PHYSICAL REVIEW B 91, 144302 (2015)

Phonon anharmonicity of monoclinic zirconia and yttrium-stabilized zirconia

C. W. Li,1,2,* H. L. Smith,2 T. Lan,2 J. L. Niedziela,3 J. A. Munoz,2 J. B. Keith,2 L. Mauger,2 D. L. Abernathy,4 and B. Fultz2

1Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA2Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California, 91125, USA

3Instrument and Source Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA4Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA

(Received 28 April 2014; revised manuscript received 12 January 2015; published 13 April 2015)

Inelastic neutron scattering measurements on monoclinic zirconia (ZrO2) and 8 mol% yttrium-stabilizedzirconia were performed at temperatures from 300 to 1373w K. Temperature-dependent phonon densities of states(DOS) are reported, as are Raman spectra obtained at elevated temperatures. First-principles lattice dynamicscalculations with density functional theory gave total and partial phonon DOS curves and mode Gruneisenparameters. These mode Gruneisen parameters were used to predict the experimental temperature dependence ofthe phonon DOS with partial success. However, substantial anharmonicity was found at elevated temperatures,especially for phonon modes dominated by the motions of oxygen atoms. Yttrium-stabilized zirconia (YSZ) wassomewhat more anharmonic and had a broader phonon spectrum at low temperatures, owing in part to defects inits structure. YSZ also has a larger vibrational entropy than monoclinic zirconia.

DOI: 10.1103/PhysRevB.91.144302 PACS number(s): 63.20.−e, 63.20.Ry, 77.84.Bw, 78.20.Bh

I. INTRODUCTION

Zirconia (ZrO2) is the most common and stable compoundof zirconium found in nature and one of the most studiedceramic materials. Zirconia is monoclinic (P 21c, baddeleyite)at ambient pressure and temperature, transforms to a tetragonalphase (P 42nmc) at approximately 2000 K [1,2], and to a cubicphase (Fm3m, which differs sightly from the tetragonal phaseby displacements of oxygen atoms) at higher temperaturesand pressures [1]. The high temperature phases of ZrO2

can be stabilized at ambient temperature and pressure bysubstituting some magnesium, calcium, cerium, or yttriumin place of zirconium to produce “stabilized zirconia.” Inparticular, 8 mol% yttrium-stabilized zirconia (YSZ), which isa composition of technological importance, primarily takes thetetragonal phase. This YSZ has about 4% oxygen vacancies,consistent with valences of Y3+ and Zr4+.

Zirconium-based oxides are leading candidates to replacesilicon oxide as gate insulators in field effect transistors [3,4],and their chemical stability and physical hardness also makethem useful as optical coatings. YSZ has applications in solidoxide fuel cells because of high ionic conductivity owingto ion hopping at temperatures near or above 800 K [5].Zirconia and YSZ both have high bulk moduli and highmelting temperatures, making them important materials forhigh temperature applications [6]. YSZ is also one of the mostwidely-used materials for thermal barrier coatings, owing toits property of transformation toughening and its surprisinglylow thermal conductivity of about 2 W/(m · K), which is muchlower than the monoclinic phase [7]. The oxygen vacancies inYSZ are believed to have a major effect on thermal transport,but their interactions with phonons are not understood.

A contribution to the heat capacity at constant pressureis expected as the crystal expands against its bulk modulus.“Quasiharmonic” shifts of phonon frequencies arise becausephonon frequencies usually decrease in an expanded crystal,

*lichen@caltech.edu

giving an increased vibrational entropy. In the quasihar-monic approximation (QHA), it is assumed that the phononmodes are harmonic and noninteracting, but with shiftedfrequencies. Anharmonic effects arise from phonon-phononinteractions, which are caused by cubic or quartic terms inthe phonon potential. Nonharmonic effects are important forunderstanding thermodynamic stability and thermal transportproperties at elevated temperature [8], but only a few studiesof phonons in metal oxides at high temperatures have beenreported. Anharmonicity in beryllia has been attributed toa change of phonon lifetime resulting from phonon-phononinteractions [9]. Phonon lifetime calculations on MgO showedanharmonicity at high pressures and temperatures [10]. An-harmonicity in cuprite Ag2O was explained by the phonon-phonon interactions between Ag and O dominated modes,and this anharmonicity contributed to the negative thermalexpansion [11].

