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Journal of Non-Crystalline Solids 353 (2007) 3947–3955

Influence of structural disorder on the dynamics of mobile oxygenions in Dy2(Ti1�yZry)2O7

Karla J. Moreno a, Antonio F. Fuentes a, Ulises Amador b,Jacobo Santamarıa c, Carlos Leon c,*

a Cinvestav-Saltillo, Apartado Postal 663, 25000-Saltillo, Coahuila, Mexicob Departamento de Quımica, Facultad de Farmacia, Universidad San Pablo CEU, 28668-Boadilla del Monte, Madrid, Spain

c GFMC, Departamento de Fısica Aplicada III, Facultad de Fısica, Universidad Complutense de Madrid, 28040-Madrid, Spain

Available online 21 August 2007

Abstract

We report on the influence of structural disorder on the oxide-ion conductivity of Dy2(Ti1�yZry)2O7 (y = 0.55 and 0.90). A significantdisorder is induced by mechanical milling synthesis of the samples, and, depending on the Zr/Ti, a partial and progressive structuralordering can be achieved by subsequent annealing at temperatures between 800 and 1500 �C. Ionic conductivity is relatively high forboth compositions (up to 10�4 S/cm at 900 K), and the activation energies for dc conductivity (in the range 1.02–1.32 eV) are foundto be larger in samples with more structural disorder. This result is quantitatively explained, by using Ngai’s coupling model, in termsof the enhancement of interactions between mobile oxygen vacancies in a more disordered structure.� 2007 Elsevier B.V. All rights reserved.

PACS: 66.30.�h

Keywords: X-ray diffraction; Fast ion conduction

1. Introduction

Pyrochlore oxides A2B2O(1)6O(2) are drawing a greatdeal of attention in many areas of materials science of tech-nological interest because of their, frequently, unique prop-erties induced by a remarkable chemical and structuralflexibility (see Fig. 1 and Ref. [1] for a detailed descriptionof the pyrochlore crystal structure). Thus, composition elec-troneutrality can be achieved by a large combination of cat-ion species A and B with different oxidation states renderinga great variety of physical and chemical properties. Theirstructural flexibility is perhaps best illustrated, as pointedout by Vanderah et al. [2], by the existence of a pyrochloreform of WO3 where the whole O(2)A2 substructure is com-pletely absent. Since the O(2) oxygen atoms are only bonded

0022-3093/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2007.04.037

* Corresponding author. Tel.: +34 913944435; fax: +34 913945196.E-mail address: carletas@fis.ucm.es (C. Leon).

to A-type cations and do not participate into the networkforming (BO(1)6)z�polyhedra, defective pyrochlores areeasily formed and neither A nor O(2) ions are essential tostabilize the pyrochlore crystal structure. Indeed, manyproperties of pyrochlores are very much influenced by iondistribution and site occupancies. Thus, a large increase isobserved in ionic conductivity values due to the appearanceof mobile oxygen ions when all the three crystallographi-cally possible anion sites in the structure, 48f, 8a (both ini-tially fully occupied) and 8b (initially empty), are partiallyoccupied as in systems of solid solutions, A2(Ti1�yZry)2O7

(A = Y3+, Ln3+), and it is well established that oxygenmotion takes place through available oxygen vacancies at48f sites [3,4]. As disorder in both the anion and cationsublattices seems to proceed at different rates [5], these sys-tems offer the possibility of manipulating pyrochlores intrin-sic concentration of anion vacancies between highlydisordered (high Zr content) and highly ordered forms (highTi content), making them ideally suited for analyzing the

Fig. 1. Projections of four fluorite unit cells (left) and one pyrochlore unit cell (right) evidencing that pyrochlores might be considered as ‘ordered’ aniondeficient fluorites. Larger circles in both figures represent oxygen atoms whereas smaller circles represent cations (only one type in fluorites and two inpyrochlores).

