Volume 153, number8,9 PHYSICSLETTERSA 18 March 1991

On theelectricalconductivity, thermoelectricpoweranddielectricconstantof ErKMo2O8 singlecrystal

A.K. Pandit,T.H. Ansari, R.A. SinghDepartmentofPhysics,UniversityofGorakhpur,Gorakhpur273009.India

and

B.M. WanklynClarendonLaboratory,DepartmentofPhysics,UniversityofOxford, Oxford,UK

Received14 December1989; revisedmanuscriptreceived18 October1990;acceptedforpublication3 December1990Communicatedby J.I. Budnick

Theelectricalconductivity,thermoelectricpoweranddielectricconstantof ErKMo2O8singlecrystalin thetemperaturerange300—1000K havebeenstudied.ErK~Mo2O8is a p-typesemiconductorwith energybandgap2.6eV. It exhibitsanextrinsicnatureup to 625K andabove625K it exhibitsan intrinsic nature.The thermoelectricpowerincreaseswith temperaturein theregion300—625 K whereasit decreaseswith temperaturein theregion 625—1000K. The dielectric constantincreasesslowly in thetemperatureranges300—600K and750—1000K whileits increasebecomesfastin thetemperaturerange600—750K.

I. Introduction 2. Experimental

A greatdealof interesthasbeenwitnessedin the Singlecrystalsof ErKMo2O8 weregrown by thelastthreedecadeson thestudyofrare-earthelements flux methodat the ClarendonLaboratory,Oxford,andtheir compounds,becauseof the fact that they UK. Details aboutthe crystalgrowth andidentifi-showuniquephysicalpropertiesandpromisepoten- cation techniquesaregivenelsewhere[71.Thesin-tial technicalapplications[1—3].Not evena single gle crystalsof ErKMo2O8havea pink colourandthepropertyof ErKMo2O8hasbeenstudiedup till ~ crystalon which the measurementswerecarriedoutKeepingthisin view, wehavechosenthiscrystalfor hada dimension6.6x4.0x 1.1 mm

3. The dc elec-study. It belongs to the series of compounds trical conductivity andthermoelectricpower haveRM (MoO

4)2, whereR is a rare-earthelementand beenmeasuredwith the helpof a digital multimeterM is an alkali atom. It hasbeenindicatedthat the PM 2522/90Philips, India, with an accuracybettercompoundsof this seriesmay undergoa crystallo- than ±0.25% and ±0.20%for resistanceande.m.f.graphicphasetransition,possiblyof theJahn—Teller measurementsrespectively.The ac electrical con-type arounda temperatureof 10 K [4,5]. At room ductivity and dielectric constanthavebeendeter-temperatureErKMo2O8 is isomorphicto YKMo2O8 minedusinganautocomputingdigital LCE.-Qmeterwhosestructurehasbeendeterminedby Klevtsova 4910,Applied ElectronicsLtd., Thane,India, at anandBorisov [6], it is anorthorhombicdistortionof internalfrequencyof 1 kHz. Fordielectricmeasure-the scheelite structure and has the spacegroup ment, the crystal is usedas dielectric medium.ForD1~( Pbcn). all measurementsperpendiculartothec-axis,thetwo-

probemethodwas employed.Platinumfoils andsil-verpaint were usedas electrodematerials.Thetwoelectrodesformedan ohmic contact.The tempera-

488 0375-9601/91/$ 03.50© 1991 — ElsevierSciencePublishersB.V. (North-Holland)

Volume153, number8,9 PHYSICSLETFERSA 18 March1991

turesare recordedwith the help of chromel—alumel below 625 K andthe otherabove625 K, asfollows,thermocouplewires attachedto the platinum elec-trodes.Thedetails regardingthe sampleholderas- a1 = l.314x i0~exp(—0.04eV/kT)c�’cm—’,sembly and measuringtechniquesare given else- 300K~T~625K, (2)where [8].

a,1=0.Ollx 102 exp(—1.30 eV/kT) ~‘ cm—’,

625K~T~l000K. (3)3. Resultsanddiscussion

Thevalueof the activation energy,a0(T) andtheThe electric conductivity (a) of single crystal chargecarriermobility havebeentabulatedin table

