Oxide Materials with Low Thermal Conductivity

Michael R. Winter and David R. Clarkew

Materials Department, College of Engineering, University of California, Santa Barbara, California 93160-5050

A heuristic approach to identifying candidate materials withlow, temperature-independent thermal conductivity above roomtemperature is described. On the basis of this approach, a num-ber of compounds with thermal conductivities lower than that of8 mol% yttria-stabilized zirconia and fused silica have beenfound. Three compounds, in particular, the Zr3Y4O12 deltaphase, the tungsten bronzes, and the La2Mo2O9 phase, exhibitpotential for low thermal conductivity applications. As each canexhibit extensive substitutional solid solution with other, highatomic mass ions, there is the prospect that many more com-pounds with low thermal conductivity will be discovered.

I. Introduction

WITH some exceptions, the majority of non-metallic com-pounds exhibit a thermal conductivity that decreases with

increasing temperature above room temperature.1–4 Two not-able exceptions are fused silica2 and stabilized zirconia4–6 (andthe structurally related defect fluorite compounds ceria, thoria,and urania3). These two materials also have the lowest thermalconductivity of any fully dense oxide (Fig. 1).

One of the applications of yttria-stabilized zirconia (YSZ)that takes advantage of its unusually low thermal conductivity isas a thermal barrier coating for combustors and turbine bladesin gas turbine engines, enabling them to operate at higher gastemperatures than without the coating. To further increase en-gine performance, there has been interest in finding an alterna-tive material with still lower, temperature-independent thermalconductivity up to high temperatures. The discovery that certainrare-earth zirconates4,7 with the pyrochlore crystal structurehave lower thermal conductivity than YSZ and also exhibit analmost flat temperature dependence has demonstrated that sta-bilized zirconia is not unique among crystalline oxides in thisrespect and has spurred interest in the search for other oxidesthat also have low thermal conductivity. Although the pyro-chlore zirconates have a crystal structure closely related to thebasic fluorite structure of stabilized zirconia, the fact that theirconductivity is lower than YSZ suggests that there is potentialfor many other materials with low thermal conductivity.

In this contribution, we describe some of the results of oursearch for oxide materials having low thermal conductivity. Thispaper is organized as follows: after a description of our ap-proach to identifying candidate materials with low thermal con-ductivity and a brief description of experimental details, wepresent our results in sections devoted to different classes ofmaterial. For the purposes of this work, we include only thosematerials that proved to have thermal conductivities lower thanthat of dense YSZ. Although arbitrary, it serves to identify thosematerials that might, for instance, be of interest in future ther-mal barrier coating systems. Our focus has been on fully dense

materials so that we can compare the intrinsic thermal conduct-ivity of materials as it is well known that porosity can signifi-cantly decrease the measured thermal conductivity.

II. Criteria for Low Thermal Conductivity

Although no theory exists for predicting which compounds willhave a low thermal conductivity at high temperatures, there area number of guidelines that we have used to identify candidatematerials. The first are expressions for what has become knownas the minimum thermal conductivity, kmin.

8–10 This is the low-est thermal conductivity that a non-metallic solid can exhibitbased on its atomic number density, its phonon spectrum, andother parameters.8 Of particular interest to our work is the high-temperature limit to the minimum thermal conductivity, whichis based on the assumption that the phonon mean free path ap-proaches the mean inter-atomic distance. A number of similarexpressions have been derived for this high-temperaturelimit.8–10 For instance, Cahill and Pohl9 have expressed this as

kmin ¼kB

2:48n2=3 2vt þ vlð Þ (1)

where n is the number of atoms per unit volume and vt and vl arethe transverse and longitudinal sound velocities. An alternativeexpression, based on the same limiting conditions for the pho-non mean free path and the effective atomic masses, that alsogives almost the same values for simple compounds but is ex-pressed in more easily obtained physical parameters is:10,11

kmin ¼ 0:87kBO�2=3

E=rð Þ1=2 (2)

where Oa is an effective atomic volume

Oa ¼M

mrNA(3)

whereM is the mean atomic mass of the ions in the unit cell,m isthe number of ions in the unit cell, r is the density, and E isYoung’s modulus. kB and NA are Boltzmann’s constant andAvagadro’s number.

These expressions indicate that a large mean atomic mass anda low elastic modulus favor low thermal conductivity. Althoughhelpful as a first step in selecting materials, one would not iden-tify silica glass as having an especially low thermal conductivityon this basis nor do they provide any additional insight into thetypes of crystal structure that may exhibit low thermal conduct-ivity.

To proceed, we have been guided by two additional concepts.One is to introduce randomly distributed point defects into astructure at a sufficiently high density that they will cause in-elastic phonon scattering, thereby decreasing the phonon meanfree path and decreasing the attainable thermal conductivity.There are a number of classic examples of this effect. These in-clude the decrease in thermal conductivity of AlN with the con-centration of oxygen impurities12 and the increase in thermalconductivity of diamond when it is made of isotopically purecarbon.13 Similarly, both the alloying of germanium with sili-con14 and the alloying of indium with GaAs15 decrease the ther-

N. Padture—contributing editor

This work was supported by the Office of Naval Research as part of the TBC MURIgrant through contract N014-02-1-0801.

wAuthor to whom correspondence should be addressed. e-mail: clarke@engineer-ing.ucsb.edu

Manuscript No. 21956. Received June 29, 2006; approved October 4, 2006.

