Characterization of Electromaterials using ac Impedance Spectroscopy


 Barry Day
 1 years ago
 Views:
Transcription
1 BOLETÍN DE LA SOCIEDAD ESPAÑOLA DE Cerámica y Vidri A R T I C U L O DE REVISION Characterizatin f Electrmaterials using ac Impedance Spectrscpy DEREK C SINCLAIR Departament f Chemestry. University f Aberdeen, Mestn Walk, Aberdeen, U. K. AB9 2UE Caracterización de electrmateriales mediante el emple de espectrscpia de impedancia Se discute y revisa la tería básica de la espectrscpia de impedancia y se expnen varis ejempls de electrmateriales/dispsitivs, dnde las medidas de impedancia cmpleja dan una excelente infrmación, que n puede ser btenida pr técnicas ac y de cnvencinales. Se hace énfasis en las técnicas avanzadas de adquisición y elabración de dats; pr ejempl la cmbinación de ls diagramas de espectrscpia de impedancia cn la espectrscpia del mdul eléctric, para caracterizar eléctricamente materiales cerámics inhmgénes cm ls materiales basads en BaTi3 que sn resistencias cn ceficiente de temperatura psitiv. Se presenta un análisis eléctric detallad de mncristales ferreléctrics de L Ta3 en función de la rientación cristalgráfica. Ls resultads demuestran la utilidad de la técnica de impedancia para visualizar prcess tan cmplejs cm la inversión de dminis en materiales ferreléctrics. Se discute también el us de estas técnicas insitu para mntrizar variacines en las capas intercaras en las intercaras electrdelectrlit en las baterías de liti de estad sólid. Palabras clave: Electrmateriales, Espectrscpia de impedancia, Espectrscpia de módul eléctric. The basic thery f ac impedance spectrscpy is reviewed and then several examples f electrmaterials/devices are discussed where ac impedance measurements have prvided infrmatin which is nt readily available frm dc r cnventinal fixed frequency ac measurements. Emphasis is given t advanced data handling techniques, such as cmbined impedance and electric mdulus spectrscpic plts fr characterising electrically inhmgeneus ceramics such as psitive temperature cefficient f resistance BaTi3 ceramics. A detailed electrical analysis f ferrelectric LiTa3 single crystals as a functin f crystallgraphic rientatin is presented. These results demnstrate the usefulness f the technique in mnitring cmplex prcesses such as dmain reversal in ferrelectric materials. The use f insitu ac impedance measurements t mnitr variatins in interfacial layers at electrdeelectrlyte interfaces in slid state lithium batteries is als discussed. Key wrds: Electrmaterials, Impedance Spectrscpy ElectricMdulus Spectrscpy. 1. INTRODUCTION Electrical applicatins f slidstate materials cver the cmplete spectrum frm electrical insulatrs t supercnductrs. The desired prperties are many and varied but can be subdivided int fur main categries: (i) ntragranular r "bulk" prperties, e.g. high levels f inic cnductivity, such as Na"*" in cnductin in betaalumina ceramics, used as an Na"*" in cnducting membrane in Na/S batteries ^'^ (ii) intergranular r ''grain bundary" prperties, e.g. resistive grain bundary cmpnents and cnducting cres, such as dped SrTi3 internal barrier layer capacitrs ^^\ (iii) a cmbinatin f bth inter and intragranular prperties, e.g. psitive temperature cefficient f resistance (ptcr) devices, such as dnrdped BaTi3, which depend n resistive grain bundary cmpnents and ferrelectric semicnducting grains ^^\ r (iv) surface prperties, e.g. gas sensrs ^^\ such as Sn2. Invariably these hightechnlgy ceramics require specialised knwledge regarding the structural, cmpsitinal, ceramic prcessing and electrical behaviur í the material(s) in questin. Cnsequently there are many aspects f electrceramics which need t be studied and cmbined in rder t btain a cmplete characterisatin f the material under investigatin. By far the largest applicatin f ferrelectric materials is the develpment f varius types f capacitrs ^^\ All these devices rely n the material being an electrical insulatr with a large bulk permittivity value. In recent years, ferrelectric materials have fund increasing applicatin in ther diverse areas f electrceramics and cmpsite materials, namely as ptcr devices, pyr and piezelectric sensrs and electrptic devices. As further applicatins f these plar slids emerge, characterisatin f their behaviur, by existing and new techniques becmes imperative. The tw main techniques emplyed in the characterisatin f electrceramics are micrscpy and electrical measurements. Scanning, SEM, and transmissin micrscpy, TEM, are cmmnly emplyed t characterise the micrstructure. Advanced techniques, such as dark and bright field imaging have been develped in recent years t detect thin layers, 1 nm, f amrphus Bl. Sc, Esp. Cerám. Vidri, 34 [2] (1995) 55
2 DEREK C. SINCLAIR secnd phase material in the grain bundary regins f electrceramics ^^\ such as ZnO varistrs. Cmbining such techniques with EDAX, energy dispersive analysis f Xrays, allws the cmpsitin f these regins, r the distributin f a dpant between the bulk and grain bundary regins t be determined. Decratin techniques, such as integral, ICL, and spectral, SCL, cathdluminescence have been develped t make grain bundary ptential barriers visible in materials such as ptcr BaTi3 {7ß)^ These techniques, which ''bridge the gap" between micrstructural and electrical measurements, depend n the number f electrns in the cnductin band. Resistive regins appear dark whereas cnductive regins are bright. Thus, resistive regins in a ceramic may be identified by cmbining CL techniques and electrn micrscpy. These techniques are becming increasingly ppular in characterising the micrstructure f many electrceramics. DC electrical measurements, tw r fur terminal, are the mst cmmnly emplyed methd f establishing electrical characteristics f electrceramics, althugh they are nt the mst cnvenient methd f btaining inter and intragranular resistance values. Recently, several grups (^/'O) have develped techniques invlving micrelectrdes which permit direct measurements f the resistances assciated with individual grains and grain bundaries. Such techniques are extremely useful but are very difficult t implement experimentally. A much mre cnvenient methd in which t separate surface, grain bundary and bulk cmpnents f a material is t emply ac impedance techniques ver a wide frequency range, 1"^ t 1'^ Hz. Althugh this technique is cmmnly emplyed t establish the bulk resistance f slid electrlytes ^^ ^\ applicatins f this technique t grain bundary r interfacial layer dminated electrmaterials/devices, such as ZnO varistrs, ptcr devices and slid state batteries, etc., r t ferrelectric materials have been limited. In the present paper, the basic thery f ac impedance spectrscpy is reviewed and several applicatins f the technique discussed in rder t demnstrate hw ac impedance spectrscpy can, under certain circumstances, yield infrmatin abut electrmaterials/devices which is nt readily available frm dc r cnventinal, fixed frequency ac measurements. 2. AC THEORY AC impedance methds have been widely used t characterise electrical materials ('2/'3) ^^^j electrdeaqueus electrlyte systems ^'^^\ The mst cmmn methd emplyed t study the ac respnse f a test system, i.e. an electrdematerial arrangement, is by the direct measurement f the impedance in the frequency dmain. The impedance f any system is defined as Z = V^/IQ and usually cntains bth resistive (R) and reactive (L and/r C) cmpnents, bth f which must be determined. By applying a single frequency vltage V = VQ.sin(ct), where c represents the angular frequency 2Tcf, acrss the test system, the phase shift and amplitude f the resultant current i = lq.sin(cût i ( )) can be determined. Unless the test system behaves as an ideal resistr there will be a phase difference, ( ) between the applied vltage and the resultant flwing current. The phase shift is related t the reactive cmpnent f the system. In general, bth the magnitude (resistive) and phase shift (reactive) f the impedance f a sample is frequency dependent. Impedance is a vectr quantity which can be defined as a cmplex number, whse magnitude and directin can be expressed by real, Z' and imaginary, Z" cmpnents. Z* = Z' (resistive) jz" (reactive) where j = V1. Three ther cmplex frmalisms can be measured r derived frm the cmplex