ARTICLE IN PRESS - Harvard University · 2016-09-15 · +Model ARTICLE IN PRESS JECS-9584; No.of Pages10 Available online at ScienceDirect Journal of the European Ceramic Society

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ARTICLE IN PRESS+ModelECS-9584; No. of Pages 10

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ScienceDirect

Journal of the European Ceramic Society xxx (2014) xxx–xxx

Thermal conductivity of single- and multi-phase compositions in theZrO2–Y2O3–Ta2O5 system

Andi M. Limarga a,1, Samuel Shian a,∗, Rafael M. Leckie b,2, Carlos G. Levi b, David R. Clarke a

a School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, Unites Statesb Materials Department, University of California, Santa Barbara, CA 93106, United States

Received 9 December 2013; received in revised form 4 March 2014; accepted 15 March 2014

bstract

ompositions in the ZrO2–Y2O3–Ta2O5 system are of interest as low thermal conductivity, fracture resistant oxides for the next generation thermalarrier coatings (TBC). Multiple phases occur in the system offering the opportunity to compare the thermal properties of single, two-phase,nd three-phase materials. Despite rather large variations in compositions almost all the solid solution compounds had rather similar thermalonductivities and, furthermore, exhibited only relatively small variations with temperature up to 1000 ◦C. These characteristics are attributed tohe extensive mass disorder in all the compounds and, in turn, small interfacial Kapitza (thermal) resistances. More complicated behavior, associatedith the transformation from the tetragonal to monoclinic phase, occurs on long-term annealing in air of some of the compositions. However, the
hases in two of the compositional regions do not change with annealing in air and their thermal conductivities remain unchanged suggesting theyay be suitable for further exploration as thermally stable TBC overcoats.
2014 Elsevier Ltd. All rights reserved.

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eywords: Thermal conductivity; Thermal barrier coatings; Mass disorder; Pha

. Introduction

There is currently an on-going world-wide quest for thermalarrier coating materials capable of higher temperature opera-ion than the state-of-the-art oxide based on ZrO2–7 wt.%Y2O37YSZ).1,2 Although many oxides have low thermal conductiv-ty, in several instances even lower than 7YSZ,3,4 they lack theequisite fracture toughness needed to resist delamination andmpact. The task is complex because of the stringent require-

ents of a TBC, a combination of low thermal conductivityt high temperature, compatibility with alumina as well asigh fracture toughness.5 Previous studies have identified the

Please cite this article in press as: Limarga AM, et al. Thermal conductivitsystem. J Eur Ceram Soc (2014), http://dx.doi.org/10.1016/j.jeurceramsoc

rO2–Y2O3–Ta2O5 system as particularly promising, especiallyetragonal compositions lying along the ZrO2–YTaO4 join, aarrow compositional range formed by equi-molar tri-valent

∗ Corresponding author. Tel.: +1 617 496 4295.E-mail address: [email protected] (S. Shian).

1 Present address: Corning Incorporated, Palo Alto, CA 94304, United States.2 Present address: MST-6, Powder Materials Processing, Los Alamos Nationalaboratory, NM 87545, United States.

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ttp://dx.doi.org/10.1016/j.jeurceramsoc.2014.03.013955-2219/© 2014 Elsevier Ltd. All rights reserved.

nsformation; Kapitza resistance

nd penta-valent additions.3,6 In particular, these compositionsre phase stable at 1500 ◦C and particularly resistant to sul-ate/vanadate corrosion.7 Moreover, they exhibit very high levelsf tetragonality which results in indentation fracture toughnessalues comparable or higher than 7YSZ.8,9 Furthermore, bothaghavan6 and Shen et al.10 have demonstrated that composi-

ions along the ZrO2–YTaO4 join have especially low thermalonductivity provided the transformation to monoclinic zirconias prevented from occurring. The low thermal conductivities arettributed to the extensive mass disorder associated with compo-itions along the join. They are also resistant to moisture-inducedow-temperature transformation.11