Vibrational spectroscopy studies and theoretical work onzirconia have been performed [1,12–15], and other studieswere focused on phase transitions under pressure [16–18].In recent studies of the phonon dynamics of hafnia andzirconia, we reported measurements of Raman line positionsand shapes to temperatures of about 1000 K, and correlatedanharmonic effects to the vibrational displacements of oxygenatoms in the unit cell [19,20]. Similar work on YSZ showed anunexpectedly large softening in one of the phonon modes and alarge thermal broadening of Raman-active modes [21]. CubicYSZ is also known to have large thermal parameters andDebye-Waller factors [22]. Some phonon dispersion curveswere measured with triple-axis neutron spectrometry on cubicYSZ. The longitudinal and transverse acoustic phonon modeswere extremely broad, but curiously, no optical modes weredetected [23].

Here we report results from inelastic neutron scatteringmeasurements on zirconia and YSZ, together with Ramanspectrometry measurements of the temperature dependenceof specific phonon modes. DFT calculations of the phononsand their Gruneisen parameters are reported for monoclinicand tetragonal zirconia to provide insight into quasiharmonic

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behavior, where the phonon frequencies depend on tem-perature only through thermal expansion. Comparisons ofcalculations to the Raman and neutron measurements showthat zirconia and YSZ exhibit substantial anharmonic thermalbroadenings and shifts of phonon frequencies that differ fromquasiharmonic predictions. The oxygen-dominated modes athigher energies were especially anharmonic. The thermaltrends of the phonon peaks are similar in both zirconia andYSZ. In comparison to zirconia, the experimental phononspectra of YSZ showed substantial broadening at low temper-atures, however. The experimental phonon spectrum of YSZwas in some disagreement with the phonon spectrum calcu-lated for the tetragonal structure, unlike the good agreementfound for calculation and experiment for monoclinic zirconia.It appears that defects have a significant effect on the phononspectrum of YSZ. The phonon entropy of YSZ was found to belarger than that of zirconia, as expected for the monoclinic-to-tetragonal phase transition of zirconia at elevated temperature.

II. EXPERIMENTAL

Monoclinic zirconia and 8 mol% YSZ powder (99.99%and 99.95% purity, respectively) were loaded into an annularvolume between two concentric aluminum cylinders (givingan outer diameter of 2.9 cm, a wall thickness of 1 mm, anda height 6.4 cm), or were loaded into niobium sachets formeasurements at higher temperatures. The effective samplethickness for neutron scattering was about 2 mm, giving aratio of multiple to single scattering of approximately 5%. TheYSZ sample was characterized by x-ray powder diffraction tobe primarily tetragonal with 8% monoclinic phase. Inelasticneutron scattering measurements were performed with thetime-of-flight Fermi chopper spectrometer, ARCS [24], at theSpallation Neutron Source at Oak Ridge National Laboratory.For measurements at 300, 450, 600, and 750 K, the sampleswere measured in aluminum sample cans inside a low-masselectrical resistance furnace (“stick furnace”). For 300, 673,1073, and 1373 K, an electrical resistance furnace withniobium radiation shields (“MICAS furnace”) was used.Zirconia and YSZ are stable to much higher temperatures, butsince small anharmonic effects are linear in temperature, theessential effects of phonon anharmonicity can be determinedfrom the temperatures of these measurements. The incident

neutron energies, calculated from experimental data, were163 meV for measurements with the stick furnace, and 90and 175 meV for measurements with the MICAS furnace.ARCS has an energy-dependent energy resolution that variedfrom about 4% at the elastic line to 1% at the highestenergy transfer. Temperature was monitored with severalthermocouples and is believed accurate to within 5 K overmost of the sample. Furnace backgrounds were measured withempty sample cans at each temperature and later subtractedfrom the measurements of the sample.