ErKMo2O8 has beenmeasuredin the temperature 1. In a semiconductingmaterial,the electricalcon-range300—1000K perpendicularto the c-axis.The ductionat low temperaturesis alwaysassociatedwithvariationof log awith the reciprocalof theabsolute impurities, defectsandinterstitials,etc.,which aretemperature(10

3/T) is shownin fig. 1. Thecurve generallypresentin the forbiddenenergygapof thefollows the well known exponentialrelation [9] materialandlowerthevalueof theactivationenergy

toagreaterextent.Suchimpuritiespresentin mixeda=aoexp(—W/kT), (1) oxidescannotberemovedeasily [10]. Thelow valuewith two different slopesbelow and above625 K. of the activationenergy W= 0.04 eV andthe chargeThedatacanbe expressedby two straightlines,one carrier mobility 3.913X 10’ cm2 V’ s’, calcu-

0

~. •.D.

‘a

t 8a,

0.

0

0

I I I1.0 1.5 2.0 2.5 3.0 3.5

‘o~/~(K1)—

Fig. 1. Variation of ac and dcelectricalconductivitieswith reciprocalof absolutetemperature(103/T); it~:ac conductivity; 0: dcconductivity.

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Volume 153, number8,9 PHYSICSLETTERSA 18 March 1991

Table 1Electricaltransportparametersof ErKMo

2O5single crystal.

Electricaltransportparameter Temperaturerange300—625K Temperaturerange625—1000K

activationenergy(W) 0.04eV 1.30 eVu0(T) l.314x l0

9L2~cm~ 0.011 X 102Q~cm~chargecarriermobility (p) 3.913x l0—~cm2 V s_I 1.368 cm2V~s

lated from the electricalconductivity andthermoe- by the thermalexcitationof electronsfrom 4f or 5plectric powermeasurements,suggestextrinsiccon- bands,andholesleft therebyareresponsiblefordcc-duction in ErKMo

2O8 below 625 K. The trical conductionaboveT—625 K. So the only ap-contributionsof defectsor impuritiestowardsthe propriatebandsfor high mobility electricalconduc-conductionin a solid canbeexplainedin termsof tion arethe Er

3~:Sdempty bandand02_: 2p filleddonorsoracceptorsandisrepresentedby theexpres- band.The2pbandisexpectedto bean ordinarybandsion [11] (about4 eV wide) andthe largepolaron theoryof

conductionshouldbe appliedin this band.The Sdad=Aexp(—EI/kT), (4) . .

bandis in compansona narrowband,the mobilitywhereE, is the ionization energyof donorsor ac- of chargecarriersin the Sdbandis thusexpectedtoceptorsandusuallyE, 0.1 eV for semiconducting be low in comparisonto the mobility of chargecar-materials.Theactivationenergyfoundbelow625 K riers in the O2_: 2p band.Thus the intrinsic con-is approximatelycomparableto the ionization en- ductivityshouldbedominatedby largepolarons.Theergy E,, andthereforethe conclusionthat the elec- electronor holecurrentdominationwill dependupontricalconductioniscertainlydueto impurities,point theeffectivemassofthechargecarriersin theemptydefectsor interstitials,seemsto be reasonable.The bandEr3~: Sdandthefilled band02_: 2p [16,17].highvalueof the activationenergy W= 1.30 eV and However, both these holes and electrons are cx-chargecarrier mobility 1.368cm2 V’ s’, suggest pectedto interactwith the latticeandthis may leadintrinsic conductionin thecompoundabove625 K. to the formationof large polaronsas discussedbySo, thechangein the natureof the log aversus1 0~/ severalauthors[18—20].TheelectricalconductionTcurveat T—~625K is due tothe changein thecon- of a largepolaronis of bandtypeandthe expressionduction mechanism,i.e. a transitionfrom extrinsic for the conductivity isto intrinsic conduction.However,this changemayalsobedue toa magneticor phasetransition.In our a=a

0 exp(— Eg/2kT) , (5)measurements,no precautionswere takento elimi-nateoxygenlossor gainathighertemperatures,which whereE8 is the energybandgapof the solid anda0mayalso be a reasonof the changein the electrical is a constant.In thetemperaturerange625—1000K,propertiesat 625 K. the log aversus10