The purpose of this work was to investigate the thermalonductivity over a broader range of compositions in therO2–Y2O3–Ta2O5 system and compare the behavior of sin-le and multi-phase oxides. The compositions investigated arehown superimposed on the phase diagram in Fig. 1. Theynclude two single-phase solid solutions (the 7YSZ baseline

y of single- and multi-phase compositions in the ZrO2–Y2O3–Ta2O5

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nd 16Y16Ta), two compounds (YTaO4 and δ-Zr3Y4O12), aair of two-phase materials (22Y13Ta and 20Y20Ta) and oneomprising three phases (18Y28Ta). The ternary compositions

dx.doi.org/10.1016/j.jeurceramsoc.2014.03.013

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ARTICLE IN PRESS+ModelJECS-9584; No. of Pages 10

2 A.M. Limarga et al. / Journal of the Europea

Fig. 1. Isothermal section of the ZrO2–YO1.5–TaO2.5 phase diagram at 1500 ◦C.The compositions of the single phase, two-phase and three-phase materialsinvestigated in detail are indicated by the stars. The inverted triangles indi-cate compositions with known thermal conductivity data, either reported oru

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The microstructures of the conventionally sintered samples

npublished work.

ere selected to encompass the non-transformable tetragonalhase as one of the constituents, with the expectation thathis would provide a toughness benefit based on prior work.8

aterials having compositions lying in the two-phase fieldetween the co-doped tetragonal ZrO2 and the orthorhombicO’ phase were found to partially transform on cooling and con-equently, they were not studied further. Also shown in Fig. 1 areompositions whose thermal conductivities have been reportedlsewhere.10,12,13 Compositions within the fluorite single-phaseeld were also not explored since their thermal conductivitiesave already been reasonably well studied14 and were foundarlier to have lower fracture toughness.15

. Experimental methods

The experimental procedures were chosen to producehemically-homogeneous, fully-dense materials so that thentrinsic thermal conductivities could be measured without need-ng to apply corrections for the presence and shape of anyorosity. In the few cases that the materials could not be madeully dense, particularly for YTaO4 composition, correctionactors were applied with the assumption of spherical pores.amples were prepared by both current assisted densificationrocess (CADPro)16 and conventional sintering. The latter pro-ess yielded micron-sized grains whereas the former producedano-scale grains, which enabled the study of the effect of grain


ize on thermal conductivity upon aging at prospective use tem-eratures.

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n Ceramic Society xxx (2014) xxx–xxx

.1. Synthesis of powders

Powders were synthesized by a reverse co-precipitationethod17 in which yttrium nitrate and zirconium oxychloride

queous solutions were mixed with tantalum chloride solutionsn ethanol and then precipitated in ammonium hydroxide.15

he resulting precipitates were separated from the solvents byentrifugation, repeatedly washed in water and ethanol beforerying and then calcined in air at 950 ◦C for 4 h. These powdersere then cold-pressed and sintered at 1500 ◦C in air for 35–40 h

o form a dense pellet.

.2. Densification and annealing

For samples prepared by sintering, the powders were cold-ressed (300 MPa) and heat treated at 1500 ◦C in air for 20 ho form dense pellets. For CADPro specimens, the powdersere loaded into a graphite die and were simultaneously pressed

130 MPa) and heated (at 100 ◦C/min) to 1150 ◦C for 10–15 minn vacuum (6.7 Pa), and then quickly cooled to room temper-ture. To restore the oxygen stoichiometry after densificationn the reducing atmosphere of the CADPro chamber the sam-les were subsequently heat treated in air at 900 ◦C for 4 h.pecimens were characterized using methods described in theollowing subsections after annealing times of 1, 10, 50 and00 h at 1200 ◦C in air.

.3. Thermal property measurement

For thermal diffusivity (α) measurements, specimens wereoated with gold and then graphite on both sides. The measure-ents were conducted in flowing argon gas with a laser flash

nstrument (Micro Flash® LFA 457, Netzsch, Selb, Germany),rom room temperature to 1000 ◦C. The thermal conductivityκ) was obtained from the standard relationship,

= α · ρ · Cp (1)

here Cp is the heat capacity obtained from calculation usinghe Kopp–Neumann rule18 from literature data of pure zirconia,ttria, and tantala, and ρ is the mass density measured usingrchimedes method.

