Journal of Alloys and Compounds 605 (2014) 63–70

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Journal of Alloys and Compounds

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Structural and crystal chemical properties of rare-earth titanatepyrochlores

http://dx.doi.org/10.1016/j.jallcom.2014.03.1530925-8388/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Address: 1 Bethel Valley Road, Oak Ridge, TN 37831,United States. Tel.: +1 865 574 5492; fax: +1 865 574 4814.

E-mail address: boatnerla@ornl.gov (L.A. Boatner).

J. Matt Farmer a, Lynn A. Boatner a,b,⇑, Bryan C. Chakoumakos c, Mao-Hua Du a,b, Michael J. Lance a,Claudia J. Rawn a,d, Jeff C. Bryan e

a Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United Statesb ORNL Center for Radiation Detection Materials and Systems, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United Statesc Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United Statesd Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996-2100, United Statese Department of Chemistry and Biochemistry, University of Wisconsin–La Crosse, La Crosse, WI 54601, United States

a r t i c l e i n f o

Article history:Received 7 March 2014Received in revised form 25 March 2014Accepted 26 March 2014Available online 5 April 2014

Keywords:Rare earth compoundsPyrochloresSingle crystal X-ray diffractionCrystal growthThermal expansionDensity functional theory

a b s t r a c t

Rare-earth titanates, RE2Ti2O7 (where RE = a rare-earth) with the pyrochlore structure continue to beinvestigated for use as potential stable host materials for nuclear and actinide-rich wastes. Accordingly,the present work is directed towards the elucidation of the fundamental structural, physical, and thermo-chemical properties of this class of compounds. Single-crystals of the rare earth pyrochlores were synthe-sized using a high-temperature flux technique and were subsequently characterized using single-crystalX-ray diffraction. The cubic lattice parameters display an approximately linear correlation with the RE-site cation radius. Theoretical calculations of the lattice constants and bond lengths of the subject mate-rials were carried out using density functional theory, and the results are compared to the experimentalvalues. The Sm and Eu titanates exhibit a covalency increase between the REO8 and TiO6 polyhedralresulting in a deviation from the increasing linear lattice parameter through the transition series. Gd2Ti2-

O7 with the 4f7 half-filled f-orbital Gd3+ sub-shell exhibits the lowest 48f oxygen positional parameter.The coefficient of thermal expansion for the rare-earth titanate series is approximately linear, and ithas a range of 10.1–11.2 � 10�6 �C�1. Raman spectroscopy indicated that the �530 cm�1 peak associatedwith the Ti–O stretching mode follows a general trend of decreasing frequency with increasing REreduced mass.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Pyrochlore-structure compounds of the form, A2B2O7, havebeen the subject of extensive research due to their broad rangeof physical, chemical [1], and magnetic properties that depend onthe substitution of ions on the A and B cation sites. These com-pounds are important candidate materials for electrolytes andanodes in solid-oxide fuel cell (SOFC) applications [2]. In fact at727 �C, the ionic conductivity of these pyrochlore compositionscan reach 5 � 10�2 S/cm – a value that is comparable to yttriumstabilized cubic zirconia (YSZ) – an electrolyte for the developmentof SOFC. Rare-earth titanates, RE2Ti2O7 (where RE = a rare-earthion) with the pyrochlore structure also continue to be investigatedfor use as potential nuclear and actinide waste storage/disposal

forms. They are, in fact, a key component phase in Synroc (syn-thetic rock)-based pyrochlore-rich ceramics for the proposed geo-logical immobilization of surplus plutonium from dismantlednuclear weapons [3,4], and single-crystals of these materials repre-sent the basis for continuing heavy-particle radiation-damage andactinide-doping investigations. The magnetic behavior of the tita-nate pyrochlores are also of interest due to their varied and oftenunconventional magnetic ground states [5]. In these materials,the magnetic RE ions form a lattice of corner-sharing tetrahedra,which is the 3D archetype for geometric frustration. This frustra-tion underlies a range of exotic disordered magnetic states at lowtemperature, such as spin-liquid, spin-glass, and spin-ice states.

Pyrochlores are also an important mineral structure-type withpyrochlore minerals occurring in a wide variety of high-tempera-ture geologic settings including pegmatites and other igneous for-mations that often preferentially incorporate U and Th in theirstructure. Naturally occurring pyrochlores are often found in thedisordered, metamict state due to radiation damage from a-decay

64 J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70

events of nuclides in the decay series of 238U, 235U and 232Th impu-rities [6,7]. Studies involving Cm-doped Gd2Ti2O7 have shown acrystalline transformation to an amorphous state as a result ofalpha-decay of the incorporated Cm [8]. Synthetic Gd2Ti2O7 dopedwith 244Cm is, in fact, very susceptible to a-decay damage andtransforms to an amorphous structure after a dose of 2.3 � 1025

a-decays/m3 [9]. Radiation effects due to bulk doping of actinidesresult in volume swelling and micro-fracturing due to theincreased size of the network as the structure expands. A practicalhost material for storing actinide waste would, of course, not be anisotropic phase. It would, instead, be an anisotropic polyphasematerial, and the determination of the thermal expansion for eachphase of a pyrochlore-containing host material is essential forwaste storage applications to prevent thermo mechanical phasemismatch. The coefficient of thermal expansion (CTE) can be calcu-lated from the lattice parameters as a function of temperature, andthe present study presents the first comprehensive determinationof the CTE values for the RE2Ti2O7 (RE = Lu–Sm and Y) pyrochlores.Accordingly, precise temperature-related structural data and sin-gle-crystal structural and crystal chemical analyses are pertinentto the interpretation of previous and ongoing rare-earth titanateirradiation-induced amorphization, chemical stability and thermomechanical studies [10].