3948 K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955

relationship between electrical properties and atomic order-ing (disordering). Additionally, the activation energy foroxygen migration in partially ordered pyrochlore typeLn2Zr2O7, is in general lower than that of the correspondingdefect fluorite-type forms with the same chemical composi-tion, which has been explained as due to the existence ofpreferential pathways in the former that leads to a decreasein the strain energy term of the activation energy for oxide-ion conduction [6]. This fact makes these materials goodcandidates to substitute the currently used yttria stabilizedzirconia as electrolyte in solid oxide fuell cells, and thus ofmuch technological interest nowadays. However, completeorder, as in ‘ideal’ pyrochlores, renders very low conductiv-ity values because oxygen vacancy ordering with optimalconductivity is obtained for partially ordered phases where,in addition, ionic interactions penalizing ion migration canbe minimized. In previous works [7–9], we have shown theinfluence of disorder on the electrical properties of ionicallyconducting Gd2(Ti1�yZry)2O7 and Gd2(Sn1�yZry)2O7

pyrochlores by analyzing samples with different Zr/Ti andZr/Sn ratios. Increasing Zr content gives rise to a more dis-ordered structure, and Ngai’s coupling model [10] has beenshown to provide a quantitative explanation of theobserved changes in the dispersive behavior of ionic con-ductivity in terms of the existence of cooperative effectsamong mobile oxygen ions. In this work we will continueanalyzing the relationship between structure and electricalproperties in A2(Ti1�yZry)2O7 (A = Ln3+) pyrochlores byexamining oxygen dynamics in two compositions preparedby mechanical milling within the Dy2(Ti1�yZry)2O7 solidsolution, keeping a fixed Zr/Ti ratio in this case, and anneal-ing at various temperatures to promote a different degree ofstructural order. Isostructural with the better knownY2(Ti1�yZry)2O7 solid solution (as Y2Zr2O7 and Y2Ti2O7,Dy2Zr2O7 and Dy2Ti2O7 are respectively, defect fluoriteand ordered pyrochlore materials), this is an appropriatesystem to carry out this type of studies by simple and widelyavailable techniques such as laboratory X-ray diffraction

because of the large difference in the Dy3+ and Zr4+ scatter-ing factors, as opposed to the Y3+ and Zr4+ couple.

2. Experimental

Two compositions in the title solid solution Dy2(Ti1�y

Zry)2O7 (y = 0.55 and 0.9) were prepared as described indetail elsewhere [4], by dry milling stoichiometric mixturesof the constituent oxides (high purity (>99%) monoclinicZrO2, anatase-TiO2 and C-Dy2O3), in a planetary ball millusing zirconia vials and balls. Portions of these powdersamples were subjected to post-milling thermal treatments(12 h) at selected temperatures and analyzed by X-ray pow-der diffraction (XRD) at room temperature. The structuralfeatures at room temperature of all the above samples wereobtained from precise diffraction data obtained on a h–2hhigh-resolution X-ray powder diffractometer of Bragg–Brentano geometry equipped with a position sensitivedetector (PSD) using monochromatic CuKa1 radiation(k = 1.5406 A), obtained with a germanium primary mono-chromator. The measured angular range, the step size andcounting times were selected to ensure enough resolution(the step size should be at least, 1/10 of the fwhms) and sta-tistics. The instrumental contribution to line broadeningwas evaluated using NIST LaB6 standard reference mate-rial (SRM 660a; l = 1138 cm�1, linear absorption coeffi-cient for CuKa1 radiation). The structural refinementswere carried out by the Rietveld method using the FullProfprogram [11] and taking into account, simultaneously, theeffects of the sample microstructure on the diffraction pat-terns according to a phenomenological approach describedin detail elsewhere [12,13].

Admittance spectroscopy measurements were carriedout on annealed pellets (10 mm diameter and �1 mm thick-ness) by using a Solartron 1260 Frequency Response Ana-lyzer to obtain electrical conductivity relaxation data. Inorder to analyze the relationship between electrical andstructural (degree of ordering) properties in our powder

K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955 3949

samples, we selected three annealing temperatures for thestudy: 800, 1200 and 1500 �C (soaking time 12 h; heatingand cooling rate 2 �C/min). Electrodes were made by coat-ing opposite faces of the pellets with SPI-ChemTM conduc-tive platinum paint and firing them at 800 �C to eliminateorganic components and harden the Pt residue. Data wererecorded in air for each sample from 300 to 600 �C over the100 Hz–1 MHz frequency range.