Data reduction was performed with the software packageDRCS [25] for ARCS. For each incident energy, the rawdata of individual neutron detection events were first binnedto get S(E,2θ ), where 2θ is the scattering angle and E isthe energy transfer, and normalized by the proton currenton target. Bad detectors were identified and masked, and thedata were corrected for detector efficiency using a white-beammeasurement from vanadium. The S(E,2θ ) was then rebinnedinto intensity, S(Q,E), where �Q is the momentum transferto the sample. The elastic peak was removed and replaced bya function of energy determined from the inelastic scatteringjust past the elastic peak [26]. Intensities of the imaginarydynamical susceptibility, χ ′′(Q,E) = S(Q,E)/(nT (E) + 1),with nT (E) the Planck distribution, are shown in Fig. 1 formeasurements at 300 K. The phonon DOS curves, shown inFigs. 4 and 5 for the incident energies of 163 or 175 and90 meV, were obtained after corrections for multiphononand multiple scattering using the getdos package [27], asdescribed previously. [26] Neutron diffraction patterns werealso obtained by taking elastic scattering cuts. Pair-distributionfunctions (PDF) were also calculated using S(Q), as detailedin the Supplemental Material [28], and showed overall goodagreement with simulations of monoclinic and tetragonalstructures. The crystal structure of YSZ remained tetragonalat all temperatures, and that of zirconia remained monoclinic,as expected.

For Raman spectroscopy measurements, samples weremounted on the silver block of a Linkam thermal stage withthe chamber sealed and purged with nitrogen gas flow. A tem-perature controller drove a 200 W power supply for heating thesamples for measurements from 300 to 853 K. Raman spectrawere measured with a Renishaw micro-Raman system withan Olympus LMPlanFI microscope lens. The spectrometerwas configured in backscattering geometry, minimizing issues

FIG. 1. (Color online) Intensity of χ ′′(Q,E) for (a) zirconia and (b) 8 mol% YSZ at 300 K from the time-of-flight inelastic neutronscattering measurements with background subtracted. The color scales are in log scale and with the same range. YSZ shows fewer features atlow energy transfers.

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with the thickness of the sample [29]. A depolarized solid-statelaser operated at a wavelength of 514.5 nm excited the samplewith the low incident power of 10 mW to avoid additionalthermal heating. Each Raman spectrum was accumulated in20 measurements with 5 s exposure times. The measurementson zirconia were performed on a Raman system describedelsewhere [19,20], but the resolutions of both spectrometerswere much narrower than the peaks in the measured Ramanspectra and can be safely ignored. The Raman spectra werecorrected for background and fitted with multiple Lorentzianpeaks to obtain the mean phonon energies and their linewidths.

III. RESULTS

The χ ′′(Q,E) results in Fig. 1 show different phononscattering from zirconia and YSZ at 300 K. The χ ′′(Q,E) fromYSZ has fewer distinguishable energy-dependent featuresbelow 60 meV. The peaks in the measured phonon DOS arebroader in YSZ than zirconia at the same temperature. Thisis consistent with the Raman results shown in Figs. 2 and 3.At 300 K, the linewidths of some Raman peaks of YSZ areup twice as large as the same peaks of ZrO2. Nevertheless, forboth zirconia and YSZ, the Raman peak center energies havesimilar temperature dependencies, and both sets of Ramanpeaks have similar increases in linewidths with temperature.

FIG. 2. (Color online) Comparison of the Raman spectra ofzirconia [red, top (773 K) and bottom (300 K)] and YSZ (black)at temperatures as labeled.