The pyrochlore, A2B2O7, structure (Fd-3m, Z = 8), is an anion-deficient derivative of fluorite, AX2 (Fm3m, Z = 1), with two typesof cations ordered on the A- and B-sites and one eighth of theanions removed. The structure can be envisioned as interpenetrat-ing networks of BO6 octahedra and A2O chains of distorted cubes.One-eighth of the oxygen atoms are removed from the fluoritestructure giving the pyrochlore formula of A2

3+B24+O7, in which the

A-site contains the large cations (rare-earth ions) and the B-siteconsists of smaller (e.g., titanium), higher-valence cations. The lar-ger RE3+ cations are eight-fold coordinated with oxygen andlocated within a distorted cubic coordination polyhedron. The lossof oxygen atoms causes a reduction in the coordination of the Ti-site cation from eight to six in a distorted octahedron. The generalcoordinates are shown in Table 1. There are two unique oxygensites noted by the Wyckoff notation (48f and 8b): the 48f site oxy-gen at ðx; 1

2 ;12Þ is coordinated with two Ti4+ and two RE3+ cations,

while the 8b site oxygen at ð38 ; 38 ;

38Þ is in a tetrahedral coordination

with only RE3+ cations. The x positional parameter for the 48f siteoxygen is the only variable coordinate for each rare-earth titanatepyrochlore compound. An unoccupied interstitial site, 8a, is sur-rounded by four Ti4+ ions, and the ‘‘vacancies’’ at the 8a site areordered on the anion sub-lattice.

For the ordered pyrochlore structure, A2B2O7, the chemical sta-bility is mainly determined by the cation ionic radius ratio (rA/rB).The larger A3+ cations are eight-fold coordinated with oxygen andlocated on the 16c site at (½,½,½) within the distorted cubic poly-hedron. The smaller B4+ cation is six-coordinated with oxygen andlocated in a distorted octahedron on the 16d site at (0,0,0). Theionic conductivity that makes these materials of interest for SOFCapplications is attributed to the cation disordering at the A and Bsites [11].

The essential crystallographic feature of the pyrochlore struc-ture consists of sheets of corner-sharing BO6 octahedra parallelto the (111) plane. These sheets are arranged into three- andsix-membered rings. When actinides are substituted into the

Table 1Atomic positions for RE2Ti2O7 (RE = Lu–Sm and Y).

Atom Wyckoff notation x y z

RE 16d 1/2 1/2 1/2Ti 16c 0 0 0O(1) 48f x 1/8 1/8O(2) 8b 3/8 3/8 3/8

pyrochlore structure, they preferentially occupy the A-site [12].This octahedral framework structure is an ideal host in which tosubstitute actinide elements at the A-site. As a result of the stablebonding, the rare-earth pyrochlores are important candidate cera-mic waste forms for actinide immobilization [13], and they are oneof the principal host phases being considered for the disposition ofPu from dismantled nuclear weapons [14].

An upper A-cation radius exists, above which the cubic titanatepyrochlore cannot form (rA3+ > rSm3+, RE = Nd, Pr, and La), and thesecompositions then crystallize in the monoclinic space group P21

(No. 4).Rare-earth titanate compounds have previously been character-

ized using routine powder XRD methods and other physical tech-niques [15,16]. Prior to the present investigations the synthesisof these compounds, however, has been limited primarily to theformation of powder samples. We have now grown single-crystalsamples of the rare-earth titanate pyrochlore series, RE2Ti2O7

(RE = Lu to Sm, and Y) by using a high-temperature flux technique[17]. The present study investigates the details of the single-crystalstructures, plus the coefficients of thermal expansion of this serieswere determined using high-temperature X-ray diffraction. Spec-tral characterizations were also made by using Ramanspectroscopy.

2. Experimental

2.1. Crystal growth

Single-crystals of the compounds RE2Ti2O7 (RE = Sm to Lu, plusY) were grown at T = 1235 �C in a molten mixture consisting ofthe specific rare-earth oxide (RE2O3), titanium oxide (TiO2), andlead fluoride (PbF2). Octahedral crystals of RE2Ti2O7 up to 3 mmon a side were formed by the slow evaporation of the PbF2 flux dur-ing a 5-day high-temperature synthesis period. The resulting crys-tals were yellow to brown in color depending on the particularrare-earth oxide used in the synthesis. The excess PbF2 flux thatremained on the crystals was superficial and was removed byphysical methods before analysis. The growth process was com-pleted in air in a Pt crucible that was placed in a temperature-pro-grammable furnace employing SiC heating elements.