3. Results and discussion

3.1. Structural evolution of powder samples with post-milling

thermal treatments

As the pyrochlore crystal structure might be consideredas a superstructure of an anion-deficient fluorite-likeatomic arrangement, its X-ray diffraction pattern containsa set of strong reflections characteristic of the underlyingfluorite-type subcell plus an additional set of superstructurereflections with intensities depending on factors such as thedegree of ordering, the differences in the average scatteringfactors of the elements involved, or the distribution of oxy-gen vacancies [5]. There are two different disordering mech-anisms operating in compositions prepared by mechanicalmilling in the title solid solution. Thus, disordering inducedby milling has also to be considered in addition to theintrinsic chemically induced disordering when replacingTi atoms by Zr. As a far-from-equilibrium processingmethod, mechanical milling frequently leads to uniquemetastable defect structures unattainable by any other syn-thetic route. Therefore, in powder samples prepared bymechanical milling, changes in the relative intensity of

Fig. 2. Experimental (circles), calculated (solid line) and difference (bottom)sample after firing 12 h at 1500 �C.

the superstructure peaks with the temperature of post-mill-ing thermal treatment can be used as a direct evidence ofthe evolution of cation distribution in the structure whilekeeping chemical composition fixed.

Fig. 2 shows graphically the fitting result of the X-raydiffraction pattern corresponding to Dy2(Ti0.1Zr0.9)2O7

powders prepared by mechanical milling and fired 12 h at1500 �C. Similar X-ray diffraction patterns were obtainedfor all samples belonging to this series, independent ofthe temperature of post-milling thermal treatment. Table1 contains the final refined structural parameters obtainedfor the whole Dy2(Ti0.1Zr0.9)2O7 series fired at differenttemperatures. Since no superstructure reflections character-izing the pyrochlore long-range atomic ordering were evi-dent in any of the X-ray diffraction patterns collected forthis series (i.e. the (111) or (331) lines at �15� and 38�(2h) respectively), the Dy2(Ti0.1Zr0.9)2O7 powders preparedby mechanical milling consist of a single phase anion-defi-cient fluorite-type of structure which remains stable up to,at least, the highest firing temperature used in this work,1500 �C. As Table 1 shows, cell parameters for these fluor-ites remain almost temperature independent, as previouslyobserved for similar systems in samples prepared bymechanical milling [14].

Fig. 3(a) and (b) shows the graphic results of the profilefitting corresponding to the X-ray diffraction data obtainedfor the as-prepared Dy2(Ti0.45Zr0.55)2O7 powders afterpost-milling thermal treatments at 800 and 1200 �C, respec-tively. The final structural refined parameters for the wholeseries are presented in Table 2. As observed in the similarGd2(Ti1�yZry)2O7 system [14], the tendency to adopt apyrochlore structure in powder samples prepared by

X-ray diffraction patterns for the as-prepared Dy2(Ti0.1Zr0.9)2O7 powder

Table 1Structural evolution of the as-prepared Dy2(Ti0.1Zr0.9)2O7 powders with the temperature of post-milling annealing treatments

Treatment T(�C)/Time (h) Just-milled 600/12 800/12 1000/12 1200/12 1500/12

a (A) 5.2131(4) 5.209(1) 5.2092(4) 5.2113(3) 5.20774(7) 5.21026(3)RB 0.027 0.040 0.033 0.028 0.021 0.040Rwp 0.02 0.039 0.036 0.042 0.040 0.044Rexp 0.017 0.038 0.034 0.042 0.035 0.037v2 1.27 1.05 1.12 1.03 1.29 1.42

All samples have fluorite-like structure (S.G. Fm3m, n. 225) with metals at 4a (000) and oxygen at 8c (0.250.250.25). The respective occupations being thosegiven by the chemical formula; i.e. 0.5/0.05/0.45 for Dy/Ti/Zr and 7/8 for oxygen. Cell content is obtained as the site multiplicity times the occupancy; Z = 1.RB = R|Io � Ic|/RIo; Rwp = [Rw|yo � yc|

2/Rw|yo|2]1/2; Rexp ¼ ½ðN � P þ CÞ=Rðwy20Þ�

1=2; v2 = [Rwp/Rexp]2; N = number of data points; P = number of refinedparameters; C = number of constrains; wi = 1/variance(yo) (weight for every data point).

Fig. 3. Experimental (circles), calculated (solid line) and difference (bottom) X-ray diffraction patterns for as-prepared Dy2(Ti0.45Zr0.55)2O7 powdersamples fired at 800 �C, (a) and 1200 �C (b).