Journal

J. Am. Ceram. Soc., 90 [2] 533–540 (2007)

DOI: 10.1111/j.1551-2916.2006.01410.x

r 2006 The American Ceramic Society

533

mal conductivity of both these semiconductors. Kingery1 alsoshowed that solid solution alloying in the NiO–MgO systemdecreased the thermal conductivity. However, in each of thesematerials, as well as alloying in a variety of minerals16 and mixedhalides, cyanides, and fluorides,17 the effect is to decrease thethermal conductivity in the 1/T regime of thermal conductivity.No effect has been reported in the high-temperature regime butthere is no reason to suppose that alloying, or mass disorder, willalso not be effective in the high-temperature regime. As we willshow, this can, in fact, be quite effective in reducing thermalconductivity at high temperatures, especially when alloying isused to create disorder on more than one of the sub-lattices in acrystal structure.

The second concept is to seek structures that have the op-posite characteristics of materials with very high thermal con-ductivity.18 Such materials, for instance diamond, berylliumoxide, silicon carbide, aluminum nitride, and gallium nitride,have low atomic mass; highly directional, usually covalent,bonding; high lattice stiffness; high purity; low defect concen-tration; and minimum disorder in addition to being electricalinsulators. These common characteristics lead to high phononvelocities and minimization of phonon scattering. Silica glassesare the classic example of materials that exemplify this set ofopposite characteristics. Although silica glass has a low densityand is primarily covalent, it has a flexible structure consisting ofcorner-shared SiO4 tetrahedra that can rotate and flex about oneanother. The contrary behavior of silica glasses was attributed,as long ago as 1949 by Kittel,19 to being a consequence of the

amorphous structure precluding the existence of long wave-length phonons so that the phonon mean free path is limited bythe size of the SiO4 tetrahedral structure. Using the simple De-bye model for thermal conductivity and using the measuredthermal conductivity, first Kittel19 and then Kingery1 calculatedthat the phonon mean free path corresponds closely to the sizeof the tetrahedral unit. Although no non-silicate glass is knownto be stable to high temperatures, it does suggest that crystalstructures with various forms of short-range disorder and con-sisting of structural units that are loosely connected may alsoexhibit low thermal conductivity.

Taken together, these guiding concepts suggest that materialshaving low thermal conductivity at high temperature will bethose that have high mean atomic mass, weak, non-directionalbonding as well as extensive disorder at a variety of length scalesdown to that corresponding to inter-atomic spacings. Not all ofthese structures will be stable to the very highest temperaturesrequired for thermal barrier application but may help identifyother compounds with higher melting temperatures. This is analternative to the search approach based on first identifyingcompounds that have the highest melting temperatures, such asappears to be the basis for a number of other searches.7,20,21

III. Experimental Procedure

Unless otherwise described, all the materials studied in this workwere performed by what will be referred to as standard powderprocessing routes in which commercially available oxide pow-ders were first mixed together, milled, ground, and then sinteredto full density. Deviations from this method were necessary forcompositions that did not densify easily and these are describedwhere appropriate in the sections devoted to specific materials.In the standard process, the powders were mixed together andattrition milled for 3 h in deionized water with zirconia grindingmedia. The milled powder was passed through a o325 meshsieve, dried, and ground to break up large agglomerates. Then,the powders were formed into disks by uniaxial cold pressing (80MPa) without a binder and sintered in air, typically at 16001C.Once dense samples were created, they were machined to size forthermal diffusivity measurements using a surface grinder. Somematerials had to be hot pressed. These were also ground to sizeafter removing any graphite that had adhered to the surfaces aswell as any reaction zone. Finally, all the samples were annealedin air at 10001C for 30 min to equilibrate them before testing.The density was measured using the Archimedes technique. Thevalues are listed in Table I, together with the method used tomake the samples.

X-ray diffraction analysis and Raman spectroscopy wereused to confirm that the materials had the desired crystal struc-ture and were single phase. The thermal conductivity, k, of eachof the materials was determined from separate measurements ofthe thermal diffusivity, a, heat capacity, C, and density, r, using

