ExtendedrigiditypercolationandchemicalthresholdsinGeTePbglassesasrevealedbyMDSCP.ZaheerudeenSahebb,B.H.Sharmilaa,S.Asokana,*,K.AppajiGowdabaDepartmentofInstrumentation,Indian InstituteofScience,Bangalore560012, IndiabDepartmentofPhysics,Bangalore University,Bangalore 560056, IndiaReceived6October2003;receivedinrevisedform27November 2003;accepted24December 2003byA.K.SoodAbstractThermal analysis of Ge20Te802xPbx 2 # x # 8 glasses has been undertaken using modulated differential scanningcalorimetry(MDSC).Thecompositionaldependenceofthermalparametersisinvestigated.ThecrystallizationtemperaturesTc estimated from the total heat ow show detectable changes at compositions x 4; 6.5 and 7.5. Further, the heat capacitychange at the glass transition temperature, measured from the reversible heat ow curve DCRp ; is found to exhibit a maximumand an inexion at compositions x 4 and 6.5 and minimum at x 7:5; respectively. Also, the relaxation enthalpy, estimatedfromtheareaunderthenon-reversingheatowcurve DHNR;exhibitssimilarfeaturesatthesaidcompositions. Fromtheobserved MDSC results, it has been proposed thatthe compositions x 4 and x 6:5 denote to the onset and completionofrigiditypercolationandx 7:5correspondstothechemicalthresholdofthesystem.q 2004ElsevierLtd.Allrightsreserved.PACS:61.43.Fs; 64.70.Pf; 67.80.Gb; 65.40. g;64.75. g;72.80.NgKeywords:A.Disorderedsystems;D.Heatcapacity;D. Thermodynamicproperties1.IntroductionThedifferential scanningcalorimetry(DSC) is exten-sively used in studying the thermal events that occur when asample is subjectedtoatemperatureregime. Therecenttechnique of modulated differential scanning calorimetry(MDSC) uses the deconvolutionprocedure inwhichthetotalheatowisresolvedintoacomponentthattracksthetemperaturemodulationleadingtothereversingheat owand the other which does not track the temperaturemodulation giving rise to the non-reversing heat ow.This information provides unique insights into the structureofglassymaterials[1].Chalcogenide glassesare known to exhibit two networktopological thresholds namely, the rigidity percolationthreshold (RPT) and the chemical threshold (CT). Theformer is indicative of a transformation froma oppypolymericglasstoarigidamorphoussolid[28],whereasthe later corresponds to an ordered glass with onlyheteropolarbonds[25,8].DSCstudiesareroutinelyusedtoidentifythe networktopological thresholds inchalco-genideglasses.The recent MDSC studies have revealed that the rigiditypercolation may span over a range of compositions/averagecoordinationnumbers[9,10],contrarytotheearlierunder-standing that the rigidity percolation is sharp occurring at adenitecomposition(RPT). Anextendedrigiditypercola-tionleads toanintermediatephase existingbetweentheoppy and the rigid phases. The presence of an intermediatephase is however, not revealed in many investigations otherthanMDSC.The earlier electrical studies on GeTePb glasses [11]haverevealedthesignatureofrigiditypercolation, thoughthe occurrence of an intermediate phase has not been0038-1098/$-seefrontmatter q 2004 ElsevierLtd.Allrightsreserved.doi:10.1016/j.ssc.2003.12.043SolidStateCommunications129 (2004)765768www.elsevier.com/locate/ssc*Corresponding author. Tel.: 91-80-3344411; fax: 91-80-3341683.E-mailaddress: sasokan@isu.iisc.ernet.in(S.Asokan).noticed. Inthepresent work, MDSCmeasurements havebeen carried out to explore the possibility of extendedtopologicalthresholdsinGe20Te802xPbxglasses.2.ExperimentalBulk Ge20Te802xPbx glasses 2 # x # 8werepreparedbymeltquenchingtechnique.Thesampleswereconrmedfor the amorphous nature by X-ray diffraction. MDSCstudieswereundertakenusingaTAInstrumentsMDSCe(model 2910). Thebaselinecorrectionwasdonewithanempty pan and the calibration for enthalpy and temperaturewas performed using high purity indium. The calibration forspecicheat wasachievedwithhighpuritysapphire. Allcalibrations wereconductedusingthesameexperimentalparameters that were used for the samples. Samples of about1016 mginweightweregroundintoapowderandweresubsequently transferred to an Al pan and sealed; an emptypan was taken as a reference. The sample was initiallyequilibrated at 30 8C for 2 min with the data storagecapability switched on. The MDSC experiments werecarriedout withthe heatingrate maintainedat 5 8Cpermin, the modulation amplitude at ^1.00 8C and modulationperiodof 60 s. The temperature evolutionof the MDSCsignals was deconvoluted from the modulated heat ow intothe total heat ow, reversing heat ow and the non-reversingheatow.The thermal parameters, namely the glass transitiontemperature Tg andthe crystallizationtemperature Tcwere estimated from the various MDSC curves;the changein specic heat was established fromthe step transitionintheglasstransitionregionfromthereversingheat owDCRp ; the relaxation enthalpy was calculated by measuringtheareaunderthenon-reversingheatowcurve DHNR:3.Resultsand discussionFig.1(a)showsthevariationofcrystallizationtempera-ture Tcof the GeTePb glasses, obtainedfrom the totalheat ow curve, with the composition/average coordinationnumber krl: Here, for the calculation of krl; thecoordinationnumbersofGeandTearetakentobe4and2, respectively. Based on the Kastners proposition thatmetal impuritiesinchalcogenideglassescoordinatetetra-hedrally [12], a coordination of 4 has been assumed for Pb.However, thereisnoclear experimental evidencefor theactual coordination of Pb in GeTePb glasses. Hence, theaverage co-ordinations used here are only suggestive and itmaybemoreappropriatetousetheactualcompositions.It can be seen fromFig. 