3950 K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955

Table 2Structural evolution of the as-prepared Dy2(Ti0.45Zr0.55)2O7 powders with the temperature of post-milling annealing treatments

TreatmentT(�C) /Time (h)

Just-milled 600/12 800/12 1000/12 1200/12 1500/12

a (A) 5.119(2) 5.1670(5) 5.1679(6) 5.1600(3) 10.3143(1) 10.3290(1)Dy/Zr/Ti in 16c, (000), Occ. 0.95(2)/1.05(2)/0.0 1.69(1)/0.31(1)/0.0Dy/Zr/Ti in 16d, (1/21/21/2), Occ. 1.05(2)/0.05(2)/0.90 0.31(1)/0.79(1)/0.90O(1) in 48f, (x1/81/8), Occ. 1 1x 0.399(6) 0.413(1)O(2) in 8a, (1/81/81/8), Occ. 1 1

RB 0.031 0.035 0.021 0.031 0.021 0.082Rwp 0.021 0.016 0.036 0.040 0.023 0.044Rexp 0.019 0.014 0.035 0.040 0.020 0.037v2 1.19 1.26 1.07 1.04 1.34 1.41

As prepared sample and those treated at 600 �C, 800 �C and 1000 �C have fluorite-like structure (S.G. Fm3m, n. 225) with metals at 4a (000) and oxygenat 8c (0.250.250.25). The respective occupations being those given by the chemical formula; i.e. 0.5/0.225/0.275 for Dy/Ti/Zr and 7/8 for oxygen. Cellcontent is obtained as the site multiplicity times the occupancy; Z = 1. Samples treated at 1200 �C and 1500 �C have pyrochlore structure, (S.G. Fd3m, n.227). The occupations are given by the chemical formula; cell content is obtained as the site multiplicity times the occupancy; Z = 8.RB = R|Io � Ic|/RIo; Rwp = [R w|yo � yc|

2/Rw|yo|2]1/2; Rexp ¼ ½ðN � P þ CÞ=Rðwy20Þ�

1=2; v2 = [Rwp/Rexp]2; N = number of data points; P = number of refinedparameters; C = number of constrains; wi = 1/variance (yo) (weight for every data point).

Fig. 4. Frequency dependence of the real part of the electrical conduc-tivity, r 0(x), at different temperatures from 300 to 700 �C for the as-prepared Dy2(Ti0.45Zr0.55)2O7 powders annealed at 1500 �C.

K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955 3951

mechanical milling in the title solid solution, increases asthe Ti content increases and as the temperature of post-milling thermal treatment rises. Thus, as preparedDy2(Ti0.45Zr0.55)2O7 powders present a defect fluorite-typeof structure that remains stable up to at least 1000 �C,the cell parameters being almost temperature independent.However, powders fired at 1200 and 1500 �C show diffrac-tion patterns similar to those characteristic of pyrochlore-like materials showing superstructure peaks, (h k l)p with h,k and l odd, due to the cation (and anion) partial ordering.While these reflections are clearly evident in Fig. 3(b) andobviously in the XRD pattern of the powder fired at1500 �C (not shown), differences in their relative intensitiessuggest different metal distribution. To carry out the struc-tural analysis, we assumed as a starting model in our refine-ments all the Dy ions to be constrained into the 16c sites andcorrespondingly, the existing Ti and Zr ions sharing the 16dposition. However, it was evident during the fitting processthat much more scattering power should be located in the16d sites which could only be accomplished by allowingDy ions to move into the latter and consequently, removingeither Ti or Zr. From crystallochemical considerations, theobvious choice was Zr(r(Ti4+) = 0.61 A; r(Zr4+) = 0.72 A;r(Dy3+) = 0.912 A, all in octahedral coordination) [15].Thus, we refined the occupation of both sites allowing Zrions to move to the 16c sites and consequently, also permit-ting Dy ions to occupy the octahedral sites. Although othercation distributions could be possible (formally the numberof unknowns is larger than the information available), theywere discarded on the basis of crystallochemical consider-ations because they are artificial and unnecessarily complex.The oxygen array in our structural refinements was assumedto be ordered as in the ideal pyrochlore structure whereas influorite 1/8 of the oxygen positions are empty at random.The final refined structural parameters obtained forDy2(Ti0.45Zr0.55)2O7 powders fired at 1200 �C (Table 2)show the larger eight-coordinated 16c site to be equally occu-pied by Dy3+ and Zr4+ ions, the latter constraint by stoichi-

ometry, whereas the smaller and hexa-coordinated 16d site isoccupied by the remaining 50% of the Dy3+ ions and all theTi4+ ions, as imposed by the sample chemical formula. Forthe sample fired at 1500 �C, the structural refinement sug-gests a more ordered atomic distribution, closer to thatexpected for equilibrium configurations, with 80% of allDy ions confined to the larger 16c site and 70% of the existingZr atoms in the smaller 16d position. Finally, we want toremark that although some degree of short-range or localorder (pyrochlore-like) could exist in some fluorite-like sam-ples [14], it cannot be detected by averaging (long-range) dif-fraction techniques such as XRD.