impedance: (i) The cmplex admittance, Y, r A, is defined as the inverse f the cmplex impedance, Z : Y = (Z )' =Y' + Y'\ The real cmpnent, Y', is mre cmmnly knwn as the cnductivity, G. (ii) The cmplex electric mdulus, M, is related t the cmplex impedance, Z*, thrugh the relatin: M* = JCOCQZ* = M' + M" where CQ = e^a/l is the vacuum capacitance f the empty measuring cell with electrde area. A, and separatin, I. The permittivity f free space 8Q = x 1"^^ Fcm"^. (iii) The cmplex permittivity, 8*, can be defined as the inverse f the cmplex electric mdulus, M*: * = (M*)"'^ = Y*(JCOCQ)'' = 8' + 8''. Althugh the fur basic frmalisms are interrelated they can be subdivided int tw sets, i.e. (Z*, M*) and (Y*, 8*) frm the equatins abve. The main effect f the transfrmatin within each set is t exchange the real and imaginary cmpnents n multiplicatin byco, as shwn abve. Thus, all fur frmalisms are valuable, because f their different dependence n, and weighting with, frequency. It is this feature f versatility, where the varius plarisatin and charge transfer prcesses which ccur in a test system, ver the measured frequency range, are highlighted by different frmalisms, which gives ac techniques such pwer in the studies f electrical prperties f matter. There are varius frms in which the data may be pltted: (i) a lcus f pints in the cmplex plane, i.e. imaginary against the real cmpnent, (ii) a spectrscpic plt, i.e. the real and imaginary cmpnents as a functin f lg (f), (iii) a cmbined spectrscpic plt, i.e. the real r imaginary cmpnents f the different frmalisms as a functin f lg (f), (iv) a three dimensinal plt, with lg (f) perpendicular t the cmplex plane. Despite this versatility, the majrity f wrkers present the ac respnse f dielectric/ferrelectric and cnducting materials nly in the 8* and Z* planes, respectively. The different regins f a test system are nrmally characterised by a resistance and capacitance, usually placed in parallel. The characteristic relaxatin time r time cnstant, x f each parallel RC element is given by the prduct f R and C, i.e. T = RC. In the frequency dmain, RC elements are separable due t the relatinship coppigx'^^  ^ which hlds at the frequency f the maximum lss, ^^x/ '"^ ^^^ impedance spectrum. Frm the impedance spectrum, it is usually pssible t identify different RC elements, based n the capacitance values, and assign them t the apprpriate regins f the test system. The values f the individual R and C cmpnents may then be quantified. In this analysis, different physical features in the test system are represented by layers f varying thickness, as in Maxwell's mdel f the layered dielectric ^^^^ (fig. 1). This mdel assumes that the permittivity f the varius regins, namely, any surface layer adjacent t the electrdes, the grain bundary regins and the grain interirs, all have the same value. The equatin fr a parallel plate capacitr is defined as: C = 8'CQ where 8' is the permittivity f the material placed between the plates and CQ is the vacuum capacitance. The capacitance values assciated with these three regins discussed abve differ nly in the value f I. Differences in capacitance are therefre, a direct 56 Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril 1994
3 CARACTERIZACIÓN DE ELECTROMATERIALES MEDIANTE EL EMPLEO DE ESPECTROSCOPIA DE IMPEDANCIA ELECTRODE 1 ELECTRICAL DOUBLE LAYER GRAIN BOUNDARY CRYSTAL GRAINS Figure 1. Physical representatin f a sample/electrde arrangement in terms f Maxwell's layered dielectric mdel. result f the relative thickness f each regin. The grain bundary regins are 1"^  1""^ and the electrde interface < ^~^, f the cell length. Typical capacitance values and their pssible interpretatin fr a unit cell are listed in table I. Thus, small capacitance values e.g. 1"^ ^ Fcm"^ are assciated v^ith large vlume fractins, i.e. bulk material, whereas larger capacitances, e.g. 1"^ Fem"' t 1"^ Fcm"^ are assciated with prgressively smaller vlume fractins r with the bulk respnse f ferrelectric materials with large values f permittivity. These "rder f magnitude" values enable a crrelatin between the bserved electrical prperties and the varius regins within a test system. TABLE I. CAPACITANCE VALUES AND THEIR POSSIBLE INTERPRETATION"^' Capacitance/ Fcm"^ 112 bulk Phenmenn Respnsible 111 minr, secnd phase Ö grain bundary 11 _ 19 bulk ferrelectric near Tç. (Curie Temperature) surface layer sampleelectrde interface 14 electrchemical reactins The central prblem assciated with ac measurements arises ver the interpretatin f the data cllected. The ac respnse fr a test system defines nly the relatinship between the applied vltage and the current thrugh the test system, as a functin f frequency. The physical nature f the test system i.e. single crystal, plycrystalline, blcking r nnblcking electrdes, etc, and its electrical prperties i.e. inic, electrnic r mixed cnductr, ferrelectric, etc, must be cnsidered. Plausible equivalent circuits, i.e. sme netwrk cntaining ideal resistive and reactive cmpnents may then be suggested which can represent these prperties f the system and mdel the cllected data. There are materials whse electrical behaviur is such that ideal resistive and capacitive circuit elements are inadequate t describe the ac respnse. This has led t the intrductin f distributed impedance elements ^1 ^'' ^\ e.g. CPE, the cnstant phase element. which "mix" "ideal" resistive and reactive elements t mdel the bserved respnse. The degree f success in any ac analysis depends n hw well the experimental data fit that predicted by an apprpriate equivalent circuit. An equivalent circuit that cntains three r mre elements may be rearranged in varius cmbinatins but still yield the same verall ac respnse. This leads t the ntin that there is n unique equivalent circuit fr a particular test system. The values f the elements fr the circuits have t be different in rder t yield the same verall respnse. Thus, the prblem arises as t which equivalent circuit shuld be emplyed fr the analysis and interpretatin f the electrical behaviur f a test system. Usually, the equivalent circuit is chsen based n the fllwing: (i) intuitin as t what kind f impedances are expected t be present in the test system and whether they are cnnected in series r parallel, (ii) examinatin f the experimental data t decide whether the respnse is cnsistent with the prpsed circuit, (iii) inspectin f the R and C values that are btained in rder t check that they are realistic and their temperature dependence, if any, is reasnable. The equivalent circuit shwn in figure 2 is widely used t represent bulk and grain bundary phenmena in plycrystalline materials. It is desired t separate each f the parallel RC elements and measure their cmpnent R and C values. This is best achieved using a cmbinatin f the impedance and electric mdulus frmalisms since each parallel RC element gives rise t a semicircle in the cmplex plane ( Z" vs Z'; M" vs M') r a Debye peak in the spectrscpic plts f the imaginary cmpnent ( Z", M" vs lg f ). This is seen frm the equatin fr the impedance f the circuit: Z* = (1/Ri + jcci)! + (I/R2 + jcc2r'' Z* = Z'  jz" where r = Ri/{1 + (côrici)2} + R2/ÍI + (cûr2c2)2) and Z" = R, [crici/{1 + ((RiCi)2}] + R2[(R2C2/{1 + (cûr2c2)2)] The crrespnding equatins fr M' and M" are btained by substituting int the equatin M* = JCOCQZ*. These are M' = (C/Ci).{(cRiCi)2/(1 + ((RjCi)2)l+ (C/C2).{((ûR2C2)2/ (1 + ((ûr2c2)2)l and M" = (CQ/CI).[(ORICI/{1 + (crici)2)] + (C/C2).[cûR2C2/ 11 + (CR2C2P)] Nte that the terms in square brackets fr the Z" and M" cmpnents is a mathematical representatin f a Debye peak. The respnse f this circuit in the tw cmplex plane plts is shwn in figure 3. Fr cnvenience and t illustrate the relative weightings that impedance and mdulus plts apply t data, the values f Ri and R2 are chsen t differ by a factr f 1, but the capacitances are chsen t be equal. In the cmplex impedance laaa/v I R2 wwv Figure 2. An equivalent circuit cmmnly used t represent the electrical prperties f a plycrystalline material. The subscripts 1 and 2 refer t electrically distinct regins within the material, e.g. bulk and grain bundary cmpnents. Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril
