Thomson phenomenon. Thermoelectric phenomena. Seebeck effect. Peltier effect. Thomson effect. See what the "Thomson Effect" is in other dictionaries

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"Thomson effect"

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Introduction. 3

1. Thomson effect in semiconductors. 5

2. Applying the effect. 12

Introduction

Thomson effect- one of the thermoelectric phenomena, which consists in the fact that in a homogeneous unevenly heated conductor with direct current, in addition to the heat released in accordance with the Joule-Lenz law, additional Thomson heat will be released or absorbed in the volume of the conductor, depending on the direction of the current.

The amount of Thomson heat is proportional to the strength of the current, time and temperature difference, depends on the direction of the current.

The effect was discovered by W. Thomson in 1856.

The explanation of the effect in the first approximation is as follows. Under conditions when there is a temperature gradient along the conductor through which the current flows, and the direction of the current corresponds to the movement of electrons from the hot end to the cold end, when moving from a hotter section to a colder one, the electrons transfer excess energy to the surrounding atoms (heat is released), and when in the opposite direction of the current, passing from a colder area to a hotter one, replenish their energy at the expense of the surrounding atoms (heat is absorbed).

In semiconductors, it is important that the concentration of carriers in them strongly depends on temperature. If the semiconductor is heated unevenly, then the concentration of charge carriers in it will be greater where the temperature is higher, so the temperature gradient leads to a concentration gradient, resulting in a diffusion flow of charge carriers. This leads to a violation of electrical neutrality. Separation of charges generates an electric field that prevents separation. Thus, if a semiconductor has a temperature gradient, then it has a bulk electric field.

Suppose now that through such a sample is passed electricity under the action of an external electric field. If the current goes against the internal field, then the external field must do additional work when moving the charges relative to the field, which will lead to the release of heat, in addition to the Lenz-Joule losses. If the current (or external field) is directed along, then it itself does the work of moving charges to create a current. In this case, the external source spends less energy to maintain the current than in the case when there is no internal field. The work of the field can only be performed due to the thermal energy of the conductor itself, so it is cooled. The phenomenon of heat generation or absorption in a conductor due to a temperature gradient during the passage of current is called the Thomson effect. Thus, matter heats up when the fields and are oppositely directed, and cools when their directions coincide.

In the general case, the amount of heat released in the volume dV is determined by the relation:

Where is the Thomson coefficient.

Thomson effect in semiconductors

Volumetric release or absorption of heat in a semiconductor under the combined action of an electric current and a temperature gradient

Description

The Thomson effect refers to thermoelectric effects and consists in the following: when an electric current is passed through a semiconductor (or conductor) along which there is a temperature gradient, in addition to Joule heat, an additional amount of heat will be released or absorbed in it, depending on the direction of the current (Thomson heat ).

Uneven heating of an initially homogeneous sample changes its properties, making the substance inhomogeneous. Therefore, the Thomson phenomenon is, in essence, a peculiar Peltier phenomenon, with the difference that the inhomogeneity is not caused by the difference chemical composition sample, but not the same temperature.

Experience and theoretical calculations show that the Thomson phenomenon obeys the following law:

where is the Thomson heat released (or absorbed) per unit time per unit volume of the semiconductor (specific thermal power);

j is the current density;

Temperature gradient along the sample;

t is the Thomson coefficient, which depends on the nature of the semiconductor and its temperature.

The above formula (the so-called differential form of the law) can be applied to a section of the sample x, along which the current I flows and there is a certain temperature difference: (see Fig. 1)

Semiconductor with mixed conductivity

Thomson's law in integral form determines the total amount of Thomson's heat Qt released (or absorbed) in the entire volume of the semiconductor under consideration (DV=SЧDx) during time t:

or finally:

Qt= tHDT HCH t.

In this case, the Thomson effect is considered positive if the electric current flowing in the direction of the temperature gradient (I dT/dx) causes the semiconductor to heat up (Qt>0), and negative if it cools down at the same current direction (Qt<0).

