ON THE EFFECTIVE KINETIC COEFFICIENTS OF THERMOELECTRIC NANOCOMPOSITES

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1 ON THE EFFECTIVE KINETIC COEFFICIENTS OF THERMOELECTRIC NANOCOMPOSITES Bula L.P., Osvensky V.B., Pivovarov G.I. 3, Snarskii A.A. 4, Tayanin E.V. 3, Tay A.A.O. 5 -S. Peersburg Sae Universiy of Refrigeraion, S. Peersburg, 9, Ul. Lomonosova, 900, Russia -GIREDMET, Mosow, B. Tolmahevskii per. 5, 907, Russia 3-Tehnologial Insiue of Superhard and New Carbon Maerials, 7a, Tsenralhaya S. Troisk, Mosow reg., 490, Russia 4-Naional Tehnial Universiy of Ukraine KPI, 37, Prospe Peremohy, 03056, Kyiv- 56, Ukraine 5-Naional Universiy of Singapore, 9 Engineering Drive, Singapore, 7576 Cona auhor: LBula@mail.ru Inroduion Inreasing he figure of meri is he main hallenge in hermoeleri insrumenaion ehnologies and in hermoeleri energy onversion. Apparenly highly effiien hermoeleri elemens based on planelaminaed nanosruures suh as uanum well (QW) superlaies are no sable; and o dae no laboraory in he world an repea he bes ahieved resuls. The hea diffusion proesses mos likely redue he lifeime of suh sysems. The oher hallenge is very high fabriaion os of he hermoeleri QW-superlaies. Agains o QW and QD hermoeleris bulk rysalline nanosruured omposies are probably prospeive hermoeleri maerials [-4]. Really here are a leas wo mehanisms ha an inrease he hermoeleri figure of meri σ Z = α () κ in suh nanoomposies (s is he eleri onduiviy, a oeffiien of hermoe.m.f., κ hea onduiviy): (i) elerons unneling hrough inerfaes beween nanopariles in he omposie; and (ii) addiional phonons saering on he inerfaes beween nanopariles. Influene of elerons unneling on inrease of he effiieny of hermoeleris wih fla vauum gaps where he phonons hea onduiviy is negligible, has been sudied in []. In he heoreial paper [] deail and all-round invesigaion of hermioni sruure (differene beween hermoeleri and hermioni proesses disappears in nanosruures) wih fla vauum gaps was fulfilled; he possibiliy of signifian inrease of he hermoeleri figure of meri was found. A perolaion sruures below he hreshold of ourse an be a perspeive good hermoeleri wih elerons unneling; his idea was saed in [3]. Also usage of ball milling of a rysalline hermoeleri o nanopowder sae and hen ho pressing of he powder o bulk nanoomposies was suggesed in [3]. In he reen paper [4] he value ZT =.4 a 00 C and ZT abou. a room emperaure (T absolue emperaure) was ahieved in p-ype nanorysalline bismuh animony elluride bulk alloy. These nanorysalline bulk maerials were made by hopressing nanopowders ball-milled from rysalline ingos. Auhors [4] explained inrease of ZT as he resul of low hermal onduiviy aused by he inreased phonon saering by grain boundaries and defes. Our preparaion of hermoeleri bulk nanoomposies, mehanisms of improvemen of he figure of meri, problem of alulaion of effeive kinei oeffiien of omposie medium inluding perolaion nanosruures below he hreshold of ourse and heoreial problems whih should be solved are disussed in he presen paper. I-03-