4 DEREK C SINCLAIR Z" / MQ 6 (a) I AAW^ I AMW, C^ = 112F C2 = 112F RTRI R, = losfi R2 = 16a A Z'/Ma CR2C2 = 1 Figure 3. Cmplex impedance (a) and electric mdulus (b) plane plts fr the circuit shwn. Z" / MQ M" C, = I12F C F /; > ^ / \ r 1 \ \ M" / \ i.4.3 ~.2 t _ ^ I I. [ J^L 1 1 1^ 1^ 1^ 1' 1' 1' 1^ 1'.1 Figure 4. Impedance, Z", and electric mdulus, M'\ spectrscpic plts against frequency, ( = 2ïïf fr the circuit shwn. plane, a single semicircle is seen since the impedance respnse is dminated ttally by the parallel RC circuit with the larger resistance, R. In the mdulus plane, tw semicircles, f equal size, are seen because the mdulus respnse is dminated by the RC element with the smaller parallel capacitance, and in this case, the capacitances are equal. The spectrscpic plts shw a similar effect, figure 4, with a single peak in Z" but tw peaks in M". An advantage f the cmbined Z", M" plt such as this is that the M", Z" peaks fr a particular RC element shuld be cincident n the frequency scale, as indeed they are fr the lwer frequency f the tw peaks. A rapid assessment can therefre be made frm a visual inspectin f such a cmbined plt. This cmparisn is nt s easy t d fr the cmplex plane plts since, whereas the Z* plane plt terminates at the rigin at the high frequency limit, the M* plane cmmences at the rigin at the lw frequency limit. The frequencies f peak maxima in Z" and M" spectrscpic plts are given by the respective relaxatin time cnstants fr the given parallel RC element. The RC prduct fr each peak is a fundamental parameter as als is the value f copp^x ^'^'^ '^ because the RC prduct is usually independent f the gemetry f the regin respnsible fr the RC element. In the particular example shwn in figures 3 and 4, the mdulus plts shw up bth parallel RC elements, whereas the impedance plts nly shw the mre resistive element. On varying the magnitudes f R and C cmpnents, hwever, different situatins may arise. Fr instance, if ne f the capacitances is much larger than the ther, its assciated peak and semicircle will effectively disappear frm the mdulus plts. The key pint in determining whether RC elements are detected depends n which plt is used and the relative magnitudes f the capacitances. Thus mdulus plts give emphasis t thse elements with the smallest capacitances, whereas impedance plts highlight thse with the largest resistances. The respnse in the Z* plane fr a single parallel RC element ideally takes the frm f a semicircular arc which passes thrugh the rigin and gives a lw frequency intercept n the real axis crrespnding t the resistance, R f the element, figure 5. In practice, semicircles assciated with bulk relaxatin prcesses in the Z* plts f many cnducting materials and in the 8* plts f dielectric (insulating) materials, are fund t be nnideal. Depressed semicircles are btained whse centres are displaced belw the real axis; they ccur fr bth single crystal and plycrystalline materials. There are tw main reasns fr such nnideal behaviur: (i) the presence f a distributin in relaxatin times within the bulk respnse, and (ii) distrtin by ther relaxatins, e.g. grain bundary relaxatins, whse time cnstants are within tw rders f magnitude f that f the bulk. These reslutin prblems can limit smewhat the use f ac techniques in characterisatin f individual electrical and electrchemical prcesses. Curve fitting prgrams fr tw verlapping arcs and mre generally, cmplex nnlinear least squares (CNLS) analysis can be emplyed ^'^' ^^^ in an attempt t vercme such prblems. In general, metal electrdes are applied t inic and electrnic cnducting materials. Fr inic cnducting materials there are tw extreme types f metal cntacts, blcking and nnblcking. Gld electrdes are cmmnly emplyed and are blcking. Fr Li''"cnductrs, the gld/li"*" cnductr interface has been mdelled by a vltage independent parallel plate capacitr ^^^' ^ ^^ The mdel cnsists f an electrnically charged metal surface in direct cntact with an equal but ppsitely charged Li^ layer residing within the first atmic layer f the Li"*" cnducting material. Several assumptins are made in this mdel; namely, n specific adsrptin r in migratin t r frm the interfaces ccur and that the uter surfaces f the material are smth and cntain n vids. Figure 5 (a) summarises the equivalent circuit and ideal ac respnse in the Z* plane fr a single crystal inic cnductr with blcking electrdes. The semicircular arc, with intercepts n the real axis at and R, represents the respnse f a parallel RjCj bulk element. At lw frequencies the Z* plane respnse is dminated by the blcking nature f the electrde interface, where Z" = 1/cC. This respnse is illustrated by a vertical lcus f pints, ften referred t as an electrde ''spike'', in which Z" decreases with increasing c. This data can be mdelled by an equivalent circuit whereby the bulk parallel RC element is cnnected in series with an ideal capacitr which represents the blcking nature f the electrde interface. In practice, hwever, electrde cntacts are jagged and cntain 58 Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril 1994
5 CARACTERIZACIÓN DE ELECTROMATERIALES MEDIANTE EL EMPLEO DE ESPECTROSCOPIA DE IMPEDANCIA Figure 5. Cmplex impedance plts and equivalent circuits prpsed fr materials exhibiting bulk; (a) inic cnductin with blcking electrdes, (b) electrnic cnductin with hmic cntacts and (c) infinite, Warburgtype inic diffusin with an assciated charge transfer element, ^2^2 This results in an inclined lw frequency spike in the Z* plane plt f angle ca. 7i/6 t TÍ/I. In additin t an inclined spike, a lw frequency semicircle is cmmnly bserved in the Z* plane plt, figure 5 (c). This respnse, with an assciated capacitance in the rder f 1'^Fcm"^, permits a resistance value (R2 in figure 5 (c)) fr the charge transfer mechanism f the mbile ins between the electrde/sample interface t be calculated. Partial blcking behaviur f gld electrdes als nrmally identifies inic cnductin within a sample. An inclined spike f angle 7r/4, where IZ'I = IZ'1 invlves infinite diffusin f the mbile species int the electrde material. This type f respnse is cmmnly referred t as Warburgtype behaviur, and is represented by the symbl W in equivalent circuit analyses, figure 5 (c). The varius cmbinatins f electrde behaviur likely t ccur fr inic cnducting materials with bth negatively and psitively charged cnducting species, their equivalent circuits and ac respnse in the Z* plane have been extensively reviewed in the literature ^^^' ^^^ and are utside the scpe f the present paper. Fr electrnic materials such as insulatrs, semicnductrs and metals there are als tw types f electrde behaviur, referred t as hmic and nnhmic cntacts. Ohmic cntacts prduce a minimum ptential drp at the electrde interface when current is flwing thrugh the material. Ohmic cntacts are achieved by careful matching f the cntact ptentials, r wrk functins (^6) f the material and metal electrde. Failure t match the cntact ptentials results in the creatin f ptential barrier at the interface. This results in a measurable ptential drp at the electrde interface and is referred t as a cntact resistance. Such electrdes are called nnhmic cntacts and wuld give rise t a lw frequency semicircle in the Z* plane plt. In summary, the lw frequency respnse in the Z* plane can usually prvide infrmatin n the nature f the predminant charge carriers respnsible fr the bserved electrical cnductin and n the physical prcesses which ccur at the sample/electrde interface. 