The rare-earth pyrochlore crystal composition was confirmedby a semi-quantitative X-ray fluorescence analysis employing anInternational Systems Instrument (ISI-40) scanning electronmicroscope (SEM) equipped with an energy dispersive system(EDS). Trace amounts of lead (Pb) from the PbF2 flux were observedon the crystal surface. The majority of the PbF2 was physicallyremoved before any further analyses was undertaken, however,and the interior surfaces of fractured crystals did not show tracesof lead flux that might have been incorporated in the crystal lattice.Additionally, examination of the crystal samples using polarizedlight microscopy showed no evidence for impurity phases in thecrystal matrix and confirmed the optical homogeneity of the singlecrystals that were selected for subsequent X-ray diffractionanalysis.

2.2. Single-crystal X-ray diffraction studies

2.2.1. Collection methodsIntensity data for all of the rare-earth pyrochlore compounds

were collected using an Enraf-Nonius CAD4-F auto-diffractometerequipped with a graphite monochromator (take-off angle at 2.8�).Using Mo Ka radiation (kmean = 0.71073 Å). The orientationmatrix and unit cell lattice parameters were obtained throughthe application of the CAD4 subroutine program SEARCH [18]. Datasets were collected for each compound in the range of 3.0 < 2h < 56

Table 3Experimentally measured and calculated bond lengths (Å) for RE2Ti2O7 (RE = Lu–Smand Y).

RE2Ti2O7 RE–O(1)48f RE–O(2)8b Ti–O(1)48f

Exp. Cal. Exp. Cal. Exp. Cal.

Lu 2.459(7) 2.437 2.169(1) 2.173 1.943(4) 1.963Yb 2.454(3) 2.172(1) 1.950(3)Tm 2.474(3) 2.457 2.179(1) 2.184 1.950(1) 1.967Er 2.488(6) 2.469 2.182(1) 2.190 1.946(3) 1.969Ho 2.489(4) 2.479 2.187(1) 2.195 1.954(2) 1.971Dy 2.503(3) 2.490 2.192(1) 2.201 1.953(2) 1.974Tb 2.505(3) 2.503 2.199(1) 2.207 1.963(2) 1.976Gd 2.524(4) 2.517 2.205(1) 2.214 1.961(3) 1.979Eu 2.523(2) 2.533 2.207(2) 2.223 1.965(1) 1.983Sm 2.524(5) 2.549 2.209(1) 2.231 1.968(4) 1.986

Y 2.477(3) 2.491 2.187(1) 2.187(1) 1.960(2) 1.973

J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70 65

(h:0 ? 10, k: 0 ? 10, l: 0 ? 10) using the x�2h technique at a var-ied scan rate (0.54–5.17� min�1). Intensity variations selected fromdifferent zones of reciprocal space were negligible during the datacollection (<1.0%). Intensity measurements were corrected for Lor-entz and polarization factors. The data were also corrected byapplying either a numerical absorption correction based on sixcrystal-face measurements or a semi-empirical absorption correc-tion based on azimuthal scans of w-data [19].

2.2.2. Structural refinement methodsThe rare-earth titanate single-crystal structures were solved

using isomorphic substitution [16]. Refinements were made by afull-matrix least squares method on all F2 data, using the SHELX-97 program [20]. All atoms were refined anisotropically. The rele-vant crystallographic data are listed in Table 2. Final differenceFourier maps indicated some residual density near the positionsof the rare-earth ions. Elsewhere, the residual map was virtuallyfeatureless revealing only random fluctuating backgrounds. Atomicscattering factors with related anomalous dispersion correctionfactors were obtained from the International Tables [21]. Thestructural parameters of the rare-earth titanate pyrochloresobtained from refinements of the single-crystal X-ray diffractiondata are summarized in Table 2. Atomic positions for the RE2Ti2O7

pyrochlores are found in Tables 1 and 2.

2.3. First-principles calculations

Structural properties of the subject rare-earth pyrochlores werecalculated using Density Functional Theory (DFT) as implementedin the VASP codes [22]. Perdew–Burke–Ernzerhof (PBE) functionalswere used in all calculations. The electron-ion interactions aredescribed by the projector augmented wave method [23]. The 4felectrons of the rare-earth cations are frozen in the core becausethe 4f states are highly localized and have little interaction withvalence states. The valence wavefunctions are expanded in aplane-wave basis with a cutoff energy of 500 eV. The Yb compoundwas not calculated here because of the lack of a good pseudopoten-tial for Yb3+. Lattice constant and internal coordinates of the rare-earth pyrochlores were fully optimized. The results of the DFT–PBEcalculations are compared to the experimental values in the appro-priate corresponding tables and figures (see Tables 2–4 and Figs. 1and 3–5).

2.4. High-temperature X-ray diffraction

High-temperature X-ray diffraction (HTXRD) measurementswere made using a Scintag PAD V vertical h/h goniometer equippedwith a Buehler HDK-2 diffraction furnace. The diffractometer uti-lized Cu Ka radiation (45 kV and 40 mA) and a Si(Li) Peltier-cooled

Table 2Crystal structure refinement results for RE2Ti2O7 (RE = Lu–Sm and Y). The calculated lattic

RE Lattice parameter(exp.) (Å)

Lattice parameter(cal.) (Å)

O(1)48f x parameter(exp.)