3.2. Electrical conductivity relaxation

Fig. 4 shows the frequency dependence of the real part ofthe electrical conductivity, r 0(x), at different temperatures,

Fig. 5. Frequency dependence of the real (empty symbols) and imaginary(solid symbols) parts of the electric modulus, at selected temperatures, forthe sample Dy2(Ti0.45Zr0.55)2O7 annealed at 1500 �C. Solid lines are fitsaccording to a KWW relaxation function (see text).

Fig. 6. Values of the exponent n obtained from the fits of electricalconductivity relaxation data to KWW functions for samples of both seriesDy2(Ti0.45Zr0.55)2O7 and Dy2(Ti0.1Zr0.9)2O7 at various annealingtemperatures.

3952 K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955

for the pyrochlore Dy2(Ti0.45Zr0.55)2O7 sample annealed at1500 �C. Similar conductivity plots were obtained for allsamples analyzed in this work. As Fig. 4 shows, the fre-quency dependence of conductivity at low temperaturemay be well described by the so-called Jonscher empiricalexpression [16], r 0(x) / xn with a fractional exponent n,consistent with a power law-type dependence at high fre-quencies and a frequency-independent conductivity valueat low frequencies which is the dc conductivity or the bulkconductivity value, rdc. Increasing temperature leads to aregime with an almost frequency-independent conductivityvalue, with the dispersive region observed as a power lawfrequency dependence shifting towards higher frequenciesand eventually out of the experimental window. Thus, rdc

at a given temperature can be directly obtained from ac con-ductivity measurements as the conductivity value in the‘plateau’ region of the isothermal curves in Fig. 4. Theobserved decrease in conductivity values for every tempera-ture above 350 �C is due to blocking effects at grain bound-aries. The presence of the above mentioned dispersiveregion has been related to the existence of cooperativeeffects in the dynamics of hopping ions [10], with the frac-tional exponent n (0 6 n < 1) determined by the degree ofion–ion interactions existing in the ionic hopping process;i.e. in the absence of interactions among mobile ions (com-pletely independent and random ion hopping), the exponentn would be 0.

Electrical relaxation data might be also described interms of the electric modulus which is the inverse of thedielectric permittivity and thus, is directly related to theconductivity through the equation:

M�ðxÞ ¼ 1=e�ðxÞ ¼ jxe0=r�ðxÞ: ð1Þ

The ion hopping ac conductivity can be expressed then bythe Fourier transform of the time derivative [17,18]

M�ðxÞ ¼ 1

e11�

Z 1

0

� dUdt

� �e�jxt dt

� �; ð2Þ

of the so-called Kohlrausch–Williams–Watts (KWW)relaxation function of the form [18,19]:

UðtÞ ¼ expð�ðt=sÞ1�nÞ; 0 < ð1� nÞ 6 1; ð3Þ

where e1 is the dielectric permittivity at high frequenciesand s the characteristic relaxation time of the ion-hoppingprocess that is thermally activated with the same activationenergy of the dc conductivity. Correspondingly, the timedependence indicated in Eq. (3) is reflected by the spectralshape of the imaginary part of the electric modulus as anasymmetric relaxation peak at a characteristic frequencyxp � s�1, which increases with increasing temperature.This behavior is illustrated in Fig. 5, which shows the fre-quency dependence of the real and imaginary parts of theelectric modulus at three selected temperatures for the samesample shown in Fig. 4, Dy2(Ti0.45Zr0.55)2O7 annealed at1500 �C. The figure also shows best fits according to Eqs.(2) and (3), in excellent agreement with experimental data,

and from which the values of the exponent n are obtainedand found to be temperature independent. The fractionalvalue of the exponent n in the KWW function gives riseto the power law frequency dependence of the ac conduc-tivity at high frequencies and low temperatures, and asmentioned above, is a measure of the departure from thepure exponential or Debye behavior expected for uncorre-lated ion hopping.