3. APPLICATIONS OF AC IMPEDANCE SPECTROSCOPY electrically pen and clsed circuits as well as a hst f adsrbed and freign species, all f which influence the lcal electric field. In general, the interface impedance is partly resistive and partly capacitive. This results in a lw frequency electrde spike in the Z* plane whse angle is less than 7i/2. T mdel such systems ften requires the use f CPE's r transmissin lines t accunt fr any frequency dispersin f the electrde respnse (2325) \^ ^ ^g ppg_ sent paper such cmplexities are ignred: instead, blcking electrde interfaces are represented as duble layer capacitances in series with the sample impedance. Nnblcking r reversible electrdes allw cnductin f bth electrns and mbile ins, at very high discharge rates, acrss the electrde/sample interface. Since there is n charge buildup r plarisatin, such as ccurs with blcking electrdes, C \ = and the Z* plane respnse des nt cntain a lw frequency spike, figure 5 (b). Fr gld electrde systems this behaviur wuld nrmally identify electrnic species as the predminate charge carriers f a sample. In ther cases, the rates f discharge f mbile ins at the electrdes may be slw enugh t be measurable; such electrdes are said t be partially blcking. In this case, finite r infinite diffusin f the mbile charge carriers ccurs int the electrde material. In this sectin three applicatins f ac impedance spectrscpy are discussed. (I) SlidState Lithium Batteries AC Impedance techniques prvide ne pssible means f mnitring the cell perfrmance f slid state batteries, e.g. Li [ande] / (PEO).LiCF3S3 [ plymer electrlyte] / V5O13 [cathde] and fr yielding infrmatin n the chemical reactins and interfacial effects that ccur during cell assembly and peratin. Such techniques are cmmnly used t mnitr plymer electrlyte cnductivity and the frmatin f passivatin layers at the ande/electrlyte and/r cathde/electrlyte interfaces (2729) An effect in these cells that has nt been explained satisfactrily cncerns their pen circuit vltage (OCV) behaviur. Immediately after assembly and heating t their nrmal perating temperatures, e.g. 12^C, cells with plyethlene xide electrlytes, e.g. PEO.LÍCF3SO3 have reprducibly high OCV values, e.g. 3.65V at 12^C fr cells cntaining V5O13  based cathdes. On standing, hwever, the OCV quickly falls befre levelling ut t a steady value, e.g. 3.2V fr V^O] 3. In a previus study we ^^^"^ were invlved in using ac impedance spectrscpy t mnitr the OCV stabilisatin perid. Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril
6 DEREK C. SINCLAIR 4 I 31 O Fg 2 h 1 ( a ) U/PEO. LÍCF3SO3/cathde 12^C. OCV = 3.52V R, Ri + R2 V^^.1 '^ «J I I I [ \ \ \ \ I Z' hm R/hm 3, 2,5 2, 1,5 (b) Equilibratin f cell : U/PEO. LÍCF3SO3/ cathde at 13 C "] I! I I ( c ) Li / PEO, LÍCF3SO3 / cathde 1, 5 3 r OCV/V 4 (d J I U C. ti^ht^ H/V I^VNAAJ L_A^AAJ R2 1K/T Figure 6. (a) Cmplex impedance plane plt at UO^C fr a freshly prepared cell, (b) Resistances R^ and R2 against OCV during the OCV stabilisatin and (c) their variatin temperature, (d) The equivalent circuit used t mdel the ac impedance data. with The cmplex impedance spectra had a similar frm thrughut the equilibratin perid t that btained initially, figure 6 (a). This cmprised a single semicircle with a lw angle spike at lwer frequencies. The high frequency end f the semicircle clearly did nt pass thrugh the rigin and gave a nnzer intercept, Rj. Frm the lw frequency intercept n the real, Z' axis, a secnd resistance, R2 culd als be btained, as shwn. During the perid f OCV stabilisatin, the resistance R2 decreased markedly, by between 1 and 2 rders f magnitude, as shwn in figure 6 (b), but Rj shwed little, if any, variatin. The capacitance C2 was als essentially unchanged thrughut, with a value f 31±8nF. In rder t gain further insight int the rigins f the tw resistances R and R2/ ac impedance measurements were made ver the temperature range ambient t 12OC. A Li/(PEO).LiCF3S3A^5i3. cell was left at 12 C fr tw days and then cled slwly t rm temperature ver a perid f 24h. The ac measurements were then made n the reheating cycle. Results are given in figure 6 (c) in the frm f lg cnductance versus reciprcal abslute temperature (n crrectins were made fr the cell cnstants). The resistance R shwed marked nnlinear behaviur, with a change in slpe at abut 7^C, characteristic f PEO electrlytes. The R2 data, by cntrast, shw essentially linear temperature dependence with n discntinuity. The impedance data btained belw 5^C cnfirmed that R was the bulk resistance f the electrlyte. An additinal high frequency semicircle was als seen between the rigin and the intercept Rj in the impedance plts, nt shwn. This had an assciated capacitance value cnsistent with the bulk capacitance f thin layer cells. Symmetric ande and cathde cells, e.g. Li/PEO.LiCF3S3/Li were prepared and their ac impedance recrded at different temperatures ver the range 25 t 12^C. Only the symmetric ande cells shwed evidence fr the semicircular arc at intermediate frequencies, characterised by the R2 C2 element. The ac impedance results n cells with different electrdeelectrlyte cmbinatins enables identificatin f certain features f the cells. The impedance data may be analysed in terms f the ideal equivalent circuit shwn in figure 6 (d). The resistance R represents the electrlyte resistance and is shunted by the cell gemetric capacitance, Cj. Given the gemetry f the cells, a value f C in the range 33pF is reasnable. Arrhenius plts f the [R ]"^ values were f a similar frm and, by cmparisn with literature reprts, R is cnsistent with the resistance f the plymeric electrlyte. The parallel R2C2 element f figure 6 (d) was evident nly in the impedance data fr cells cntaining at least ne lithium electrde. The presence f this element is therefre interpreted in terms f the Li/electrlyte interface. The magnitude f the capacitance C2, in the range 34nF, suggests a thin layer extending ver the range 6 Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril 1994
7 CARACTERIZACIÓN DE ELECTROMATERIALES MEDIANTE EL EMPLEO DE ESPECTROSCOPIA DE IMPEDANCIA 1 I ^ ^ T" (a) C S N ^ O ^ 1 1 J 1 e 3.2 (b) ^ * 2.4 ~» ^ O ^ Ñ 1.6.» 2 S LT X L *^ RT=RI Z' / M hm lg(f/h2) 1^ (c) 1' 4 E 1^ e CJ LL. c 3  O n.il '^.L^O <^^i i*^ n 2 C, 1 _. J_ % ^ ^2^ 1 Te T/^C a: ^QS 1^ 1*^ 1^ 1' RT frm Z* R2 frm M" vs lg ( f ) j _ j _ 1 Te T/^C (e) f) m t p FERROELECTRIC S:^/ CONDUCTIVE CORE R3 NON FERROELECTRIC GRAIN BOUNDARY REGION Rl Ri R2 R3 I v^aar^ nwna^ pvvvvn HH HH HH Figure 7. Impedance data fr a ptcr BaTiO^ ceramic at 327^C. The same data are used in (a) and (b) but are presented in different ways. Resistive and capacitance data as a functin f temperature are shwn in (c) and (d) and a schematic mdel and equivalent circuit f plycrystalline ptcr BaTiOj are shwn in (e) and (f), respectively. Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril
8 DEREK C.SINCLAIR 11Â. This value f C2 was relatively independent f bth temperature and time. This wuld indicate, fr such a mdel, that the layer thickness remains essentially cnstant. The bserved variatins f this R2C2 element are assciated directly with the presence f a high initial pen circuit vltage and its subsequent decline. Since it is knwn that PEO.LÍCF3SO3 electrlytes decmpse at vltages greater than V versus lithium at 12^C it is pssible that the initial OCV decay is assciated with a lcal decmpsitin f the electrlyte. The Warburg resistance, figure 6 (d), is evidenced in the cmplex impedance plts by a lw frequency spike, inclined ideally at 45^. The rigin f the Warburg lies in the cathde material r at the electrlyte/cathde interface where significant intercalatin f Li"^ in the V5O13 based cathde is expected. Results such as these demnstrate the usefulness f ac impedance measurements in btaining infrmatin regarding interfacial phenmena at bth the ande and cathde interfaces with the plymer electrlyte. Such measurements are nn destructive and can be used t mnitr electrical phenmena in situ. (II) Ptcr BaTi3 Ceramics. The psitive temperature cefficient f resistance, ptcr, effect is a well dcumented (3i34) (3^^ prly understd phenmenn in which the electrical resistivity f certain materials underges a dramatic increase, ften by several rders f magnitude, with increasing temperature. In dnrdped, semicnducting barium titanate, the ptcr effect ccurs as the temperature is raised thrugh the ferrelectric Curiepint, 12^C and in which the resistivity typically increases frm 1 Qcm t 1 MQcm ver an interval f abut 1 C. The effect is fully reversible with temperature cycling and leads t applicatins in thermal fuses and current verlad prtectin devices. The rigins f the ptcr effect are nt wellunderstd. It is usually regarded as being assciated with acceptr traps at the grain bundaries, e.g. adsrbed xygen ^^^' ^^\ metal vacancies ^^^^ and/r segregated additives/impurities i.e. manganese ^^^\ Varius theries have been prpsed t explain the effect, e.g. the Heywang mdel (394) whereby Schttky barriers are develped at the grain bundaries due t the acceptr traps, hwever many dubts remain (4143) In plycrystalline ceramic materials which exhibit mdest