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Materials Science and Engineering A 527 (2009) 93–97

Contents lists available at ScienceDirect

Materials Science and Engineering A

journa l homepage: www.e lsev ier .com/ locate /msea

rW2O8/ZrO2 composites by in situ synthesis of ZrO2 + WO3: Processing,oefficient of thermal expansion, and theoretical model prediction

i Sun, Patrick Kwon ∗

epartment of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA

r t i c l e i n f o

rticle history:eceived 13 April 2009eceived in revised form 17 July 2009ccepted 23 July 2009

a b s t r a c t

The in situ synthesis of WO3 and ZrO2 in a particular mass ratio enables us to produce ZrW2O8, a materialwith negative coefficient of thermal expansion (CTE). By increasing the proportion of ZrO2, the productswere made into a wide variety of ZrW2O8/ZrO2 composites. The temperature dependences of the CTEsof those materials were measured and the experimental data were compared with the predictions from

eywords:rW2O8

oefficient of thermal expansionn situ synthesis

several models. The Levin model yielded the predictive values most close to the experimental CTEs. Thiswas the first time the micromechanics models were applied to predict the CTEs of composite materialscontaining a negative thermal expansion material. A ZrW2O8/ZrO2 composite with a designed CTE canbe fabricated and utilized to meet a special thermal requirement in many industrial applications.

© 2009 Elsevier B.V. All rights reserved.

oung’s modulusicromechanics model

. Introduction

Most materials exhibit positive thermal expansion with theemperature increase. However, some materials with negativeoefficient of thermal expansion (CTE) exist. Among those materi-ls, zirconium tungstate (ZrW2O8) has been the subject of intensetudy [1–10] due to its isotropic, large negative CTE over a wideange of temperatures (0.3–1050 K) [1–5]. The CTE of ZrW2O8 isearly constant for a wide range of temperatures except around60 ◦C where a sharp change occurs due to the �-to-� phase tran-ition [1]. One possible application of the negative CTE materialsuch as ZrW2O8 is to combine them with positive CTE materials,hus producing a composite with a desirable CTE. The compos-tes such as Cu/ZrW2O8 [6], Al/ZrW2O8 [7], cement/ZrW2O8 [8] andrO2/ZrW2O8 [9,10] have been studied.

In this paper, several ceramic–ceramic composite materialsade of ZrW2O8 and ZrO2 were fabricated by mixing, compact-

ng and sintering a series of WO3 + ZrO2 powders with varying theroportion of ZrO2. The focus of the paper is to develop a process-

ng method designed to yield a set of composites with desirablehermomechanical properties. The CTEs and Young’s moduli of

he samples were measured using a Thermomechanical AnalyzerTMA: Setaram 95, France). Comparisons were made between thexperimental CTE data and several micromechanics model predic-ions, including the rule of mixture (ROM), the Turner model [11],

∗ Corresponding author. Tel.: +1 5173550173; fax: +1 5173539842.E-mail address: pkwon@egr.msu.edu (P. Kwon).

921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2009.07.050

the Kerner model [12], the Rosen–Hashin bounds model [13] andthe Levin model [14].

A ZrW2O8/ZrO2 composite with a desirable CTE can be fabri-cated to meet particular thermal expansion requirements for agiven industrial application. For example, the thermal expansionof a composite can be designed to match the thermal expansionof other adjacent mechanical or electronics components. Specifi-cally, a ZrW2O8/ZrO2 composite with near-zero CTE can be usedas the ceramic substrate of optical fiber Bragg gratings in orderto keep the constant dimension under the temperature-changingenvironment.

2. Background

Many micromechanics models have been presented to predictthe effective or bulk physical properties of composite materials[11–17]. For particulate composites, the Mori–Tanaka method [15]is widely used to determine the effective elastic stiffness tensor[16,17]. The effective stiffness tensor is given by

Cc = Cm + Vp(Cp − Cm)Ap (1)

where the subscripts c, p and m represent the composite, inclusionmaterials and matrix material, respectively, C represents stiffnesstensor, V is volume fraction and Ap is the inclusion strain concen-

trator tensor which relates the average strain in the inclusion to theapplied homogeneous boundary strain. The Mori–Tanaka methoddefines Ap to be

Ap = T[VmI + VpT]−1 (2)

9 e and Engineering A 527 (2009) 93–97

wd

T

ws

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˛

w

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˛

T

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wu

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wM

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3

TS(ccds

Table 1Mean features of raw powders used in this study.