Table I. Sample Density and Processing

Compound Measured density (kg/m3) X-ray density (kg/m3) Density (%) Processing

7YSZ 6.04 6.134 98.5 Hot pressed/16001C/60 minGdPO4 5.94 6.061 98.0 Hot pressed/12001C/30 minLaPO4 4.60 5.067 90.8 Hot pressed/11501C/45 minYPO4 3.63 4.262 85.2 Hot pressed/15501C/60 minGd0.5La0.5PO4 5.48 5.564 98.5 Hot pressed/12001C/30 minZr3Y4O12 5.45 5.49 99.3 Sintered in air/16001C/2 h0.1WO3–0.9Nb2O5 4.70 4.74 99.2 Hot pressed/12751C/30 minWNb12O33 4.70 4.76 98.7 Hot pressed/12751C/30 minW4Nb26O77 4.78 4.93 97.0 Hot pressed/12751C/30 minW3Nb14O44 5.02 5.02 100 Hot pressed/12751C/30 min(3.5Eu–3.5Tm–7Y) SZ 6.25 6.24 100 Hot pressed/15501C/60 min(3.5Eu–3.5Yb–7Y) SZ 6.17 6.25 98.7 Hot pressed/15501C/60 minLa2Mo2O9 5.02 5.564 90.2 Sintered in air/10501C/10 h

m-ZrO2 [1]

5

4

3

2

1

00 500 1000 1500

Th

erm

al C

on

du

ctiv

ity,

W/m

K

Dense YSZ [4] Nano-YSZ

(dense) [5]

Fused SiO2(excluding

radiation) [2]

Gd2Zr2O7 [6]

Temperature (°C)

Fig. 1. Thermal conductivity of a number of oxide materials includingmonoclinic zirconia,1 dense yttria-stabilized zirconia (YSZ),4,6 theGd2Zr2O7 pyrochlore,6 and, for comparison, fused silica.2 There areseveral reports of the thermal conductivity of the pyrochlores but onlyWu et al. 6 is for fully dense material.

534 Journal of the American Ceramic Society—Winter and Clarke Vol. 90, No. 2

the relationship

k ¼ rCPk (4)

Thermal diffusivity was measured with an Anter Flashline3000 thermal flash system (Pittsburgh, PA) based on the tech-nique pioneered by Parker et al.22 This instrument uses a high-speed xenon lamp and measures the corresponding increase inbackside temperature with an InSb infrared detector. All thesamples were ground coplanar to a thickness of approximately 1mm and a diameter of approximately 12.4 mm. To minimizeradiative heat transport through the sample, which can lead toan apparently higher diffusivity, both sides were coated with a10 nm Ti adhesion layer and a 750 nm of Pt layer via electronbeam physical vapor deposition. Both sides were also spraycoated with a colloidal graphite approximately 10 mm thick toensure full absorption of the flash at the front surface and max-imum emissivity from the backside. The samples were thenheated to drive off any remaining solvents. The mass of thesample was measured before and after the test to ensure that thegraphite coating remained intact. Thermal diffusivity was meas-ured at 1001C intervals from 1001 to 10001C and then allowed tocool to 1001C before a final measurement was made. A com-parison of the diffusivities measured at 1001C at the beginningand end of the test series was made to ensure that there were nochanges in the sample or in the coating integrity. All the meas-urements were made in nitrogen. The thermal diffusivity wasdetermined using the correction described by Clarke and Tay-lor,23 which accounts for radiative losses that occur due to non-adiabatic conditions. Calibration of the thermal flash systemwas performed with a standard sample of pyroceram 9606 glass–ceramic. The pyroceram sample was purchased from Anter Cor-poration (Pittsburgh, PA). The day-to-day variation in the ther-mal diffusivity of the pyroceram sample was 2%–3%. Togetherwith variations in the heat capacity measurements, the uncer-tainty in the reported values here of thermal conductivity is es-timated to be 75%.

Heat capacity was measured with a Netzsch Pegasus 404Cdifferential scanning calorimeter (Estes, CO). Samples wereground coplanar to approximately 1 mm thickness and approxi-mately 5.5 mm diameter. Heat capacity was determined accord-ing to the ASTM standard E1269-95 in a platinum crucible fromroom temperature to 10001C in an argon atmosphere.24

IV. Decreasing Thermal Conductivity of Zirconia bySubstitution on the Cation Sub-Lattice

YSZ has several of the characteristics of low conductivity de-scribed in Section II. Without stabilization by yttria (or anotherstabilizer ion, such as the trivalent rare-earth ion, divalent cat-ions, or mixed-valence ions), zirconia is monoclinic and exhibitsthe classic 1/T temperature dependence.1 The substitution ofY31 for Zr41 in the fluorite structure of ZrO2 stabilizes the te-tragonal phase by introducing vacancies into the oxygen sub-lattice. At typical concentrations of 8 m/o YO1.5, the spacing ofthe oxygen vacancies is B1.25 nm. (At higher yttria concentra-tions, the concentration of vacancies increases but clusteringbegins to occur.) The unusually low thermal conductivity ofYSZ is generally attributed to enhanced phonon scattering fromoxygen vacancies. Although the Y31 ions substitute for Zr41

ions in the cation sub-lattice, their atomic mass is almost iden-tical to that of the Zr41 ions and hence are unlikely to cause anymass disorder on the cation sub-lattice.