levels f electrnic cnductivity, ac impedance techniques prvide a pwerful methd fr prbing electrical inhmgeneities assciated with crystal interirs, grain bundaries and surfaces. This is particularly the case when the results f different methds f data analysis are cmpared since ften, ne methd alne, such as the use f cmplex impedance plane plts may give infrmatin that is incmplete r misleading. Recently we have shwn that by use f cmbined impedance and mdulus spectrscpy t analyse ac impedance data, it is pssible t characterise bth grain bundary and bulk phenmena in ptcr barium titanate ceramics (4446) j , 5 has lead us t develp a creshell mdel t characterise these electrically inhmgeneus ceramics (4^^ ). A typical cmplex impedance plane plt fr a grain bundary dminated ptcr BaTi3 ceramic sample is shwn in figure 7 (a). The spectrum cnsists essentially f a single semicircular arc (capacitance Cj = 3 nfcm"') assciated with the resistive grain bundary cmpnent, such that the dc resistance f the sample, Rj apprximates t Rj at lw frequencies, figure 7 (a). Given that impedance plane plts are dminated by the mst resistive regins within a sample such plts are insensitive t the mre cnductive regins within the sample and therefre cannt be used as a methd t prbe such regins in ptcr BaTi3 ceramics. A methd f data prcessing which has been fund t be very sensitive t prbe the electrically inhmgeneus nature f these ceramics has been cmbined spectrscpic plts f the imaginary cmpnents f impedance, Z" and electric mdulus, M''. As described in the previus sectin such plts place different weighting n, and highlight different features f the cllected data. Z" spectra are dminated by the mst resistive element f the sample whereas M" spectra are inversely prprtinal t capacitance and are mre sensitive t the "bulk" r grain respnse f the sample, table 1. Plts such as that shwn in figure 7 (b) have prvided infrmatin which has nt previusly been btained frm traditinal Z* plane plts f such materials (48/ 49) jp,g 2" spectra are dminated by the mre resistive grain bundary cmpnent, R and thus shw nly a single peak in the Z" spectra, crrespnding t the semicircle in figure 7 (a). In striking cntrast t the single peaks in the Z" plts, M" plts based n the same raw data, shw much mre cmplexity with tw (fig. 7 b), r in sme cases three (4^), verlapping peaks. Furthermre, M" plts as a functin f temperature shw a marked variatin in shape. The smaller, lwerfrequency peak which is cincident with the Z" peak, fig 7 (b), stays at abut the same size, indicating that its capacitance value is cnstant. The higherfrequency M" peak increases in size with temperature, indicating that its capacitance value is decreasing. The assciated capacitance values and temperature dependence f the tw M" peaks is shwn in figure 7 (c); Cj is essentially independent f temperature, whereas C2 rises increasingly rapidly as the temperature decreases twards the Curie pint. A CurieWeiss plt fr C2, nt shwn, cnfirmed that C2 was assciated with a ferrelectric regin f the sample abve the Curie pint and represents the plarisatin f the residual dmains which are present in the paraelectric regin. In rder t determine the magnitudes f the tw resistances, a cmbinatin f impedance and mdulus plts is used. The value f the larger f the tw resistances, Rj, is given directly frm the cmplex impedance plane plts since, effectively, R^j^. = Rj = R. The value f R2 cannt be btained frm the impedance plts, but may be estimated frm the c^nax ^^'^^ ^^ ^^^ highfrequency M" peak using the equatin cop^^x '^2^2 ~ ^' ^^^^^ '^^ capacitance value has been determined( M^'^^^ = CQ/C2). This resistance value fr R2 is pltted in figure 7 (d) and als exhibits a ptcr effect. Such an effect has nt been previusly discvered by use f dc r Z* plane plts frm ac measurements. Detailed analysis f ac impedance data f such ptcr BaTi3 ceramics has led us t prpse (4^) the creshell type mdel shwn in figure 7 (e). in this mdel bth R] (grain bundary) and R2 (shell f individual grains) shw ptcr effects, whereas R3 (cre f grains) remains semicnducting as the temperature is raised thrugh the Curie pint. The predminant acceptr states f the grain bundary and uter grain regins are thught t be adsrbed xygen and metal vacancies (Ba and/r Ti), respectively. The capacitance assciated with the grain bundaries, C, is independent f temperature and nnferrelectric whereas the capacitance f the shelltype regins f the grains, C2, has been shwn t be ferrelectric. Due t the lw resistivity f the cre regin, < 2 ßcm, nthing is currently knwn abut C3 r its temperature dependence. The equivalent circuit used t mdel the ac respnse f the ptcr BaTi3 ceramics is shwn in figure 7 (f) and cmprises f a series array f parallel RC elements: each parallel RC element represents an electrical regin f the sample, such as the grain bundaries r the crystal interirs. Results such as these demnstrate hw alternative frmalisms f data presentatins can yield additinal infrmatin that is nt easily 62 Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril 1994
9 CARACTERIZACIÓN DE ELECTROMATERIALES MEDIANTE EL EMPLEO DE ESPECTROSCOPIA DE IMPEDANCIA (a) c \[ W Ci ww R K/T a N Figure 8. Impedance data fr single crystal LiTaOj with the applied vltage parallel t the plar c axis. The equivalent circuit, resistive and capacitive data and a cmplex impedance plane plt at 528^C fr this rientatin are shwn in (a) t (d), respectively. accessible frm the cmplex impedance plane alne and thus lead t a mre cmplete characterisatin f electrically inhmgeneus electrceramics such as ptcr BaTi3 ceramics. (Ill) Single Crystal LiTa3 LiTa3 is a ferrelectric material and a mdest cnductr f lithium ins/electrns at high temperatures which finds numerus applicatins assciated with its nnlinear ptical and pyrelectric prperties. Studies n single crystals have the advantage that grain bundary phenmena shuld be absent and a mre detailed analysis f the bulk prperties may be made, ac Impedance measurements n single crystals f LiTa3 abve and belw the Curie temperature, ca 59 C, with the plar c axis rientated bth parallel and perpendicular t the electric field, has allwed a detailed breakdwn f the electrical prperties fr the different crystallgraphic rientatins ^^^>. in the ferrelectric rientatin i.e. applied electric field parallel t the plar c axis, the mst useful methds f data analysis fr R and C values was by cmplex admittance plane plts, Y*, and spectrscpic plts f the real cmpnent f permittivity, e', respectively. The equivalent circuit and temperature dependence f the cmpnent R and C values are shwn in figures 8 (a), (b) and (c) respectively. In this ferrelectric rientatin, at temperatures belw the Curie pint the ac respnse f the sample indicates the presence f five cmpnents: Cj, crrespnds t the charge plarisatin assciated with the ferrelectric dmains. It passes thrugh a sharp maximum at Tc, figure 8 (c), and shws very gd CurieWeiss behaviur, extraplating t the Curie temperature. Dmain reversal is easiest in the regin f the Curie pint, as evidenced by the maximum in Cj arund 59^C. Well belw the Curie temperature the value f C^ is lw since the dmains are essentially fixed in their rientatin and cannt be reversed at the small applied vltages, i.e. loomv used in the impedance measurements. Abve the Curie temperature, Ci decreases as the dmains break up int smaller clusters thus reducing the net plarisatin. Rj, in series with the ferrelectric capacitance Cj, figure 8 (a). This resistance is assciated with the rerientatin f the ferrelectric dmains and has a marked temperature dependence. Well belw the Curie temperature the activatin energy assciated with cmplete dmain reversal within the applied field is large and the Bletin de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril
10 DEREK C.SINCLAIR E a NI e a en O 12 (a) 6  / / / (c) / 1 R K/T 669^C ' \ \ \ transitin. The plarisatin f the individual diples starts t ccur at temperatures well belw the Curie temperature and is essentially ptimised at the Curie temperature. R2, is in parallel with the ther three elements and represents the leakage resistance f the crystal which is caused by the lng range migratin f Li+ ins in this crystallgraphic rientatin. It gives a linear resistance plt with an activatin energy f 1.27eV, figure 8 (b). C3, is in series with the ther fur elements f the equivalent circuit, figure 8 (a) and represents the blcking dublelayer capacitance assciated with the crystalelectrde interface since the gld electrdes are blcking transprt f the Li"*" ins. The magnitude f the capacitance was estimated frm the lw frequency spike in the cmplex impedance plane plts, figure 8 (d), using the equatin T'  1/(ûC and had a typical value f 2JLIF. The angle f the electrde spike is less than the ideal 9^ due t the gld electrdes being nly partially blcking twards Li"^ at such elevated temperatures. In the nnferrelectric rientatin the impedance respnse is very simple and can be mdelled by a single parallel RC element, figure 9 (a). There was n evidence f the resistance, Ri and capacitance, Cj attributed t the ferrelectric dmains. Instead the material is a pr electrnic cnductr with a small, temperatureindependent bulk capacitance. Resistance values were btained frm the lw frequency intercept f the semicircular arc in the cmplex impedance plane plts. An Arrhenius plt f the data shws a slight change in slpe at the Curie temperature with linear regins t either side, figure 9 (b). The lw frequency regin f the cmplex impedance plane plts did nt shw the existence f any characteristic electrde spike; instead a residual tail is bserved, figure 9 (c). The absence f an electrdespike indicates that the material is an electrnic cnductr in the nnferrelectric rientatin. These results n LiTa3 indicate the ptential f ac impedance techniques fr prbing the electrical prperties f ferrelectric crystals and demnstrate that ferrelectric dmain rerientatin can be characterised by macrscpic resistance and capacitance values. Such detailed characterisatin f dmain behaviur is much sught after but, as yet cannt be btained frm cmmnlyused fixed frequency r dc measurements. R Z' / k Q cm 4. SUMMARY Figure 9. Impedance data fr single crystal LITaOj with the applied vltage perpendicular t the plar c axis. The equivalent circuit, resistive data and a cmplex impedance plane plt at 669^C fr this rientatin are shwn in (a) t (c), respectively. refre the assciated resistance is large. As the Curie temperature is apprached, switching f the ferrelectric dmains in the applied field ccurs mre easily and the assciated resistance Rj decreases rapidly, with prnunced curvature, figure 8 (b) and the assciated capacitance, C^ increases, figure 8 (c). The small residual resistance abve the Curie temperature can be attributed t the existence f lcal regins r clusters f ferrelectric plarisatin. C2, in parallel with resistance Rj represents the intrinsic lattice plarisatin f the sample. Capacitance C2 is nt ferrelectric but it is very large and increases markedly n passing thrugh the Curie temperature, figure 8 (c). This capacitance prvides a measure f the small, individual atmic displacements f the Li and Ta ins within their distrted ctahedral envirnments. The smth increase in C2 as the Curie temperature is apprached can be related t the strng secndrder character f the ferrelectric t paraelectric The basic thery, versatility and usefulness f ac impedance spectrscpy in characterising electrmaterials and slid state devices has been reviewed. In these materials/devices, impedance spectrscpy has permitted detailed electrical characterisatin f thin, interfacial layers between electrdes and electrlytes in slid state batteries and between grain and grain bundary regins in ptcr BaTi3 ceramics. The usefulness f the technique in studying intrinsic prperties f ferrelectric materials, such as electrical cnductin and ferrelectric dmain reversal is demnstrated by an indepth study f single crystal LiTa3 in different crystallgraphic rientatins. Data analysis fr a given material/device nrmally requires mre than ne cmplex frmalism t be studied and frequently, spectrscpic plts f either the real r imaginary cmpnents f a cmplex frmalism have t be used in cnjunctin with cmplex plane plts. The results fr LiTa3 and ptcr BaTi3 represent majr advancements in characterisatin ver previus analyses which emplyed nly dc r cnventinal fixed frequency and/r cmplex impedance plane plts f ac measurements. 64 Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Niím. 2 MarzAbril 1994
11 CARACTERIZACIÓN DE ELECTROMATERIALES MEDIANTE EL EMPLEO DE ESPECTROSCOPIA DE IMPEDANCIA REFERENCES D.P.Almnd, A.R.West and R.J.Grant, Temperature Dependence f the ac Cnductivity f NaBetaAlumina, Slid State Cmms., (1982). 2. H.D.Park and D.A.Payne, Characterisatin f Internal Bundary Layer Capacitrs, Advances in Ceramics, 1, 242, Ed. L.M.Levinsn, The American Ceramic Sciety lnc.,clumbus, Ohi (USA) B.M.Kuiwicki, PTC Materials Technlgy, , Advances in Ceramics, 1, 147, Ed. L.M.Levinsn, The American Ceramic Sciety Inc.,Clumbus, Ohi (USA) P.T.Mseley and B.C.Tfield, "Slid State Gas Sensrs.", 225, Adam Hilger, A.J.Mulsn and J.M.Herbert, ''Electrceramics.", 189, Chapman and Hall, 199,. 6. D.R.Clarke, The Micrstructural Lcalisatin f the Intergrannular MetalOxide Phase in a Zinc Oxide Varistr, J. Appl. Phys., (1978). 7. H.Ihrig and M.Klerk, Visualisatin f the Grain Bundary Ptential Barriers f PTCtype BaTi3 Ceramics by Cathdluminescence in an ElectrnPrbeMicr Analyser, Appl. Phys. Letts., (198). 8. G.Kschel and E.KubaIek, GrainBundary Characteristics and their Influence n the Electrical Resistance f Barium Titanate Ceramics, J. Amer. Ceram. Sc, (1985). 9. D.Dims, P.Chaudhari, J.Mannhart and F.K.LeGues, Orientatin Dependence f GrainBundary Critical Currents in YBa2Cu37_x Bicrystals, Phys. Rev. Letts., (1988). 1. H.Sumin, O.Sakurai, K.Shinzaki, M.Kat and N.Mizutani, A New Instruement t Measure the Electrical Prperties in Very Narrw Regins in Ceramics, J. Mater. Sei. Letts., 1 126(1991). 11 P.Wd, D.C.Sinclair and P.P.Classer, Electrical Characterisatin f Bismuth Orthvanadate Using ac Impedance Spectrscpy, Slid State Inics, (1993). 12. K.S.Cle and R.H.Cle, Dispersin and Absrptin in Dielectrics I. Alternating Current Characteristics, J. Chem. Phys., (1941). 13. J.E.Bauerle, Study f Slid Electrlyte Plarisatin by a Cmplex Admittance Methd, J. Phys. Chem. Slids, (1969). 14 J.H.SIuyters and J.J.C.Omen, The Impedance f Galvanic Cells. II. Experimental Evidence, Rec. Trav. Chim., (196). 15 L.Page and N.J.Adams, "Principles f Electricity" 2nd ed"^.. Van Nstrand, J.T.S.Irvine, D.C.Sinclair and A.R.West, Electrceramics: Characterisatin by ac Impedance Spectrscpy, Adv. Mater., (199). 17. A.K.Jnscher, "Dielectric Relaxatins in Slids.", Chelsea Dielectric Press, P.G.Bruce and A.R.West, The ac Cnductivity f Plycrystalline LISICON LÍ2+x^n _xge4 and a Mdel fr Intergrannular Cnstrictin, J. Electrchem. Sc, (1983). 19. J.R.Macdnald and J.A.Garber, Analysis f Impedance and Admittance Data fr Slids and Liquids, J. Electrchem. Sc, (1977). 2. J.R.Macdnald, "Impedance Spectrscpy", 18, Jhn Wiley, R.D.Armstrng, The MetalSlid Electrlyte Interface, J. Electranal. Chem., 52 ( 413(1974). 22. R.D.Armstrng, Specalist Peridical Reprts in Electrchemistry, (198). 23. R. delevie, The Influence f Surface Rughness f Slid Electrlytes n Electrchemical Measurements, Electrchim. Acta., (1965). 24. S.H.Liu, Fractal Mde fr the ac Respnse f a Rugh Interface, Phys. Rev.Letts., (1985). 25. M.Kleifz and J.Dupuy, "Electrde Prcesses in Slid State Inics.", 149 Reidel Pub. C., S.N.Sze, "Semicnductr Devices, Physics and Technlgy.", Jhn Wiley, N.C.Chaklanabish and H.S.Maiti, Discharge Characteristics and Interface Impedance f a Li/1 MLiCI4(PC)/V25 Cell, J. Pwer Surces, (1985). 28. J.Thevenin, Passivating Films n Li Electrdes  an Apprach by means f Electrde Impedance Spectrscpy, J. Pwer Surces, (1985). 29. D.Fauteux, Frmatin f a Passivating Film at the LithiumPEOLiCF3S3 Interface, Slid State Inics, (1985). 3. C.C.Hunter, D.C.Sinclair, A.Hper and A.R.West, ac Impedance Studies f the Lithium/Plymer Electrlyte Interface in Slid State Batteries, J. Pwer Surces, (1988). 31. O.Saburi, Prperties f Semi Cnducting Barium Titanates, J. Phys. Sc. Jpn., (1959). 32. R.Wernicke, The Kinetics f Equilibrium Restratin n Barium Titanate Ceramics, Philips Res. Rep., (1976). 33. T.R.N.Kutty and P.Murugaraj, ElectrnParamagneticResnance Study n the Rle f Mn in Enhancing the PTC f BaTi3, Mat. Letts., (1985). 