Bismuth-induced dielectric relaxation in the„1−x…La„Mg1/2Ti1/2…O3–xBi„Mg1/2Ti1/2…O3 perovskite system

Andrei N. Salak,1,a� Victor M. Ferreira,2 José L. Ribeiro,3 Luís G. Vieira,3

Robert C. Pullar,4 and Neil McN. Alford4

1Department of Ceramics and Glass Engineering/CICECO, University of Aveiro, 3810-193 Aveiro, Portugal2Department of Civil Engineering/CICECO, University of Aveiro, 3810-193 Aveiro, Portugal3Department of Physics, University of Minho, 4710-057 Braga, Portugal4Centre for Physical Electronics and Materials, Department of Materials, Imperial College London,Exhibition Road, London SW7 2AZ, United Kingdom

�Received 30 January 2008; accepted 26 April 2008; published online 7 July 2008�

The temperature variation of the dielectric permittivity and loss of the solid solutions�1−x�La�Mg1/2Ti1/2�O3–xBi�Mg1/2Ti1/2�O3 ��1−x�LMT–xBMT� �0�x�0.3� measured at radio,microwave, and far infrared frequency ranges has been analyzed in comparison with that observedin other bismuth-containing and bismuth-free perovskite ceramics based on LMT. It has been foundthat the low temperature dielectric response of the �1−x�LMT–xBMT compositions with x�0 isfrequency dependent over a wide range from radio to microwave frequencies. The considerablecompositional growth of the dielectric permittivity and loss associated with the amount of bismuthin the system was revealed to be not contributed by the lattice polar phonon modes. The effect wassuggested to be related to the low-temperature dielectric relaxation process due to a hoppingmovement of charge carriers in crystallographic A-sites of the perovskite lattice. Particular role oflocal lattice distortions caused by the anisotropic chemical bonds involving bismuth 6s2 electrons ina localization of hopping charge carriers in perovskites and other oxygen-octahedral compositionsis considered. The characteristic features of the Bi-induced dielectric relaxation and those typical ofthe ferroelectric relaxors are compared and discussed. © 2008 American Institute of Physics.�DOI: 10.1063/1.2951890�

I. INTRODUCTION

Lead-free compositions have been intensively explored,both as potential replacements for some toxic/expensive ma-terials traditionally used in electronics, and as possible can-didates for novel areas of application. Environment-friendlymaterials with extended temperature and frequency operatingranges are required. In this respect, bismuth-based perovs-kites, pyrochlores, and other oxygen-octahedral composi-tions are closely considered. The prominent electromechani-cal characteristics of solid solutions in the systemsPbTiO3-BiBO3 �Refs. 1 and 2� and PbTiO3–Bi�B� ,B��O3

�Refs. 3–6� have recently been reported. Moreover, there isalso evidence that some Bi-containing metastable perovs-kites are structural and are likely dielectric analogs of leadtitanate.7,8 The low sintering temperatures of the ceramicsbased on bismuth make them attractive for another area ofapplication—in low-temperature cofired ceramic �LTCC�packages. It is suggested that Bi2�B� ,B��2O7 and�Bi,B��2�B� ,B��2O7 pyrochlores9–12 are promising materialsfor LTCC technology. In spite of their increased andfrequency-dependent dielectric loss induced by low-temperature dielectric relaxation,11 such compositions arewidely examined with regard to their use in high-frequencycircuits.

Recently, the system �1−x�La�Mg1/2Ti1/2�O3–xBi�Mg1/2Ti1/2�O3 ��1−x�LMT–xBMT� was investigated re-

garding the formation of perovskite solid solutions based onlanthanum magnesium titanate.13 A limited solubility �x�0.3� has been revealed in the system. It has also beenfound that within the solubility range, the crystal structure ofBi-substituted LMT possesses monoclinic symmetry �spacegroup P21 /n�, allowing for B-site cation ordering andoxygen-octahedra rotations. Although the crystal structure ofthe �1−x�LMT–xBMT solid solutions is the same over thewhole range of existence, their values of temperature coeffi-cient of capacitance ��C� at radio frequencies demonstrate anonmonotonic compositional variation. The low-temperaturedielectric response of the LMT-BMT ceramics is frequencydependent. The appearance and localization of the dispersiveranges are certainly governed by the amount of bismuth inthe system. It was also suggested13 that this dielectric relax-ation process, as well as conduction of the localized chargecarriers, are the most likely reasons for the �C�x� behaviorobserved in �1−x�LMT–xBMT.

