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§ 4.3. An estimate of thermodynamic efficiency kaloricheskih effects in a double-layer composite.

Now solid-state cooling draws the increasing attention of researchers of all world thanking the advantages before traditional (parokompressionnymi) methods. Constructive solutions of solid-state coolers allow to avoid use of moving parts, therefore they are more unobstructive, are trusty and practically silent.

Moreover, materials used in them are ecologically safe - unlike set of the coolants applied now in the refrigerating technics. Solid-state cooling is parted on two parts: thermoelectric [121] and on kaloricheskih effects [49]. As effect Pelte underlying operation of a thermoelectric cooler, is nonreversible its efficiency makes no more than 7 % from efficiency of a Carnot cycle. Much more effective is cooling on kaloricheskih effects [32,49]. For the working bodies possessing magnetocaloric effect, efficiency makes the order of 70 % [1], for coolers on

Electrocaloric effect (EKE) - 62 % [122], that essentially surpasses corresponding values for parokompressionnyh cooler bodies and aerial refrigerators (20 % [121]). However,
Despite high efficiency, the technology of cooling grounded on kaloricheskih effects, has not gained a wide circulation because of high cost of materials and lack of trusty and high-efficiency thermal valves. So it was offered to use not single kalorichesky effect, and the compounded complex action of the several physical strengths leading to occurrence multikaloricheskogo of effect (rke) [37-40]. In this case the efficiency magnification, but quantitatively this question is possible earlier was not considered. One of the basic performances of efficiency of any cooler is the dimensionless refrigerating coefficient ε. It is spotted as the relation of quantity of heat Qcотнятой from cooled object (holodoproizvoditelnosti), to operation W spent for the organisation of a cycle, ε =Qc∣W.Для any thermodynamic cycle featured in a frame (S,) closed curve L, ε is expressed as follows

Here S - entropy, T - temperature, Lc - inferior half L (drawing 4.9). For example, for a Carnot cycle curve Lявляется a rectangle, for a cycle of Brighton - a curvilinear trapezoid (a parenthesizing in drawing 4.9). Integration in a curvilinear integral, as well as for all refrigerators, is carried out counter-clockwise. Quantity ε is not quite objective as at small differences of temperatures in a cycle it can be as much as major. So for an estimate of efficiency of cycle Lобычно use the relative coefficients η = ∖QQo∕o ∙ε j εκ apm, where =karno - refrigerating coefficient of a Carnot cycle.

As an example of calculation of efficiency of a thermodynamic cycle for multikalorika we will view the linear ferroelectromagnetic, which free energy Fимеет a view

Here P - polarisation, M - magnetisation, Eи H - intensity of electrical and magnetic water, ε0и μ0 - electrical and magnetic stationary values, and - permanent-magnet coefficient.

Coefficients a, χe, χm are guessed not dependent on fields E, N, but depend on T.Imenno's temperature temperature dependence of these coefficients and causes presence kaloricheskih effects [27]. From a requirement of extremeness (4.7) we find communication between E, P, H, M

For available materials permanent-magnet interaction is small [123] we Will enter one more permanent-magnet

koeffitsienti we will copy equality (4.8) in a view

The written out relations allow to find thermal performances of a ferroelectromagnetic. Most simply there is entropy S

From (4.10) follows, that entropy change at an isothermal change consists of three addends, each of which answers corresponding kaloricheskomu to effect. The first sets EKE, second - magnitoelektrokalorichesky effect (MEKE), the third - MKE. Heat capacity C a usual fashion is from entropy and it is represented in the form of the total of two addends

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Where C0теплоёмкость in lack of a field. In theory Landau C0считается a symmetric function of temperature [124], but for room temperatures and small change of temperature in a cycle it is possible to consider From a stationary value. Piroelektricheky and pyromagnetic coefficients look like

The gained formulas (4.10) - (4.12) allow to write out the equations for the basic thermodynamic processes

The first of the equations (4.13) features change entropiii, and second - change of temperature in the adiabatic process. In viewed model vsledstvii guesses of lack of dependence of the material stationary values from values of external fields change of temperature in process

Drawing 4.9. The diagrammatical image of dependence of temperature from entropy for thermodynamic cycles Karno () and Brighton ().

85 it is spotted only by initial and terminating values of electrical and magnetic water E, N.

It is necessary to score, that for entropy change it is the statement validly at any dependences ∕ςот E, N.Primenim the output relations for a finding of efficiency of a cycle of Brighton which often meets both in parokompressionnyh cooler bodies [121], and in cooler bodies on MKE [125]. We will view this cycle for the working body possessing tske. The cycle of Brighton consists of two adiabats of 1-2 and 3-4 and two iso-field curves 2-3, 4-1 (drawing 4.9).