(a) (b)

FIG. 3. (Color online) Temperature dependencies of fit parame-ters for Raman peaks, numbered as in Fig. 2. Solid black lines are forYSZ, and dashed red for ZrO2. (a) Center energy. (b) Full width athalf maximum.

Room temperature neutron results from different furnaceswere in good agreement after completing data deduction andcorrecting for the background (Fig. 4). The phonon DOScurves from measurements with an incident energy of 90 meVhave higher resolution (Fig. 5) but otherwise are in goodagreement with the results in Fig. 4 from higher incidentenergies. Thermal broadening is the most salient feature ofthe phonon spectra of zirconia and YSZ measured by bothneutron and Raman scattering. Compared to YSZ, the spectrafrom zirconia have sharper features at low temperatures.Thermal shifts are also apparent, with spectral features from40 to 80 meV shifting to lower energies (softening) withtemperature.

At about 750 K the phonon modes near 87 meV broaden forboth zirconia and YSZ; phonon modes around 70 meV softenand also broaden. The spectra of YSZ are mostly featurelessbetween 20 and 60 meV, even for the higher resolution spectrameasured with 90 meV incident energy.

IV. CALCULATIONS

First principles DFT calculations were performed withVASP [30–32] and used to calculate the total and partialphonon DOS curves for pure monoclinic and tetragonalphases. The generalized gradient approximation (GGA) andprojector augmented wave (PAW) pseudopotentials were usedin all calculations. Electronic structure was calculated selfconsistently using primitive cell and a 6 × 6 × 6 k-point grid.Experimental lattice parameters [33,34] for ambient conditionsof monoclinic zirconia and high-temperature tetragonal phasewere used for the calculations. Phonon energies were calcu-lated using the finite displacement method on a 2 × 2 × 2supercell and interpolated to a 16 × 16 × 16 k-point grid,which was used to calculated the total and atom-projected

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(a) (b)

FIG. 4. Normalized neutron-weighted phonon DOS curves of (a) zirconia, and (b) 8 mol% YSZ from inelastic neutron scattering with 163or 175 meV incident energies at temperatures from 300 to 1373 K with background subtracted. The solid lines are the results from the MICASfurnace, dashed lines from the stick furnace. The vertical lines are aligned with peaks at 300 K.

phonon DOS. Results for the monoclinic and tetragonalphases are presented in Fig. 6. Figure 6(a) shows that inmonoclinic zirconia, the heavier metal-dominated modes arein the low-energy end of the DOS below 40 meV, while thelighter oxygen atoms tend to dominate the high-energy partof the spectrum. This separation is somewhat less strongfor the tetragonal phase, as shown in Fig. 6(c), but againmetal-dominated modes are found below 40 meV and themajority of the oxygen-dominated modes are between 40 and70 meV. This approximate separation into metal modes andoxygen modes is expected from the large difference in themass of zirconium and oxygen atoms.

For comparison with experimental results, the calculatedphonon partial DOS curves of Zr and O were multipliedby σscat/m, where σscat is the total cross section for neutron

scattering and m is the mass of the atom. (The σscat/m for Yis nearly the same as for Zr.) Summing these corrected partialDOS curves gave “neutron-weighted” curves for comparisonto experiment. Good agreement was found between the experi-mental DOS for monoclinic zirconia and the neutron-weightedcalculation convoluted with the ARCS instrument resolutionfunction, which varies with energy transfer [Fig. 6(b)]. Theexperimental phonon DOS of the YSZ agreed far less wellwith the calculations for the tetragonal structure. (It is betterfit by a mixture of calculated DOS curves, for example,70% tetragonal and 30% monoclinic phase). Some calculatedfeatures at energies below 60 meV are conspicuously absentin the experimental spectra from YSZ. Similar calculations forcubic zirconia are shown in Supplemental Material Fig. 2 andprove that the cubic phase does not produce the neutron results.

