Ferroelectric and piezoelectric properties of tungsten substituted SrBi 2Ta 2O 9ferroelectric ceramicsIndrani Coondoo *,S.K.Agarwal a ,A.K.Jha ba Superconductivity and Cryogenics Division,National Physical Laboratory,Dr K.S.Krishnan Road,New Delhi 110012,India bDepartment of Applied Physics,Delhi College of Engineering,Bawana Road,Delhi 110042,India1.IntroductionDefects in crystals significantly influence physical and various other properties of materials [1].For instance,as it is well known,doping by other elements leads to significant changes in the electrical properties of silicon.Historically,‘‘defect engineering’’has been developed in the field of semiconducting materials such as compound semiconductors as well as in diamond,Si and Ge [2–4].Subsequently,the concept of defect engineering has been applied to other functional materials,and the significant improve-ment in material properties have been achieved in high transition-temperature superconductors [5],amorphous SiO 2[6],photonic crystals [7]and also in the field of ferroelectrics,such as BaTiO 3,Pb(Ti,Zr)O 3(PZT),etc.[8,9].Various structural and electrical properties of bismuth layer-structured ferroelectrics (BLSF)are also strongly affected on deviation from stoichiometric composi-tions and defects have been recognized as a crucially important factor [10–13].It has been found that in BLSF small changes in chemical composition result in significantly altered dielectric and ferroelectric properties including dielectric constant and remanent polarization.In SrBi 2Ta 2O 9(SBT)and SrBi 2Nb 2O 9(SBN),orthor-hombic structural distortions with non-centrosymmetric spacegroup A 21am cause spontaneous ferroelectric polarization (P s )along a axis [14,15].SBT,a member of the BLSF family,has occupied an important position among the Pb-free ferroelectric memory materials [16–18].Tungsten (W 6+)has recently been investigated as a dopant for bismuth titanates and lanthanum doped bismuth titanates,in which the remanent polarization was observed to enhance when a small amount of Ti 4+was substituted by W 6+[19,20].With the objective to improve structural,dielectric and ferroelectric proper-ties,the hexavalent tungsten (W 6+)was chosen as a donor cation for partial replacement of the pentavalent tantalum (Ta 5+)SBT.In this report,the effect of tungsten substitution in SBT (SBTW),on the microstructural,ferroelectric and piezoelectric properties is reported.The results including the improvement in polarization properties have been discussed.2.ExperimentalSamples of compositions SrBi 2(W x Ta 1Àx )2O 9(SBWT),with x =0.0,0.025,0.050,0.075,0.10and 0.20were synthesized by solid-state reaction method taking SrCO 3,Bi 2O 3,Ta 2O 5and WO 3(all from Aldrich)in their stoichiometric proportions.The powder mixtures were thoroughly ground and passed through sieve of appropriate size and then calcined at 9008C in air for 2h.The calcined mixtures were ground and admixed with about 1–1.5wt%polyvinyl alcohol (Aldrich)as a binder and then pressed at $300MPa into disk shaped pellets.The pellets were sintered at 12008C for 2h in air.Materials Research Bulletin 44(2009)1288–1292A R T I C L E I N F O Article history:Received 3October 2008Received in revised form 5December 2008Accepted 6January 2009Available online 15January 2009Keywords:A.CeramicsC.X-ray diffractionD.FerroelectricityA B S T R A C TTungsten substituted samples of compositions SrBi 2(W x Ta 1Àx )2O 9(x =0.0,0.025,0.050,0.075,0.10and 0.20)were synthesized by solid-state reaction method and studied for their microstructural,electrical conductivity,ferroelectric and piezoelectric properties.The X-ray diffractograms confirm the formation of single phase layered perovskite structure in the samples with x up to 0.05.The temperaturedependence of dc conductivity vis-a`-vis tungsten content shows a decrease in conductivity,which is attributed to the suppression of oxygen vacancies.The ferroelectric and piezoelectric studies of the W-substituted SBT ceramics show that the remanent polarization and d 33values increases with increasing concentration of tungsten up to x 0.05.Such compositions with low conductivity and high P r values should be excellent materials for highly stable ferroelectric memory devices.