Pressure evolution of resistance in framework structured materials α - Zr Mo 2 O 8 andα - Hf Mo 2 O 8A. S. Karandikar, G. D. Mukherjee, V. Vijayakumar, B. K. Godwal, S. N. Achary, and A. K. Tyagi Citation: Journal of Applied Physics 100, 013517 (2006); doi: 10.1063/1.2211312 View online: http://dx.doi.org/10.1063/1.2211312 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/100/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Resistive switching characteristics of nickel silicide layer embedded HfO2 film Appl. Phys. Lett. 100, 112901 (2012); 10.1063/1.3694045 Effect of ZrO x / HfO x bilayer structure on switching uniformity and reliability in nonvolatile memory applications Appl. Phys. Lett. 97, 172105 (2010); 10.1063/1.3491803 Oxygen diffusion in atomic layer deposited ZrO 2 and HfO 2 thin films on Si (100) J. Appl. Phys. 96, 144 (2004); 10.1063/1.1753080 Chlorine mobility during annealing in N 2 in ZrO 2 and HfO 2 films grown by atomic layer deposition J. Appl. Phys. 92, 7675 (2002); 10.1063/1.1521802 Pressure-induced cubic-to-orthorhombic phase transformation in the negative thermal expansion material HfW 2O 8 J. Appl. Phys. 89, 3184 (2001); 10.1063/1.1347412

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Pressure evolution of resistance in framework structured materials�-ZrMo2O8 and �-HfMo2O8

A. S. Karandikar,a� G. D. Mukherjee, V. Vijayakumar, and B. K. GodwalHigh Pressure Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

S. N. Achary and A. K. TyagiApplied Chemistry Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

�Received 23 February 2006; accepted 3 May 2006; published online 11 July 2006�

The ac resistance measurements on the trigonal ��-� phase of ZrMo2O8 and HfMo2O8 carried outup to 5 GPa using the toroid anvil apparatus are reported. The ac resistance data in both thematerials are found to be strongly frequency dependent and show a transition between two powerlaw regimes with a crossover frequency ��c� near 1 kHz. For both the compounds slope changesand anomalies are observed in the ac resistance data at the structural transition pressures. Theactivation volumes at room temperature are obtained by analyzing the ac conductance data in termsof the pressure dependent activation volume model. The main conduction mechanism at 12 Hz isbelieved to be the diffusion of oxygens ions, whereas hopping of point defects is responsible for acconductuance above 33 kHz. At 1 KHz, a crossover from hopping to diffusion of point defects isobserved at the �-� �monoclinic� phase transition pressure. © 2006 American Institute of Physics.�DOI: 10.1063/1.2211312�

I. INTRODUCTION

In recent years there have been a considerable amount ofinvestigations on the framework structured materials withgeneral formula such as MX2O8 �M =Zr, Hf and X=W,Mo�,M2��XO4�3 �M�=Sc,Lu,Al�, etc. Many of the above materi-als and their various polymorphs show isotropic as well asanisotropic negative thermal expansion �NTE� behavior1–5

and numerous phase transitions under moderate pressure ortemperature variations.6–14 Such materials may be used toform composites with specific properties, such as tunablethermal expansion. During preparations and applications thelocal pressure inside the composites will change, which mayaffect the phase stability of these NTE materials. Thus apartfrom the interest in basic sciences, the high pressure charac-terization of the structural and electrical properties of thesematerials is of technological importance also.

Many investigations on ZrMo2O8 that belongs to theMX2O8 family have been performed owing to its possibleuse as catalysts,15 ion exchangers,16 and in nuclear fuelprocesses.17 At ambient pressure several polymorphs ofZrMo2O8 are reported in literature: the metastable cubic��-� phase �space group Pa−3�; trigonal ��-� phase �spacegroup Pa−31c�; and monoclinic ��-� phase �space groupC2/c�.5,18–21 Trigonal ��� phase is found to be the only stablepolymorph of HfMo2O8 at ambient conditions and is iso-structural to �-ZrMo2O8. Both �-ZrMo2O8 and HfMo2O8

exhibit highly anisotropic NTE with negative expansionalong the a axis only.22,23