O(1)48f xparameter

Lu 10.0172(4) 10.037 0.3297(9) 0.3336Yb 10.0325(3) 0.3309(4)Tm 10.0638(5) 10.087 0.3292(3) 0.3324Er 10.0787(3) 10.114 0.3278(8) 0.3316Ho 10.1041(2) 10.137 0.3285(5) 0.3310Dy 10.1240(3) 10.164 0.3275(5) 0.3304Tb 10.1589(6) 10.193 0.3281(5) 0.3296Gd 10.1860(2) 10.226 0.3263(6) 0.3287Eu 10.1943(9) 10.266 0.3267(3) 0.3278Sm 10.2056(6) 10.304 0.3270(8) 0.3269

Y 10.1002(6) 10.163 0.3300(4) 0.3302

solid-state detector. The single-crystals were crushed into a pow-der form for all of these analyses. The data were collected asstep-scans with a step size of 0.02� in 2h and a count time of 1 s/step size between 10� and 68� 2h. The sample temperature wasmonitored with a Pt/Pt-10% Rh thermocouple spot-welded to thePt-30% Rh heater strip on which a thin layer of the RE2Ti2O7 pow-ders was dispersed.

The data were collected in vacuum at 20 �C and on heating toset points at 10 �C/min beginning at 100 �C – and then increasingwith increments of 100 �C up to 1000 �C. The data were analyzedusing the JADE 6.0 program [24]. The (111) and (200) diffractionpeaks from the Pt/Rh heater strip at approximately 40.5� and47.1� 2h, respectively, were omitted from the refinements.

2.5. Raman spectroscopy

Raman spectra for the pyrochlore single crystals were obtainedusing a Dilor XY800 triple-stage Raman microprobe (Horiba Scien-tific, Edison, NJ) using an Innova 308C Ar+ ion laser (Coherent Inc.,Santa Clara, CA) at 5145 Å and 6 mW power at the sample. AllRaman spectra were recorded at room temperature over the rangeof 50–1000 cm�1. The spot diameter and penetration depth wereboth �10 lm in size. Anti-stokes spectra were acquired to deter-mine if anomalous peaks were caused by fluorescence effects.

3. Results and discussion

3.1. Single-crystal structure analysis

3.1.1. Lattice parametersThe values of the cubic lattice parameters of the rare-earth

pyrochlores, RE2Ti2O7 (RE = Lu–Sm and Y), determined from thesingle-crystal X-ray structural refinements are given in Table 1.

e constant and the x positional parameter for 48f-site oxygen are also shown.

(cal.)Density (g/cm3)

R1 Rall Residual/(e� �3) max.

Residual/(e� �3) min.

7.371 0.0373 0.0384 2.03 �1.897.287 0.0144 0.0174 0.54 �1.047.112 0.0225 0.0237 1.82 �1.087.037 0.0367 0.0401 2.54 �1.446.926 0.0272 0.0292 1.25 �2.186.821 0.0174 0.0219 1.83 �0.796.661 0.0224 0.0227 1.19 �0.656.566 0.0251 0.0297 1.03 �0.736.417 0.0213 0.0223 0.93 �2.446.355 0.0239 0.0258 1.77 �0.85

4.972 0.0206 0.0291 0.38 �0.44

Table 4Selected measured and calculated bond angles (�) for RE2Ti2O7 (RE = Lu–Sm and Y).

RE O(1)ii–RE–O(2) O(1)ii–RE–O(2)i O(1)ii–RE–O(1)iv O(1)xii–Ti–O(1)xvii

Exp. Cal. Exp. Cal. Exp. Cal. Exp. Cal.

Lu 79.19(18) 78.54 100.81(18) 101.46 116.57(11) 116.15 96.6(4) 97.92Yb 78.99(8) 101.01(8) 116.44(6) 96.9(1)Tm 79.27(6) 78.74 100.73(6) 101.26 116.62(3) 116.29 96.40(12) 97.51Er 79.52(14) 78.88 100.48(14) 101.12 116.77(8) 116.37 95.9(3) 97.23Ho 79.40(9) 78.97 100.60(9) 101.03 116.70(5) 116.43 96.12(19) 97.04Dy 79.62(8) 79.08 100.38(8) 100.92 116.83(5) 116.50 95.65(17) 96.81Tb 79.46(8) 79.21 100.54(8) 100.79 116.73(5) 116.58 96.00(18) 96.54Gd 79.76(10) 79.37 100.24(10) 100.63 116.91(6) 116.67 95.3(2) 96.20Eu 79.69(6) 79.51 100.31(6) 100.49 116.87(3) 116.76 95.50(13) 95.89Sm 79.65(8) 79.66 100.35(8) 100.34 116.84(9) 116.85 95.6(1) 95.56

Y 79.15(6) 79.11 100.85(6) 100.89 116.54(4) 116.51 96.67(13) 96.75

Symmetry transformations used to generate equivalent atoms: (i) �x + 1, �y + 1, �z + 1 (ii) �y + 1/2, �z + 1/2, �x + 1 (iii) y + 1/2, z + 1/2, x, (iv) �z + 1/2, �x + 1, �y + ½ (xii)y�1/4, �z, x-1/4 (xvii) �x + 1/4, �y + 1/4, z, (xxiv) �x + 1/4, y, �z + 1=4.