ß2009Elsevier Ltd.All rights reserved.*Corresponding author.Present address:Liquid Crystal Group,National Physical Laboratory,Dr K.S.Krishnan Road,New Delhi 110012,India.Tel.:+919810361727;fax:+911125170387.E-mail address:indrani_coondoo@ (I.Coondoo).Contents lists available at ScienceDirectMaterials Research Bulletinj o ur n a l h o m e p a g e :w w w.e l se v i e r.c om /l oc a t e /m a t r e sb u0025-5408/$–see front matter ß2009Elsevier Ltd.All rights reserved.doi:10.1016/j.materresbull.2009.01.001X-ray diffractograms of the sintered samples were recorded using a Bruker diffractometer in the range 108 2u 708with CuK a radiation.The sintered pellets were polished to a thickness of 1mm and coated with silver paste on both sides for use as electrodes and cured at 5508C for half an hour.Electrical conductivity was performed using Keithley’s 6517A Electrometer.The polarization–electric field (P –E )hysteresis measurements were done at room temperature using an automatic P –E loop tracer based on Sawyer–Tower circuit.Piezoelectric charge co-efficient d 33was measured using a Berlincourt d 33meter after poling the samples in silicone–oil bath at 2008C for half an hour under a dc electric field of 60–70kV/cm.3.Results and discussion3.1.Structural and micro-structural studiesThe phase formation and crystal structure of the ceramics were examined by X-ray diffraction (XRD),which is shown in Fig.1.The XRD patterns of the samples show the characteristic peaks of SBT.The peaks have been indexed with the help of a computer program–POWDIN [21]and the refined lattice parameters are given in Table 1.It is observed that a single phase layered perovskite structure is maintained in the range 0.0 x 0.05.Owing to the same co-ordination number i.e.6and the smallerionic radius of W (0.60A˚)in comparison to Ta (0.64A ˚),there is a high possibility of tungsten occupying the tantalum site.The observance of unidentified peak of very low intensity in the compositions with x >0.05indicates the solubility limit of W concentration in SBT.The unidentified peak is possibly due to tungsten not occupying the Ta sites in the structure as the intensity of this peak is observed to increase with tungsten content.Composition and sintering temperature influences the micro-structure such as grain growth and densification of the specimen,which in turn control other properties of the material [11,13].The effects of W substitution on the microstructure have been examined by SEM and the obtained micrographs are shown in Fig.2.It shows the microstructure of the fractured surface of the studied samples.It is clearly observed that W substitution has pronounced effect on the average grain size and homogeneity of the grains.Randomly oriented and anisotropic plate-like grains are observed in all the samples.It is also observed that the average grain size increases gradually with increasing W content.The average grain size in the sample with x =0.0is $2–3m m while that in the sample with x =0.20the size increases to $5–7m m.3.2.Electrical studiesThe electrical conductivity of ceramic materials encompasses a wide range of values.In insulators,the defects w.r.t.the perfect crystalline structure act as charge carriers and the consideration of charge transport leads necessarily to the consideration of point defects and their migration [22].Many mechanisms were put forward to explain the conductivity mechanism in ceramics.Most of them are approximately divided into three groups:electronic conduction,oxygen vacancies ionic conduction,and ionic and p-type mixed conduction [22].Intrinsic conductivity results from the movement of the component ions,whereas conduction resulting from the impurity ions present in the lattice is known as extrinsic