2 Preparaion of hermoeleri nanoomposies We used he following ehnologial proess for reaion of bulk hermoeleri nanoomposies: a. Fine rushing and learing of iniial maerial. The maerial should be a good radiional rysalline hermoeleri (suh as solid soluions based on bismuh elluride). We used as he iniial maerial he p-ype of Bi 0,5 Sb,5 Te 3 polyrysalline solid soluion. A B Fig.. HRTEM images of p-bi 0,5 Sb,5 Te 3 powder afer hours mehani-aivaion proessing Fig.. EDS sperum of bismuh elluride powder afer ball milling b. Weigh and high energy ball milling. We used he so alled mehani-aivaion proessing he proesses of fine rushing and homogenizaion was arried ou in a high-power and a high-speed planeary mill whih provides he effeive rushing and hashing of powders a impa of working bodies wih aeleraion up o 0g. To exlude polluion all operaions wih nanosruured powder were arried ou in he argon amosphere. HRTEM images and EDS sperum of he nanopowder are presened a Fig. and Fig. aordingly.. Exraion of he aivaed mixed powders from drums of mehanial aivaor in he argon amosphere. d. Assembly of high pressure onainers. e. Consolidaion under pressure of he aivaed powder mixes. Sinering of he powder a high emperaure and high pressure o form bulk nanoomposies. The powder mix was exposed o simulaneous influene of high pressures (P=,5GPa) and high emperaure (up o C); see Fig.3. We see from Fig., ha he average size of nanopariles afer ball milling is 0 nm, he minimal size nm and he greaes (very seldom) 40 nm. Surfaes of he nanopariles are lean (Fig. B). The lines of Cu in he Fig. onne wih he supporing grid; he rae of Fe was aused by he seel balls and he seel onainer. I-03-

3 bulk sruures o be sable and o have good mehanial haraerisis. Fig.3. Surfaes of bulk nanoomposie («NanoSan» mirosope). The area of sanning is (5.8 * 5.8) mm. The upper image he surfae are polished, he lower he same surfae afer pikling by feeble hydrohlori aid soluion. Traes of polishing are visible on a surfae (Fig. 3.); pinholes and borders of grains are no looked hrough. The sruure is homogeneous and isoropi. Afer pikling «sruural elemens» are visible; he sizes are (50 00) nm. These elemens onsis of finer formaions. The given mehod for fabriaion of bulk nanosruured hermoeleri maerials is heap enough in omparison wih preparaion of uanum wells and uanum dos hermoeleri nanosruures. Moreover here exis ways o make suh Effeive kinei oeffiiens To sudy he eleron unneling he orresponden oeffiien of ransparene of a poenial barrier should be alulaed as he funion of he barrier s widh and he work funion of a maerial. If we have vauum gap beween nanopariles he work funion is eual o few ev, and a he room emperaure he gap should be less hen 5-0 nm for effeive unneling. However suh gap is sill large omparing wih ineraomi disane, herefore phonons an no move hrough he gap. Then he oal hea onduiviy κ = κ + κ he sum of elerons and ( e p phonons hea onduiviies) will redue in omparison wih he iniial bulk maerial. So he figure of meri () will inrease. If he gaps beween nanopariles filled by solid layers (semionduor or oxide) he work funion will be redued up o few enh of ev [5,6]. In his ase phonons will ake par in he hea onduiviy bu he onribuion of phonon hea ranspor will be less han he phonon hea onduiviy of he iniial bulk maerial. Addiional phonons saering on he inerfaes beween he nanopariles will also redue he phonon hea onduiviy; he onribuion of his mehanism hardly gives in exa alulaion. The sruure of he nanoomposies an be simulaed as a se of elemenary idenial ells sruural elemens. The kinei oeffiiens of eah ell should be alulaed aking ino onsideraion he uanum unneling and he addiional phonon saering. Then he effeive kinei oeffiiens (EKC) of hermoeleri nanoomposies of he bulk sample an be alulaed. Properies of marosopi inhomogeneous medium in whole are desribed by EKC. Aording o definiion EKC relae among hemselves average on volume he hermodynami flows and he generalized fores [7]. I-03-3