In a very important practical development, Zhu and Mill-er25,26 at NASA Glenn have demonstrated that coatings stabil-ized with a combination of trivalent ions have exceptionally lowthermal conductivity. These coatings have been referred to as‘‘cluster-doped’’ coatings and are based on the substitution ofthree different trivalent cations, typically Y31 ion plus one ionlarger and one smaller. Unlike other coating materials, the ther-mal conductivity of these coatings did not change substantiallyover extended periods of time at high temperatures.27

An alternative approach to reducing thermal conductivity isto replace some of the Zr41 ions with Hf41 ions. In contrast tothe rare-earth substitutions used in the ‘‘cluster’’-doped zirconia,Hf41 ions do not introduce vacancies into the oxygen sub-latticebut produce random mass disorder into the cation sub-lattice. Apeculiar feature of Hf41 ions is that they are chemically similarto Zr41 ions, have a similar ionic radius but are almost twice asmassive.

(1) Multiple Dopant Substitution

To evaluate the possible effect of multiple stabilizer dopants infully dense material as distinct from coatings, we produced twosets of dense zirconia material stabilized with three different tri-valent ions, Y31 and Eu31, and either Yb31 or Tm31. The ionicradii are listed in Table II. The total concentration of the sta-bilizer ions was 14 m/o, so that the material was tetragonal, anexpectation confirmed by X-ray diffraction and Raman spec-troscopy. The stabilizer concentration was chosen as the work ofZhu and Miller25 indicates that coatings made with this totalstabilizer concentration had the lowest thermal conductivity intheir thermal gradient testing. The powders of these materialswere prepared in the standard way but were then densified byhot pressing at 20 MPa for 1 h at 15501C as they could not bedensified by sintering. Even after sintering for 2 h at 16001C,they only attained a density of B70%.

The thermal conductivity of two of the fully dense materials isshown in Fig. 2. One, the composition stabilized with7YO1.513.5 EuO1.5 and 3.5 TmO1.5, had a temperature-inde-pendent conductivity of B2.0 W/mK, independent of tempera-ture. This value is almost the same as has been reported forzirconia stabilized with 14 m/o YO1.5

28 but much higher thanthat reported for the NASA coatings. The other, the one sta-bilized with 7YO1.513.5 EuO1.5 and 3.5 YbO1.5, exhibited very

Table II. Atomic Mass and Ionic Radii (Ionic Radii after Shannon43)

Ion Zr41 Hf41 Y31 Tm31 Eu31 Yb31 La31 Gd31

Atomic mass (amu) 91.2 178.58 88.91 168.93 151.96 173.04 138.91 157.25Ionic radius (nm) 0.084 0.083 0.1019 0.0994 0.1066 0.0985 0.1160 0.1053

1.0

1.5

2.0

2.5

3.0

0 200 400 600 800 1000 1200

7YSZ+ 3.5 EuO + 3.5 TmO

7YSZ+ 3.5 EuO + 3.5 YbO

Temperature (°C)

The

rmal

Con

duct

ivity

(W

/mK

)

(Zr,Hf) Y O

Fig. 2. Comparison of the thermal conductivity of two tri-dopedzirconias and the equi-molar hafnia-zirconia material.

February 2007 Oxide Materials with Low Thermal Conductivity 535

pronounced radiative transport effects from almost 3001C on-wards. Why radiative effects are so pronounced in this compos-ition is not known but was duplicated with a second sample. Allthe samples were white indicating extensive internal optical scat-tering. Nevertheless, at 1001C, the thermal conductivity wassomewhat lower atB1.8 W/mK. Two conclusions can be drawnfrom these results. The first is that it is the mean value of theionic mass of the stabilizer ions that is important rather than thevariation in ionic mass or size. The second, and of crucial im-portance for the design of coatings, is that the low thermal con-ductivity of the ‘‘cluster’’-doped coatings is not intrinsic to thecomposition per se but most probably due to the presence ofporosity incorporated during the deposition of the coating andits resistance to densification during deposition and subsequenthigh-temperature exposure.

(2) Hafnia Substitution

As described in detail elsewhere, hafnia substitution de-creases the thermal conductivity of YSZ across the full solid–solution series.29 The most notable reduction, however,occurs close to the equi-molar mixtures of hafnia and zir-conia, such as ðZr0:5Hf0:5Þ0:87Y0:13O1:94 tetragonal and theðZr0:4Hf0:6Þ0:76Y0:24O1:88 cubic phase. The data for the formercomposition are shown in Fig. 2 and, for comparison, with thethermal conductivity of the multiple-stabilizer zirconia, illus-trates the effectiveness of mass disorder on the cation sub-lattice.In contrast to the cluster-doped materials, these could be readilydensified to better than 96% by sintering in air at 16001C for 2 h.The measured lattice parameters and molecular weight wereused to calculate the X-ray density of the individual compos-itions.

V. Thermal Conductivity of the Delta Phase Zr3Y4O12

Previous studies have shown that the thermal conductivity ofzirconia decreases with increasing yttria concentration up toabout 20 m/o YO1.5 but then is approximately constant.28 Thissaturation behavior has been attributed to ordering of the sub-stitutional Y31 ions and the oxygen vacancies, limiting the ran-dom disordering on the oxygen sub-lattice.30,31 The maximumconcentration that seems to have been studied is 30%Y2O3, wellwithin the cubic, fluorite phase. However, the ZrO2–YO1.5 phasediagram indicates that another crystalline phase, the delta phase,Zr3Y4O12, exists.