Fig. 1. Lattice parameter vs. RE+3 crystal radius for RE2Ti2O7 (RE = Lu–Sm and Y). Thestandard deviations are smaller than the symbol size. The slow-down of theincrease of the experimentally measured lattice constant in Eu and Sm compoundsshould be due to the increased hybridization between RE–4f and O–2p states. Thecalculations do not consider RE–4f–O–2p hybridization, therefore, the trend ofincreasing lattice constant as a function of the ionic radius does not slow down forEu and Sm compounds.

Fig. 2. Edge-sharing REO8 and TiO6 polyhedra in the pyrochlore structure.

Fig. 3. O(1)48f x-coordinate vs. crystal radius RE+3 for RE2Ti2O7 (RE = Lu–Sm and Y).

Fig. 4. RE–O(1)48f vs. RE+3 crystal radius for RE2Ti2O7 (RE = Lu–Sm and Y).

66 J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70

These results are in fairly reasonable agreement with the valuesreported earlier by Subramanian et al. [1]. The lattice constantincreases approximately linearly with the RE cation ionic radiusfrom Lu to Gd compounds, but increases more slowly from theGd to Sm compounds [25]. The ‘‘slowdown’’ of the lattice constantincrease from Gd to Sm may be related to the increasing hybridiza-tion between the empty RE 4f states and the O 2p states. The RE 4fstates are usually considered to be highly localized, i.e., not partic-ipating in the covalent bonding, but it has been found in both

experiments and in calculations that the RE 4f states can hybridizewith the 6s and 5d states in RE metals and in semiconducting REcompounds. Since the RE 6s and 5d states hybridize with anionstates in RE compounds, the RE 4f states should, in turn, alsohybridize with anion states – thus participating in covalentbonding.

The hybridization strength between the empty RE 4f states andthe anion states in a RE compound should increase from La3+ toEu3+ as the gradual filling of the RE 4f states lowers the empty RE4f states. The reduced energy separation between the RE 4f states

Fig. 5. O(1)ii–RE–O(1)iv vs. RE+3 crystal radius for RE2Ti2O7 (RE = Lu–Sm and Y).

J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70 67

and the valence band should increase the hybridization. From Eu3+

to Gd3+, a sudden decrease in hybridization between the RE 4f andthe anion states should occur because the 4f states of Gd3+ are halffilled and the empty minority spin 4f states are high in energy dueto the exchange splitting. The hybridization increases again fromGd3+ to Lu3+ as the minority spin 4f states are being filled, whichlowers the energy of the empty 4f states.

For titanate pyrochlores, the hybridization between the RE 4fand the O 2p states decreases from Lu to Gd, which contributesto the increase in the lattice constant, but the change of the REionic radius is the dominant factor in the increase of the latticeconstant. From Gd to Eu, an abrupt increase in the RE–4f–O–2phybridization occurs, which reduces the increase of the RE–O bondlength and consequently the lattice constant.

DFT calculations freeze the RE 4f states in the core and, there-fore, no hybridization between the RE–4f states and the O 2p statesis allowed. The calculated lattice constants of titanate pyrochloresshow a nearly linear increase from the Lu to the Sm compounds(see Fig. 1) with no slowdown of the trend in going from Gd toSm. The difference between the calculated and the experimentallymeasured lattice constants suggests that the RE 4f state may play arole in the slowdown of the lattice constant increase from Gd toSm. The lattice parameter of the yttrium titanate compound devi-ates slightly from the general trend due to an absence of the f-orbi-tal sub-shell electron shielding.

3.1.2. Oxygen parameterAn ordered pyrochlore structure can be described by the cubic

lattice parameter, a, and the 48f site oxygen positional parameter,x [15,6,26]. The atomic positions for RE2Ti2O7 pyrochlores are givenin Tables 1 and 2. The oxygen at the 48f site is located at (x,½,½).The parameter x of the 48f oxygen defines the degree of distortionof the Ti–O octahedron, and the limiting values of x are 5/16 and 3/8 for the pyrochlores. For x = 5/16, the B ions in the A2B2O7 struc-ture are in regular octahedral coordination, BO6, and the A ionsare in a distorted cubic coordination, AO8. When x ¼ 3

8, the coordi-nation around the A ion is a perfect cube, AO8, and the BO6 octahe-dron is unrealistically flattened; the atomic positions correspond tothe fluorite-type with ordered oxygen vacancies. The oxygenvacancy at the 8a site, located at (1/8, 1/8, 1/8), is surrounded byfour B4+ cations in the ordered pyrochlore structure. The electro-static repulsion between exposed B-site cations is compensatedfor by the displacement of the 48f site oxygen towards the exposedB-site cations. The polyhedral distortion can be seen in Fig. 2. Thus,the 48f-site oxygen x parameter is a measure of the degree of struc-tural distortion and the extent of deviation from the ideal fluoritestructure.