Similar dependence of the dielectric response has re-cently been observed in the LMT– �Na1/2Bi1/2�TiO3 �NBT�ceramics.14 In this system, the range of the frequency-dependent behavior is also shifted with increasing NBT con-tent. The dielectric relaxation and its compositional variationin the �1−y�LMT–yNBT ceramics has been attributed to thecontent of bismuth. This effect is also believed15 to be theuniversal feature of oxygen-octahedral systems with disor-dered Bi3+ cations at the A-site. Dielectric studies over awide frequency range �100 Hz–100 THz� performed on bis-muth pyrochlores suggested that their dielectric permittivitya�Electronic mail: salak@cv.ua.pt.

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and losses at low temperatures are mainly contributed by thedielectric relaxation rather than the polar phonons.11,16 What-ever the case, this phenomenon certainly needs detailed in-vestigation and generalization.

In this paper, we present and describe the dielectric re-sponse of the perovskite ceramics �1−x�LMT–xBMT �0�x�0.3� at radio, microwave, and far infrared �FIR� fre-quency ranges. The macroscopic dielectric studies werecomplemented with the investigation of the local microwavedielectric properties using an evanescent microwave probe�EMP�. Possible contributions to the dielectric permittivityand loss of the Bi-substituted LMT ceramics have been con-sidered and analyzed in comparison with those revealed inother bismuth-containing oxygen-octahedral systems.

II. EXPERIMENT

Solid solutions �1−x�LMT–xBMT with the composition0�x�0.3 were prepared by the conventional ceramic routefrom the respective oxides and carbonates. A detailed de-scription of the preparation procedure and the crystal struc-ture characterization of the ceramics can be foundelsewhere.13 Cylindrical samples of about 7 mm in diameterand 6–8 mm length were used in microwave dielectric mea-surements and EMP studies. Shorter samples of the samediameter were polished to form disks 0.4–0.5 mm thick forradio-frequency dielectric measurements and FIR spectros-copy.

EMP, otherwise known as Scanning Evanescent Micro-wave Microscopy �SEMM�, measurements were carried outon samples polished to a 1 �m finish. The relative permit-tivity ���� of the ceramics was evaluated from the observedshift in the resonant frequency of EMP tip ��2.4 GHz�.17

Single crystals of MgO, LaAlO3, and SrTiO3 were used asthe EMP calibration standards.

The samples for radio-frequency dielectric investigationswere electroded with platinum paste and annealed at 1270 K.Dielectric permittivity ���� and loss tangent �tan �� weremeasured as a function of temperature within a frequencyrange of 100 Hz–1 MHz using a Precision LCR meter �HP4284A� and an Impedance/Gain-Phase Analyzer �Solartron1260�. The measurements were performed over the intervalof 10–480 K both upon heating and cooling with a rate of1.5 K min−1 using a cryostat �Displex APD Cryogenics,10–300 K� and an environment chamber �Delta Design9023, 95–480 K�. The room temperature permittivity, qual-ity factor �Q�, and resonant frequency �f� of the samples at amicrowave frequency range were estimated by an adaptationof the Hakki–Coleman method18,19 using a 10 MHz–20 GHzScalar Analyzer �IFR 6823�. Temperature variations of the fand Q values were measured using a Transmission/ReflectionNetwork Analyzer �HP 8722ET� in the range of 15–300 Kupon cooling at a rate of 2 K min−1. The measurements werecarried out in an oxygen-free cavity of high-conductivitycopper cooled by a CTI Cryogenics Model 22 Refrigeratorwith an 8200 Compressor coupled to a Lakeshore 330 Tem-perature Controller

The samples investigated by FIR spectroscopy were pol-ished to 0.25 �m finish. IR reflectivity measurements were

carried out with a Bruker IFS-66V spectrometer. Room tem-perature pyroelectric detectors of deuterated triglycine sul-fate with high density polyethylene or KBr windows andMylar 6�-M8 or KBr beam splitters were used to cover thespectral range of 40–2000 cm−1. The complex dielectricfunctions at IR frequencies were evaluated by fitting the re-flectivity spectra with the factorized form of the dielectricfunction,20

�*��� = ����� + i����� = ���j=1

n jLO

2 − �2 + i� jLO

jTO2 − �2 + i� jTO

, �1�

where �*��� is related to the reflectivity R��� by

R��� = ���*��� − 1��*��� + 1

�2

, �2�

jTO�LO� and jTO�LO� represent the frequency and dampingcoefficient of the jth transversal �longitudinal� optical mode,respectively, and �� is the permittivity at optical frequencies.