32

The experiment indicates that this compound does have a lowand temperature-independent thermal conductivity as shown bythe data in Fig. 3. Its thermal conductivity parallels the thermalconductivity of YSZ but has a value almost 30% lower up to atleast 10001C. The delta-phase composition was readily sinteredin air at 15501C for 2 h but could not be fully ordered even after3 weeks at 12501C.

(1) Hafnia Substitution in the Delta Phase

Based on the success in lowering the thermal conductivity bysubstituting Zr41 ions with Hf41 ions,29 the equi-molar com-position ðZr0:5Hf0:5Þ3Y4O12 was prepared in a fully dense form.Its thermal conductivity as a function of temperature is shown inFig. 3 and demonstrates clearly that introducing mass disorderinto the cation sub-lattice can significantly reduce thermalconductivity from room temperature up to at least 10001C.

VI. Tungsten Niobates

In contrast to the zirconia-based oxides, the basis for selectingthe tungsten niobates, sometimes referred to as the ‘‘tungstenbronzes,’’ for study is that their crystal structures have somefeatures common to silica. They consist of blocks of corner-shared NbO octahedra linked together with W ions.33,34 This isillustrated for the W3Nb14O44 compound in Fig. 4 showing theblocks of 4� 4 corner-sharing octahedra joined by W ions and

arranged in a tetragonal structure. According to the first crystalstructure determination, the W and Nb ions were randomlydistributed among all the octahedral sites. Further structuralrefinement by neutron diffraction indicates that, at room tem-perature at least, there is a preference for the W to be in anoctahedral co-ordination and to be distributed among the octa-hedra in the vicinity of the block-sharing W ions. In selectingthese compounds for study, it was also hypothesized that thecorner sharing of the blocks and the disorder along the c-axisassociated with the W ions might provide the vibrational free-dom that would lead to low thermal conductivity. In addition,several of the tungsten bronzes have some of the highest meanatomic masses and densities of the oxides and several are stableto well over 14001C. Also, the size of the blocks varies with theW/Nb ratio, leading to a series of line compounds in the phasediagram, as shown in Fig. 4.

Four compounds were investigated and are indicated in thediagram of Fig. 4. Three were single-phase line compounds hav-ing different W/Nb ratios, W3Nb14O44, (D), WNb12O33 (B), andW4Nb26O77 (C). The fourth was a deliberately made two phasemixture of Nb12WO39 and Nb60WO183 marked A on Fig. 4. Allthe compounds were made from oxides and were calcined at11001C for 2 h in air. They then had to be hot pressed and thenannealed in air at 10001C for 1 h.

The measured thermal conductivity (Fig. 5) indicates that thetungsten bronzes do indeed have low thermal conductivity andare temperature independent. The actual values are similar tothose of both YSZ and fused silica. Notably, both the single-phase materials and the two-phase material exhibited similarconductivities.

VII. Lanthanide Orthophosphates

Orthophosphates have crystal structures that are analogous tothe network silicates with various arrangements of corner- andedge-sharing PO4 tetrahedra rather than the SiO4 tetrahedra.

35

Based on the guidelines described in ‘Section II,’ they are a nat-ural choice of compounds for searching for low thermal con-ductivity. Perhaps the best known example is the aluminumphosphate (AlPO4) but an extensive series of lanthanide-basedorthophosphates (LnPO4), also exist, which have a significantlyhigher density because of the higher atomic mass of the lantha-nide ion. They form two distinct, but closely related, crystalstructures, the monazite and the xenotime structures, dependingon the ionic size of the lanthanide ions.36 The monazite structureis typically formed with the larger lanthanide ions and the xeno-time structure with the smaller lanthanide ions. Both structures

1.0

1.5

2.0

2.5

3.0

100 200 300 400 500 600 700 800 900 1000

Temperature (°C)

The

rmal

Con

duct

ivity

(W

/m K

)

Zr3Y4O12

(Zr,Hf)3Y4O12

8YSZ

Fig. 3. Comparison of the thermal conductivity of the Zr3Y4O12 deltaphase and the hafnia–zirconia counterpart with that of dense yttria-stabilized zirconia (8YSZ).