FIG. 5. Neutron-weighted phonon DOS curves of (a) zirconia, and (b) 8 mol% YSZ from inelastic neutron scattering with 90 meV incidentenergies at temperatures from 300 to 1373 K in the MICAS furnace with background subtracted. The lower incident energy gives betterresolution than the results of Fig. 4.

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(a) (b)

(c) (d)

FIG. 6. (Color online) Total and partial phonon DOS curves of (a) monoclinic, (c) tetragonal phases from first principles DFT calculations.The thick gray lines are the phonon DOS with proper neutron weighting and ARCS instrument resolution at 163 meV incident energy. Theyare compared with the results from neutron experiments on monoclinic zirconia (b), on YSZ (d) at 300 K on the right.

Mode Gruneisen parameters

γj = − V

ωj

∂ωj

∂V(1)

were calculated for modes throughout the Brillouin zone usingfirst-principles and finite displacement methods. The resultsfor monoclinic and tetragonal phases are plotted versus phononenergy in Fig. 7. The inset in Fig. 7 shows that some phononbranches have distinct correlations between γj and energy.The monoclinic phase has more negative γj than the tetragonaland a broader distribution. Some mode Gruneisen parametersat low energies are quite large. A large γj suggests that thephonon mode is very anharmonic and may not be describedreliably by the quasiharmonic approximation [35].

V. DISCUSSION

A. Quasiharmonicity and anharmonicity

The temperature dependence of the phonon frequency ωj

can be written as

dωj

dT= ∂ωj

∂T

∣∣∣∣V

+ ∂ωj

∂V

∣∣∣∣T

dV

dT. (2)

FIG. 7. (Color online) Gruneisen parameters for monoclinic andtetragonal phases calculated from first-principles and finite displace-ment methods. The energy-dependent averages are shown as solidlines.

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The second term, where the ωj depends on volume, gives thequasiharmonic softening of a phonon mode owing to thermalexpansion

ωj (T ) = ωj (0) exp

(−γj

∫ T

0β(T ) dT

), (3)

where β is the volume thermal expansivity and γj was definedin Eq. (1).

In a test of the quasiharmonic contributions to the thermalshift of phonon DOS curves, Gruneisen parameters calculatedusing the quasiharmonic approximation (as shown in Fig. 7)and experimental thermal expansion data [36,37] were used topredict how the phonon DOS should evolve with temperature.The phonon DOS curves measured at 300 K were binned intohistograms of 1 meV intervals. For each mode in the interval,its Gruneisen parameter was assessed, and with the thermalexpansion the intensity from this mode was shifted to anotherenergy bin. This procedure was repeated for all modes, andthe redistributed intensity gave a new DOS from the QHAand mode Gruneisen parameters. The results are comparedwith the measured phonon DOS curves in Fig. 8. For themonoclinic zirconia the agreement with the experimental DOScurve at high temperature is moderately good, consideringthat the QHA does not account for any increase in phononlinewidth with temperature. The softening of the spectralfeature near 40 meV for monoclinic zirconia is underestimated,however. The agreement is less good for the YSZ, usingeither the Gruneisen parameters calculated for the monoclinicphase or the tetragonal phase. Neglecting thermal changesof specific features, the quasiharmonic approximation wasreasonably successful for the metal-dominated low-energymodes. The oxygen-dominated high-energy modes were notwell described by the QHA. This is consistent with the signifi-cant thermal broadening of this part of the spectra, indicative ofanharmonicity.

B. Thermal broadening

At low temperatures, the phonon DOS and Raman spectraof YSZ are broader than in the pure zirconia, especiallyat lower energies. This probably originates with a dis-tribution of phonon frequencies caused by vacancies andother structural disorder in the YSZ. It could be related tothe low thermal conductivity of YSZ at low temperatures.Nevertheless, the high-energy parts of the phonon DOS,dominated by oxygen atom motions, are rather similar inthe two materials. With increasing temperature, there is asimilar broadening and shift of the two peaks in the phononDOS curves of zirconia and YSZ at approximately 70 and85 meV.