The explanation of the Thomson phenomenon for semiconductors with one type of carriers (electrons or holes) is similar to the case of metallic conductors. First, it is necessary to take into account the change in the average energy of charge carriers along the sample due to its uneven heating. In the hotter part of the semiconductor, the average energy of electrons (or holes) is greater than in the less heated part. Therefore, if the direction of the current in the semiconductor corresponds to the movement of current carriers from the hot end to the cold one, then they will transfer their excess energy to the crystal lattice, resulting in the release of Thomson heat (Qt>0).

In the reverse direction of the current, charge carriers, moving from the cold end to the heated end, will replenish their energy due to the lattice, i.e. the corresponding amount of heat is absorbed (Qt<0).

In semiconductors with mixed conductivity, in the presence of a current, electrons and holes move towards each other, and the heat fluxes transferred by them will be compensated. So, in fig. 1, holes move from the hot end to the cold end, which, in the absence of electronic conduction, should lead to the release of Thomson heat. However, with the movement of electrons (from the cold end to the hot end), heat absorption is associated. As a result, when the concentrations and mobilities of electrons and holes are equal, Thomson heat is not released (Qt=0).

The second factor that must be taken into account is related to the thermopower electric field that arises under conditions of temperature inhomogeneity (Fig. 2, 3).

Release and absorption of Thomson heat in an electronic semiconductor

n-conductor

Release and absorption of Thomson heat in a hole semiconductor

p-conductor

Consider a semiconductor with electronic conductivity. Let Т1>Т2, i.e. the temperature gradient is directed from point 2 to point 1 (Fig. 2). Diffusion of electrons from the hot end to the cold one leads to charge separation; against the temperature gradient. If the current flows in the direction of the temperature gradient (electrons move in the direction of the ET field), then the ET field will slow down the electrons, and the semiconductor section 1-2 will cool (Qt<0). Если ток течет в обратном направлении, то произойдет нагревание участка 1-2.

In a hole semiconductor, the ratios will be inverse (Fig. 3). The phenomenon looks as if an additional heat flow associated with the passage of an electric current is superimposed on the usual heat flux caused by thermal conductivity. In hole semiconductors, the additional heat flux is directed in the same direction as the electric current flows. In electronic semiconductors, the directions of current and heat are opposite.

The considered factors act in opposite directions, determining not only the magnitude, but also the sign of t and Qt.

For a quantitative study of the Thomson phenomenon, an experiment can be used, the scheme of which is shown in Fig. 4

Experiment scheme for observing the Thomson effect

Two identical rods AB and CD are taken from the material being tested (for example, a p-type semiconductor). Ends A and C are connected together and maintained at the same temperature (eg, TA=TC=100°C). The temperatures of the free ends B and D are also equal (for example, TB=TD=0°C). In the experiment, the temperature difference is measured for two points a and b, chosen in such a way that in the absence of current their temperature is the same (Ta=Tb=T0). When an electric current is passed in one rod (in the figure, this is the CD rod), an additional heat flow passes from left to right (Qt> 0), and in the other rod (AB) - from right to left (Qt<0). В результате между точками а и b возникает разность температур DТ=Тa -Тb, которая регистрируется термопарами. При изменении направления тока знак разности температур изменяется на противоположный.

The Thomson effect, like other thermoelectric phenomena, has a phenomenological character.

The Thomson coefficient is related to the Peltier coefficients p and thermopower a by the Thomson relation:

For a chain composed of two dissimilar materials, we have:

Taking into account these relations, one can obtain the value of the dependence of t on temperature, carrier concentration, etc.

From measurements of the Thomson coefficient, one can determine the thermoelectric coefficient of one material, and not the difference in the coefficients of two materials, as in the direct measurement of a and p. This allows, by measuring t and determining a from it. in one of the metals, get the absolute thermoelectric scale.

The Thomson effect has no technical application, but it must be taken into account in accurate calculations of thermoelectric devices.

The effect was described and discovered in 1854 by William Thomson, who developed the thermodynamic theory of thermoelectricity.

Timing

Initiation time (log to -3 to 2);

Lifetime (log tc 13 to 15);

Degradation time (log td -3 to 2);

Optimal development time (log tk -2 to 1).

