесса от температуры подчиняется закону Кирхгофа:!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_26.jpg" alt="(!LANG:>So, we got in the differential (and for some special cases - and in the integral)"> Итак, мы получили в дифференциальной (а для некоторых частных случаев – и в интегральной) форме !} mathematical expression, which establishes a strict relationship between the thermodynamic parameters p and T, which characterize the equilibrium between two different phases in a one-component system. However, in the general case, we do not know the integral form of the equations of state for various phases, even for one-component systems. The only exception is the Mendeleev-Clapeyron equation, which is applicable when the components of the gaseous phase obey the laws ideal gases, and a number of more or less well-chosen, but quite complex equations describing the state of real gases and real individual liquids.

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_27.jpg" alt="(!LANG:>Phase transformations of the second kind occur in crystals when point defects are ordered (when structure changes"> Фазовые превращения второго рода происходят в кристаллах при упорядочении точечных дефектов (когда изменения структуры минимальные), при превращении ферромагнитных веществ в парамагнитные, при переходе в сверхпроводящее и сверхтекучее состояние и т.д. Наиболее общей и полной термодинамической теорией ФП второго рода в настоящее время является теория Ландау, разработанная им в 1937 г. Теория фазовых переходов II рода!}

Src="https://present5.com/presentacii/20170502/Lekcija_4-5.ppt_images/Lekcija_4-5.ppt_28.jpg" alt="(!LANG:>In the Landau theory, it is assumed that the individual phases of the system differ from each other physical properties,"> In the Landau theory, it is assumed that the individual phases of the system differ from each other in physical properties, the change of which is characterized by some additional parameters. That is, in addition to the usual thermodynamic parameters (T and p for G), parameters η1 are also introduced for the thermodynamic potential , η2 ... ηn, which are called the ordering parameters of the corresponding subsystems.Let a phase have only one ordering parameter η.The ordering parameter characterizes the physical state of an individual phase and is usually chosen in such a way that it is equal to 0 for one phase and nonzero for the second.Phase , for which η=0, is conventionally called the disordered phase, and the phase with η≠0 is called ordered.In this interpretation, the phase transition is associated with the transition of the system from an ordered state to a disordered one.