.4. Phase and microstructural characterization

The phase contents of the samples were analyzed by X-ay diffraction (D8 Bruker, Karlsruhe, Germany) and Ramanpectroscopy (LabRAM Aramis, Horiba–Jobin Yvon, Edison,J). Grain size was measured from SEM images (Ultra, Zeiss,ermany) of sintered surfaces and fracture surfaces using a

inear-intercept method.

. Results


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nd the CADPro samples after 100 h annealing are shown inig. 2. They clearly demonstrate the considerably smaller grain



A.M. Limarga et al. / Journal of the European Ceramic Society xxx (2014) xxx–xxx 3

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ig. 2. Microstructures of specimens prepared by conventional sintering (left col00 h and consisted of nano-sized grains. The average grain size, d, are indicatemages for direct comparison of grain size, where the top and bottom images re

izes of the materials produced by CADPro, even after 100 hnnealing at 1200 ◦C. The phases present after densificationere consistent with the reported phase diagram at 1500 ◦C,

hown in Fig. 1, although as will be described later some ofhe phases transform on prolonged aging at 1200 ◦C. These arellustrated in the X-ray diffraction patterns, Fig. 3. The peaksn the diffraction patterns recorded from the samples immedi-tely after CADPro densification were broader due to the smallrain size and the peaks subsequently narrowed with prolongedeat treatment. The patterns recorded after different annealingimes indicated, though, that the phases were unchanged withhe exception of the solid solution 16Y16Ta and the two-phase0Y20Ta, which slowly transformed to monoclinic zirconia


nd a zirconia containing YTaO4 monoclinic solid solution.he formation of monoclinic zirconia in the 16Y16Ta and0Y20Ta materials is shown most clearly by the appearance of

few

and by CADPro (right column). CADPro samples were annealed at 1200 C forhe bottom left. The center column shows equal magnification of microstructurent conventional sintering and CADPro, respectively.

he characteristic monoclinic lines (arrowed) in the Raman spec-ra reproduced in Fig. 4. Interestingly, samples of the same twoompositions prepared by conventional sintering for at least 4 hut at the higher temperature 1500 ◦C did not undergo the sameransformation as the CADPro samples annealed at 1200 ◦C.

The thermal conductivities of the single phase, two-phase andhree-phase materials, prepared by CADPro, as a function ofemperature are shown in Fig. 5 together with data for other sin-le phase, polycrystalline phases in the system prepared as partf this work. Fig. 5(a) compares the thermal conductivities withhose of dense 7YSZ, the orthorhombic phase, the delta phasend the pure YTaO4 phases. The evolution of thermal conduc-ivity with aging is also shown in Fig. 5 together with the data


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or the larger grain sintered materials. Consistent with the phasevolution upon aging, the conductivities of the compositionshose phases remain stable do not change appreciably whereas



4 A.M. Limarga et al. / Journal of the European Ceramic Society xxx (2014) xxx–xxx

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ig. 3. X-ray diffraction patterns of the indicated compositions produced bynnealing at 1200 ◦C for 100 h.

hose that do transform change, with an initial increase followedy a steady decrease with aging time. Despite these variations,he thermal conductivities of all the materials are largely inde-endent of temperature with the exception of those two in whichartial transformation to monoclinic occurred on aging at 50 hnd line compound YTaO4.

. Discussion

The most striking feature of the results presented in thisork is that the thermal conductivities of all but the compounds

ying along the edges of the ZrO2–Y2O3–Ta2O5 phase diagramre almost independent of composition and are also indepen-ent of temperature above room temperature (Fig. 5). As wille described, both of these characteristics are related and canualitatively be understood as being a consequence of the largeean atomic mass of the compounds and the extensive site dis-

rder possible resulting from different atomic arrangements ofhe individual ions on equivalent crystallographic sites within


he crystal structures of the phases involved. Less obvious ishe finding that there is little difference between the thermalonductivities of the single phase, two-phase and three-phaseompositions. These findings will be discussed in the following

iado

entional sintering (Conv.), by CADPro (0 h), and by CADPro followed with

ub-sections in terms of the Klemens–Callaway phonon scat-ering model19,20 which relates the thermal conductivity, �i, toemperature, T, and the concentration of randomly distributedoint defects through the phonon scattering term, Γ , introducedn the following sub-section:

i = κmin + kB√

vs√π3

√Ω0Γ

1√C

1√T

tan−1

×(

kBTD

�

(Ω0Γ

4πv3sCT

)1/2)