III. RESULTS

A. Crystal structure

It has been recently shown13 that the crystal structuresymmetry of �1−x�LMT–xBMT remains the monoclinicP2�n over the whole range of existence of the single-phasesolid solutions �0�x�0.3�. Moreover, their unit cell volume�Vp� was found to be weakly dependent on x, varying in anonmonotonic way. The observed weak Vp�x� dependenceseems normal, since being equally coordinated, La3+ andBi3+ have essentially similar ionic radii. Nevertheless, oneshould take the different character of the chemical bond in-volving either lanthanum or bismuth into consideration. Inparticular, LMT is principally an ionic solid,21 in contrast tothe perovskite BMT where the interatomic coupling �particu-larly, Bi–O: 6s2-2p6� is suggested to be mainly of covalenttype.22 Indeed, it is known that some compositions BiBO3

and Bi�B� ,B��O3 preferentially adopt pyrochlore structure inwhich the spontaneous polarization of bismuth 6s2 electronsstabilizes a less symmetric coordination of Bi3+ with asmaller coordination number.23 However, the majority ofcomplex Bi-based compositions of the above types, includ-ing BMT, does not exist as a single phase at normal pressureand their metastable perovskite phase can be obtained in spe-cial conditions only.7,22 The metastable perovskite BMT hasbeen revealed at room temperature to have the orthorhombicstructure �most likely, Pnnm� with both the antiferroelectri-clike displacements of Bi3+ cations and the antiphase tiltingof oxygen octahedra.22 At the same time, it has been statedthat the spontaneous polarization of the 6s2 core may inducea ferroic displacement of bismuth in preference to anoxygen-octahedra tilting.24 It appears that an origin of anti-parallel displacement of A-cation is distinct in LMT andBMT. Unlike LMT, magnesium and titanium are not orderedin BMT. Unit cell volume of BMT is �2.5% larger than thatof LMT, indicating the less close-packed structure of thebismuth-based composition. One can suggest these two per-ovskites to be more different than similar in terms of theircrystal chemistry. We believe that this difference is a reason

014105-2 Salak et al. J. Appl. Phys. 104, 014105 �2008�

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of the limited solubility observed in LMT-BMT and othersystems where Bi3+ substitutes for La3+ in A-site. Chen etal.25 have recently reported that the single-phase perovskitecompositions �1−x�LaCrO3–xBiCrO3 are only for 0�x�0.35 and adopt LaCrO3-type structure over the range ofexistence. These authors25 suggested that a volatilization ofbismuth oxide prevents the forming of the single perovskitephase when the amount of bismuth is more than 35 mol %.However, it has been shown13 that sintering in a Bi2O3-richenvironment does not increase the bismuth substitution ratein the �1−x�LMT–xBMT ceramics. Hence, the volatilizationseems not to be the main reason for the limited solubilityin these systems. It should be pointed out that in both�1−x�LMT–xBMT and �1−x�LaCaO3–xBi /CrO3, substitu-tion is allowed up to about one Bi3− cation per three unitcells. Moreover, the character of the Vp�x� dependence forboth systems changes in the middle of the solubility range �atx�0.15�.13,25 In this respect, it does not seem an accidentalcoincidence that the anomalylike variation of the unit cellvolume is also observed in the �1−y�LMT–yNBT perovskiteceramics at the same bismuth content �Fig. 1�. The disconti-nuity in the compositional variation of the crystal structureparameters of the �1−y�LMT–yNBT solid solutions at abouty=0.3 has been suggested to be due to possible appearanceof–Bi–O–Bi–chains when the relative amount of bismuth isclose to one per six primitive perovskite unit cells.14 Thecrystal structure of all the aforementioned solid solutions atsmall amounts of bismuth is certainly determined by the La-based matrix. At the same time, some stable atomic configu-rations caused by anisotropy of the 6s2-2p6 chemical bondare suggested to arise when the relative Bi /La ratio in theunit cell is close to some threshold values. These configura-tions �local lattice distortions� are believed to deflect a com-positional dependence of the crystal structure parameterseven if the macroscopic crystal symmetry remains the same.

The crystal structure of the �1−x�LMT–xBMT compo-sitions with 0�x�0.3 is mainly governed by the LMT-

based atomic network. At larger amounts of bismuth the per-ovskite structure is no longer stable enough to adjust to boththe ionic-type LMT-based atomic arrangement and the con-figuration determined by anisotropic chemical bond involv-ing bismuth 6s2 electrons. At the same time, some solubilityfrom the side of BMT in the LMT-BMT system is also pos-sible.

B. Infrared reflectivity

The room temperature IR reflectivity spectra of the�1−x�LMT–xBMT ceramics �0�x�0.3� are shown in Fig.2. A visual inspection reveals that the spectra become morediffuse with increasing bismuth content, although their es-sential features remain the same.