Diagram:

Technical realizations of the effect

Implementation of the Thomson effect in semiconductors

Description of the technical implementation of the Thomson effect (scheme of experience for a quantitative study of the phenomenon) is given in the “essence” section, see fig. 4 and comments on it.

Applying an effect

The Thomson effect has no technical applications, but must be taken into account in relatively accurate calculations of thermoelectric devices.

For example, when determining the efficiency of thermoelectric generators to account for Thomson's heat, the thermoelectric coefficient is calculated as the average value of the values at both ends of the thermoelement.

1. Physical Encyclopedia.- M.: Great Russian Encyclopedia, 1998.- T.3.- S.552.- T.5.- S.98-99.

2. Sivukhin S.D. General course of physics.- M.: Nauka, 1977.- V.3. Electricity.- S.481-490.

3. Stilbans L.S. Physics of semiconductors.- M., 1967.- S.75-83, 292-311.

4. Ioffe A.F. Semiconductor thermoelements. - M., 1960.

Time and temperature difference, depends on the direction of the current.

The explanation of the effect in the first approximation is as follows. Under conditions when there is a temperature gradient along the conductor through which the current flows, and the direction of the current corresponds to the movement of electrons from the hot end to the cold end, when moving from a hotter section to a colder one, the electrons transfer excess energy to the surrounding atoms (heat is released), and in the opposite direction of the current, passing from a colder area to a hotter one, they replenish their energy at the expense of the surrounding atoms (heat is absorbed).

Let us now assume that an electric current is passed through such a sample under the action of an external electric field. If the current goes against the internal field, then the external field must do additional work when moving the charges relative to the field, which will lead to the release of heat, in addition to the Lenz-Joule losses. If the current (or external field) is directed along, then it itself does the work of moving charges to create a current. In this case, the external source spends less energy to maintain the current than in the case when there is no internal field. The work of the field can only be performed due to the thermal energy of the conductor itself, so it is cooled. The phenomenon of heat generation or absorption in a conductor due to a temperature gradient during the passage of current is called the Thomson effect. Thus, matter heats up when the fields and are oppositely directed, and cools when their directions coincide.

In the general case, the amount of heat released in the volume dV is determined by the relation:

, where is the Thomson coefficient.

Electrothermal Peltier effect.

In 1834, the French watchmaker J. Peltier noticed that when current passes through a junction of two different conductors, the temperature of the junction changes. Like Seebeck, Peltier did not at first see this as an electrothermal effect. But in 1838, E.Kh. Lenz, a member of the St. Petersburg Academy of Sciences, showed that with a sufficiently large current strength, a drop of water deposited on a junction can either be frozen or brought to a boil by changing the direction of the current. In one direction of the current, the junction heats up, and in the opposite direction, it cools down. This is the Peltier effect (Fig. 3), the opposite of the Seebeck effect.

Electrothermal Thomson effect.

In 1854, W. Thomson (Kelvin) discovered that if a metal conductor is heated at one point and an electric current is simultaneously passed through it, then a temperature difference arises at the ends of the conductor equidistant from the heating point (Fig. 4). At the end where the current is directed towards the heating point, the temperature decreases, and at the other end, where the current is directed away from the heating point, the temperature rises. The Thomson coefficient is the only thermoelectric coefficient that can be measured on a homogeneous conductor. Thomson later showed that all three phenomena of thermoelectricity are interconnected by the Kelvin relations already mentioned above.

Thermocouple.

If the materials of the circuit in Fig. 2 are homogeneous, then the thermo-EMF depends only on the selected materials and on the temperatures of the junctions. This experimentally established position, called the Magnus law, underlies the application of the so-called. thermocouples devices for measuring temperature, which is of great practical importance. If the thermoelectric properties of a given pair of conductors are known and one of the junctions (say, with temperature T 1 in fig. 2) maintained at a precisely known temperature (e.g. 0°C, the freezing point of water), the thermo-emf is proportional to the temperature T 2 other junctions. Thermocouples from platinum and platinum-rhodium alloy measure temperatures from 0 to 1700 ° C, from copper and a multicomponent alloy of constantan from - 160 to + 380 ° C, and from gold (with very small additions of iron) and multicomponent chromel up to values, only a fraction of a degree higher than absolute zero (0 K, or - 273.16 ° C).