conductivity.At low temperature region (ferroelectric phase),the conduction is dominated by the extrinsic conduction,whereas the conduction at the high-temperature paraelectric phase ($300–7008C)is dominated by the intrinsic ionic conduction [23,25].Fig.3shows the temperature dependence of dc conductivity (s dc )for the undoped and doped SBT samples.The curves show that the conductivity increases with temperature.This is indicative of negative temperature coefficient of resistance (NTCR)behavior,a characteristic of dielectrics [22].It is observed in Fig.3that throughout the temperature range,the dc conductivity of the doped samples are nearly two to three orders lower than that of the undoped sample.Two predominant conduction mechanisms indicated by slope changes in the two different temperature regions are observed in Fig.3.Such changes in the slope in the vicinity of the ferro-paraelectric transition region have been observed in other ferroelectric materials as well [23,24].In addition,it is also observed (Table 2)that the activation energy calculated using the Arrhenius equation [22]in the paraelectric phase increase from $0.80eV for the undoped sample to $2eV for the doped samples.The X-ray photoemission spectroscopic study has confirmed that when Bi 2O 3evaporates during high-temperature processing,vacancy complexes are formed in the (Bi 2O 2)2+layers [26].As a result,defective (Bi 2O 2)2+layers are inherently present in SBT.The undoped SBT shows n-type conductivity,since when oxygen vacancies are created,it leaves behind two trapped electrons [27]:O o !12O 2"þV o þ2e 0(1)where O o is an oxygen ion on an oxygen site,V o is a oxygen vacant site and e 0represents electron.The conductivity in the perovskites can be described as an ordered diffusion of oxygen vacancies [28].Their motion is manifested by enhanced ionic conductivity associated with an activation energy value of $1eV [26].These oxygen vacancies can be suppressed by addition of donors,since the donor oxide contains more oxygen per cation than the host oxide it replaces [29].It has been reported that conductivity in Bi 4Ti 3O 12(BIT)can be significantly decreased,up to three orders of magnitude with the addition of donors,such as Nb 5+and Ta 5+at the Ti 4+sites [23,30].A few other studies on layered perovskites have also reported a decrease inconductivityFig.1.XRD patterns of SrBi 2(W x Ta 1Àx )2O 9samples sintered at 12008C.Table 1Lattice parameters of SrBi 2(W x Ta 1Àx )2O 9samples.Concentration of W a (A ˚)b (A ˚)c (A ˚)0.0 5.5212 5.513924.92230.025 5.5214 5.520225.10790.05 5.5217 5.519925.05850.075 5.5191 5.504525.05670.10 5.5142 5.506125.0850.205.51335.493925.0861I.Coondoo et al./Materials Research Bulletin 44(2009)1288–12921289with addition of donors [23,24,31].In the present study,the Ta 5+-site substitution by W 6+in SBT can be formulated using a defect chemistry expression as WO 3þV o!Ta 2O 512W Ta þ3O o (2)It shows that the oxygen vacancies are reduced upon the substitution of donor W 6+ions for Ta 5+ions.Hence,it is reasonable to believe that the conductivity in SBT is suppressed by donor addition.As per the above discussion,the high s dc observed in the undoped SBT (Fig.3)can be attributed to the motion of oxygen vacancies.As already discussed,the doped samples show reduced conductivity because the transport phenomena involving oxygen vacancies are greatly reduced.The high E a value of $1.75–2eVcorresponding to the high-temperature region in the doped ceramics is consistent with the fact that in the donor-doped materials,the ionic conduction reduces [32].The activation energy E a in the low temperature ferroelectric region (Table 2)corre-sponds to extrinsic conduction.At lower temperatures the extrinsic conductivity results from the migration of impurity ions in the lattice.Some of these impurities may also be associated with lattice defects.Pure SBT has large number of Schottky defects (oxygen vacancies)in addition to impurity ions whereas in the doped