The first evaluation of the frequency and compositionaldependence of the complex dielectric function was obtainedby Kramers–Kronig inversion of the reflectivity spectra.Based on this preliminary analysis, both the number of re-flectivity bands discriminated and the approximate values ofthe corresponding transversal and longitudinal mode fre-quencies for each composition were estimated. A more pre-cise evaluation of �*��� was then performed by fitting thefactorized form of the dielectric function to the reflectivityspectra via Eq. �1�. Given the complexity of the spectra, we

FIG. 1. �Color online� Primitive perovskite unit cell volume �Vp� in�1−x�LMT–xBMT �Ref. 13� and �1−y�LMT-yNBT �Refs. 14 and 26� as afunction of the Bi content.

FIG. 2. �Color online� IR reflectivity spectra of the �1−x�LMT–xBMTceramics: experimental data �open symbols� and fit �solid lines�.

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have imposed the condition TO=LO in order to ensure thatthe fitted dielectric loss remained non-negative. The best fitsobtained in this manner are also shown in Fig. 2 for thedifferent compositions. The number of IR active modes de-tected by the fitting was found to be 15 for LMT �x=0� and14 for other compositions of the system. In general, this alsotestifies to the identical symmetry of the compositions overthe solubility range. The detailed consideration of the ob-served and expected number of the IR active modes based onthe results of the factor group analysis for LMT and theLMT-type structure compositions can be foundelsewhere.27,28

Figure 3 represents the calculated compositional varia-tion of the imaginary part of �*� for the �1−x�LMT–xBMT system. One should note that although the dielectricloss peaks widen when x is increased, these peaks are nota-bly sharper and narrower than those observed for LMT-NBTat the same bismuth-substitution rates.15 This reflects somecharacteristics of the phonon spectra of the LMT-BMT com-positions; in particular, the relatively smaller damping valuesof their TO phonons. Indeed, the average weighted sum ofthe TO phonon dampings, TO=� j=1

n jTO�� j /� j=1n �� j

�where �� j is the dielectric strength of the jth mode�, calcu-

lated as a function of x for �1−x�LMT–xBMT �Fig. 4�, dem-onstrates lesser growth with increasing bismuth content thanthat for LMT-NBT. This is not unexpected since the formeris less disordered than the later �in particular, the LMT-NBTsystem presents more disorder in both A- and B-sites�. Anexperimental error in the TO determination related to thefitting procedure was estimated not to exceed 8%. In thisrespect, the composition with x=0.05 certainly falls awayfrom the tendency of monotonic compositional variation ofthe average weighted dampings �Fig. 4�. The cause of theobserved deviation is not clear. Definitely, the TO valuefor x=0.05 should not be less than that for pure LMT. At thesame time, we note that the overall experimental error maybe higher since many other factors apart from fitting param-eters can affect the result. Thus, the improbably small valueof the average damping for the x=0.05 composition may bedue to some experimental inaccuracy, such as surface rough-ness effects.

The contribution of the polar lattice phonons to the di-electric response at microwave frequency range was evalu-ated by the extrapolation of the real and the imaginary partsof the IR dielectric function down to 0.26 cm−1 �7.8 GHz�.

C. Microwave dielectric properties

Figure 5 depicts the compositional variation of the di-electric permittivity and loss estimated by different methodsfor the �1−x�LMT–xBMT ceramics at room temperature. Asseen, both �� and tan � gradually increase with x. However,the ���x� value extrapolated from IR data demonstrates aweaker dependence on bismuth content in the system. Inaddition, although the extrapolated tan ��x� follows qualita-tively the same trend as that measured at microwave frequen-cies, the former varies within a much smaller range. Thedifference between the respective values of both ���x� andtan ��x� grows as x is increased starting from as small as10 mol % of bismuth. It should be noted that bismuth-freeceramic systems based on LMT show much better agreementbetween the values of the dielectric permittivity and lossestimated at different frequency ranges �including those ex-

FIG. 3. Imaginary part of the dielectric function ���� calculated from IRreflectivity data on the �1−x�LMT–xBMT system.

FIG. 4. Average weighted sum of the TO phonon dampings as a function ofBi content in �1−x�LMT–xBMT.