In this study, the 48f site oxygen positional parameter, x, variesfrom 0.3263 to 0.3309 over the series of titanate pyrochlores(Table 2). A significant change in the x parameters for the rare-earth titanate pyrochlores is obtained by varying the size of theRE-site cation, (Fig. 3). There is a general trend of a monotonicincrease of the x positional parameter as the RE-site cation radiusdecreases relative to the Ti4+ cation [1,16]. The trend of theO(1)48f x values vs. the crystal radius is relatively consistent withthe values determined by Knop et al. [16], which were based onan X-ray structural refinement made using powder samples. Therelative discrepancies between the x value determined in thisstudy and Knop’s results might be attributed to differences in sys-tematic errors, given that the present study used single-crystal X-ray diffraction as opposed to powder X-ray diffraction. In bothstudies, Gd2Ti2O7 has the smallest O(1)48f x value, which deviatesfrom the general trend as a function of ionic size. This suggests thatother factors can play an important role in determining the oxygenpositional parameter.

The fact that Gd2Ti2O7 has the smallest 48f oxygen positionalparameter (0.3263), as compared with other rare-earth titanatepyrochlores correlates with the largest deviation from the idealfluorite structure. The relatively low O(1)48f x value for Gd2Ti2O7

obtained here (and consistent with Knop et al. [16]) can beexplained by considering the electronic configurations. There is astrong hybridization of the Ti 3d and O 2p valence states forrare-earth titanate pyrochlores, and this interaction is responsiblefor the chemical bonding in the distorted Ti–O(1)48f octahedron[27]. The Ti–O(1)48f overlap is evidenced by the relatively shorterbond distance of Ti–O(1)48f for Gd2Ti2O7 (see Table 3). Further-more, the O 1s binding energy for Gd2Ti2O7 is the lowest withinthe RE2Ti2O7 pyrochlore compositions, which also confirms theincreasing Ti–O48f overlap in Gd2Ti2O7. Nemoshkalenko et al. [28]also observed an anomalous build-up of electron density on theO(1)48f atoms in Gd2Ti2O7. The increased Ti 3d and O 2p orbitaloverlap leads to the lower oxygen positional parameter, x, for Gd2-

Ti2O7. This displaces the oxygen atoms toward the Ti4+ anddecreases the O(1)48f positional parameter, x, for Gd2Ti2O7 and Lu2-

Ti2O7, as compared with the neighboring rare-earth titanatepyrochlores. The large O(1)48f x value found for Y2Ti2O7 in thisstudy could be related to some residual disordering that, forinstance, can be induced by Zr substitution in Y2Ti2O7 [29], how-ever, we saw no evidence for any such disorder from the single-crystal X-ray diffraction refinement.

3.1.3. Bond distances and anglesThe bond distances and angles for the RE pyrochlores are shown

in Tables 3 and 4, respectively. The RE–O(1)48f bond distances ofthe RE2Ti2O7 single-crystals for the RE’s from Lu to Tb show anapproximate linear dependence on the cation radius (Fig. 4), andreach a maximum constant value for Gd, Eu, and Sm. The bond dis-tances indicate a significant hybridization between RE 5p–O(2)8b

and RE 5p–O(1)48f 2s for the RE2Ti2O7 [25]. The shorter bond dis-tance for RE–O(2) compared to RE–O(1), indicates a strongerhybridization of RE 5p–O(2)8b. As the rare-earth atomic numberincreases, the hybridization becomes weaker. This effect is consis-tent with a predominant ionic character with decreasing crystalradius, and it explains the relationship of the cubic lattice param-eter, and bond distances of the RE–O(1)48f and RE–O(2)8b withchanging rare-earth crystal radius. The unusual environment atthe RE site also results in anisotropic atomic displacement param-eters for the RE cations, since they cannot readily vibrate againstthe nearby 8b oxygen atoms.

The bond angles for the RE titanate series are shown in Table 4.A representation of the general trend of the angles can be seen inthe O(1)ii–RE–O(1)iv angle change vs. RE, see Fig. 5. In general,the angle increases from the Lu to the Gd pyrochlores, and a slight

Fig. 6. Coefficient of thermal expansion vs. crystal radius RE+3 for RE2Ti2O7

(RE = Lu–Sm and Y).

68 J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70

decrease is found for the Eu and Sm analogs. The O(1)ii–Gd–O(1)iv

angle, 106.13(8)�, is the largest angle for the series. The angles rep-resent the degree of distortion of the polyhedral. Thus, Gd2Ti2O7

has the largest polyhedral distortion. A second general trend canalso be seen from the O(1)ii–RE–O(2)i angles. These values showa decreasing value in going from the Lu to the Gd pyrochloresand a slight increase for Eu and Sm. In this case, Gd2Ti2O7 hasthe smallest O(1)ii–RE–O(2)i angle, 100.24(10)�, found for the ser-ies, which once again indicates that Gd2Ti2O7 has the largestdegree of polyhedral distortion.