samples,due to charge neutrality,there is relatively less content of oxygen vacancies.Thus,in the doped samples the conductivity in the low temperature region is largely due to the impurity ions only.This explains the high activation energy in pure SBT in the low temperature region compared to doped samples (Table 2).In the high-temperature region,the value of E a in the doped samples is observed to increase with W concentration up to x =0.05but beyond that,it decreases (Table 2).The decrease in the activation energy for samples with x >0.05suggests an increase in the concentration of mobile charge carriers [33].This observation can be ascribed to the existence of multiple valence states of tungsten.Since tungsten is a transitional metal element,the valence state of W ions in a solid solution most likely varies from W 6+to W 4+depending on the surrounding chemical environment [34].When W 4+are substituted for the Ta 5+sites,oxygen vacancies would be created,i.e.one oxygen vacancy would be created for every two tetravalent W ions entering the crystal structure,whichFig.3.Variation of dc conductivity with temperature in SrBi 2(W x Ta 1Àx )2O 9samples.Fig.2.SEM micrographs of fractured surfaces of SrBi 2(W x Ta 1Àx )2O 9samples with (a)x =0.0,(b)x =0.025,(c)x =0.050,(d)x =0.075,(e)x =0.10and (f)x =0.20Table 2Activation energy (E a )in the high-temperature paraelectric region and low temperature ferroelectric region;Curie temperature (T c )in SrBi 2(W x Ta 1Àx )2O 9samples.Concentration of W E a (high temp.)(eV)E a (low temp.)(eV)T c (8C)0.00.790.893110.025 1.920.593080.05 1.960.543250.075 1.940.543380.10 1.860.573680.201.740.54390I.Coondoo et al./Materials Research Bulletin 44(2009)1288–12921290explains the increase in the concentration of mobile charge carriers which ultimately results in an decrease in the E a beyond x>0.05. Hence it is reasonable to conclude that W ions in the SBWT exists as a varying valency state,i.e.at lower doping concentration they exist in hexavalent state(W6+)and at a higher doping concentra-tion,they tend to exist in lower valency states[8].The P–E loops of SrBi2(Ta1Àx W x)2O9are shown in Fig.4.It is observed that W-doping results in formation of well-defined hysteresis loops.Fig.5shows the compositional dependence of remanent polarization(2P r)and the coercivefield(2E c)of SrBi2(Ta1Àx W x)2O9samples.Both the parameters depend on W content of the samples.It is observed that2P rfirst increases with x and then decreases while2E cfirst decreases with x and then increases(Fig.5).The optimum tungsten content for maximum2P r ($25m C/cm2)is observed to be x=0.075.It is known that ferroelectric properties are affected by compositional modification,microstructural variation and lattice defects like oxygen vacancies[10,35,36].In hard ferroelectrics, with lower valent substituents,the associated oxide vacancies are likely to assemble in the vicinity of domain walls[37,38].These domains are locked by the defects and their polarization switching is difficult,leading to an increase in E c and decrease in P r[38]. On the other hand,in soft ferroelectrics,with higher valent substituents,the defects are cation vacancies whose generation in the structure generally increases P r.Similar observations have been made in many reports[38–41].Watanabe et al.[42]reported a remarkable improvement in ferroelectric properties in the Bi4Ti3O12ceramic by adding higher valent cation,V5+at the Ti4+ site.It has also been reported that cation vacancies generated by donor doping make domain motion easier and enhance the ferroelectric properties[43].Further,it is known that domain walls are relatively free in large grains and are inhibited in their movement as the grain size decreases[44].In the larger grains, domain motion is easier which results in larger P r.Also for the SBT-based system,it is known that with increase in the grain size the remanent polarization also increases[45,46].Based on the obtained results and above discussion,it can