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trapolated from IR data�.27–29 It seems that a huge increase inmicrowave dielectric loss of the Bi-substituting LMT ceram-ics is the characteristic feature of their dielectric properties.Increasing amount of bismuth in �1−x�LMT–xBMT resultsin the growth of the lattice contribution to the imaginary partof the dielectric response at room temperature by about afactor of 2 �see Fig. 4 and inset on Fig. 5�. At the same time,the observed rise in the tan ��x� value measured at a micro-wave frequency range when x is changed from 0 to 0.3 wasfound to be more than two orders of magnitude �Fig. 5�. Toemphasize a distinction between Bi-containing and bismuth-free systems based on LMT, their key dielectric propertiesare compared in Table I. It should be stressed that a near-zerovalue of the temperature coefficient of the resonant fre-quency �� f� for Bi-containing solid solutions is achieved atsmaller substitution rates. At the same time, the value ofquality factor of these zero-� f compositions is seen to beabout one order of magnitude lower than that for the respec-tive bismuth-free solutions. It suggests another �nonlattice�contribution to the dielectric response of both the LMT-BMTand LMT-NBT ceramics. This contribution is thought tomake these ceramics more lossy �dissipating� and may alsoimpact the temperature behavior of their dielectric permittiv-ity modifying the values of both �C and � f �as these arelinearly related to each other�.34,35

Since EMP can reveal variations in the dielectric permit-tivity and loss at a gigahertz range due to grain boundaries,mixed phases, orientation of grains, impurities, etc., thistechnique was applied to study and to compare the micro-wave dielectric properties of the �1−x�LMT–xBMT ceram-ics obtained by two independent �the conventional macro-scopic and the novel nanoscale� methods. Unfortunately, thedielectric permittivity estimated from EMP scans was foundto vary within a wide range and this range extends withincreasing Bi content in the system. Limits of the permittiv-ity variation according to the EMP data, their average values,and the �� values measured by the microwave resonatormethod13 are listed in Table II for comparison. As seen, thevalues measured by different methods are in satisfactoryagreement only at small substitution rates. It has not beenobserved any certain correlation between the variation in thenanoscale permittivity of the ceramics and their surface to-pography �Fig. 6�. At the same time, in spite of some uncer-tainties, the EMP data suggest no contribution of microstruc-ture to the dielectric response of LMT-BMT at microwavefrequencies.

Unlike the bismuth-free compositions based on LMT,the microwave dielectric loss measured in the LMT-BMTand LMT-NBT ceramics has the same order of magnitude�for equal rates of Bi-substitutions�13–15 and its nature andbehavior seems to be of the same origin associated with acontent of bismuth in these systems.

D. Low-temperature dielectric relaxation

The dielectric response of the �1−x�LMT–xBMT ce-ramics was also investigated below room temperature. It has

FIG. 5. Relative permittivity ���, top panel� and dielectric loss tangent�tan �=1 /Q, bottom panel� for �1−x�LMT–xBMT as a function of x: mea-sured at a microwave range ���, radio frequencies ���, and extrapolatedfrom IR data ���. The inset shows the compositional variation of tan �=�� /�� estimated from the IR dielectric function.

TABLE I. The microwave dielectric properties of the solid solutions basedon LMT.

Systems of solid solutions Zero �C at �� Q · f �GHz� Reference

�1−z�LMT–zBaTiO3 z�0.5 60 9600 30�1−z�LMT–zSrTiO3 z�0.5 48 5800 28�1−z�LMT–zCaTiO3 z�0.5 43 12400 31�1−z�LMT–zLa2/3TiO3 z�0.5 47 8300 32�1−z�LMT–z�Na1/2Nd1/2�TiO3 z�0.6 42 7000 33�1−y�LMT–y�Na1/2Bi1/2�TiO3 y�0.3 57 905 14�1−x�LMT–xBi�Mg1/2Ti1/2�O3 x�0.15 47 765 13

TABLE II. Relative permittivity of the �1−x�LMT–xBMT ceramics mea-sured by EMP and conventional microwave resonant cavity method at agigahertz range.

x

�� estimated from EMP data�� measured by the

conventionalmethoda

Maximumvalue

Minimumvalue

Averagevalue

0.05 27.0 36.4 31.7 32.60.10 31.8 44.6 38.2 36.80.15 41.8 60.7 51.2 47.00.20 65.3 129.3 97.3 55.30.25 83.2 114.0 98.6 59.30.30 59.9 106.4 83.2 76.9

aReference 13.

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been revealed that the low-temperature dielectric permittivityand loss of the ceramics starting from x�0.1 are frequencydependent. Both �� and �� measured as a function of tem-perature over 10–300 K at a radio-frequency range areshown in Fig. 7. As expected, the ranges of the dispersivedielectric response regularly shift to higher temperatureswhen x is increased. The observed behavior of the dielectricresponse of the �1−x�LMT–xBMT ceramics is seen to bevery similar to that of the �1−y�LMT–yNBT compositionswith the same bismuth content �x=y /2�.15 At the same time,some distinct features of the dielectric behavior should bepointed out. Firstly, the �� value estimated at the range of thedispersive shoulder has a different rate of compositionalvariation in these ceramic systems. This is obviously causedby the different dielectric characteristics of NBT and BMT.Secondly, when comparing at the same amount of bismuth,

the �� peaks for LMT-NBT are regularly more diffuse thanthe respective peaks for LMT-BMT. This observation is con-sistent with the IR spectroscopy results and can be attributedto the fact that the former system is more disordered than thelatter with respect to the relative number, and the size andcharge differences of the atoms involved.