(2)

here C describes anharmonic phonon–phonon scattering in theure, defect-free compound and is independent of defect concen-ration, vs is the acoustic velocity, TD is the Debye temperature,

0 is the unit cell volume, and kB and � are the Boltzmann andlanck constants, respectively. The first term expresses the min-


.2014.03.013

mum value of the thermal conductivity at high temperaturesnd is temperature independent. It has the same form as firsterived by Roufosse and Klemens21 and notably is independentf the defect concentration. Its value is related to the minimum



A.M. Limarga et al. / Journal of the European Ceramic Society xxx (2014) xxx–xxx 5

Fig. 4. Raman spectra show the evolution on high temperature annealing for the hours indicated. Transformation to monoclinic in the two of the compounds isr

ie

κ

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4

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satdirte

p ( ) p ( )2

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epresented by the overlapping doublet, as indicated by the arrows.

nter-atomic distance and the mass of the compound, and can bexpressed as3,22

min = 0.87kB

(nρNA

M

)2/3(E

ρ

)1/2

(3)

here M̄ and n are the mean atomic mass and the number of theons in the unit cell, respectively, E is Young’s modulus, ρ is theensity and NA is Avogadro’s number. The second term in Eq.2) is the conductivity derived by Callaway–von Baeyer20 ands identical to their equation 23.

.1. Similarity of thermal conductivities

In contrast with the pure oxides and stoichiometric YTaO4, inhich there is no significant site disorder, each composition in

he ZrO2–Y2O3–Ta2O5 ternary (Fig. 1) is either a solid solutionr a mixture of two or more solid solution phases. This has twomportant implications. The first is that there can be local massariations due to a heavier or lighter atom substituting for the


tom that usually occupies a particular crystallographic site. Forxample, as Y and Ta are added in equal amounts to ZrO2, theyubstitute onto the Zr-site producing spatial variations in atomicass throughout the solid solution. A vacancy is an extreme case

Γ

f such a mass variation but other variations in the ternary solidolution are also associated with Y3+ and/or Ta5+ ions substi-uting on a Zr4+ site. Along the ZrO2–YTaO4 line, no structuralacancies are required for charge neutrality but for all otherompositions inside the ternary phase field, either oxygen oration vacancies will form to maintain charge neutrality. Theecond implication, discussed in Section 4.3 below, is that thenterfaces between the phases and grains may lower the thermalonductivities.

According to the Klemens–Callaway model above, phononcattering is proportional to the product of the variances intomic mass at each crystallographic site and their concentra-ions. Specifically, if each solid solution compound contains pistinct crystallographic sub-lattice sites and several differentons, j, can occupy each of these sites, the mass disorder iselated to the concentration of the different ions on each crys-allographic site and the scattering cross-section is given by thexpression23–25:


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=∑i=1

ni

n

Mi

M̄

2

Γi =∑i=1

ni

n

M̄i

M̄

j

(M̄i)2

(4)




Fig. 5. (a) Thermal conductivity of samples before annealing compared with thermal conductivity of stoichiometric phases, YTaO4, the orthorhombic-phaseTa2Zr6O12, 7YSZ, and the delta-phase Zr3Y4O12. Note that the thermal conductivity of pure Y2O3 and pure ZrO2 are not shown because they are off-scale. (b)–(f)T r the

c e with

wtms

m

hermal conductivities of the CADPro specimens after annealing at 1200 ◦C foonventionally-sintered samples. The mean grain sizes are shown but for sampl

here n is the total number of atoms in the unit cell, ni is


he number of atoms on the sub-lattice, i, M̄ is the meanass of the unit cell, M̄i is the mean mass on the i’th

ub-lattice and Γ i is the phonon scattering coefficient from

m(c

indicated times are shown along with thermal conductivities of the large grain multiple phases, the rate of grain growth for each phase may not be the same.

ass variance on the i’th sub-lattice. The variance of the


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asses on each sub-lattice, in effect the “mass disorder”,ΔMi)2 = (Mj − Mi)

2in Eq. (4), is weighted by their fractional

oncentrations, fj. For example, for the 16Y16Ta solid solution



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A.M. Limarga et al. / Journal of the Eu

omposition, the fractional concentrations of Zr, Y and Ta ionsn the cation sublattice would be 0.68, 0.16 and 0.16, respec-ively.