The structure of �-ZrMo2O8 ��-HfMo2O8� consists ofZrO6 �HfO6� octahedra, which share all the corners with theMoO4 tetrahedra. While only three oxygen atoms at the api-ces of the tetrahedra form part of the three adjacent octahe-

dra, the oxygen atom at the fourth apex is “nonbridged” andpoints towards the interlayer region. This kind of frameworkarrangement gives rise to a two-dimensional layered struc-ture perpendicular to the c axis. The electrically neutral lay-ers �built from corner sharing ZrO6 or HfO6 and MoO4 poly-hedra� are bonded together by the van der Waals forcesbetween the oxygen atom pointing into the interlayer spaceand its closest neighbor. This interlayer oxygen can executelarge amplitude low frequency vibrations; can flip betweentwo crystallographically equivalent positions; or hop to adja-cent defect sites leading to dynamic oxygen disorder andionic conduction. In fact, the evidence of dynamic oxygendisorder has been found in ZrMo2O8 at temperatures as lowas 200 K.24,25 At high pressures �-ZrMo2O8 undergoes twosuccessive phase transformations: � phase to a monoclinic��� phase �space group: C2/m� at 1.06–1.11 GPa and �phase to a triclinic ��� phase at 2.0–2.5 GPa,26,27 withvolume reductions of about 5% and 10%, respectively. Thesetransformations take place mainly by the displacive move-ments of the oxygen ions with most of the pressure increasebeing accommodated by decreasing the interlayer distance.In recent high pressure structural investigations on �-HfMo2O8, similar phase transformations are observed: �-�transition at 1.3 GPa and �-� phase transition at 2.7 GPa.28

However, for �-HfMo2O8 a significant distortion of HfO6

polyhedra is observed in addition to the oxygen ion displace-ment during the structural evolution with pressure.28 There-fore structural transitions are expected to be reflected in theionic �ac� conductivity. Such conductivity variation can alsoreveal the feasibility of these materials as pressure sensingelements. In view of the above more detailed investigationsof the phase transformations under pressure in these systemsare desired.

In this paper we report high pressure ac electrical resis-a�Electronic mail: amol@apsara.barc.ernet.in

JOURNAL OF APPLIED PHYSICS 100, 013517 �2006�

0021-8979/2006/100�1�/013517/7/$23.00 © 2006 American Institute of Physics100, 013517-1

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tance measurements up to 5 GPa on both �-ZrMo2O8 and�-HfMo2O8 to gain more insight into their high pressurephase transitions.

II. EXPERIMENT

Trigonal ��� phases of ZrMo2O8 and HfMo2O8 wereprepared by the conventional solid-state reaction of ZrO2

with MoO3 at 600 °C and HfO2 with MoO3 at 650 °C, re-spectively, for 18 h. Pure phases of �-ZrMo2O8 and �-HfMo2O8 were obtained with the regrinding and annealingof the samples at 750 °C for 5 h and at 650 °C for 8 h,respectively. The final products were characterized separatelyby powder x-ray diffraction measurements.