Thermo-EMF of a metal thermocouple with a temperature difference at its ends equal to 100 ° C, a value of the order of 1 mV. To increase the sensitivity of the temperature transmitter, you can connect several thermocouples in series (Fig. 5). A thermopile is obtained in which one end of all thermocouples is at a temperature T 1 , and the other at a temperature T 2. The thermo-emf of a battery is equal to the sum of the thermo-emf of individual thermocouples.

Since thermocouples and their junctions can be made small and convenient to use in a variety of conditions, they have found wide application in devices for measuring, recording and controlling temperature.

Thermoelectric properties of metals.

The Seebeck effect is usually easier to measure than other thermoelectric effects. Therefore, it is usually used to measure the thermoelectric coefficients of unknown materials. Since thermo-EMF is determined by the properties of both thermocouple branches, one branch must be made of some kind of "reference" material, for which the "specific" thermo-EMF (thermo-EMF per one degree temperature difference) is known. If one branch of the thermocouple is in a superconducting state, then its specific thermo-EMF is zero and the thermo-EMF of the thermocouple is determined by the value of the specific thermo-EMF of the other branch. Thus, a superconductor is an ideal "reference" material for measuring the specific thermo-EMF of unknown materials. Until 1986, the highest temperature at which a metal could be maintained in a superconducting state was only 10 K (-263°C). At present, superconductors can be used up to approximately 100 K (-173° C). At higher temperatures, measurements must be made with non-superconductive reference materials. Up to room and somewhat higher temperatures, lead is usually used as a reference material, and at even higher temperatures, gold and platinum. Cm. Also SUPERCONDUCTIVITY.

The Seebeck effect in metals has two components: one of them is associated with the diffusion of electrons, and the other is due to their phonon drag. Diffusion of electrons is caused by the fact that when a metal conductor is heated from one end, there are many electrons with high kinetic energy at this end, and few at the other. High-energy electrons diffuse towards the cold end until further diffusion is prevented by repulsion from the excess negative charge of electrons accumulated here. This accumulation of charge determines the thermo-EMF component associated with the diffusion of electrons.

The component associated with phonon drag arises because when one end of the conductor is heated at this end, the energy of thermal vibrations of atoms increases. The vibrations propagate towards the colder end, and in this motion the atoms, colliding with electrons, transfer to them part of their increased energy and drag them along in the direction of propagation of phonons, vibrations of the crystal lattice. The corresponding charge accumulation determines the second component of thermo-emf.

Both processes (diffusion of electrons and their phonon drag) usually lead to the accumulation of electrons at the cold end of the conductor. In this case, the specific thermo-EMF is by definition considered negative. But in some cases, due to the complex distribution of the number of electrons with different energies in a given metal and due to the complex patterns of scattering of electrons and vibrating atoms in collisions with other electrons and atoms, electrons accumulate at the heated end, and the specific thermo-EMF turns out to be positive. The highest thermo-EMFs are typical for thermocouples made up of metals with specific thermo-EMFs of the opposite sign. In this case, the electrons in both metals move in the same direction.

Thermoelectric properties of semiconductors.

In the 1920s and 1930s, scientists discovered a number of low-conductivity materials, now called semiconductors, whose specific thermoelectric power is thousands of times greater than that of metals. Therefore, semiconductors are more suitable than metals for the manufacture of thermopiles, which require high thermoelectric power or intense thermoelectric heating or cooling. As in the case of metals, the thermo-EMF of semiconductors has two components (related to the diffusion of electrons and to their phonon drag) and can be negative or positive. The best thermopiles are obtained from semiconductors with thermo-EMF of the opposite sign.

Thermoelectric devices.