Fig. 6 shows the values of the exponent n determinedfrom the fits of electrical conductivity relaxation data toKWW functions, as a function of the annealing tempera-ture, and for both compositions analyzed in this work. Thisfigure suggests that the value of the exponent n is relatedto the degree of structural order in the samples, decreasingn with increasing structural order. As deduced from

Fig. 7. Arrhenius plots obtained for both set of samples,Dy2(Ti0.45Zr0.55)2O7 (a) and Dy2(Ti0.1Zr0.9)2O7 (b), annealed at differenttemperatures (800 �C (diamonds), 1200 �C (circles), 1500 �C (squares)),showing the activated temperature dependence of the dc conductivity.

K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955 3953

the structural characterization, as prepared Dy2(Ti0.45

Zr0.55)2O7 powders present the highly disordered anion-deficient fluorite-type of structure which remains stablewhen firing the samples at temperature 61000 �C whereasincreasingly ordered (pyrochlore) structures are obtainedby raising the annealing temperature above 1000 �C. Thisprogressive ordering leads to a significant decrease in thevalue of the exponent n when the annealing temperatureincreases from 800 to 1500 �C, changing from n = 0.52 ±0.02 to 0.38 ± 0.01. In the case of the as-preparedDy2(Ti0.1Zr0.9)2O7 series, the XRD study shows theanion-deficient fluorite-type of structure remaining essen-tially unchanged with increasing annealing temperature,and correspondingly the value of the exponent n is almostconstant for the series, changing from n = 0.48 ± 0.02 forthe sample annealed at 800 �C to n = 0.44 ± 0.02 for thatfired at 1500 �C. The small decrease observed in this seriessuggests the existence of some ordering, perhaps of shortrange, taking place when firing. This kind of local orderwas evidenced by spectroscopic or local diffractometrictechniques such as SAED (selected area electron diffrac-tion). Although nominally anion-deficient fluorite-typematerials when y > 0.9 [20], complete randomization ofthe cation and anion substructures in the similarY2(Ti1�yZry)2O7 system is really never achieved, and evi-dences of pyrochlore-like local ordering has been detectedeven in Y2Zr2O7 [21].

Fig. 7 presents Arrhenius-type plots showing the tem-perature dependence of the dc conductivity for both seriesof samples annealed at different temperatures. Although allsamples show a thermally activated behavior of the formrdc ¼ ðr1=T Þ expð�Edc=kT Þ, changes in the dc conductivitywith the annealing temperature are markedly different forboth series. Thus, rdc in the Dy2(Ti0.45Zr0.55)2O7 seriesshowing the anion-deficient fluorite to pyrochlore phasetransition on heating, increases markedly by more thanthree orders of magnitude when the annealing temperatureis raised from 800 to 1500 �C whereas the conductivityincrease for the Dy2(Ti0.1Zr0.9)2O7 series is less than oneorder of magnitude for the same annealing temperaturerange. Interestingly, dc conductivity values obtained forboth series at high temperatures are very similar despitethe large difference in their Zr content, that is, in the degreeof atomic ordering/disordering. Activation energy valuesfor dc conductivity, Edc, obtained from the slopes of theseplots for the Dy2(Ti0.1Zr0.9)2O7 defective fluorites arealmost constant, with a value of 1.30 ± 0.02 eV irrespectiveof the annealing temperature used, whereas those obtainedfor the Dy2(Ti0.45Zr0.55)2O7 samples show a markeddecrease from 1.32 ± 0.02 eV to 1.02 ± 0.01 eV when theannealing temperature is increased from 800 to 1500 �C.Thus, lower dc activation energies in pyrochlores withincreasing ordering (lower Zr content and higher annealingtemperature) lead to the same conductivity values obtainedfor highly defective fluorites.

In the following we discuss the observed relationshipbetween structural order and ionic conductivity in terms

of cooperative effects among mobile oxygen vacancies. Dif-ferent models have been proposed to analyze electricalrelaxation data in ionic conductors [10,22,23] which takeinto account the existence of cooperative effects amongmobile ions in the diffusion process. Interestingly, ourresults of a concomitant decrease of the activation energyEdc for the dc conductivity (see Fig. 8) and of the valueof n (see Fig. 6), with decreasing disorder, can be rational-ized in terms of the Coupling Model (CM) [10,22,24,25].The CM starts with the consideration of independent hopsof ions to vacant adjacent sites with exponential correlationfunction, UðtÞ ¼ expð�t=s0Þ, and relaxation time s0. Suchindependent hops cannot occur for all ions at the same timebecause of ion–ion interactions and correlations. The resultof ion–ion interactions is the slowing down of the relaxa-tion rate at times longer than tc of the order of 2 ps, chang-ing the correlation function from a pure exponential to aKWW function, UðtÞ ¼ expð�ðt=sÞ1�nÞ, wherein the valueof the fractional exponent n is a measure of the cooperative