3/Tcurveis a straightlineandtheTherelevantbandsforconductionin thissolid are conductionis probablyofbandtypedue to largepo-

02: 2p filled; Er3~: 4f partially filled; Mo6~:4d and larons.From this part of the curveonegets the en-Er3~:Sdemptybands.Theonly partially filled band ergy bandgapE

8=2.6 eV anda0=0.Ollx 102 ç~-i

expectedin thissolid is the 4f band,but it hasbeen cm—’.shown that 4f electronshavealmostatomicchar- The ac conductivity is slightly larger than the dcacter,even in rare-earthsolids,andform only very conductivity in the extrinsic region, but in the in-narrow and highly correlatedbands [12,131. The trinsic region the two conductivitiesbecomealmostvalueusuallyquotedfor the bandwidth is 0.05 eV. equal. This showsthat the conductivity is ionic asHencetheparticipationof4felectronsinconduction well as electronicin theextrinsicregionbut it is en-is improbable [14,15]. The 5d band in rareearth tirely electronicin theintrinsic region.solidsis regardedastheconductionband[13]. Thus Thethermoelectricpower(S) hasbeenstudiedinit seemslikely thatelectronsin the Sdband,caused the temperaturerange300—1000K andits valueat

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Volume 153, number8,9 PHYSICSLETTERSA 18 March1991

differenttemperatureshasbeendeterminedby using conclusionof achangein the conductionprocess.the relation Thethermoelectricpowerdecreaseswith increas-

ingtemperatureabove625 K, which isinaccordanceS= lim ~, (6) with our conclusionof largepolaron bandconduc-

tion. In the largepolaronbandconduction,the num-

whereAE is the thermoe.m.f. producedacrossthe berof chargecarriersincreasesexponentiallywithcrystal due to a temperaturedifferenceL~T—~20°C. temperatureandthe mobility of chargecarriersde-The variationof thethermoelectricpower (S) ver- creaseswith temperature.sus 1 03/T is shown in fig. 2. The polarity of the Thestatic dielectricconstant(t’) of a singlecrys-thermo e.m.f. (+ye) showsthatErKMo2O8 is a ~ tal of ErKMo2O8 hasbeenmeasuredperpendiculartype semiconductorandthemajoritychargecarriers to the c-axisin the temperaturerange300—1000K.are holes.We haveestimatedthe valuesof charge Due to the small sizeof the crystal, dielectric con-carriermobility below andabove625 K. The value stantmeasurementparallelto thec-axiswasnotpos-of chargecarriermobility is 3.913x 10’ cm

2 V—’ sible. The dielectric constantat various tempera-s’ below 625 K and1.368cm2V’ s’ above625 tureshasbeencalculatedusingthe relation [22]K. Theincreaseof thermoelectricpowerversustem- 11 3tperatureshowsthat the mobility of the chargecar- ~‘ = C—~--—, (7)riersincreaseswith temperaturebelow625 K. Sincethe conductionin ErKMo

2O8is of extrinsictypebe- where C is the capacitancein picofarads, t is thelow 625 K, governedby impurities,pointdefects,etc., thicknessof the crystal in centimetersandA is thethe numberof chargecarrierswill becomeconstant areaof theelectrodein cm

2.Thevariationof thedi-abovea certaintemperature,thereforeonly increase electricconstant(c’) with absolutetemperatureisin the mobility of chargecarrierswill be responsible shownin fig. 3. Thedielectricconstantof ErKMo

2O8forelectricaltransportbelow625 K [211. At T—~625 increasesslowly up to 600 K andafter that it in-K, the changein the plot of fig. 2 also supportsour creasesveryrapidlywith increasingtemperatureand

finally becomesalmostconstantat higher tempera-

_____________________________________ tures.Theslow variationof the dielectric constantwith temperatureis the usual trendin ionic solids

2h [23]. Thetemperaturehasa complicatedinfluence

Oh” -i 1.1 1111111

~1). ~0 45) 5CC 5CC 15) 800 900 1000

Fig. 2. Variation of thermoelectricpowerwith reciprocalof ab- I

solutetemperature(103/T). Fig. 3. Variationofdielectricconstantwith absolutetemperature.