Figure 8 shows the �� peak temperature �Tm� measuredover a range of frequencies as a function of x in �1−x�LMT–xBMT. One can see that the difference �Tm be-tween the Tm’s measured at higher and lower frequency forthe same composition gradually increases with x. Since thisdifference can be considered as a measure of dispersion, weconclude that the LMT-NBT system is dielectrically moredispersive than the LMT-BMT one. In particular, the value of�Tm=Tm�1 MHz�−Tm�1 kHz� for LMT-BMT is regularlysmaller than that for LMT-NBT at the same Bi content.Moreover, when the amount of bismuth is changed from15 to 30 mol %, �Tm for the former system increases byonly �26% up, while the respective value for the latter in-creases by about a factor of 3.

The frequency variations of Tm for the LMT-NBT ce-ramics have been recently found15 to be well fitted to theempirical Vogel–Fulcher equation,36

FIG. 6. �Color online� Three dimensional maps of the topography �top� andrelative permittivity �bottom� for the �1−x�LMT–xBMT ceramics with x=0.15. Changing contrast from dark to bright corresponds to increasing thepermittivity value.

FIG. 7. Low-temperature dielectric re-sponse of the �1−x�LMT–xBMT ce-ramics at the range of 1 kHz–1 MHz�increasing frequency is denoted byarrows�.

FIG. 8. Compositional variation of the �� peak temperature �Tm� measuredover 316 Hz–1 MHz in �1−x�LMT–xBMT.

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� = �0 exp�−EA

k�Tm − TVF� , �3�

where � is the circular frequency of the applied field and theadjustable parameters, TVF, �0, and EA are the Vogel–Fulcherfreezing temperature, a pre-exponential factor �characteristicfrequency� and activation energy, respectively. It has turnedout that for LMT-BMT, Tm’s measured as a function of � atradio frequencies also obey this equation. The Tm��� datafitted to Eq. �3� are shown in Fig. 9, and the fit parametersare summarized in Table III. A comparison of these param-eters for the compositions of the LMT-BMT and LMT-NBTsystems15 with equivalent Bi content gives the values of TVF

for the former to be slightly smaller but close to those for thelatter. The respective values of both �0 and EA are of thesame order of magnitude. This strongly suggests that thelow-temperature relaxation phenomena in both systems areessentially similar.

The observed nonmonotonic dependence of temperaturecoefficient of capacitance �C on x is another feature of thedispersive dielectric response of the �1−x�LMT–xBMTceramics.13 Figure 10 shows this dependence as well as theway to estimate the coefficient from the near-linear ���T�variation. It has been suggested13 that the sudden increase of�C�x� when x�0.175 is caused by the frequency-dependentpart of the dielectric permittivity which shifts to higher tem-peratures as x is increased �stages A–C in Fig. 10�. Indeed, in

the vicinity of room temperature the ���T� curves becomemore rounded resulting in a smaller averaged slope.

A similar dielectric behavior has been observed in theLMT-NBT ceramics.14,15 In this system the range of thefrequency-dependent permittivity also shifts when increasingBi content �Fig. 11�. This range is seen to transform into thedispersive shoulder on the ���T� curves �stage D in Fig. 11�followed by the diffuse maximum.26

IV. DISCUSSION

The limited solubility from the side of LMT has beenfound in the perovskite LMT-BMT system, while the whole-range perovskite solid solutions are obtained in LMT-NBT.Nevertheless, the evident similarities revealed in the compo-sitional variations of the crystal structure parameters and thedielectric behaviors of both systems allow us to considerthese as analogous materials. In particular, although the per-ovskite compositions from the BMT-side of the former sys-tem can be sintered at special conditions only �e.g., usinghigh-pressure technique22�, it seems that some features of thedielectric properties of the BMT-rich solid solutions as wellas BMT itself can be discerned. However, this aspect is outof scope of the present work and will be considered else-where.