34. M.Kuwabara, Effect f Micrstructure n the PTCR Effect in Semicnducting Barium Titanate Ceramics, J. Amer. Ceram. Sc, (1981). 35. G.H.Jnker, Halgen Treatment f Barium Titanate Semicnductrs, Mat. Res. Bull., 2 41 (1967). 36. G.V.Lewis and C.R.A.Catlw, PTCR Effect in BaTi3, J. Amer. Ceram. Sc, (1985). 37. J.Daniels, K.K.Hardtl, D.Hennings and R.Wernicke, Defect Chemistry and Electrical Cnductivity f Dped Barium Titanate, Philips Res. Rep., (1976). 38. T.R.N.Kutty, P.Murugaraj and N.S.Gajbhiye, EPR Evidence fr Activatin f Trap Centres in PTCR BaTi3 Ceramics, Mat. Res. Bull., (1985). 39. W.Heywang, Semicnducting BaTi3, J. Mater. Sei., (1971) 4. G.H.Jnker, Sme Aspects f SemiCnducxting Barium Titanate, Slid State Electrn., (1964). 41. H.Nemt and I.Oda, Direct Examinatin f PTC Actin f Single Grain Bundaries in Semi Cnducting BaTi3 Ceramics, J. Amer. Ceram. Sc, (198). 42. T.R.N.Kutty, Behaviur f Acceptr States in Semicnducting BaTi3 and SrTi3, Prc Indian Acad. Sei., (1986). 43. P.Gerthsen and B.Hffmann, CurrentVltage Characteristics and Capacitance f Single Grain Bundaries in SemiCnducting BaTi3, Slid State Electrn., (1973). 44. D.C.Sinclair and A.R.West, Bulk PTCR Effect n Dped BaTi3^ J. Mater. Sei. Letts., (1988). 45. D.C.Sinclair and A.R.West, Impedance and Mdulus Spectrscpy f Semicnducting Barium Titanate Shwing Psitive Temperature Cefficient f Resistance, J. Appl. Phys., (1989). 46. D.C.Sinclair and A.R.West, Variatin with Prcessing Cnditins f Bulk and Grain Bundary PTCR Phenmena in Dped BaTi3, "Surfaces and Interfaces f Ceramic Materials.", 535, Kluwer Acad. Pub., D.C.Sinclair and A.R.West, Effect f Atmsphere n the PTCR Prperties f BaTi3 Ceamics, J. Mater. Sei., (1994). 48. R.N.Basu and H.S.Maiti, PTC Behaviur f Semicnducting BaTi3 Ceramics, Trans. Indian Ceram. Sc, (1986). 49. T.Y.Tseng and S.H.Wang, ac Electrical Prperties f HighCuriePint Barium Lead PTCR Ceramics, Mater. Letts., (199). 5. D.C.Sinclair and A.R.West, Electrical Prperties f LiTa3 Single Crystal, Phys. Rev., B (1989). Recibid: Aceptad: In Memnam JOSE RIVAS SANCHEZ Falleció el día 17 de ener de 1995, a ls 82 añs de edad. Nacid en Ovied, gran parte de su vida y actividades, transcurriern entre Lugnes y su ciudad natal. Desde su juventud, participó activamente en la industria cerámica Refractaris dnde llegó a alcanzar, ls más alts puests de mand y respnsabilidad; primer en MERSA y después en DIDIER, S.A. hasta su jubilación. En una larga etapa, década de ls 4, hasta principi de ls 9, desarrlló una intensa actividad, en defensa de ls intereses de ls fabricantes de prducts refractaris. En una primera etapa, presidió el grup de Refractaris, dentr del rganigrama del Sindicat Vertical de Cerámica y Vidri, y más tarde estuv al frente de la Asciación Nacinal de Fabricantes de Prducts Refractaris (ANFRE) hasta que, al finalizar 1992, cesó a petición prpia, siend nmbrad Presidente de hlnr, de dicha Sciedad. Miembr fundadr de la Sciedad Españla de Cerámica y Vidri, tuv una participación activa en la rganización de reunines tant nacinales cm sectriales de la sección de refractaris. Durante 4 añs, representó a nuestr país, en su calidad de Presidente de ANFRE, ante la Federación Eurpea de Fabricantes de Prducts Refractaris (P.R.E.). Jsé Rivas Sánchez, fue un ejecutiv fiel cumplidr de sus deberes y cmprmiss en ls cargs que ejercía, de extrardianria capacidad de trabaj y entrega, prestó siempre genersa ayuda a las industrias del ram, en la slución de sus prblemas. Hmbres cm Jsé Rivas Sánchez, deberíams tener siempre presente cm ejempl y acicate. Entre tras cndecracines, estaba en psesión de la Medalla de Or del Cnsej Superir de Cámaras de la Prpiedad Urbana y de la Encmienda de la Orden del Mérit Civil. La Sciedad Españla de Cerámica y Vidri testimnia su más prfunda cndlencia a su Viuda Dña Laudivina Alvarez Padrón, a sus hijs y familiares pr tan irreparable pérdida. Bletín de la Sciedad Españla de Cerámica y Vidri. Vl. 34 Num. 2 MarzAbril
12 Publicacines de la Sciedad Españla de Cerámica y Vidri KZ. < Q_ Preci sin IVA Sci N sci I Semana de estudis cerámics (Madrid, 1961) II Semana de estudis cerámics (Madrid, 1963) III Semana de estudis cerámics (Madrid, 1965) IV Semana de estudis cerámics (Madrid, 1967) < û u E u XI Cngres Internacinal de Cerámica (Madrid, 1968) Terminlgía de ls defects del vidri (Madrid, 1973) Hrn eléctric de arc (I Reunión Mngráfica de la Sección de Refractaris, Marbella, 1973). AGOTADO El calín en España (Madrid, 1974). E. Galán Huerts y J. Espinsa de ls Mnters Refractaris en clada cntinua (Madrid, 1974) Refractaris en la industria petrquímica (III Reunión Mngráfica de la Sección de Refractaris, Puert de la Cruz, 1976) Refractaris para la industria del cement (Madrid, 1976). AGOTADO Refractaris para tratamient de acer y cucharas de clada, incluyend sistemas de cierre de cucharas (XX Clqui Internacinal sbre Refractaris, Aquisgrán, 1977) (Edit. E. Criad) Primeras jrnadas Científicas. El clr en la cerámica y el vidri (Sevilla, 1978) Pastas cerámicas (Madrid, 1979). E. Gippini. AGOTADO Segundas Jrnadas Científicas. Reactividad de sólids en cerámica y vidri (Valencia, 1979) Terceras jrnadas Científicas (Barcelna, 198) Cuartas jrnadas Científicas (Ovied, 1981) Separación de fases en vidris. El sistema Na2O.B2O3.SiO2 (Madrid, 1982). j. Ma. Rincón y A. Duran I Cngres Iberamerican de Cerámica, Vidri y Refractaris (ds vlúmenes) (Trremlins, 1982) (Madrid, 1983) Quintas jrnadas Científicas (Santiag de Cmpstela, 1984) Tablas Cerámicas (institut de Química Técnica, Universidad de Valencia). AGOTADO Vcabulari para la industria de ls materiales refractaris (españlfrancésinglésrus). UNE 61 (Madrid, 1985) (Edit. E. Criad) jrnadas sbre materiales refractaris y siderurgia (Arganda del Rey, 1984) (Madrid, 1985) (Edit. E. Criad) Diccinari cerámic científicpráctic (españlinglésalemánfrancés). C. Guillem Mnznis y M. C. Guillem Villar (Valencia, 1987) Curs sbre materias primas para cerámica y vidri (Edit. j. M. Gnzález Peña, M. A. Delgad Méndez y j.j. García Rdríguez) (Madrid, 1987). AGOTADO Prcessing f Advanced Ceramics (Edit. j. S. Mya y S. de Aza) (Madrid, 1987) Ls materiales cerámics y vitres en Extremadura (Edit. J. Ma. Rincón) (Mérida, 1988) Glasses and GlassCeramics fr Nuclear Waste Management (Edit. j. Ma. Rincón) (2. Edición) (también en micrficha) Materiales refractaris en siderurgia. Revisión bibligráfica Refractry Materials in Irn & Steelmaking a Bibligraphic Review (Edit. E. Criad, A. Pastr y R. Sanch) Ciencia y Tecnlgía de ls Materiales Cerámics y Vitres. España'89 (Edit. J. Ma. Rincón) (Faenza Editrice y SECV) (Castellón, 199) Cerámica y Vidri'91 (Edit. j. Ma. Rincón, F. Capel y A. Caballer) (Palma, 1991) Nuevs prducts y tecnlgías de esmaltes y pigments cerámics (Edit. j. Ma. Rincón, j. Carda y j. Alarcón) (1991) (Faenza Editrice y SECV) PEDIDOS Ls pedids pueden dirigirse a: Sciedad Españla de Cerámica y Vidri Ctra. de Valencia, Km. 24, Arganda del Rey (Madrid) Ls envís se realizarán pr transprte urgente a prtes debids. DOCUMENTACIÓN La Sciedad Españla de Cerámica y Vidri frece a sus scis ls siguientes servicis de dcumentación: ftcpias de artículs; traduccines de artículs; perfiles bibligráfics; revisines mngráficas.
The Synchronization of Periodic Routing Messages
The Synchrnizatin f Peridic Ruting Messages Sally Flyd and Van Jacbsn, Lawrence Berkeley Labratry, One Cycltrn Rad, Berkeley CA 9470, flyd@eelblgv, van@eelblgv T appear in the April 994 IEEE/ACM Transactins
More informationAn Introduction to Statistical Learning
Springer Texts in Statistics Gareth James Daniela Witten Trevr Hastie Rbert Tibshirani An Intrductin t Statistical Learning with Applicatins in R Springer Texts in Statistics 103 Series Editrs: G. Casella
More informationCreación de un motor de render para una plataforma móvil
UNIVERSIDAD CARLOS III DE MADRID INGENIERÍA INFORMÁTICA GRUPO DE INTELIGENCIA ARTIFICIAL APLICADA Creación de un mtr de render para una platafrma móvil Autr: Tutr: Antni Berlanga de Jesús Fecha: Ener 2008
More information
THE INTERNATIONAL FRAMEWORK
THE INTERNATIONAL FRAMEWORK ABOUT THE IIRC The Internatinal Integrated Reprting Cuncil (IIRC) is a glbal calitin f regulatrs, investrs, cmpanies, standard setters, the accunting prfessin and NGOs.