The Raman spectra of YSZ and zirconia, although limitedto phonons at the point, do show considerable thermalbroadening that provides further information about anhar-monicity [38,39]. A quasiharmonic analysis cannot, of course,account for linewidth broadening of phonons at elevatedtemperatures. Anharmonic phonon perturbation theory showsthat the leading term in phonon lifetime broadening originatesfrom the cubic anharmonicity [40,41]. The cubic anhar-monicity may be especially large in monoclinic zirconiabecause its atoms do not have inversion symmetry, so it

is possible for some phonons to have an odd-order termin their potential energy. The YSZ shows similar thermalbroadening of Raman lines to those of zirconia that we reportedrecently, [20] although YSZ also has broad linewidths at lowtemperatures.

C. Phonon entropy

The entropy of zirconia originates primarily from phonons,which can be described as a sum of harmonic, quasiharmonic,and anharmonic contributions

Sph = Sharm + Sqh + Sanh . (4)

The harmonic contribution, which is the largest, originateswith phonons that undergo no change in frequency withchanges in either temperature or volume. The Planck oc-cupancy of harmonic phonon modes increases with temper-ature, giving an increased entropy. The quasiharmonic andanharmonic contributions to entropy can be separated by theirdependence on volume and on temperature

dS(T ,V )

dT= ∂S

∂T

∣∣∣∣V

+ ∂S

∂V

∣∣∣∣T

dV

dT. (5)

After accounting for the Planck occupancy change of harmonicphonons, the remainder of the first term on the right ofEq. (5) is the anharmonic contribution, and the second termis the quasiharmonic. Using calculated Gruneisen parametersto describe the frequency change with temperature, thequasiharmonic contribution was approximately successful forphonons in zirconia with energies below about 50 meV,correctly predicting the smaller shift for the feature around20 meV. On the other hand, the quasiharmonic calculationspredicted a distinct softening of spectral features between50 and 70 meV, and between 80 and 100 meV, but thesefeatures stiffened and remained unchanged with temperature,respectively. It appears that the oxygen-dominated modesin zirconia are more anharmonic than the metal-dominatedmodes, as indicated from previous Raman spectroscopy results[20]. This may originate with the larger average displacementsof oxygen atoms than zirconium atoms in higher-energyphonon modes, as expected from the large difference in atomicmass.

The only material parameter needed to calculate the phononentropy is the phonon DOS, g(ε)

Sph(T ) = 3kB

∫ ∞

0gT (ε)([n(ε) + 1] ln[n(ε) + 1]

− n(ε) ln[n(ε)]) dε, (6)

where n(ε) is the Planck distribution for phonon occupancy attemperature T . Equation (6) is reliable for the harmonic, quasi-harmonic, and anharmonic entropy (approximately), if gT (ε) isthe phonon DOS at the temperature of interest. Unfortunately,our experimental phonon DOS curves are “neutron-weighted”because phonon scattering by different elements with differentefficiencies, proportional to their neutron scattering crosssection divided by atomic mass. To determine the absoluteentropies of zirconia and YSZ, the neutron weighting wascorrected by the calculated partial DOS of monoclinic andtetragonal zirconia, respectively. (The neutron weight correc-tion was largely insensitive to the choice of structure and the

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FIG. 8. (Color online) Experimental phonon DOS curves of (a) monoclinic zirconia and (b) tetragonal YSZ compared with the QHA modelcalculations described in the text. Predictions with mode Gruneisen parameters for both the monoclinic and tetragonal materials are shown inpanel b.

details of the DFT calculation.) The difference in phononentropy between YSZ and monoclinic zirconia is shown inFig. 9. (For comparing entropies, we selected the low back-ground measurements performed with the low-mass sampleand the low-mass stick furnace, for which we had four pairs ofmeasurements.)