4 The hermoeleri effes is an example of he physial phenomena, when wo hermodynami flows ( j densiy of an eleri urren and densiy of hea flow) are reaed simulaneously by wo hermodynami fields: E - eleri field and Т emperaure gradien j=σ E+σα( T ), () =σα E +κ ( + ZT )( T ) T Then EKC an be deermined as oeffiiens ha onne he volume average of hermodynami fields and flows. ì j = s * E + s * a * - ÑT, ï í ï = s * a * E + k *( + Z * T) - Ñ T (3) ïî T s * a * Z* T = T k * he aserisk means EKC of a omposie. As we see he figure of meri of omposies deermines by EKC, and here orre alulaion is he key problem o invesigae he effiieny of omposies. Calulaion of EKC represens raher a hallenge problem whih in no solved ill now in a general form [7,8]. The soluion of he problem of deermining of EKC srongly depends on a form of inhomogeneiies. The ask appears espeially diffiul if we deal wih doubleflow sysem as in hermoeleriiy. In some ases he mehod [9] an be used ha allows o redue double-flow problem wih ross omposed o single-flow problem, for example o alulaion of onduiviy. So his mehod allows esablishing exa onformiy (isomorphism) beween problems on finding EKC for sysem wih he hermoeleri phenomena and he effeive eleri onduiviy in a media wihou hermoeleri phenomena (see also [7]). EKC of perolaion sruures One of varians of marosopi inhomogeneous medium is he perolaion sruure. Suh sruures are very ineres for our porpoises beause hey give a basi possibiliy of signifian inreasing he figure of meri of nanoomposies. Really, le us reae a omposie maerial wih he perolaion sruure below he hreshold of ourse. I is known ha he number of so alled single disonneed bonds below he hreshold of ourse inrease wih onoming o he hreshold of ourse p as N ( p p) a =, where parameer a has he order of one. I is known also ha he role of single disonneed bonds an play unnel junions. I is known also ha effeive eleri onduiviy σ * above and below of he hreshold of ourse p is a degree funion on affiniy o he hreshold of ourse τ = ( p p ) / p as a firs approximaion: σ * σ * σ τ, τ > 0, τ, τ < 0, σ σ σ where and - riial indexes of onduiviy higher and lower hen p ; in praially ineresing, hree-dimensional ase, hey gave values: =.0, = The behavior of effeive hermo-e.m.f α * a he ases κ κ and κ κ are ualiaively differs (he indexes and are numbers of phases in a omposie). In he ase κ and when κ σ + ασ ake σ ασ he ineualiies plae, he oeffiien α * essenially hanges in he riial area (Fig. 4): ìï (I) a*» a, р> р, a s a s, D s æ a s ö - (II) a* a, p p, = > D s a s ç ï è ø í + æs ö (III) a* a = a, s = D <D ç è ø ï ïî (IV) a* = a, p< p, D where ( σ / σ ) + = he area of spreading, ( ) / τ = p p p. I-03-4

5 Fig 4. Conenraion dependene of effeive hermo-e.m.f. in he riial area if values of hea onduiviy of phases are lose κ. κ Oherwise, when hea onduiviies of phases onsiderably differen ( κ κ ) hanging of α * from α up o α ours in he riial area, Fig.5: α + (I) α* α, τ, p> p α σ α + (II) α* α, σ α (III) α* = α, τ < + (IV) αe = α, τ, p< p ( + ) τ τ, p> p Fig.5. Conenraion dependene of effeive hermo-e.m.f. in he riial area if α α, ασ ασ and σ / σ = κ / κ. Exep of onenraion dependenes of usual EKC (eleri and hea onduiviies and hermo-e.m.f.) he signifian ineres represens he hermoeleri figure of meri of a omposie. If he loal figure of meri of phases Z and Z are small he effeive one Z *( p ) has usual properies. Really Z *( p ) inrease wih inrease of hermoe.m.f. of phase/phases, i inrease wih derease of hea