The high pressure ac electrical conductance measure-ments were carried out up to 5 GPa in a modified pressurecell of the toroid anvil �TA� apparatus. The TA apparatus ispressure calibrated using Bi I-II and Yb hcp-bcc transitionsat 2.65 and 4 GPa, respectively. The two-probe techniquewas used for the resistance measurements, in which, thepressurizing rams of the TA apparatus themselves act asprobes for voltage measurement and sourcing the current. Acylindrical sample assembly and the graphite electrodes arearranged inside the cylindrical central hole �inside diameter�I.D.� of 6 mm, and length of 7 mm� of the toroid shapedpyrophillite gasket. The sample assembly was prepared asfollows. The powder sample was pressed by hand to form apellet �thickness: 1 mm; diameter: 6 mm� and was sand-wiched between two thin graphite plates �thickness: 1.8 mm;diameter: 6 mm�. The faces of graphite plates facing thesample were insulated leaving a tiny circular area exposed atone corner �diagonally opposite for the upper and lowergraphite plates� for electrical contact to the sample. The ex-posed faces of the graphite plates were painted with silverpaste for good electrical contact. The remaining emptyspaces inside the cylindrical hole of the pyrophyllite gasketwere filled with talc disks, which acted as pressure transmit-ting medium. The gasket containing the sample was placedin between the toroid-shaped anvils. The electrical contactamong the anvils and graphite plates were made by two thingraphite rods �2 mm diameter� of appropriate length passingthrough the central holes of the talc disks. The whole assem-bly was then slowly compressed to an initial pressure of0.4 GPa. The TA is kept locked at that pressure for sometime. This ensures a good Ohmic contact between the sampleand the electrodes. The initial thickness of the hand-pressedsample pellet reduces �irreversibly� to about 0.46 mm at thispressure. Further compression to 6 GPa and decompressionback to ambient pressure do not change the sample thicknessfrom the above-mentioned value. This ensures reproducibledata in the pressure range of 0.4–6 GPa not affected by theirreversible densification of the hand-pressed powder sample.

The ac resistance measurements were carried out usingthe GR 1689 Precision RLC Digibridge at the frequencies of12 Hz, 513 Hz, 1 kHz, 33 kHz, 67 kHz, and 100 kHz withan accuracy of about 1%. The pressure variation of the leak-age resistance, coming mainly from the pyrophillite gasket,was found to be within the precision of the bridge and can beconsidered practically constant. The precision in resistance

measurements was improved by taking the mean value of afew successive measurements at every pressure point. Thecontact resistance due to the graphite electrodes, pressurerams, etc., was estimated by replacing the sample with agraphite plate of same dimensions, which yielded a value of15 � and remained almost constant with pressure and fre-quency.

III. RESULTS AND DISCUSSION

A. Pressure evolution of ac conductance

The pressure variation of ac resistance of both the com-pounds normalized with respect to 0.4 GPa is shown in Fig.1. The data show different pressure behaviors at differentfrequencies. For �-ZrMo2O8, at 12 Hz the ac resistance datashow large anomalous changes; at 513 Hz and 1 kHz show apeak near 1 GPa, and at high frequencies �33–100 kHzrange� the pressure evolution of normalized ac resistance in-creases with a slope change near 1 GPa and follows almostthe same path �Fig. 1�a��. The R�P� /R�0.4� data for �-HfMo2O8 fall sharply up to about 2 GPa �by about 60%� at12 Hz; at 513 Hz continue to decrease up to the highest pres-sure studied with a slope change at about 2 GPa; at 1 kHzshow a broad peak in the range of 1.2–1.35 GPa; and at33-100 kHz continue to increase up to about 5 GPa and fol-low almost the same path. From Fig. 1 it is clear that thepressure evolution of ac resistance of both the compoundsshows anomalies near high pressure structural transitions.

The ac electrical resistance measurements under pressurecan probe the volume changes, which take place by the re-laxation or distortion of lattice induced by the mobile ions.29

This volume change is known as the activation volume �vact�

FIG. 1. Fractional ac resistance with respect to the ac resistance value at0.4 GPa �R�P� /R�0.4�� as a function of pressure at certain frequencies of12 Hz, 513 Hz, 1 kHz, 33 kHz, 66 kHz, and 100 kHz for �a� �-ZrMo2O8

and �b� �-HfMo2O8.