1(a) that the crystallizationtemperature of Ge20Te802xPbxglasses increases withcomposition, exhibitingamaximumat x 4 krl 2:48:TheTcdecreasessubsequentlyandacuspisseeninTcatx 6:5 krl 2:53: Beyondthis, thereis a sharp decreaseinTcwhichculminates ina minimumat x 7:5 krl 2:55:In the recent study by Boolchand et al., [10,13,14] it hasbeen proposed that the rigidity percolation transition occursover a range of mean coordination numbers leading to threedistinctphasesnamely;oppy,intermediateandrigid.Theoccurrence of extended rigidity percolation has beenobservedinglasses suchas Si Se[10], AsSe[14] andGeSe[15].Basedonthepresentresults,weproposethatthe oppyrigid transition in Ge20Te802xPbx glasses occursoverarangeofaveragecoordinationnumbers/compositionwith the existence of an intermediate phase. Here, thecomposition x 4 krl 2:48 corresponds to the onset andx 6:5 krl 2:53tothecompletionofrigiditypercola-tion. The composition x 7:5krl 2:55 at which aFig. 1. Variation with composition/average coordination number of(a)Crystallizationtemperature Tcobtainedfromtotalheatow.(b) Heat capacityjumpduringglasstransitionobtainedfromthereversibleheatow DCRp :(c)Relaxationenthalpyobtainedfromthenon-reversing heatow DHNR:P.Zaheerudeen Sahebetal./SolidStateCommunications 129(2004)765768 766pronounced minimum is seen in Tc is likely to correspond tothe chemical threshold of the system. The compositiondependenceofTc(atwhichthematerialdevitries)canbecompared with the composition dependence of crystal-lizationpressures PT: Theearlier studies haverevealedthat PTof many chalcogenide glasses exhibit a sharpmaximumat the rigidity percolation threshold and aminimum at the chemical threshold [16], which areconsistentwiththepresentobservation.Fig. 1(b)showsthevariationofthechangeinspecicheatcapacityduringtheglasstransition,obtainedfromthereversing heat ow curve DCRp as a function ofcomposition/averagecoordinationnumber. It canbeseenfrom this gure that a maximum and an inexion is seen inDCRpat the onset and the completion of the rigiditypercolation. Further, a minimum is observed at the proposedchemicalthresholdofthesystem.The change in the specic heat DCp at the glasstransition is the manifestation of the congurational degreesoffreedomofthesystemcharacteristicoftheliquidstateabove the transition [17]. The motions available in the liquidstate, whichare lockedinbelowthe glass transitionareexclusively congurational and DCp; which reects these, isthereforeknownas thecongurational heat capacity. Anideal glassisexpectedtoshowonlysmall congurationalchanges as it is taken through the supercooled liquidstate. When a glass is heated along the transition region, theliquidlikecongurationisregainedwhichisregisteredasa small change in DCp: Tatsumisago et al., [18] in thestudies on composition dependence of thermal properties ofGeAsSeglasseshaveinterpretedthatDCpvaluescouldbe related to the ease of glass formation. The smaller DCp isa characteristic feature of a fragile glass, which has a greaterglass forming ability, whereashigher DCpcorresponds to astrongglass,whichhasalesserglass-formingtendency.Inthis context it is interestingtocompare the compositiondependence of glass forming difculty (GFD, which isinverse of glass forming ability) of GexSe1002x glasses. TheGFDof these samples exhibits a minimumaround therigidity percolation threshold and a maximum at the chemi-cal threshold[5], whichisconsistent withour conclusionthat the maximum and minimum seen in DCRpisassociatedwithrigiditypercolationandchemical threshold, respec-tively. It isinterestingtonoteherethat earlier studiesonGexSb5Se952x 12:5 # x # 35;GexSb10Se902x, 10 # x #32:5andGe10AsxTe902x 15 # x # 50glasses[19]haverevealedsimilarmaximaandminimainDCpvaluesattherigiditypercolationand chemical threshold,respectively.Itis also suggested by Boolchand et al. [20] that a minimum inDCpindicates the maximization of hetero-polar bondsoccurringnearthiscomposition(chemicalthresholdofthesystem).Enthalpyof relaxationmeasures the latent heat (con-gurationenergychanges) betweentheglassyandliquidstates, andit vanishes(or leadstoaminimum) whenthenetworkisoptimallyconstrained[21]. Fig. 1(c)showsthecompositional dependence of the relaxationenthalpyforGe20Te802xPbx glasses obtained from the non-reversing heatow curve DHNR; during a heating scan. It can be seen thatDHNRshows two distinct maxima at x 4 and 6.5, similarto the crystallization temperature, followed by a globalminimumat x 7:5: The minimumor vanishingof theDHNRat x 7:5isusuallytakenasanevidencefor theabsence of network stress [22]; the global minimum seen inDHNRalsoconrmsthatx 7:5isthechemicalthresholdforthepresentsystem.4.ConclusionThermal analysis of Ge20Te802xPbx 2 # x # 8 glasseshasbeenundertakenusingmodulateddifferentialscanningcalorimetry(MDSC).Thecrystallizationtemperatures Tcestimated from the total heat ow show detectablechangesat compositions x 4; 6.5 and 7.5. 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