onduiviy of phase/phases, and Z *() p inrease wih inrease of Z and Z. As i appeared suh endeny is fair only for small values of loal figure of meri [0]. I an be shown ha for ases of large loal figure of meri Z *( p ) anno be higher han some erain value, even a somehow large figure of meri of one of phases. Theoreial problems whih should be solved A oordinae dependene of emperaure = r is negleed a sandard T T() alulaion of hermoeleri EKC; his approximaion gives an opporuniy o solve he problem, and i is possible only if a emperaure gradien is small enough. I is obvious ha in various geomerial sruures he rierion ha gradt is small an be ompleely various. Espeially ompliaed is he uesion abou smallness of gradt near o he hreshold of ourse. Here on he basi geomerial elemens of perolaion sruures single onneed bonds and single disonneed bonds [7] onsiderable urrens, volage and emperaures differenes are onenraed. Espeially ompliaed is he uesion abou a smallness of gradt near he hreshold of ourse. Aordingly, ourrene large gradt here is possible []. Then he rierion of smallness of gradt should inlude no only an average emperaure gradien, bu also loal gradiens. On he oher hand he neessiy of aoun of emperaure dependene of loal kinei oeffiiens always akes plae in real semionduors. If we an ake ino aoun suh emperaure dependene of I-03-5

6 kinei oeffiiens a fixed average gradt he value of loal kinei oeffiiens will be differen in differen poins of a sample. Therefore i is impossible o use suh essenial onep as homogeneiy in a whole o deerminaion of EKC (in oher words, he onep of orrelaion lengh an no be used). I means ha we an no inrodue orre definiion of EKC in his ase. The oher problem is he anisoropy of loal kinei oeffiiens. The mehod of isomorphism for a biphase hermoeleri medium anno "onsul" wih he siuaion, when one (or boh) phases have anisoropi ranspor properies. The speifi ineres is represened wih researhes of EKC near he hreshold of ourse for omposies formed from pariles wih he differen sizes. This problem is no invesigaed ye even for he simples siuaion "pure" onduiviy. This problem is espeially imporan beause differen sizes have nanopariles in sudies hermoeleri nanoomposies. The lose one is he problem abou layers beween rysallies in polyrysals when omposies made from pariles wih an enlosure. In his ase one of phases he enlosure, oupies uie deermined (insead of asual, as in usual models) posiion onerning anoher. For a biphase bidimenional ase wih deermined, srily periodi arrangemen of pariles wih an enlosure suh problem was sudied in []. 5. Mahan G. D. and Woods L. M. Phys. Rev. Le. 998, v.80, No.8, p Mahan G. D., Sofo J. O., Barkowiak M. J. Appl. Phys. 998, v. 83, p Snarskii A.A., Bezsudnov I.V., Sevryukov V.A. Transpor proesses in unordered mediums. Mosow, URSS, 007, 303 p. (In Russian). 8. Snarskii A.A., Bezsudnov I.V. J. of Thermoeleriiy, 005, No. 3, p Sraley J.P. J. Phys. D. 98, v.4, p Snarskii A.A., Zenirovskii M.I. Semionduors, 008, v.4, p. 8.. Anayhuk L.I., Bula L.P. Semionduors in exreme emperaure ondiions. S. Peersburg, Nauka, 00, 4. (In Russian).. Balagurov B.Ya., Kashin V.A. Zurn. Tekhn. Fiz., 00, v. 7, p. 00. Referenes. Lidorenko N.S. e al. DAN SSSR, 969, v. 85, p Hishinuma Y, Geballe T.H., Moyzhes B.Y, Kenny T.W Appl. Phys. Le. 00, v.78. p Bula L.P, Pivovarov G.I., Snarskii A.A. In Thermoeleri and is appliaions. S. Peersburg Ioffe Physio-Tehnial Insiue, 006, p.36. (In Russian). 4. Poudel B., Hao Q., Ma Yi e el. 0 Marh 008 / Page /0.6/siene I-03-6