013517-2 Karandikar et al. J. Appl. Phys. 100, 013517 �2006�

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and is determined from the conductance measurements in thevicinity of room temperature through the followingequation:29–36

vact = − kBT� � ln G

�P�

T, �1�

where kB is Boltzmann’s constant and G is the ionic conduc-tance. In many materials pressure variation of logarithm ofconductance �ln G� is found to be nonlinear due to the pres-sure dependent activation volume.31,35,36 This pressure de-pendence of vact is expressed through the activation com-pressibility �act, defined as �−1/vact���vact /�P�T. Themeasured conductance values are fitted to the second orderpolynomial equation,

ln G = ln G0 + aP + bP2, �2�

and the parameters vact and �act are calculated from coeffi-cients of Eq. �2� by35,36

vact = − kBT�a + 2bP�

and

�act = − 2b/�a + 2bP� . �3�

In an effort to understand the conduction mechanismsresponsible for the observed interesting pressure evolution ofac resistance data at various frequencies, we have chosenthree representative data sets collected at 12 Hz, 1 kHz, and100 kHz for analysis. The logarithms of the ac conductance�ln G� data at frequencies at 12 Hz, 1 kHz, and 100 kHz for

�-ZrMo2O8 and �-HfMo2O8 are shown in Figs. 2 and 3,respectively. The ac conductance values increase by orders ofmagnitude as the frequency is increased from 12 Hz to100 kHz, indicating a strong frequency dependence. Theanomalous pressure behavior of ac-conductance data and thefrequency variation of vact and ��act� are discussed below onthe basis of the structural evolution of both the compoundswith pressure at different frequencies separately. Also thereare certain subtle changes in the conductance data near4 GPa for both the compounds. In the reported structuralevolution study with pressure on �-ZrMo2O8 and �-HfMo2O8 no structural transitions are observed at thesepressures.26,28 However, a careful inspection shows a broad-ening in the sample x-ray diffraction �XRD� lines and in-crease in the error of the lattice parameters in the � phaseabove 3.5 GPa. This is due to the onset of pressure inducedamorphization process in both the compounds26,28 and showsup as a subtle change in conductance.

1. 12 Hz

At these low frequencies the room temperature ac con-duction in the polycrystalline materials is expected to takeplace by the migration of available thermally activated va-cancies and other small number of intrinsic defects and im-purities. With increasing pressure, the stiffening of the latticedue to decrease in volume and the pressure induced struc-tural changes, will restrict movement of the mobile chargecarriers and the ac resistance is expected to increase. How-ever, in contrast to the above scenario the ac resistance in

FIG. 2. Typical ln G�P� vs P plot for �-ZrMo2O8 at frequencies �a� 12 Hz, �c� 1 kHz, and �e� 100 kHz with the solid lines representing the second orderpolynomial fits. The pressure dependence of vact for frequencies 12 Hz, 1 kHz, and 100 kHz are shown in �b�, �d�, and �f�, respectively, along with �act�P�in �f�.

013517-3 Karandikar et al. J. Appl. Phys. 100, 013517 �2006�

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�-ZrMo2O8 decreases rapidly up to 1 GPa by a large amount�about 16%� �Fig. 1�a��. The pressure dependence of activa-tion volume is calculated from Eq. �3� by fitting the loga-rithm of conductance data �ln G� up to 1 GPa to Eq. �2� andis shown in Fig. 2�b�. The zero pressure activation volume�v0

act� is calculated to be −3.1 cm3/mol. The negative activa-tion volume indicates to a complicated conduction mecha-nism and is related to an inherent property of the crystallattice.37–40 Similar negative activation volumes were ob-served for O2− self-diffusion �v0

act�−2.8–−3.3 cm3/mol� innetwork-structured silicate melts37 and also for self-diffusionand creep in many elements and compounds.40 As discussedin the Introduction, dynamic oxygen atom disorder is presentin MX2O8 compounds even at very low temperatures �e.g., atand above 200 K in the case of cubic ZrMo2O8�.24 The acti-vation energy of oxygen atom migration has been estimatedto be 34 kJ/mol in ZrMo2O8,25 which is at the lower rangeof the activation energies in ionic solids. In view of theabove facts the self-diffusion of oxygen atoms assumes im-portance in �-ZrMo2O8 at low frequencies such as 12 Hz.

The sharp increase in ionic conductance up to 1 GPa at12 Hz can be related to the �-� pretransition effect in thesample as explained below. The � phase is known to beloosely packed and open for the anions to move. Also the�-� structural transition is driven by the displacement of thenonbridging oxygen anions. Therefore the �-� pretransitioneffect facilitates the oxygen ion self diffusion through thelattice. Hence the ionic conductance increases up to the

phase transition pressure at 12 Hz as the diffusion of thecharge carriers is the major conduction mechanism at suchlow frequencies.