Fig. 8. Values obtained for the activation energy of the dc conductivity,Edc (solid symbols), and for the energy barrier, Ea = (1 � n)Edc (emptysymbols), for both series Dy2(Ti0.45Zr0.55)2O7 (squares) andDy2(Ti0.1Zr0.9)2O7 (circles), as a function of the annealing temperature.

3954 K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955

effects. A major result from the CM is that the effectiverelaxation time s is related to s0 by

s ¼ ½t�nc s0�1=ð1�nÞ

: ð4Þ

For ions vibrating in their cages and hopping to neighbor-ing sites through barriers of energy Ea, the relaxation timefor independent ion hopping is s0ðT Þ ¼ s1 expðEa=kT Þ. Thereciprocal of s1 is the attempt frequency of ions. It followsfrom Eq. (4) that the activation energy for the dc conduc-tivity or s will be larger than the energy barrier and givenby the relation

Edc ¼ Ea=ð1� nÞ: ð5Þ

The increase of ion–ion interaction leads to a higher degreeof cooperativity in the ion hopping process which corre-sponds to a higher value of n and, consequently, to higheractivation energy for long-range ionic transport due to theenergy penalty that ion–ion interactions impose on the io-nic diffusion process.

In fact, when we estimate from our experimental resultsthe activation energy Ea for the barrier that oxygen ionsmust overcome to hop (independently) between neighbor-ing vacant sites, according to Eq. (5) and by using theexperimental values obtained for Edc and n, we find a valueof Ea = 0.64 ± 0.01 eV for the Dy2(Ti0.45Zr0.55)2O7 serieswhich remains independent of the annealing temperaturewithin experimental error. The value obtained for theDy2(Ti0.1Zr0.9)2O7 series of samples with a defect fluoritetype of structure is 0.70 ± 0.04 eV. Both sets of values areshown graphically in Fig. 8, as a function of the annealingtemperature, together with the Edc values obtained for thesame samples from the Arrhenius fits in Fig. 7. As deducedfrom the structural characterization, a lower annealing

temperature leads to a higher degree of structural disorder,where enhanced ion–ion interactions are expected, andconsequently also to higher values of the exponent n

according to the CM (see Fig. 6). The more disorderedstructure in samples annealed at lower temperatures fostersion–ion correlations, and lead to an increase of the energypenalty that these correlations impose on long-range or dcionic conductivity. The probability and direction of thehopping events performed by the mobile oxygen ionsdepend on their local potential landscape, which in a disor-dered structure will be determined by the distribution ofother mobile ions in the neighboring oxygen sites. The hop-ping probability of a particular mobile ion will be stronglydependent on the position of the neighboring mobile ions(and therefore on the previous hopping events). Thus, iondynamics become more correlated in a disordered struc-ture, and consequently higher values of the exponent nare expected according to the CM. This explains the largerdifference found between Edc and Ea (lower n), the lowerthe annealing temperature for the Dy2(Ti0.45Zr0.55)2O7 ser-ies (see Fig. 8). On the other hand, in the Dy2(Ti0.1Zr0.9)2O7

set of samples, where no significant difference in the degreeof ordering was observed on firing and the anion-deficientfluorite-type of structure is stable up to at least 1500 �C,both Edc and Ea remain almost independent of the anneal-ing temperature.

4. Conclusions

Mechanical milling synthesis of Dy2(Ti1�yZry)2O7

pyrochlores induces structural disorder and leads to a fluo-rite-type structure for as-prepared powders. In the case ofDy2(Ti0.1Zr0.9)2O7 samples, the high Zr content preventssignificant ordering of the cation distribution even afterannealing at 1500 �C. However, superstructure peaksappear in the XRD patterns of Dy2(Ti0.45Zr0.55)2O7 sam-ples after annealing at temperatures higher than 1000 �C,showing the progressive ordering towards an ideal pyroch-lore structure with increasing the annealing temperature.Thus, the degree of structural order in these samplesdepends not only on the Zr/Ti ratio but also on the temper-ature of the annealing treatment after milling.