In addition to the effects of phonon scattering from pointefects, the thermal conductivity also scales as the inverse squareoot of the mean atomic mass of the compound.26 (This depend-ncy is embedded in the phonon–phonon scattering parameter,, in Eq. (2).) Since the atomic masses of Y and Zr are almost

he same and are both only approximately half of that of Ta,here is a tendency for the thermal conductivity to also decreases the concentration of Ta increases.

.2. Temperature independence of thermal conductivity

The small variation of conductivity with temperature exhib-ted by all the compositions is in marked contrast to theemperature dependence of the thermal conductivity of rela-ively defect-free oxides, such as sapphire and MgO.27 In suchxides, the conductivity varies with the inverse of temperaturepproaching a temperature-independent value associated withhe minimum thermal conductivity at very high temperatures,ypically several times the Debye temperature. Until recently,easurements were either not made over a sufficiently large

emperature range to detect significant variations from the 1/Tependence or the increasing contribution from radiative heatransfer with temperature masked the higher-temperature behav-or arising from phonon scattering.

As is evident from the form of the Klemens–Callaway modelEq. (2)), mass variations decrease the temperature variationf the thermal conductivity. This is illustrated by the calcu-ations shown in Fig. 6 in which the thermal conductivity islotted against temperature for various defect phonon scatteringtrengths using YSZ as an example since the other parameters inq. (2) are known for this oxide (taken from Limarga et al.28).t low scattering strengths (Γ → 0), the second term in Eq. (2)

symptotes to an inverse dependence of temperature, the perfect,efect-free crystal limit, given by:

i = κmin + k2BTD

2π2vs�CT(5)

In contrast, as the scattering strength increases, the contribu-ion of the second term becomes increasingly smaller until theres no longer any temperature dependence above the Debye tem-erature and the thermal conductivity approaches the value ofmin, as illustrated in Fig. 6). This is consistent with the conduc-ivity data in Fig. 5, showing little dependence on temperaturebove room temperature, with the exception of a weak depend-nce for the 7YSZ and YTaO4. Thus, one can conclude that inhe compositional fields studied, there is sufficient mass disor-er (large Γ ) in each of the compounds that their conductivities


re close to their minimum thermal conductivities. As these cane expected to be rather similar, little variation of conductivityith composition within a single phase occurs.

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n Ceramic Society xxx (2014) xxx–xxx 7

.3. Thermal conductivity in multiple phase compositions

The observations that there is little difference in the thermalonductivity between single phase and multiple phase compo-itions require explanation. This is especially so when therere several reported instances of significant changes in ther-al conductivity in two-phase composites with volume fraction

f the two phases, most notably in SiC/Al29 and diamond/ZnSomposites.30,31 Although there is no detailed model for phononcattering in multiple phase materials, one would expect thathere would be two contributions to the thermal conductiv-ty. The first would be a volume fraction effect that weightshe fraction of the macroscopic thermal conductivity of eachhase according to their shapes and orientations. The secondould be an effect due to the phonon scattering at the interfacesetween dissimilar phases that incorporates both the crystallo-raphic mis-orientation, the origin of the grain size effect onhermal conductivity in polycrystalline materials, and the dif-erential acoustic scattering due to the two phases. The acousticismatch interface model32 accounts for scattering due to dif-

erences in the acoustic properties across a planar interface butot specifically other effects. However, macroscopically, theseffects can be described by effective medium computations thatncorporate an effective grain boundary resistance, a Kapitzaesistance, Rk, in series with the grains. A general formulationhat takes into account the shapes and orientations of the phasess well their volume fractions and thermal conductivities haseen developed by Nan et al.33 For the particular case of a two-hase material consisting of spherical particles in a matrix phaseith an interface thermal resistance between them the expression

or the thermal conductivity reduces to the simple form:

∗ = κm

(1 + 2α) + 2κr + 2fv[(1 − α) − κr]

(1 + 2α) + 2κr − 2fv[(1 − α) − κr](6)

here the second phase, the “particle”, is embedded in majorhase of conductivity, κm, and the parameter κr is the ratio of thehermal conductivities of the two phases, κm/κp, and fv is the vol-me fraction of the second phase particle. The non-dimensionalarameter, α, is the ratio of two characteristic lengths, the inter-ace thermal width, Rk κm and the second phase particle radius,:

= Rkκm

a(7)

There are two extremes of Eq. (6) and (7) with interfaceesistance. In the limit, α → 0 the interface has zero thermalesistance. Then, the thermal conductivity of the two-phaseaterials simply lies between the arithmetic and the harmoniceans of the volume fraction weighted conductivity and the

quation reduces to the well-known relationship for the conduc-ivity of randomly distributed particulate composites.34 Whenhe interfaces have very large thermal resistance, the thermalonductivity approaches a constant value of 2(1 − fv)κm/(2 +


.2014.03.013

v), independent of the thermal conductivity ratio. In between,here interfaces have finite thermal resistances, then exami-ation of Eqs. (6) and (7) indicates that unless the thermalonductivities of the constituent phases are very different, the




Fig. 6. (a) Plot of thermal conductivity, κ, as function of scattering cross section, Γ , according to Klemens–Callaway equation (Eq. (2)). The plot is based on fittedparameters of 7YSZ, taken from Limarga et al. (b) Thermal conductivity relative to the matrix phase, κm, as a function of Kapitza resistance for various volumefractions, fv, of a dispersed spherical phase. For illustration purposes, the conductivity ratio, κ, is taken to be 1.5 in these calculations. (c) and (d) Thermal conductivitya ry phai

conFctofurSas∼aooitatwa

pmqohtapsts

stpsbfn

t 100 ◦C and 1000 ◦C are color-mapped as a function of composition on ternan W/mK.

omposite’s thermal conductivity is again almost independentf the interface resistance unless the grain size is only a fewanometers. This is illustrated by the calculations shown inig. 6(b) in which the thermal conductivity, normalized by theonductivity of the “matrix” conductivity, is plotted as a func-ion of the Kapitza resistance for different volume fractionsf the “particle” phase. The Kapitza resistance is not knownor any of the compounds investigated in this work but val-es of 4.5 × 10−9 m2 K/W and 4.0 × 10−9 m2 K/W have beeneported for the grain boundaries in other oxides, 7YSZ28 andrTiO3,35 respectively. Recent measurements of grain bound-ries in twist bi-crystals of alumina, while showing somemall angular dependence, are somewhat higher but similar,10 × 10−9 m2 K/W.36 Taking these values as representative

nd the grain size of the order of 0.1 �m (Fig. 2), the valuef α is equal to 0.1 for the cases where the thermal conductivityf the matrix phase is 1.5 W/mK and the particle conductivitys 2 W/mK. Consequently, we can conclude that because thehermal conductivities of each of the phases are small, similar,nd relatively independent of composition, the thermal conduc-


ivities of the multiple-phase compositions investigated are onlyeakly dependent on the interface resistance, the variation being

bout ±10%.

aat

se diagram. The numbers within a constant color is the thermal conductivities

In the multiphase regions, the constituent solid solutionhases (indicated by the appropriate tie lines) have similarass disorder, meaning that the thermal conductivities are

uite similar. For example, the 22Y13T composition consistsf two phases, approximately 17Y17Ta and 25Y10Ta, whichave mass scattering coefficients of 0.08 and 0.13, respec-ively, and similar thermal conductivities (at around 1.5–1.6t 1000 ◦C). As a result, the thermal conductivity of the twohase mixture is only slightly lower than the single solidolution phases, with most of the difference originating fromhe increase in the grain interface because of small grainize.