The low-temperature relaxation associated with bismuthcontent in the LMT-BMT and LMT-NBT ceramics contrib-utes to their dielectric permittivity and loss thereby modify-ing these characteristics. Although this certainly causes thelosses to multiply, the effect can be considered as a possiblemethod to tune the value of �C and hence control the dielec-tric behavior. It has already been suggested15 that, in general,this effect is typical of oxygen-octahedral compositions withdisordered Bi3+ cations at the A-site. Appropriate Bi-substitutions in such systems are believed to adjust both the

TABLE III. Parameters of the fit of the ���� ,T� data on �1−x�LMT–xBMT to Eq. �3�: freezing temperature �TVF�, characteristic fre-quency ��0�, relaxation time ��0�, and activation energy �EA�.

x TVF �K� �0 �s−1� �0=2 /�0 �s� EA �eV�

0.10 Peaks of �� in the vicinity of 10 K—at low-temperaturelimit of our dielectric measurements

0.15 23 8.49�107 1.18�10−8 0.0170.20 27 2.04�109 4.90�10−10 0.0360.25 32 5.62�109 1.78�10−10 0.0440.30 55 1.42�109 7.04�10−10 0.037

FIG. 9. �Color online� Vogel-Fulcher plots for the �� relaxation in LMT-BMT using Eq. �3�.

FIG. 10. �Color online� Temperaturedependences of the dielectric permit-tivity for the LMT-BMT ceramics �thestraight lines represent linear fits�.Right panel: the temperature coeffi-cient of capacitance ��C� estimated at1 MHz as a function of Bi content in�1−x�LMT–xBMT �Ref. 13�.

014105-7 Salak et al. J. Appl. Phys. 104, 014105 �2008�

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value of the dielectric permittivity and its temperature varia-tion for the demands of a specific application. This way oftailoring seems possible provided that the assumed operatingrange for the respective material is well above the range ofits dispersive dielectric response. We suggest the oxygen-octahedral compositions with isovalent Bi3+-substitution atthe A-site �like that for La3+� can be the most promising inthis respect since their dielectric loss peaks in the ���T� de-pendence are expected to be narrower and located at lowertemperature.

One characteristic feature of the low-temperature dielec-tric relaxation in the Bi-containing oxygen-octahedral com-positions deserves particular consideration. It was initiallyfound that in Bi2O3–ZnO–Nb2O5 cubic pyrochlore the fre-quency dependence of the dielectric loss peak position Tm

measured at radio frequencies follows well the Vogel–Fulcher relation.10 However, being supplemented with thedata obtained at a gigahertz range �up to 10 GHz�, the Tm���dependence can be better fitted to the Arrhenius equation�Eq. �3� with TVF=0�.11,12 The same feature of the dielectricresponse has also been observed in LMT-NBT.15 The dielec-tric measurements performed on the �1−x�LMT–xBMT ce-ramics with x=0.10 and 0.15 at about 6 GHz have revealedthat the relaxation still occurs in the gigahertz range, butdoes not obey the Vogel–Fulcher relation with the fit param-eters valid for the radio-frequency data. In both LMT-BMTand LMT-NBT, a departure from the Vogel-Fulcher relationincreases as the frequency range is extended above hundredskilohertz to a gigahertz range. This effect is more evident atsmaller rates of Bi-substitution15 �see also Tm vs � for x=0.15 in Fig. 9�.

Two relaxation processes �at lower and higher frequen-cies� with different respective values of �0 and EA were ini-

tially suggested to occur in the Bi-containing ceramics basedon LMT.15 However, more detailed analysis of available datatestifies rather to the distinct manifestations of the same pro-cess at different frequency ranges. Firstly, although the mag-nitudes of both � and EA estimated by fitting to the Arrhen-ius equation over the extended frequency range are generallyconsistent with those characteristic for ion jumping, their re-spective uncertainties are found to be rather large. Secondly,it seems that the role of disorder as a necessary condition ofthe low-temperature relaxation in the compositions contain-ing bismuth at the A-site should be revised. This relaxation inbismuth pyrochlore compounds was considered to resultfrom local hopping of Bi3+ cations in the positions partlyoccupied by cations of a different type10,16 or which arevacant.37 However, along with such A-site disordered sys-tems, a series of the stoichiometric Bi2�B� ,B� �2O7

pyrochlores9 were reported to exhibit the same relaxationphenomena at low temperatures.