Figure 9 shows that monoclinic zirconia has a smallerphonon entropy than YSZ by 1.7 to 3.9 J/mol K (0.28 to0.65 kB/atom) between 300 and 800 K. From the relationshipSqh = Bvβ2T (B is bulk modulus, v is specific volume,β is the coefficient of volume thermal expansion) [8],which is consistent with the phonon entropy if zirconia is aquasiharmonic solid, the bulk properties of zirconia [36] giveSqh = 0.19 kB/atom over a temperature change of 1000 K.In the high temperature limit, this corresponds to an averagedecrease in phonon frequencies of approximately 6% in atemperature range of 1000 K if Sqh = −3kB ln〈ω/ω0〉 (where〈ω/ω0〉 is an average ratio of phonon frequency at hightemperature to that at low temperature). The actual decreaseof phonon frequencies is smaller than this, apparently becausethe anharmonicity in the oxygen-dominated modes causes lessthermal softening than predicted by the QHA. Interestingly,we found that using the phonon DOS curves for zirconia andYSZ measured at 300 K with Eq. (6) at elevated temperaturesgave similar results to Fig. 9. Even though individual phonons

FIG. 9. (Color online) The approximate difference betweenphonon entropies of YSZ and monoclinic zirconia, S = SYSZ −Smono, corrected approximately for neutron weighting.

stiffen or soften with temperature quite differently, the overalleffects of quasiharmonicity and anharmonicity are similarfor both materials, so surprisingly the difference in phononentropy of both materials can be obtained approximately froma harmonic model.

For comparison, the difference in vibrational entropy ofmonoclinic and tetragonal zirconia was also evaluated fromthe DFT calculations of the phonon spectra at T = 0 K. Thetetragonal zirconia had the larger vibrational entropy, but thedifference in vibrational entropy was only 0.38 J/(mol·K) at300 K. This suggests that the difference in vibrational entropybetween zirconia and YSZ may not arise from the difference inphonon spectra of perfect monoclinic and tetragonal structures.Defects in the YSZ appear to be important.

A recent study by differential scanning calorimetry onthe monoclinic-tetragonal phase transition in ZrO2 gave anentropy of this transition of approximately 3.7 J/(mol·K) at thetransition temperature of 1472 K [42]. Although the materialsand temperatures are different from the present study, theresults of Fig. 9 are consistent in sign and approximately theright magnitude to suggest that much of the entropy of themonoclinic-tetragonal transition originates from changes inthe phonon spectra.

VI. CONCLUSIONS

A comparison was made of phonons in monoclinic zirconia(ZrO2) and 8 mol% yttrium-stabilized tetragonal zirconia(YSZ) from ambient temperature to 1373 K, measured byinelastic neutron scattering spectrometry, Raman spectrom-etry, and calculated by density functional theory (DFT).Mode Gruneisen parameters were computed by DFT methodsand used to rescale the low-temperature phonon spectrumto predict spectra at high temperatures. This quasiharmonicapproximation was reasonably successful for the metal-dominated phonon modes at low energies but less successfulfor the oxygen-dominated phonon modes at the higher energiesin the spectrum. The Raman peak centers and linewidthbroadenings have similar changes with temperature for bothzirconia and YSZ. There is substantial anharmonicity inthe phonons of both zirconia and YSZ, especially for the

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oxygen-dominated modes at higher energies. In addition, thephonon spectra of YSZ are broadened significantly at lowtemperatures, likely due to structural disorder that wouldalso reduce the quality of agreement between computedand experimental phonon spectra of tetragonal YSZ, com-pared to the good agreement for monoclinic zirconia. Atall temperatures, YSZ had a larger vibrational entropy thanzirconia.

ACKNOWLEDGMENTS

We thank G.R. Rossman for his generous help on the Ramanmeasurements. This work was supported by the Departmentof Energy Office of Science Grant No. DE-FG02-03ER46055.The research at Oak Ridge National Laboratory’s SpallationNeutron Source was sponsored by the Scientific User FacilitiesDivision, Office of Basic Energy Sciences, DOE.

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