At the microscopic, phonon scattering level, the insen-itivity to the phase content within the ZrO2–Y2O3–Ta2O5ernary system is primarily due to the extremely shorthonon mean free paths in the individual phases. A con-equence of this is that the presence of interfaces cannote expected to reduce the already small phonon meanree path further and so the conductivity cannot be sig-ificantly reduced. Similarly, the same arguments provide


.2014.03.013

qualitative explanation for why the three-phase materialslso exhibit low and temperature independent conductivi-ies.



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A.M. Limarga et al. / Journal of the Eu

.4. Grain size effects on thermal conductivity.

The comparison between the thermal conductivities, in Fig. 5,easured after different annealing times at 1200 ◦C as well as

he comparison with the measurements made on sintered sam-les suggests that there is possibly a small effect of grain sizeor the three phase composition and 7YSZ but none in the oth-rs. (The grain size effect on the conductivity of 7YSZ has beeneported previously.28) More significant is the reduction in con-uctivity in the 16Y16Ta and 20Y20Ta on aging associated withhe occurrence of micro-cracking due to the de-stabilization ofetragonal zirconia and the formation of monoclinic zirconia. Inome cases, such as after 100 h at 1200 ◦C, distinct, macroscopicracks were observable but in all cases, there is a direct correla-ion between the reduction in thermal conductivity on annealingnd the volume fraction of monoclinic zirconia. Another charac-eristic of transformation-induced microcracked materials is thathe room temperature conductivities are unchanged, presumablyecause the microcracks close up on cooling, but exhibit reducedonductivities at higher temperatures, due to the transformationpening up the microcracks.

.5. Interpolations to other compositions.

While the compositions we selected for measurement werehosen to provide information on the thermal conductivity inifferent regions of the ZrO2–Y2O3–Ta2O5 phase diagram, it isf interest to estimate the conductivities of other compositionsn the same system. As described in the appendix, these con-uctivities can be obtained by an interpolation scheme basedn the models discussed in the previous sub-sections using theeasurements presented in this work together with the reported

onductivities of pure ZrO26 and Y2O3.37 The results of these

nterpolations are plotted in Fig. 6(c) and (d) and show only smallariations in thermal conductivity with composition except closeo pure ZrO2, Y2O3, and Ta2O5, particularly at 1000 ◦C.

. Concluding remarks

The thermal conductivity of materials with various composi-ions within the zirconia-rich portion of the ZrO2–Y2O3–Ta2O5hase diagram are all low (<1.7 W/mK), significantly lower thanYSZ and also exhibit only a weak dependence on temperaturerom room temperature to 1000 ◦C, unlike simple oxides suchs alumina, MgO, ZrO2, and Y2O3. The relative insensitivityo composition and phase content is attributed to three factors.ne is the small phonon mean free paths produced by extensiveass disorder within each of the crystalline phases associatedith large ranges of solubility of ions of different masses. The

econd factor, which is related, is that the small mean free pathsre close to the minimum associated with the minimum thermalonductivity. The third is that for the grain sizes investigated,


reater than about 0.2 �m, the effect of the thermal resistancef grain and inter-phase boundaries is relatively small meaninghat the conductivity is relatively insensitive to the grain size ofhe phases.

1

2

n Ceramic Society xxx (2014) xxx–xxx 9

One of the consequences of our findings and analysis is thatf compositions in the ZrO2–Y2O3–Ta2O5 field are used as ther-

al barrier coatings, controlling their composition will not bemportant, at least as far as the thermal conductivity is concerned.

cknowledgements

The work reported here has been supported by theoneywell-UC Santa Barbara-Harvard Alliance on thermal bar-

ier coatings and by the Office of Naval Research at Harvardhrough ONR N00014-012-1-0993. The authors are grateful tor. Yang Shen, Tsinghua University, for discussions and for

llowing us to use his data for the orthorhombic phase.

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ARTICLE IN PRESS - Harvard University · 2016-09-15 · +Model ARTICLE IN PRESS JECS-9584; No.of Pages10 Available online at ScienceDirect Journal of the European Ceramic Society