It is known that localization of hopping charge carriersin solids is caused by either static disorder �such as structuraland/or compositional defects� or the polarizability of crystallattice resulting from local distortions.38 As suggested in partA of Results, local lattice distortions are likely to arise in theabove considered oxygen-octahedral systems due to aniso-tropic chemical bond involving Bi3+. Then the carriers mayoccupy bound states. We suggest that in this case, a hoppingmovement requires a smaller activation energy, probablycomparable with the values estimated for LMT-BMT at aradio-frequency range �Table III�: that is, several tens ofmeV, instead of the hundreds of meV typical of ion jumping.At relatively low concentrations of bismuth in such systems,the reversible dipoles induced by hopping carriers39 are in-dependent, and the respective relaxation process is describedby the Arrhenius law. When the amount of bismuth is in-creased, a distribution of the relaxation frequencies of thedipoles broadens out, and interaction between them appearsand intensifies. Correlated interaction between the dipoles isbelieved to result in a formation of polar entities similar tothe polar nanoregions �PNRs� revealed in ferroelectricrelaxors.40 In this case, the dispersive dielectric responseconditioned by the temperature and frequency behaviors ofthese polar entities obeys the Vogel–Fulcher relation. Wealso suggest that the distribution of the relaxation frequen-cies in the systems under consideration is not uniform. Theamount of induced dipoles contributing to the relaxation pro-cess at higher frequencies is much less, and so the dipoles arevirtually independent.

It has already been pointed out15 that the dispersive di-electric response revealed in the Bi-containing oxygen-octahedral systems is very similar to that of ferroelectric re-laxors. It is known that the necessary attributes of a“classical” ferroelectric relaxor are the following: short-range structure imperfections �such as defects, local disorder,and distortions� and a highly polarizable host lattice andPNRs.40,41 Indeed, the first two ingredients are formallyfound in the materials with the Bi-induced low-temperaturerelaxation; the existence of PNRs is supposed although notproven. At the same time, there is the distinctive feature ofthe true relaxors: they all are the prototypical soft ferroelec-

FIG. 11. �Color online� Dielectric permittivity of the �1−y�LMT-yNBTceramics at the range of 1 kHz–1 MHz as a function of temperature �Refs.14, 15, and 26�.

014105-8 Salak et al. J. Appl. Phys. 104, 014105 �2008�

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tric mode systems.40 Real ferroelectric phase transitions insuch systems can be induced by external factors. This essen-tial feature is certainly missing in the B-containing “nonfer-roelectric relaxor” materials.

Although the microscopic mechanism of the Bi-induceddielectric relaxation is not well understood, we suggest theprocesses responsible for the relaxation in the true ferroelec-tric relaxors and in these nonferroelectric relaxors to be in-dependent rather than associated. In fact, Bi-substitution �ifheterovalent� can definitely increase a rate of disorder andthereby promote a relaxor state in ferroelectriclike material.However, contributions from the different types of relaxationprocesses are easy recognized in both the strong high-temperature ferroelectric relaxors, such as Bi-substitutedPb�Zr,Ti�O3,42 and the BiScO3–PbTiO3 solid solutions,43,44

and the incipient ferroelectric SrTiO3 doped with bismuth,45

although the Bi-induced relaxation in the latter is masked bymore strong processes.

V. CONCLUSIONS

Single-phase solid solutions in the �1−x�LMT-xBMTsystem exist until the Bi-substitution rate reaches as high as30 mol %. Then the perovskite structure is no longer stableenough to contain both the ionic-type LMT-based atomic ar-rangement and the configuration determined by anisotropicchemical bond involving bismuth 6s2 electrons.

Dielectric behaviors of the Bi-containing ceramics basedon LMT with bismuth content higher than about 10 mol % ismore affected by the low-temperature relaxation than the lat-tice polar phonon modes. This relaxation process correlateswith the content of bismuth in these systems, and contributesto both the dielectric permittivity and loss over a wide rangefrom radio- to microwave frequencies. It is believed that theBi-induced low-temperature dielectric relaxation occurs inoxygen-octahedral systems with disordered Bi3+ cations atthe A-site as a universal feature regardless of their macro-scopic crystal lattice symmetry. This relaxation is suggestedto arise from a hopping movement of the charge carrierslocalized at A-sites of such systems due to defects and localdisorder, as well as local lattice distortions caused by aniso-tropy of the 6s2 �Bi3+�-2p6 �O2−� chemical bond.

When concentration of bismuth in these sites is rela-tively high, a correlated interaction between the hopping car-riers may result in a formation of polar entities. Then therespective relaxation frequencies �at least their low-frequency edge� obey the Vogel–Fulcher relation. It is alsosupposed that a distribution of the relaxation frequencies isnot uniform, so amounts of the induced dipoles contributingto the relaxation process at higher frequencies is much less.It this case, the dipoles are virtually independent, and therespective relaxation process is described by the Arrheniuslaw.

ACKNOWLEDGMENTS

The first author acknowledges the Foundation for Sci-ence and Technology �FCT-Portugal, Grant No. SFRH/BPD/14988/2004�. This work was also supported in part by the

Treaty of Windsor �Anglo-Portuguese� Programme �ActionB-24/06�.

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