Above 1 GPa �in the � phase�, ZrMo2O8 has a closelypacked configuration with reduced compressibility.26,27 Fur-ther compression in the � phase takes place by a linear andsmall reduction of ZrO6 polyhedra, which is governedmainly by the anion-anion repulsion forces.27 Therefore inthe pressure region of 1.1–2 GPa, the decrease in conduc-tance at 12 Hz and small positive value of vact indicate thatthe diffusion of available defects/ions is the main conductionmechanism. The second high pressure transformation from �to the triclinic ��� phase takes place in the pressure range of2–2.5 GPa with about 10% unit cell volume reduction.26

Therefore, the resistance values were expected to increaseabove 2 GPa. But the decrease in resistance from 2 GPaalong with negative activation volume in the pressure rangeof 2–2.5 GPa �Fig. 2�b�� indicate the restart of the displace-ment of oxygen anions with the beginning of the �–� phasetransformation. At 2.5 GPa, the resistance starts increasing,indicating the completion of the above transition inZrMo2O8.

For �-HfMo2O8 the resistance falls sharply up to about2 GPa �Fig. 1�b�� by about 60% followed by a broad mini-mum in the range of 2–2.75 GPa and then starts increasingabove 2.75 GPa with a slower rate. Eventhough the pressureevolution of ac resistance at 12 Hz for �-HfMo2O8 showsalmost the same trend as in �-ZrMo2O8, no sharp anomalies

FIG. 3. Typical ln G�P� vs P plot for �-HfMo2O8 at frequencies �a� 12 Hz, �c� 1 kHz, and �e� 100 kHz with the solid lines representing the second orderpolynomial fits. The pressure dependence of vact for frequencies 12 Hz, 1 kHz, and 100 kHz are shown in �b�, �d�, and �f�, respectively, along with �act�P�in �f�.

013517-4 Karandikar et al. J. Appl. Phys. 100, 013517 �2006�

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are seen. In Fig. 3�a� the logarithm of ac conductance �ln G�is shown along with its pressure derivatives �the inset�.d ln�G� /dP show a small discontinuity at 1.1 GPa followedby an appreciable slope change at 2.1 GPa at 12 Hz.

The ln G data at 12 Hz could be fitted well up to2.1 GPa to Eq. �2� beyond which the fitting deteriorated rap-idly. Also the above data were fitted to Eq. �2� above2.75 GPa. The activation volumes calculated from the fittingparameters using Eq. �3� are shown in Fig. 3�b�. The value ofv0

act is calculated to be −3.1 cm3/mol, which is similar to thatfor �-ZrMo2O8. Therefore it can be speculated that self-diffusion of oxygen atoms is the major contributor for acconduction process in the pressure range up to 2.1 GPa. Thisis not surprising considering the fact the �-HfMo2O8 is iso-structural to �-ZrMo2O8 and shows similar structural transi-tions with pressure. However, the recent XRD studies showthat unlike ZrO6 polyhedra, the HfO6 octahedra deform sub-stantially during compression in HfMo2O8.28 Deformation ofHfO6 polyhedra can take place only by the displacement ofoxygen atoms, which probably leads to the continuous de-crease in ac resistance at 12 Hz up to above 2 GPa. Similarto �-ZrMo2O8, in the case of �-HfMo2O8, above 2.75 GPathe structure is too closely packed for the movement of an-ions and hence the conduction takes place by the randomdiffusion of the available vacancies and other point defects.Therefore at 12 Hz above 2.75 GPa vact is found to be posi-tive and decreasing with pressure.