3.1.4. First-principles calculations of structural propertiesThe calculated lattice constants of rare-earth titanate pyroch-

lores are reported in Table 2 and plotted in Fig. 1 along with theexperimental results. The calculated lattice constants are largerthan the experimental values by only 0.2–1%. A slight overestima-tion of the bond length and the lattice constant is typical for DFT/PBE calculations. The larger ionic radius of the rare-earth cationsuppresses the x positional parameter for the 48f site oxygen asshown by the calculations (see Table 2 and Fig. 3). The calculatedx positional parameters are in good agreement with the experi-mental values with discrepancies less than 1.2%. The calculatedbond lengths and bond angles are also reported in Tables 3 and 4and Figs. 4 and 5. Overall, the general trend from the calculationsis consistent with the experiments, i.e., with increasing ionic radiusof the rare-earth ions, the lattice constant increases, the x posi-tional parameter for the 48f site oxygen decreases, the O–Ti–Obond angle decreases (closer to 90�, less distortion for the octahe-dron), the RE–O bond lengths increase, and the Ti–O bond lengthsalso increase since a larger A-site ion also increases the space forthe B-site ion. The calculations show a somewhat more lineardependence of these structural properties on the RE-cations’ ionicradius than the experiments.

3.2. Thermal expansion using high-temperature powder diffraction

The lattice parameters at each temperature were analyzedusing the expression:

ða� a0Þ=a0 ¼ Da=a0 ð1Þ

where a0 is the lattice parameter at 20 �C (taken from the single-crystal X-ray diffraction results) and a is the lattice parameter at aparticular temperature. Room-temperature (20 �C) lattice parame-ters and the coefficients of thermal expansion (CTE) obtained usinghigh-temperature X-ray diffraction for RE2Ti2O7 (RE = Lu to Sm andY) are shown in Table 5 and Fig. 6. The CTE for the rare-earth tita-nate series has a range of 10.1–11.2 � 10�6 �C�1. The difference isonly 1.1 � 10�6 �C�1 throughout the series. The CTE with respectto the crystal radius is nearly linear from the Lu to the Gd. The Eu

Table 5Room temperature (20 �C) lattice parameters and coefficients of linear thermalexpansion (CTE) using high-temperature X-ray diffraction for RE2Ti2O7 (RE = Lu–Smand Y).

RE Room temperature (20 �C)a lattice parameter (Å)

CTE (�10�6 �C�1)

Lu 10.020(2) 10.1(1)Yb 10.033(2) 10.3(1)Tm 10.061(1) 10.4(1)Er 10.080(1) 10.5(1)Ho 10.109(1) 10.7(1)Dy 10.124(1) 10.9(1)Tb 10.151(1) 11.0(1)Gd 10.185(1) 11.1(1)Eu 10.204(2) 11.2(1)Sm 10.211(1) 11.2(1)

Y 10.106(1) 10.6(1)

and Sm titanate pyrochlore CTE’s indicates a slight decrease in thethermal expansion rate, exactly like that observed for the latticeparameter variation. While no previous similar studies of rare-earthtitanate pyrochlores are available with which to compare the pres-ent results, CTE values for similar compounds, such as the rare-earth zirconate pyrochlores (RE2Zr2O7) and rare-earth halfnatepyrochlores [(RE2Hf2O7) where RE = Gd–La], were previously givenby Kutty et al. [30], who used high-temperature X-ray diffractionanalysis. Both pyrochlore series had high thermal expansions(10.5–10.8 � 10�6 �C�1), and the values for these non-rare-earthpyrochlores are in reasonable agreement with the present results.

The thermal expansion of a solid material is related to its struc-ture and bonding. Compounds that exhibit more ionic bondinggenerally exhibit higher expansivity [31]. The RE2

3+Ti24+O7 pyroch-

lore structure can be viewed as two covalent networks, (RE2O)4+

and (TiO3)4�, with ionic bonding between the networks. The steady

increase of the ionic nature between the two networks can be seenin going from Lu to Gd. A decrease in the ionic character from Gdto Sm can be attributed to the steady increase of covalency that cor-respondingly decreases the thermal expansion rate.

3.3. Raman spectroscopy

Factor group analysis [32] of the RE2Ti2O7 (RE = Lu–Sm and Y)compounds predicts that six bands are Raman active. The rare-earth ion and titanium ions located at sites 16d and 16c, respec-tively, do not contribute to the Raman spectrum since they occupycentro-symmetric sites. The six Raman bands are only associatedwith the O(1) and O(2). The Raman-active vibrations per set of ionsare:

Oð1Þ48f ion : Ag þ Eg þ 3F2g

Oð2Þ8b ion : F2g

Fig. 7 shows the spectra obtained from all of the rare-earth tita-nate pyrochlore crystals grown here. The spectra are dominated bytwo large peaks at �310 cm�1 and �530 cm�1, see Table 6, whichare associated with the RE–O stretching and Ti–O stretchingmodes, respectively. Fig. 8 shows that the F2g peak, �310 cm�1, isinsensitive to a change in the rare-earth ion, but the Ag peak,�530 cm�1, associated with the Ti–O stretching follows a generaltrend of decreasing frequency with an increasing RE2Ti2O7 reducedmass. This is surprising since the 310 cm�1 peak is more correlatedto the RE–O vibration than the 530 cm�1 peak. However, factor

Fig. 7. Raman spectra (50–1000 cm�1) for RE2Ti2O7 (RE = Lu–Sm and Y).