Further values of physical quantities in four angular points of a cycle it will be supplied with corresponding coefficients. On a site 1-2 there is the adiabatic appendix of external fields E and N which vary from values EbН\to E2, H2. The temperature of a working body (PT) thus increases from T1до T2. On a site 2-3 warmly from PT it is transmitted in a surrounding medium and PT cools down to temperature T3. On a site 3-4 external fields adiabaticheski act in film, that leads to reduction of temperature PT to value T4. On last part of a cycle 1-4 PT accepts warmth from cooled object, and its temperature rises to initiating T1. Changes of temperature T2-T1, T3-T4mogut to be calculated under the formula (8). On the remained sites 2-3, 4-1 external fields are constant also change of temperature a little. Hence, on these pieces it is possible to consider a heat capacity as a stationary value, and dependence T (S) - linear, for example, T=T4 + (S-S4) ∕C4 ↑. Then integrals in definition mozhno to exchange with the areas of corresponding trapezoids. It is as a result gained the approximate formula for evaluation ε

On known values and =karnolegko there is the relative efficiency η.velichiny, entering into the formula (4.14), can be

Are gained on the basis of experimental data. As natural ferroelectromagnetics possess small permanent-magnet coefficient the two-layer composite has been created, one of which stratums possessed piezoelectric, and another - magnetostrictive properties. The composite consisted of a stratum of piezoelectric PbZro.53Tio.47O3 and a stratum of magnetic medium Fe48Rh52. Each of stratums had a thickness of 0,2 mm. For the featured composite temperature dependence of change of temperature ∆7⅛o has been explored at MKE for a magnetic field 0,62 Tl. Then on the sample the electric field 25 has been submitted In and temperature change ∖Tμj-opri tske has been measured. Parallelly with it measurings of dependence of permanent-magnet coefficient from temperature have been yielded. On the basis of the yielded measurings in drawing 4.10 dependence MEKE on temperature has been constructed. As a result of processing of experimental data it has been gained, that quantity MEKE found on the basis of experimental data under the formula ΔT Meke = ΔT μκ s - ∖T∖i κ-), with a high degree of accuracy coincides with the theoretical quantity calculated under the formula (4.13). It proves the chosen model (4.7), (4.14) for the description tske. At calculations EKE neglected, as phase transition in TSTS occurs far from room temperatures, and in a viewed temperature gamut of its property it is possible to consider not dependent on T.Na to a bottom of the gained effects the diagramme of the relation of efficiencies ημκ 3и g] mke for tske and MKE (drawing 4.11) has been constructed.

From effects of calculation follows, that use tske in a cycle can, both to increment, and to reduce η.prichyom magnification field soderzhit a small interval from 312 to 314К, and itself uvelichivaetsja no more, than by 2 %. It is caused by that circumstance, that viewed effects are small. So, temperature change at tske and MKE does not surpass 0.12 degrees. Similar calculations for the natural ferroelectromagnetic Cr2O3, executed on the basis of theoretical dependence D (), show, that

Drawing 4.10. Dependence kaloricheskih effects from temperature for double-layer composite FeRh/ЦТС.

ημκ j> ηMK3в a wide gamut from 240К to 350К. However, change of efficiency does not surpass 1 %. In the featured materials the efficiency magnification rke occurs for the account of interaction of electrical and magnetic water. The similar effect can be expected in piezoelectric materials. Really, pezoelektrokalorichesky the effect in TSTS, caused by temperature dependence of piezoelectric coefficients, can reach some degrees [126]. Calculated on the procedure given in the present operation the odds in efficiencies tske and MKE can make to 30 % (drawing 4.11) in a temperature gamut from 510 To to 520 To.

Thus, schistose structures are rather perspective material for effective solid-state coolers. Physical properties of stratums should be picked up so that the coefficients featuring interaction of various fields (permanent-magnet,
Piezoelectric and pezomagnitnye) had appreciable temperature dependence. Mechanisms of magnification of efficiency in such structures have the evident physical nature. Effects of calculations under the formulas output in operation have shown efficiency magnification in TSTS at use μK3на 30 % in comparison with EKE, that allows to hope for working out of highly effective solid-state coolers on μK3в the near future.

Drawing 4.11. Temperature dependence of the relation of thermodynamic efficiencies for TSTS-CERAMICS. On a parenthesizing - the same dependence for composite FeRh/ЦТС.

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A source: Rodionov Vladimir Vladimirovich. MAGNETOCALORIC EFFECT of PERMANENT-MAGNET COMPOSITES ON THE BASIS OF ALLOYS Fe-Rh. The dissertation on competition of a scientific degree of the candidate of physical and mathematical sciences. Kaliningrad - 2018. 2018

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