be understood that in the undoped SBT,the oxygen vacancies assemble at sites near domain boundaries leading to a strong domain pinning.Hence,as observed,well-saturated P–E loop for pure SBT is not obtained.But in the doped samples,the suppression of the oxygen vacancies reduces the pinning effect on the domain walls,leading to enhanced remanent polarization and lower coercivefield.Also,the increase in grain size in tungsten added SBT,as observed in SEM micrographs(Fig.2)contribute to the increase in polarization values.In the present study,the grain size is observed to increase with increasing W concentration.However, the2P r values do not monotonously increase and neither the E c decreases continuously with increasing W concentration(Fig.5). The variation of P r and E c beyond x>0.05,seems possibly affected by the presence of secondary phases(observed in XRD diffracto-grams),which hampers the switching process of polarization [47–50].Also,beyond x>0.05the increase in the number of charge carriers in the form of oxygen vacancies leads to pinning of domain walls and thus a reduction in the values of P r and increase in E c is observed.Fig.6shows the variation of piezoelectric charge coefficient d33 with x in the SrBi2(Ta1Àx W x)2O9.The d33values increases with increase in W content up to x=0.05.A decrease in d33values is observed in the samples with x!0.075.The piezoelectric coefficient,d33,increases from13pC/N in the sample with x=0.0to23pC/N in the sample with x=0.05.It is known that the major drawback of SBT is its relatively higher conductivity,which hinders proper poling[51].High resistivity is therefore important for maintenance of poling efficiency at high-temperature[52,53].The W-doped SBT samples show an electrical conductivity value up to three orders of magnitude lower than that of undoped sample(Fig.3).The positional variation of2P r and2E c in SrBi2(W x Ta1Àx)2O9samples.Fig.6.Variation of d33in SrBi2(W x Ta1Àx)2O9samples.Fig. 4.P–E hysteresis loops in SrBi2(W x Ta1Àx)2O9samples recorded at roomtemperature.I.Coondoo et al./Materials Research Bulletin44(2009)1288–12921291decrease in conductivity upon donor doping improve the poling efficiency resulting in the observed higher d33values.Moreover, since the grain size increases with W content in SBT,it is reasonable to believe that the increase in grain size will also contribute to the increase in d33values[54].The decrease in the value of d33for samples with x!0.075is possibly due to the presence of secondary phases as observed in diffractograms[1,51,55]and the increase in oxygen vacancies for samples with x>0.05.4.ConclusionsX-ray diffractograms of the samples reveal that the single phase layered perovskite structure is maintained in the samples with tungsten content x0.05.SEM micrographs reveal that the average grain size increases with increase in W concentration. The temperature dependence of the electrical conductivity shows that tungsten doping results in the decrease of conductivity by up to three order of magnitude compared to W free SBT.All the tungsten-doped ceramics have higher2P r than that of the undoped sample.The maximum2P r($25m C/cm2)is obtained in the composition with x=0.075.The reduced conductivity allows high-temperature poling of the doped samples.Such compositions with low loss and high P r values should be excellent materials for highly stable ferroelectric memory devices.The d33value is observed to increase with increasing W content up to x0.05.The value of d33 in the composition with x=0.05is$23pC/N as compared to$13 pC/N in the undoped sample.AcknowledgmentsThe authors sincerely thank Prof.P.B.Sharma,Dean,Delhi College of Engineering,India for his generous support and providing ample research infrastructure to carry out the research work.The authors are thankful to Dr.S.K.Singhal,Scientist, National Physical Laboratory,India for his fruitful discussion and suggestions.References[1]Y.Noguchi,M.Miyayama,K.Oikawa,T.Kamiyama,M.Osada,M.Kakihana,Jpn.J.Appl.Phys.41(2002)7062.