More informationA Call for Clarity: Open Questions on the Scope of FDA Regulation of mhealth. A whitepaper prepared by the mhealth Regulatory Coalition
A Call fr Clarity: Open Questins n the Scpe f FDA Regulatin f mhealth A whitepaper prepared by the mhealth Regulatry Calitin December 22, 2010 Authrs Bradley Merrill Thmpsn Epstein, Becker & Green P.C.
More informationEnvironmental, Health, and Safety General Guidelines
GENERAL EHS GUIDELINES: INTRODUCTION Envirnmental, Health, and Safety General Guidelines Intrductin The Envirnmental, Health, and Safety (EHS) Guidelines are technical reference dcuments with general and
More information1.3. The Mean Temperature Difference
1.3. The Mean Temperature Difference 1.3.1. The Lgarithmic Mean Temperature Difference 1. Basic Assumptins. In the previus sectin, we bserved that the design equatin culd be slved much easier if we culd
More informationWAVE FIELD SYNTHESIS A PROMISING SPATIAL AUDIO RENDERING CONCEPT. Günther Theile* and Helmut Wittek**
T be published in Jurnal f the Institute f Image Infrmatin and Televisin Engineers, 2007 WAVE FIELD SYNTHESIS A PROMISING SPATIAL AUDIO RENDERING CONCEPT Günther Theile* and Helmut Wittek** * Institut
More informationEU Subsidies for polluting and unsustainable practices
DIRECTORATE GENERAL FOR INTERNAL POLICIES POLICY DEPARTMENT A: ECONOMIC AND SCIENTIFIC POLICY ENVIRONMENT, PUBLIC HEALTH AND FOOD SAFETY EU Subsidies fr plluting and unsustainable practices STUDY Abstract
More informationAcross a wide variety of fields, data are
Frm Data Mining t Knwledge Discvery in Databases Usama Fayyad, Gregry PiatetskyShapir, and Padhraic Smyth Data mining and knwledge discvery in databases have been attracting a significant amunt f research,
More informationTowards Supporting the Adoption of Software Reference Architectures: An EmpiricallyGrounded Framework
Twards Supprting the Adptin f Sftware Reference Architectures: An EmpiricallyGrunded Framewrk Silveri MartínezFernández Universitat Plitècnica de Catalunya Jrdi Girna, 13 08034, Barcelna (Spain) +34
More informationIntegration Competency Center
Integratin Cmpetency Center ICC Handbk Versin 3.0 29 Nvember 2012 ICC  Integratin Cmpetency Center ICC is a shared service intended fr cmpanies wh wish t design, develp and maintain integratin slutins
More informationPCI DSS Cloud Computing Guidelines
Standard: PCI Data Security Standard (PCI DSS) Versin: 2.0 Date: February 2013 Authr: Clud Special Interest Grup PCI Security Standards Cuncil Infrmatin Supplement: PCI DSS Clud Cmputing Guidelines Table
More informationo Monitoring Business Critical Applications with VMware vcenter Operations Manager
Mnitring Business Critical Applicatins with VMware vcenter Operatins Manager Mnitring Business Critical Applicatins with This prduct is prtected by U.S. and internatinal cpyright and intellectual prperty
More informationInteroperability in DALLAS. Interim version 1.0 Published: September 2011
Interperability in DALLAS Interim versin 1.0 Published: September 2011 i White Paper  Interperability fr DALLAS applicants and cmmunities v1.0 ii Interperability fr DALLAS applicants and cmmunities Warning
More informationRETAIL DEVELOPER S GUIDE
RETAIL DEVELOPER S GUIDE Karina Kreja, Assciate Directr, CBRE: After tw decades f dynamic develpment the Plish retail market is nw mature. Despite increasing cmpetitin it still ffers cnsiderable develpment
More informationPROCESS MANAGEMENT IN HEALTHCARE. SANT CAMIL HOSPITAL CASE STUDY
Revista de Dirección y Administración de Empresas. Númer 20, diciembre 2013 págs. 18 Enpresen Zuzendaritza eta Administrazi Aldizkaria. 20. zenbakia, 2013 abendua 18 rr. PROCESS MANAGEMENT IN HEALTHCARE.
More informationIMD. Finding the Way: A Discussion of the Swedish Migrant Integration System
Finding the Way: A Discussin f the Swedish Migrant Integratin System Finding the way: A discussin f the Swedish migrant integratin system OECD 2014 1 July 2014 Finding the way: A discussin f the Swedish
More informationThe Elements of Statistical Learning
Springer Series in Statistics Trevr Hastie Rbert Tibshirani Jerme Friedman The Elements f Statistical Learning Data Mining, Inference, and Predictin Secnd Editin This is page v Printer: paque this T ur
More informationTOWARDS INTEGRATED REPORTING Communicating Value in the 21st Century
TOWARDS INTEGRATED REPORTING Cmmunicating Value in the 21st Century ABOUT THIS DISCUSSION PAPER Cntents Abut this Discussin Paper 1 Summary 2 What is Integrated Reprting? Why d We Need Integrated Reprting?
More informationTourmaline as a petrogenetic indicator mineral: an example from the staurolitegrade metapelites of NW Maine
American Mineralgist, Vlume 70, pages 115, 1985 Turmaline as a petrgenetic indicatr mineral: an example frm the staurlitegrade metapelites f NW Maine Dnnnnn J. HeNnyr Lunar and Planetary Institute 3303
More informationReport for the Food Standards Agency. Nutrition and Public Health Intervention Research Unit London School of Hygiene & Tropical Medicine
Cmparisn f cmpsitin (nutrients and ther substances) f rganically and cnventinally prduced fdstuffs: a systematic review f the available literature Reprt fr the Fd Standards Agency Nutritin and Public Health
More informationThe Gender Dimensions of the Green New Deal  an analysis of policy papers of the Greens/EFA New Deal Working Group. Mara Kuhl
The  an analysis f plicy papers f the Greens/EFA New Deal Wrking Grup Mara Kuhl Study cmmissined by The Greens/EFA Grup in the Eurpean Parliament, initiated by Elisabeth Schredter in cperatin with Prf.
More informationATM Security Guidelines
Standard: Versin: 1.0 Date: January 2013 Authr: PCI PIN Transactin Security Pint f Interactin Security Requirements (PCI PTS POI) PCI Security Standards Cuncil Infrmatin Supplement: ATM Security Guidelines
More informationThe Capacity Development Results Framework. A strategic and resultsoriented approach to learning for capacity development
The Capacity Develpment Results Framewrk A strategic and resultsriented apprach t learning fr capacity develpment The Capacity Develpment Results Framewrk A strategic and resultsriented apprach t learning
More informationThe Total Economic Impact Of KPN s Managed Video Services
A Frrester Ttal Ecnmic Impact Study Prepared Fr KPN The Ttal Ecnmic Impact Of KPN s Managed Vide Services As Used By A Large Financial Service Organizatin Prject Directr: Sebastian Selhrst March 2012 TABLE
More informationSECURITY GUIDANCE FOR CRITICAL AREAS OF FOCUS IN CLOUD COMPUTING V3.0
SECURITY GUIDANCE FOR CRITICAL AREAS OF FOCUS IN CLOUD COMPUTING V3.0 INTRODUCTION The guidance prvided herein is the third versin f the Clud Security Alliance dcument, Security Guidance fr Critical Areas
More informationDepartment of State Development, Infrastructure and Planning. State Planning Policy state interest guideline. Water quality
Department f State Develpment, Infrastructure and Planning State Planning Plicy state interest guideline Water quality August 2014 Great state. Great pprtunity. Preface Using this state interest guideline
More informationRisk management and internal control systems. Reference Framework
Risk management and internal cntrl systems Reference Framewrk FOREWORD This AMF Reference Framewrk fr French cmpanies whse securities are admitted t trading n a regulated market is a revised and enhanced
More informationPractical Guide to Cloud Service Level Agreements Version 1.0
Practical Guide t Clud Service Level Agreements Versin 1.0 April 10, 2012 Cntents Practical Guide t Clud Service Level Agreements Versin 1.0... 1 Acknwledgements... 4 Wrkgrup Leaders... 4 Extended Wrkgrup
More information