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Volume 153,number8,9 PHYSICSLETTERSA 18 March 1991

on the dielectric constant.Generally,increasingthe Referencestemperatureof a materialdecreasesthe electronicpolarization.The increaseof ionic distancedue to [1] S. MathfesselandD.C. Mattis, in: Encyclopediaof physics,thetemperature,influencesthe ionic andelectronic Vol. XVIII! 1, ed.S. Flugge(Springer,Berlin, 1968).

polarizations.The decreasein theelectronicdielec- [2] H.W. Katz, Solid state magneticand dielectric devices

tric constantis foundto be lessthan3% for a tern- (Wiley, NewYork, 1959).

peraturechangeof about400°C[24,251. Similarly [3] K.N.R.Taylor,Adv. Phys.20 (1971) 551.[4] T.S. Stetsenko,A.M. PshisukhaandS.D. Elechaninova,Opt.

the changesin ionic polarizationare not very large. Spectrosc.34 (1973)227.Evenassumingthepresenceof somedipolesandtheir [51A.I. Zvyagen, T.S. Stetsenko, V.G. Yurko and R.A.

contributiontothe dielectricconstant,we knowfrom Vaishnoras,JETPLett. 17 (1973)135.

Debye’s theory that the dielectric constant is in- [6] R.F.KlevtsovaandS.V. Borisov, Soy.Phys.Dold. 12 (1968)

verselyproportionaltothetemperature,thereforethe 1095.[7] B.M. Wanldyn,J.Mater.Sci. 7 (1972) 813.

dielectricconstantof ionic solidsshouldnot change [8] Y.P.YadavaandR.A. Singh,Mater. Chem.Phys. 17 (1987)

considerablywith increasingtemperature.The slow 259.

increasein e’ may also be dueto spacechargepo- [9] T.C. HermannandJ.M. Honing,Thermoelectricpowerand

larization, causedby impuritiesor interstitials,be- electromagneticeffects and applications (McGraw-Hill,

causethe conductionin this materialbelow 625 K New York, 1976) p. 142.[10] M.S. SeltzerandR.I. Jaffee,Defectandtransportin oxides

is of extrinsic type governed by impurities or (Plenum,NewYork, 1974).interstitials. [11] AJ. Dekker,Solid statephysics(MacMillan, London,1964)

The large increase in t’ above 600 K is attributed p. 305.

to the exponential increase in the number of charge [12] B. ConqulinandA. Blandin,Adv. Phys.17 (1968)281.

carriers in the intrinsic region. In the narrow band [13] C.E.T. GoncalvesDa Silva andL.M. Falicov, J. Phys.C 5(1972) 63.

semiconductors,the chargecarriersare not ableto [14] Y.A. Rocher,Adv. Phys.11(1962)233.move freely with the electric field. If thesecharges [15] R.RamirezandL.M. Falicov,Phys.Rev.B 3 (1971)2425.

are trapped,a spacechargepolarizationbuilds up [16] J.M. Ziman,Principlesof thetheoryof solids (Cambridge

anda macroscopicfield distortionresults.Dueto this Univ. Press,Cambridge,1964) p. 179.phenomenonthe dielectric constantof ErKMo2O8 [17] C. Kittel, Introductionto solid statephysics (Wiley, New

York, 1971)p. 361.increasesvery rapidly above600 K andfinally be- [18] H. ~rö~ich, Adv. Phys.3 (1954) 325.

comesalmostconstant. [19] G.R.Allcock, Adv. Phys.5 (1956)412.

[20] J. Appel, Solidstatephysics (AcademicPress,New York,1968)p. 193.

Acknowledgement [21] C.Kittel, Introductionto solid statephysics(Wiley Eastern,NewDelhi, 1977).

The authorsare thankful to the Council of Sci- [22] J.P. Suchet, Electrical conduction in solid materials(Pergamon,Oxford, 1975)p. 89.

entific and IndustrialResearch(CSIR), NewDelhi, [23] C.P.Smyth,Dielectricbehaviourandstructure(McGraw-

India, forproviding financialsupport. Hill, NewYork, 1955)p. 132.

[24] K.V. RaoandA. Smakula,J. Appl. Phys.37 (1960)319.[25] A. Smakula,Erinkristalle (Springer;Berlin,1959).

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