Table 6Selected Raman spectroscopy peak positions (cm�1) for RE2Ti2O7 (RE = Lu–Sm and Y).

RE F2g peak A1g peak

Lu 312.83 526.76Yb 297.40 522.67Tm 303.37 522.67Er 310.03 521.99Ho 311.09 522.16Dy 307.58 518.92Tb 304.77 517.22Gd 311.43 517.56Eu 304.77 514.83Sm 308.80 515.51

Y 307.22 521.65

Fig. 8. A1g and F2g Raman spectroscopy peak positions (cm�1) for RE2Ti2O7 (RE =Lu–Sm and Y).

J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70 69

group analysis predicts that these vibrations will be largely unaf-fected by the choice of rare-earth ion since the vibrations are deter-mined by the oxygen sub-lattice. Therefore, any shift in the Ramanpeaks is likely to be due to a secondary effect of changing the rare-earth ion, which may be counter-intuitive. Vandenborre et al. [33]predicted that for stannate titanate pyrochlores the only force con-stant affected by the rare-earth ion is the constant associated withthe Ti–O stretching vibration. This confirms the result shown inFig. 8. While relatively insensitive to the Ti-site ion, Raman spec-troscopy will be sensitive to the presence of vacancies on the oxy-gen sub-lattice.

3.4. Comparison with other studies

The enthalpies for our pyrochlore samples were previouslystudied using drop calorimetry methods [34]. The trend of themeasured formation enthalpies, DH0

f, decreases across the RE tita-nate series and is consistent with the observed O(1)48f x parameterdecrease. The TiO6 distortion increases as the parameter x of theO(1)48f oxygen decreases. An increase in distortion of the TiO6

polyhedron has a direct influence on the increasing exothermicnature of the DH0

f for the RE titanates across the series. A similartrend between the DH0

f and the coefficients of thermal expansioncan also be surmised. The increase in the CTE across the series (seeFig. 6) follows the increasing instability trend of the DH0

f for the REtitanate series [32].

The present coefficient of thermal expansion results are similarto the behavior observed in an irradiation investigation that wasconducted using the same single crystal samples that are the sub-ject of this study [14]. There is consistency between the CTE andthe resistance to radiation damage as indicated by the criticalamorphization temperature, Tc, for the RE2Ti2O7 pyrochlores. Thecritical amorphization temperature is the temperature abovewhich annealing processes compensate the damage processesand the crystal can no longer be amorphized. The lower the Tc

for a material, the higher the radiation damage resistance becauseannealing removes the damage domains at relatively lower tem-peratures. The Tc curve reaches a maximum for Gd2Ti2O7

(Tc = 847 �C) indicating that this material is the least ‘‘resistant’’to radiation damage [10,35–39]. For the RE-titanate pyrochlores,substituting Gd for Tb increases the stability by, presumably, bettersatisfying the bond requirements of the RE-site. This stabilizationeffect may continue until the RE-site becomes too large and beginsto have a destabilization effect as indicated by the flattening of theenthalpy curve from Gd to Sm. This is consistent with the phasetransformation associated with the substitution of RE3+ with ionicradii larger than Sm that results in the formation of a layeredperovskite-type structure [40].

4. Conclusions

Single-crystal rare-earth titanate pyrochlores RE2Ti2O7

(RE = Sm–Lu) have been synthesized, and their structures refinedby single-crystal X-ray diffraction analysis. The cubic latticeparameter for RE2Ti2O7 (RE = Lu–Gd) displays an approximatelylinear correlation with the RE-site cation ionic radius. The latticeconstant increase slows down from Gd to Sm, related to the trendchange in the x positional parameter, bond length, and bondangles. This is attributed to the abrupt increase in RE–4f–O–2phybridization when transitioning from Gd to Eu compounds.

DFT–PBE calculations of the RE pyrochlore structural parame-ters (including the lattice parameters, x positional parameters,RE–O bond lengths, and Ti–O bonds lengths) were carried out,and these theoretical results are compared with the correspondingexperimental values. The calculated results, in general, are consis-tent with the experimental results except that the trend change instructural parameters from Gd to Sm is absent from the calculationresults due to the freezing of the RE 4f orbitals in the core, whichneglects the RE–4f–O–2p hybridization.

A change in the coefficients of thermal expansion at Gd2Ti2O7

corresponds to a change in the slope of Tc that is attributed to smallvalues of the O(1)48f positional parameter, x, and increased cova-lency of the Ti–O(1)48f bond. The coefficients of thermal expansionfor the pyrochlore rare-earth titanate series have a difference of1.1 � 10�6 �C�1 throughout the series. This indicates that thethermal expansions are fairly similar and would, therefore, be

70 J.M. Farmer et al. / Journal of Alloys and Compounds 605 (2014) 63–70

compatible for possible multi-RE element radioactive waste formapplications.

Acknowledgments

Research at the Oak Ridge National Laboratory was sponsoredby the U.S. Department of Energy, Basic Energy Sciences, MaterialsSciences and Engineering Division. The contributions of Sandra Sal-men and Allison Gray to the preparation of the manuscript aregratefully acknowledged.

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