536 Journal of the American Ceramic Society—Winter and Clarke Vol. 90, No. 2

are based on chains of alternating phosphate tetrahedral and REpolyhedra. Because of the well-known lanathanide ion contrac-tion, these compounds are formed with the lighter and heavierions, respectively. The boundary between the monazite andxenotime structures occurs between the GdPO4 and theTbPO4 compounds, the monazite being formed with the Gd31

ions and the xenotime being formed with the Tb31 ions.It has been reported that the monazite compound CePO4 has

a thermal conductivity ofB3.1W/mK at room temperature anda value of B1.8 W/mK at 5001C37, suggesting a weak 1/T de-pendence. Similarly, the xenotime compounds YPO4, LuPO4,YbPO4, and ErPO4 all have a thermal conductivity of B12 W/mK at room temperature.38 The thermal conductivity of LaPO4

at room temperature has previously been reported.39

To compare the thermal conductivity of a number of themonazite and xenotime structures, we measured the conductiv-ity of YPO4 (a xenotime compound) and GdPO4 and LaPO4,both having the monazite structure. We also investigated theco-doped La0:5Gd0:5ð ÞPO4, another monazite compound. The

rationale for the last was that although it has a different crystalstructure, it has the same unit cell volume as does YPO4 and soone might expect that the average inter-atomic spacing would bethe same. The materials were made from chemically precipitatedprecursor powders prepared by adding phosphoric acid, drop bydrop, to the appropriate nitrate solution in deionized water.The powders were washed several times with deionized waterand centrifuged between washings to avoid powder loss. Then,they were calcined at 7001C for 1 h in air. Before hot pressing,the powders were heated above 5001C to remove any water asthey are hygroscopic. The YPO4 was hot pressed at 15501C,whereas the monazite compounds were hot pressed at 12001C.Even under these conditions, not all the materials were fullydense; the YPO4 samples were B85% dense and the LaPO4

samples were 90% dense. Both the GdPO4 and La0:5Gd0:5ð ÞPO4

samples were 98% dense. Two samples of each compositionwere made.

The measured thermal conductivities are shown in Fig. 6. Themost striking feature of the data is that the orthophosphate with

1365

1380

13351357 1358

1435

13401356

~1275~1265

~1210

~1115

~1090

~1270

~1245

1385

1440

1435

1464

1476

2:7

1:11 1:15

Liquid

"3.8"

4:9

9:89:16

9:17

8:513:4

1000

1100

1200

1300

1400

1500

1470

20 40 60 806:1 7:3 1:1Nb2O5

Mol.%WO3

Tem

pera

ture

(°C

)

A

B C

D

(a)

(b)

Fig. 4. (a) Schematic of the crystal structure of W3Nb14O44 looking down the tetragonal axis. The structure consists of blocks of 4� 4 corner-sharingNbO octahedra joined by the tungsten ions shown as circles in the square unit cell. (b) Section of the Nb2O3–WO3 phase diagram illustrating thecompositions of the compounds, A, B. C and D measured.

February 2007 Oxide Materials with Low Thermal Conductivity 537

the xenotime structure has the classic 1/T dependence, whereasthe three with the monazite structure are almost indepen-dent of temperature. Furthermore, the co-doped monazite,La0:5Gd0:5ð ÞPO4, clearly has quite different conductivity char-acteristics from the xenotime YPO4 even though the averageinter-atomic distance is the same. Although the atomic mass ofthe cations is rather similar, the difference in temperature de-pendence appears to be directly related to the difference in theway in which the basic building blocks are connected. We alsonote that although the three monazites have different unit cellvolumes, they have rather similar thermal conductivities. Themost obvious difference between the xenotime and monazitestructures is that the xenotime structure, which has a highercrystal symmetry, consists of REO8 polyhedra whereas the poly-hedra in the monazites are REO9.

36 This would suggest that thebonds are weaker in the monazite than in the xenotime struc-tures. The other distinct difference is that there is much greatervariation in the RE–O bond length in the monazite, with each ofthe nine bonds being different than in the xenotime structurewhere there are only RE–O bond lengths.36 Similarly, the RE–Pbond length in the xenotime is shorter than either of the twoRE–P bond lengths in the monazites. In addition, in lookingalong the [001] axis, it is evident that there is some rotation ofthe PO4 tetrahedra about the [001] direction in the monazite,whereas the tetrahedra are all parallel in the xenotime structure.Finally, in the monazite structure, the PO4 tetrahedra are linkedto the REO9 polyhedra by corner sharing, whereas in the xeno-

time structure, some of the tetrahedra are linked to the REO8

polyhedra by corner sharing and others are edge shared. Allthese facts suggest that the monazite structure is more disor-dered at the inter-atomic length scale than the xenotimestructure, consistent with the significantly lower thermal con-ductivity.

A more extensive survey of the orthophosphates is clearlywarranted but we had difficulty in making large enough, fullydense pellets for thermal diffusivity measurements to exploreother ionic substitutions.