2. 1 kHz

The conductance at 1 kHz is observed to decrease in the� phase of the both the materials. The activation volumes aredetermined by fitting the ln G data to Eq. �2� in the pressurerangs of 0.4–1 and 0.4–1.2 GPa for the � phase of ZrMo2O8

and HfMo2O8, respectively. The values v0act are calculated

to be 0.49 and 1.01 cm3/mol for �-ZrMo2O8, and �-HfMo2O8, respectively. The positive v0

act and decreasing vact

with pressure indicate the migration or hopping of point de-fects to be the main conduction mechanism in the � phasefor both the materials at 1 kHz.

Interestingly above 1 GPa the conductance starts in-creasing in both the compounds. The vact calculated from theparameters obtained by fitting ln G data in the pressure re-gions: 1–2.75 and 2.8–5 GPa for ZrMo2O8 and 1.3–2.6 and2.7–5 GPa for HfMo2O8. The vact is found to be negativeand decreasing in the � phase while negative and almostconstant in the � phase of both the compounds. The negativeactivation volume shows a diffusion of ions above 1 GPa. Itseems that in the � phase the residence time of the ion in avacancy site is reduced compared to the flight time betweendifferent sites. Therefore instead of discrete hopping a diffu-sion of charge carriers through the lattice takes place, in-duced by a relaxation of the lattice surrounding the mobileion.40 There may be a possibility that the change in conduc-tion mechanism at 1 kHz is probably induced by the struc-tural transitions. Also this may be related to the fact thatthere is a transition between two power law regimes in theionic conductivity near 1 kHz, which will be discussed inSec. III B.

3. 100 kHz

The conductance values at 100 kHz continue to decreaseup to 5 GPa, the highest pressure of this study. The pressureevolutions of vact and �act at 100 kHz are calculated from Eq.�3� after fitting the ln G data to Eq. �2� in the pressure re-gions: 0.5–1, 1.1–2.5, and 2.7–5 GPa for ZrMo2O8 and 0.5–2.1, and 2.75–5 GPa for HfMo2O8. However, for HfMo2O8

even though the data are fitted up to 2.1 GPa, from Fig. 3�e�it can be seen that the fit matches well with the experimentaldata points up to about 2.5 GPa.

The vact is found to be positive in this frequency, whichindicates a conduction mechanism mediated by point defetcs.From Figs. 2�f� and 3�f� vact is seen to be steeply decreasingwith the pressure in the � phase. It is consistent with thelarge compressibility of the � phase of both the compounds.The divergence in �act at about 1 GPa in ZrMo2O8 is consis-tent with the discontinuous volume change across the �-�transition. Eventhough the ln G data are fitted in the pressurerange of 1.1–2.5 GPa for ZrMo2O8, �act is found to divergerapidly from about 2 GPa. The divergence at 2.5 GPa islarger than at 1 GPa and is consistent with the fact that the�-� transition in ZrMo2O8 takes place in the pressure rangeof 2–2.5 GPa with a 10% discontinuous volume change.

For HfMo2O8, vact and �act calculated in the above pres-sure regions are shown in Fig. 3�f�. The values of v0

act and�0

act are calculated to be 0.5 cm3/mol and 0.45 GPa−1, repec-tively, at 100 kHz. The �act is found to diverge at 2.75 GPa,as observed in the case of ZrMo2O8 at 2.5 GPa ��-� transi-tion�. The values of both vact and �act are found to be almostconstant with pressure in the � phase. Due to the closelypacked configuration of the polyhedral structural units thenearest neighbor environment of the conducting anions doesnot change much with pressure and results in almost pressureindependent activation volume.

According to a study the ratio �0act /�0, where �0 is the

compressibility of the sample, should be equal to 5,41 whichserves as an index for the quality of the analysis employed.For �-ZrMo2O8, �0

act=0.78 GPa−1 and �0=0.051 GPa−1.27

This gives �act /�0�15. For HfMo2O8, the value of �0 isreported28 to be 4.5 GPa−1 and the ratio �act /�0 is found to be10. Thus for both the cases the value of the ratio �act /�0 isclose to the theoretical value.