We have also found that these samples show a relativelyhigh ionic conductivity, due to the existence of mobileoxygen vacancies, and the degree of structural order deter-mines the electrical properties of the samples. In particular,it is found a lower value of the fractional exponent n whichcharacterizes the dispersive ac conductivity, and a system-atic decrease in the activation energy for the dc ionic con-ductivity when increasing structural order by increasingannealing temperature for a fixed composition. From theanalysis of electrical conductivity relaxation in terms ofNgai’s coupling model we conclude this behavior is dueto the enhancement of ion–ion interactions promoted bythe more disordered structure in samples annealed at lowertemperatures.

K.J. Moreno et al. / Journal of Non-Crystalline Solids 353 (2007) 3947–3955 3955

Acknowledgements

Financial support from Mexican Conacyt (SEP-2003-C02-44075) is greatly appreciated. Authors from Spainthank financial support from MCYT (MAT2004-3070-C01 and MAT2004-3070-C05).

References

[1] M. Subramanian, G. Aravamudan, G.V. Subba Rao, Prog. SolidState Chem. 15 (1983) 55.

[2] T.A. Vanderah, I. Levin, M.W. Lufaso, Eur. J. Inorg. Chem. 14(2005) 2895.

[3] P.K. Moon, H.L. Tuller, Solid State Ionics, in: G. Nazri, R.A.Huggins, D.F. Shriver (Eds.), Mater. Res. Soc. Proc. 135 (1989) 149.

[4] K.J. Moreno, M.A. Guevara-Liceaga, A.F. Fuentes, J. Garcıa-Barriocanal, C. Leon, J. Santamarıa, J. Solid State Chem. 179 (2006)928.

[5] B.J. Wuensch, K.W. Eberman, C. Heremans, E.M. Ku, P. Onnerud,E.M.E. Yeo, S.M. Haile, J.K. Stalick, J.D. Jorgensen, Solid State Ion.129 (2000) 111.

[6] M.P. Van Dijk, K.J. de Vries, A.J. Burggraaf, Solid State Ion. 9–10(1983) 913.

[7] K.J. Moreno, G. Mendoza-Suarez, A.F. Fuentes, J. Garcıa-Barrio-canal, C. Leon, J. Santamarıa, Phys. Rev. B 71 (2005) 132301.

[8] J. Garcıa-Barriocanal, K.J. Moreno, G. Mendoza-Suarez, A.F.Fuentes, J. Santamarıa, C. Leon, J. Non-Cryst. Solids 351 (2005)2813.

[9] K.J. Moreno, A.F. Fuentes, J. Garcıa-Barriocanal, C. Leon, J.Santamarıa, J. Solid State Chem. 179 (2006) 323.

[10] K.L. Ngai, R.W. Rendell, ACS Symposium Series 676, 1997, p. 45.[11] J. Rodriguez-Carvajal, Physica B 19 (1993) 55.[12] S. Garcıa-Martın, M.A. Alario-Franco, H. Ehrenberg, J. Rodrıguez-

Carvajal, U. Amador, J. Am. Chem. Soc. 126 (2004) 3587.[13] A.F. Fuentes, K. Boulahya, M. Maczka, J. Hanuza, U. Amador,

Solid State Sci. 7 (2005) 343.[14] K.J. Moreno, A.F. Fuentes, M. Maczka, J. Hanuza, U. Amador, J.

Solid State Chem. 179 (2006) 3805.[15] R.D. Shannon, Acta Cryst. A 32 (1976) 751.[16] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric,

London, 1984.[17] K.L. Ngai, C. Leon, Phys. Rev. B 60 (1999) 9396.[18] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13

(1972) 171.[19] R. Kohlrausch, Pogg. Ann. Physik 72 (1847) 353.[20] C. Heremans, B.J. Wuensch, J. Solid State Chem. 117 (1995) 108.[21] N. Kim, C.P. Grey, J. Solid State Chem. 175 (2003) 110.[22] K.L. Ngai, C. Leon, Solid State Ion. 125 (1999) 81.[23] K. Funke, R.D. Banhatti, C. Cramer, Phys. Chem. Chem. Phys. 7

(2005) 157.[24] K.L. Ngai, C. Leon, Phys. Rev. B 66 (2002) 064308.[25] K.L. Ngai, C. Leon, J. Non-Cryst. Solids 315 (2003) 124.