VIII. Lanthanum Molybdate

Lanthanum molybdate, La2Mo2O9, is a recently discoveredcompound that has attracted considerable attention because itexhibits a two to three order of magnitude increase in ionicconductivity to a value comparable with that of YSZ, when thecrystal structure changes on heating at B5851C.40 Our originalmotivation for studying the thermal conductivity of this com-pound was simply to ascertain whether the change in crystalstructure would affect the thermal conductivity, the rationalebeing that a compound with a very high oxygen ionic conduct-ivity would have considerable vibrational entropy of the oxygensub-lattice and this might be reflected by strong phonon scat-tering and hence low thermal conductivity. However, as ourmeasurements show in Fig. 7, there was no discernable changein thermal conductivity as the crystal structure changed and al-most no variation with temperature. The samples were made byattrition milling of the oxides for 3 h in deionized water, fol-lowed by grinding and then calcination in air for 16 h at 8001C.They were then cold pressed and sintered in air at 10001C for48 h. They could not be prepared by hot pressing, presumablybecause of the reaction to form molybdenum carbides. Foursamples were made on separate occasions. Each had a density ofB90% and all showed almost identical thermal conductivity.Using Maxwell’s relation1,41 to account for the porosity, f,

kdense ¼ kmeasured1

ð1� 1:5fÞ (5)

the thermal conductivity of dense lanthanum molybdate wouldbe 17% higher than shown in Fig. 7, namely 0.82 W/mK at1001C and 0.95 W/mK at 10001C.

Remarkably, our results show that the thermal conductivity islower than that of any other crystalline compound we havemeasured or found in the literature. Part of the reason for its lowthermal conductivity is undoubtedly its large mean atomic mass.

1.0

1.5

2.0

2.5

3.0

0 200 400 600 800 1000 1200

W Nb 0

WNb O

W Nb O

Two phase

Temperature (°C)

The

rmal

Con

duct

ivity

(W

/mK

)

Fig. 5. Measured thermal conductivity of the tungsten–bronzes indicated.

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600 700 800 900 1000

Temperature (°C)

The

rmal

Con

duct

ivity

(W

/m K

)

YPO4

GdPO4LaPO4(Gd,La)PO4

Fig. 6. Comparison of the thermal conductivity of the xenotime-struc-tured YPO4 and three of the monazite compounds. The YPO4 materialtested was 85% dense and the monazites were all 90% of full density.

0.0

1.0

2.0

3.0

0 200 400 600 800 1000 1200

Temperature (°C)

La Mo O

LaPO

Tri-doped YSZ Zr Y O

W Nb O

(Zr,Hf) Y O

(Zr,Hf) Y O

The

rmal

Con

duct

ivity

(W

/mK

)

8YSZ

Fig. 7. Thermal conductivity of La2Mo2O9 compared with the othermaterials investigated in this work. The density of the La2Mo2O9

samples was 90%.

538 Journal of the American Ceramic Society—Winter and Clarke Vol. 90, No. 2

However, this alone does not explain its exceptionally low con-ductivity. It is noted, though, that in common with the zirconatepyrochlores, it also has a high concentration of ‘‘structuralvacancies.’’

IX. Discussion and Conclusions

As mentioned in Section I, it was once considered that YSZ wasexceptional for a crystalline material because it exhibits both alow thermal conductivity at room temperatures and a conduct-ivity that is constant to high temperatures. However, as the re-sults presented here indicate, several compounds with lowerthermal conductivity than YSZ have been identified. While theapproach we have used to identify these compounds is, by itsvery nature, qualitative it does suggest that there will be manyother compounds that will also have a lower thermal conduct-ivity than YSZ.

On the basis of the materials identified, three strategies ap-pear to be most promising in identifying low thermal conduct-ivity materials. One is to search for silicate-like structures with alarge effective mass that incorporate structural units that arejoined together by rather flexible linkages. A second is to seekout compounds with low crystal symmetry. The third is tointroduce mass disorder on the cation sub-lattices of a crystalstructure that is known to have rather low thermal conductivity.The concept of introducing mass disorder to lower thermal con-ductivity is not, of course, new. However, hitherto it has onlybeen shown to be effective in the temperature regime where thethermal conductivity is dependent on temperature, the 1/T re-gime. This work demonstrates that the mass disorder strategy isalso a viable one in the minimum thermal conductivity regime,the regime where the thermal conductivity is temperature inde-pendent.

At this stage, very little is known about the phase equilibria ofthe La2Mo2O9 and related compounds to ascertain whether theymight have applications as thermal insulators or in other appli-cations beyond fast-ion conductors. It is also unknown howtheir melting temperatures vary with the rare-earth ion sub-stitution for the lanthanum ion. Similarly, although theorthophosphates have attractively low thermal conductivity,controlling their stoichiometry during deposition has provenproblematic and any free phosphate is likely to corrode existingsuperalloys. Of the compounds investigated in the course of ourstudies, the zirconia–yttria delta phase therefore appears to bethe most promising for possible application in thermal barriercoatings. The delta phase is reported to be stable to B13461Cbefore transforming to cubic zirconia and the composition itselfdoes not melt until 24611C. In addition, the constituent elementsare known to have similar vapor pressures and hence it is likelythat the compound can be deposited by standard, one-sourceelectron beam deposition. As it is not phase compatible withalumina, the oxide formed by high-temperature oxidation of themajority of bond-coat alloys, it would need to be used in a two-layer configuration with standard 8YSZ as an inner layer pro-viding the thermal cycle resistance. Finally, it is noted that thezirconia–yttria delta phase is just one of a family of compoundswith the same crystal structure and that cation substitutioncan be made on both the Zr site and on the Y site, so there apossibility of systematically varying the cations to investigate theeffect on thermal conductivity as has been done for the pyro-chlore compounds through modeling.42