B. Frequency dependence of ac conductance

The ionic conductivity in solids is known to exhibitpower law behavior with frequency.42,43 To understand theanomalous behavior in ionic conductance with pressure at1 kHz, we have plotted log10 Gac vs log10 � �where � is thefrequency�, at various pressures and are shown in Fig. 4.For �-ZrMo2O8 it can be seen that at all pressures the dataare bunched together with a clear slope change just below1 kHz. For �-HfMo2O8, dispersion is observed below1 kHz, but all the data points fall on the same curveabove 1 kHz. Therefore from the above figure it is clear thatthe conductance in both the systems shows a transition be-tween two power law regimes that correspond to twoasymptotic straight lines. This transition is marked by acrossover frequency ��c�, which is found to be near 1 kHz.

013517-5 Karandikar et al. J. Appl. Phys. 100, 013517 �2006�

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Similar frequency dependence of ionic conductivity has beenobserved in many materials,44,45 which can be expressed asfollows:

Gac �n for � �c

�m for � � �c, �4�

where n is the low frequency exponent and m is the highfrequency exponent. For ZrMo2O8 the values n and m arefound to be around 0.5 and 1.2, respectively. For HfMo2O8

the value of n decreased from 0.8 to 0.7 from 0.5 to 5 GPaand the value of m remained constant at about 1.3. The highvalue of exponents is typical of hopping ion conductors andhas been observed in the case of another framework struc-tured material Al2�WO4�3 �Ref. 46� and also in layeredperovskites.45 This is associated with strong latticeresponses43,46 to the movement of anions through the struc-tural bottleneck.

The ionic conduction in these materials can be inter-preted in terms of jump relaxation model47 �JRM� throughEq. �5�. According to JRM, n1 corresponds to translationalhopping motion and m2 corresponds to the localized orreorientational hopping motion.47 At low frequencies, below�c �i.e., in the long time limit�, the neighborhood getsenough time to relax with respect to the ions position andhence the ion stays in the site In this way the ionic conduc-tion takes place by the bodily movement �or diffusion� ofanions. This gives rise to a power law exponent �around0.5–0.8 for both the systems�, which is 1. Decrease in thevalue of n for HfMo2O8 with pressure can be related to therestrictions on the translational hopping motion of anionsdue to decrease in the open spaces in the lattice.

At frequencies above �c, the observation time is shortfor the neighborhood to become relaxed with respect to theposition of the ion after its jump, and hence the ion maymove to another -position quickly. As the frequency in-creases the number of hops also increases. Therefore thehopping motion of the ions seems to take place at shorterhopping distances and can be related to the localized or re-

orientational hopping motion.47 The values m as observed byus 2, which follows JRM. The very nature of these local-ized or reorientational hopping motions indicates that theyare almost independent of lattice volume and hence fre-quency dependence of conductance is almost pressure inde-pendent above �c.

The above analysis shows that the major conductionmechanism responsible in these framework structured mate-rials slowly evolves from diffusion of oxygen atoms at lowfrequencies to the hopping of point defects at high frequen-cies and they are dependent on the structural evolution ofboth the materials with pressure. The pressure transition fea-tures in the resistance data of ZrMo2O8 are sharper as thestructural evolution takes place only by the displacement ofoxygen atoms with almost no deformation in the polyhedra.However, in the case of HfMo2O8, the pressure transitionfeatures are broader due to the fact that the polyhedra alsogets substantially deformed. This may be the reason for dif-ferent pressure evolutions of resistance of both materials at513 Hz as diffusion may be still predominant in HfMo2O8 atthat frequency.

IV. CONCLUSIONS

In this paper a detailed study of the effects of quasihy-drostatic pressure on the ac electrical conductance of theframework structured materials �-ZrMo2O8 and �-HfMo2O8 is carried out. It is observed that the pressure evo-lution of the ac conductance is mediated by structuralchanges in both the materials. The ac conductance of boththe materials is found to be strongly frequency dependentand shows a transition between two power law regimesmarked by a crossover frequency ��c�, near 1 kHz. This be-havior is associated with strong lattice responses to themovement of the ions. The different pressure behaviors of acconductance at different frequencies in both the compoundsare attributed to the different conduction mechanisms medi-ated by the structural evolution of the materials.

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