If good thermal contact is made between one group of thermopile junctions and some source of heat, such as a small amount of radioactive material, then a voltage will be generated at the output of the thermopile. The efficiency of converting thermal energy into electrical energy in such thermoelectric generators reaches 1617% (for steam turbine power plants, the thermal efficiency is 2040%). Thermoelectric generators are used in remote locations on Earth (for example, in the Arctic) and in interplanetary stations, where the power source requires a long life, small size, lack of moving mechanical parts and reduced sensitivity to environmental conditions.

It is also possible, by attaching a current source to the terminals of the thermopile, to pass current through its thermoelements. One group of thermopile junctions will heat up and the other will cool down. Thus, the thermopile can be used either as a thermoelectric heater (for example, for baby bottles) or as a thermoelectric refrigerator. see also REFRIGERATION EQUIPMENT.

The efficiency of thermoelements for thermoelectric generators is evaluated by a comparative quality index

Z = (S 2 s T)/ k,

Where T temperature, S specific thermo-EMF, k thermal conductivity, and s electrical conductivity. The more S, the greater the thermo-emf at a given temperature difference. The more s, the greater the current in the circuit. The less k, the easier it is to maintain the required temperature difference at the thermopile junctions.

In addition to the heat released in accordance with the Joule-Lenz law, additional Thomson heat will be released or absorbed in the volume of the conductor, depending on the direction of the current.

The explanation of the effect in the first approximation is as follows. Under conditions when there is a temperature gradient along the conductor through which the current flows, and the direction of the current corresponds to the movement of electrons from the hot end to the cold end, when moving from a hotter section to a colder one, the electrons transfer excess energy to the surrounding atoms (heat is released), and in the opposite direction of the current, passing from a colder area to a hotter one, they replenish their energy at the expense of the surrounding atoms (heat is absorbed).

Let us now assume that an electric current is passed through such a sample under the action of an external electric field E (\displaystyle E). If the current goes against the internal field E′ (\displaystyle E"), then the external field must do additional work when moving charges relative to the field E′ (\displaystyle E"), which will lead to the release of heat, additional to the Lenz-Joule losses. If the current (or external field E (\displaystyle E)) is directed along E′ (\displaystyle E"), That E′ (\displaystyle E") does the work of moving charges to create a current. In this case, the external source spends less energy to maintain the current than in the case when the internal field E′ (\displaystyle E") No. Field work E′ (\displaystyle E") can be performed only due to the thermal energy of the conductor itself, so it is cooled. The phenomenon of heat generation or absorption in a conductor due to a temperature gradient during the passage of current is called the Thomson effect. Thus, the substance is heated when the fields E (\displaystyle E) And E′ (\displaystyle E") oppositely directed, and cools when their directions coincide.

In the general case, the amount of heat released in the volume dV is determined by the relation:

d Q T = − τ (∇ T ⋅ j) d t d V (\displaystyle dQ^(T)=-\tau (\nabla T\cdot \mathbf (j))dtdV), Where τ (\displaystyle \tau )- Thomson coefficient.

THOMSON EFFECT

The release or absorption of heat in a current-carrying conductor, along which there is a temperature gradient, which occurs in addition to the release of Joule heat. Thomson heat Qs proportional. current strength I, time t and temperature difference (T1-T2): Qs=S(I1-I2)It. Coeff. Thomson S - character of the conductor. T. e. predicted in 1856 physicist W. Thomson (Lord Kelvin) and experimentally established by the French. physicist Leroux and others.

According to Thomson's theory, ud. the thermoelectric power of a pair of conductors is related to their coefficient. S1 and S2 ratio:

da/dT=(S1-S2)/T,

where a is the coefficient. Seebeck (see SEEBECK EFFECT).

If a current flows along the conductor, there is a temperature gradient, and the direction of the current corresponds to the movement of the electrons from the hot end to the cold, then when moving from a hotter area to a colder one, the electrons slow down and transfer excess energy to others atoms (heat is released); in the reverse direction of the current, the electrons, moving from a colder area to a hotter one, are accelerated by the thermopower field and replenish their energy due to the energy of the surrounding atoms (heat is absorbed). This explains (in the first approximation) T. e.

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