It is interesting to speculate as to why the pyrochlore zirco-nates, the delta phase, the tungsten bronzes, and the lanthanummolybdate all exhibit such low thermal conductivity. One com-mon characteristic is that they have more than one cation sub-lattice and hence the possibility of different phonon modes aswell as disorder on each. They all have a large average atomicvolume, O, as shown in Table III and calculated from publisheddata on densities and formula units per unit cell. Another com-mon characteristic of the unit cells of these compounds is thatthey all incorporate ‘‘structural vacancies.’’ These oxygen va-

cancies can be expected to limit the allowable lattice phonons aswell as produce phonon scattering when they are occupied.However, as they are not randomly distributed, by analogywith the oxygen vacancy ordering in YSZ at high yttria con-centrations, it is unlikely that they can be more effective in pho-non scattering than they are in that material. Several of thecompounds also appear to have unusually large thermal ellips-oids for the oxygen ions as measured by X-ray diffraction atroom temperature, suggesting that they may be particularly ef-fective in phonon scattering. Another characteristic, though, ofthe oxygen sub-lattice in the delta phase as well as both the cat-ion and anions sub-lattices in the pyrochlore compounds is thatthey have a Kagome arrangement.44 This is an unusual featurefor the anion sub-lattice in solids but is likely to support unusualphonon modes.

One of the correlations that we have noted is that all thesecompounds have rather broad Raman lines, and in some cases,rather poorly defined Raman spectra. An example is shown inFig. 8. Although we are not aware of any direct correlation be-tween thermal conductivity and the width of the Raman lines,the phonon lifetime, t, is inversely proportional to the FWHMof the Raman lines when the lines are not instrumentally limit-ed.45 As the phonon mean free path can be expected to be pro-portional to the phonon lifetime, then if the mean phononvelocity remains unchanged, there will be a correlation betweenthe thermal conductivity and the width of the Raman lines.

Lastly, it is appropriate to mention that although all the sam-ples were the same thickness and were either white or darkcolored before metal coating, some nevertheless showedappreciable ‘‘transparency’’ in the thermal diffusivity measure-ments even at relatively low temperatures. Interestingly, increas-ing the thickness of the platinum layer to 2.25 mm on both sidesdid not affect the observation. Also, as indicated in Fig. 2, therecould be a significant difference with only a minor change in thestabilizer ion. The transparency is not the penetration of theflash of light through the absorbing layer and the sample that is

100 200 300 400 500 600 700

Wavenumber (cm−1)

Rel

ativ

e In

tens

ity

Zr3Y4O12

(Zr,Hf)3Y4O12

(Zr0.75Y0.25) O1.875

(Zr0.75 Hf0.25) O1.875

Fig. 8. Raman spectra of the indicated compounds recorded with a 514nm argon ion laser. The spectra are characterized by broad Ramanbands much broader than that of most oxides.

Table III. Calculated Average Atomic Volume

Compound Average atomic volume O (nm3)

7YSZ 0.1158YPO4 0.1194LaPO4 0.1278Zr3Y4O12 0.1308Gd2Zr2O7 0.1330W3Nb14O44 0.1385La2Mo2O9 0.1410

February 2007 Oxide Materials with Low Thermal Conductivity 539

usually considered in papers on measuring diffusivity by theflash technique. As the center wavelength of the xenon flash is atB1.8 mm, it is unlikely that any light penetrates as it is a wave-length to which the carbon over coat is strongly absorbing andthe platinum layer is highly reflective. Instead, it appears to beassociated with radiation from the heated side through the sam-ple to the other side that the detector senses. As the majority ofthe zirconia samples are intrinsically transparent into the mid-infra-red, despite the presence of optical scattering, the radiativecontribution may be especially sensitive to the arrangement ofpores in the samples that are close to being fully dense and hencecontaining a relatively few number of pores. Under such cir-cumstances, there can be direct radiative paths through regionsof the sample between pores. This effect is likely to be dependenton the thickness of the samples tested, being particularly pro-nounced for thin samples.

X. Summary

Heuristic arguments have been used to identify possible mate-rials with low thermal conductivity at high temperatures. Thesearguments suggest that candidate materials can be identified bysearching for compounds with a combination of high atomicmass, flexible ionic structures, non-directional bonding, and ex-tensive site disorder. We also find that substitutional alloying onthe cation sub-lattices is a viable approach to reducing thermalconductivity in the kmin regime. Materials that exhibit low ther-mal conductivity generally also exhibit Raman spectra with verybroad peaks. It is also concluded that compounds with lowcrystal symmetry and with a Kagome arrangement of ions mightalso exhibit unusually low thermal conductivity.

Acknowledgments

The authors are grateful to Dr. Kurt Sickafus of Los Alamos NationalLaboratory for discussions on pyrochlore and delta phases and for providing anunpublished copy of his work on characterizing crystal structures in terms of layersof cations and anions.

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540 Journal of the American Ceramic Society—Winter and Clarke Vol. 90, No. 2