[2]A.Bonaparta,P.Giannozzi,Phys.Rev.Lett.84(2000)3923.[3]S.Connell,E.Siderashaddad,K.Bharuthram,C.Smallman,J.Sellschop,M.Bos-senger,Nucl.Instrum.Methods B85(1994)508.[4]T.Derry,R.Spits,J.Sellschop,Mater.Sci.Bull.11(1992)249.[5]K.Salama,D.F.Lee,Supercond.Sci.Technol.7(1994)177.[6]H.Hosono,Y.Ikuta,T.Kinoshita,M.Hirano,Phys.Rev.Lett.87(2001)175501.[7]S.Noda,A.Chutinan,M.Imada,Nature407(1999)608.[8]S.Shannigrahi,K.Yao,Appl.Phys.Lett.86(2005)092901.[9]G.H.Heartling,nd,J.Am.Ceram.Soc.54(1971)1.[10]H.Watanabe,T.Mihara,H.Yoshimori,C.A.Paz De Araujo,Jpn.J.Appl.Phys.34(1995)5240.[11]T.Atsuki,N.Soyama,T.Yonezawa,K.Ogi,Jpn.J.Appl.Phys.34(1995)5096.[12]T.Noguchi,T.Hase,Y.Miyasaka,Jpn.J.Appl.Phys.35(1996)4900.[13]M.Noda,Y.Matsumuro,H.Sugiyama,M.Okuyama,Jpn.J.Appl.Phys.38(1999)2275.[14]R.E.Newnham,R.W.Wolfe,R.S.Horsey,F.A.D.Colon,M.I.Kay,Mater.Res.Bull.8(1973)1183.[15]A.D.Rae,J.G.Thompson,R.L.Withers,Acta Crystallogr.Sect.B:Struct.Sci.48(1992)418.[16]H.M.Tsai,P.Lin,T.Y.Tseng,J.Appl.Phys.85(1999)1095.[17]Y.Shimakawa,Y.Kubo,Y.Nakagawa,T.Kamiyama,H.Asano,F.Izumi,Appl.Phys.Lett.74(1999)1904.[18]Y.Noguchi,M.Miyayama,T.Kudo,Phys.Rev.B63(2001)214102.[19]J.K.Kim,T.K.Song,S.S.Kim,J.Kim,Mater.Lett.57(2002)964.[20]W.T.Lin,T.W.Chiu,H.H.Yu,J.L.Lin,S.Lin,J.Vac.Sci.Technol.A21(2003)787.[21]Wu E.,POWD,An interactive powder diffraction data interpretation and indexingprogram Ver2.1,School of Physical Science,Flinders University of South Australia, Bedford Park,S.A.JO42AU.[22]R.C.Buchanan,Ceramic Materials for Electronics:Processing,Properties andApplications,Marcel Dekker Inc.,New York,1998.[23]H.S.Shulman,M.Testorf,D.Damjanovic,N.Setter,J.Am.Ceram.Soc.79(1996)3124.[24]M.M.Kumar,Z.G.Ye,J.Appl.Phys.90(2001)934.[25]Y.Wu,G.Z.Cao,J.Mater.Res.15(2000)1583.[26]B.H.Park,S.J.Hyun,S.D.Bu,T.W.Noh,J.Lee,H.D.Kim,T.H.Kim,W.Jo,Appl.Phys.Lett.74(1999)1907.[27]C.A.Palanduz,D.M.Smyth,J.Eur.Ceram.Soc.19(1999)731.[28]C.R.A.Catlow,Superionic Solids&Solid Electrolytes,Academic Press,New York,1989.[29]M.V.Raymond,D.M.Symth,J.Phys.Chem.Solids57(1996)1507.[30]S.S.Lopatin,T.G.Lupriko,T.L.Vasiltsova,N.I.Basenko,J.M.Berlizev,Inorg.Mater.24(1988)1328.[31]M.Villegas,A.C.Caballero,C.Moure,P.Duran,J.F.Fernandez,J.Eur.Ceram.Soc.19(1999)1183.[32]Y.Wu,G.Z.Cao,J.Mater.Sci.Lett.19(2000)267.[33]B.H.Venkataraman,K.B.R.Varma,J.Phys.Chem.Solids66(2005)1640.[34]C.D.Wagner,W.M.Riggs,L.E.Davis,F.J.Moulder,Handbook of X-ray Photoelec-tron Spectroscopy,Perkin Elmer Corp.,Chapman&Hall,1990.[35]Y.Noguchi,I.Miwa,Y.Goshima,M.Miyayama,Jpn.J.Appl.Phys.39(2000)1259.[36]M.Yamaguchi,T.Nagamoto,O.Omoto,Thin Solid Films300(1997)299.[37]W.Wang,J.Zhu,X.Y.Mao,X.B.Chen,Mater.Res.Bull.42(2007)274.[38]T.Friessnegg,S.Aggarwal,R.Ramesh,B.Nielsen,E.H.Poindexter,D.J.Keeble,Appl.Phys.Lett.77(2000)127.[39]Y.Noguchi,M.Miyayama,Appl.Phys.Lett.78(2001)1903.[40]Y.Noguchi,I.Miwa,Y.Goshima,M.Miyayama,Jpn.J.Appl.Phys.39(2000)L1259.[41]B.H.Park,B.S.Kang,S.D.Bu,T.W.Noh,L.Lee,W.Joe,Nature(London)401(1999)682.[42]T.Watanabe,H.Funakubo,M.Osada,Y.Noguchi,M.Miyayama,Appl.Phys.Lett.80(2002)100.[43]S.Takahashi,M.Takahashi,Jpn.J.Appl.Phys.11(1972)31.[44]R.R.Das,P.Bhattacharya,W.Perez,R.S.Katiyar,Ceram.Int.30(2004)1175.[45]S.B.Desu,P.C.Joshi,X.Zhang,S.O.Ryu,Appl.Phys.Lett.71(1997)1041.[46]M.Nagata,D.P.Vijay,X.Zhang,S.B.Desu,Phys.Stat.Sol.(a)157(1996)75.[47]J.J.Shyu,C.C.Lee,J.Eur.Ceram.Soc.23(2003)1167.[48]I.Coondoo,A.K.Jha,S.K.Agarwal,Ferroelectrics326(2007)35.[49]T.Sakai,T.Watanabe,M.Osada,M.Kakihana,Y.Noguchi,M.Miyayama,H.Funakubo,Jpn.J.Appl.Phys.42(2003)2850.[50]C.H.Lu,C.Y.Wen,Mater.Lett.38(1999)278.[51]R.Jain,V.Gupta,A.Mansingh,K.Sreenivas,Mater.Sci.Eng.B112(2004)54.[52]I.S.Yi,M.Miyayama,Jpn.J.Appl.Phys.36(1997)L1321.[53]A.J.Moulson,J.M.Herbert,Electroceramics:Materials,Properties,Applications,Chapman&Hall,London,1990.[54]H.T.Martirena,J.C.Burfoot,J.Phys.C:Solid State Phys.7(1974)3162.[55]R.Jain,A.K.S.Chauhan,V.Gupta,K.Sreenivas,J.Appl.Phys.97(2005)124101.I.Coondoo et al./Materials Research Bulletin44(2009)1288–1292 1292。