Name Material Mean particlesize (�m)

Manufacturer

W-Fluka WO3 8.22 Sigma–Aldrich, USATMDAR Al2O3 0.17 Taimei Chemical Co., Ltd., Japan

4 L. Sun, P. Kwon / Materials Scienc

here I is the fourth rank identity tensor and T is Wu’s Tensor [18]efined as

= [I + ESm(Cp − Cm)]−1 (3)

here E is Eshelby’s tensor determined by the shape of the inclu-ion [19] and S represents compliance tensor.

For the effective CTE prediction of a composite, the rule of mix-ure (ROM) is the simplest method based on the CTE and volumeraction of each of its components. The equation for the ROM is

c = ˛pVp + ˛mVm (4)

here ˛ is CTE.The ROM calculates the effective CTE by assuming a linear rela-

ionship between the CTE and volume ratio of each phase. However,he thermal strain in one phase within a composite is constrainedy the other phase and the magnitude of such strain depends onhe shear transfer at the interface. Thus, the thermal strain featurestrong dependence on the elastic constants [11–14]. Therefore, sev-ral other models were presented, which take into account thelastic constants for the CTE estimation, including the Turner model11], the Kerner model [12], the Rosen–Hashin Bounds model [13],nd the Levin model [14]. The calculation formula for each of theodels is shown below:The Turner model states

c = ˛mKmVm + ˛pKpVp

KmVm + KpVp(5)

he Kerner model states

c = ˛mVm + ˛pVp + VmVp(˛p − ˛m)Kp − Km

KmVm + KpVp + (3KmKp/4Gm)

(6)

nd the Rosen–Hashin bounds model states

˛uc = 4VmVpGp(Km − Kp)(˛m − ˛p)

3KmKp + (4Gp(Km + Kp)/2)+ (˛mVm + ˛pVp)

˛lc = 4VmVpGm(Km − Kp)(˛m − ˛p)

3KmKp + (4Gm(Km + Kp)/2)+ (˛mVm + ˛pVp)

(7)

here K is the bulk modulus, G is the shear modulus, the superscriptrepresents upper bound and l signifies lower bound.

Eqs. (5)–(7) are only suitable for the isotropic two-phase com-osites. A more general equation was presented by Levin [14]:

c = ˛m + (˛p − ˛m)(Sp − Sm)−1(Sc − Sm) (8)

here the effective compliance tensor, Sc, can be calculated by theori–Tanaka approach [15].These micromechanics models have been used widely to predict

he mechanical/thermal properties of composites. The predictionsrom the models have successfully applied in some cases. However,he main drawback has been that the applicability of these modelss usually limited to the composite with the volume fraction below.6 of reinforce phase. Beyond 0.6 value, one need to use conti-uity concept to reverse the role of each phase in the calculation17,20].

. Materials and experimental processing

Table 1 summarizes the three raw powders used in this study.hese powders were mixed in varying proportions as described inection 4 using 12 mm diameter zirconia media in a mixing jar mill

U.S. Stoneware 764AVM, USA) for 48 h. The powder mixtures wereompacted in a single-action die under the load producing 80 MPaompaction pressure. The green samples for CTE test were cylin-rical with 7.94 mm diameter and 6 mm height while the greenamples for Young’s modulus test were rectangular parallelepipeds

CERAC-2003a ZrO2 1.23 CERAC Inc., USA

a Stabilized by 3 wt% Y2O3.

whose dimension is 16.5 mm × 5.05 mm × 3.5 mm. Green compactswere sintered in a furnace (Carbolite-HTF1700, UK) under theatmospheric condition in a covered platinum crucible, which candecrease the sublimation of WO3 at temperatures above 800 ◦C[21]. The volume of each fully sintered sample was measured inwater using Archimedes’ principle, which was then used to calcu-late the relative densities.

Before CTE and Young’s modulus measurement, the sampleswere heat-treated (3 ◦C/min for both heating and cooling cycles,and soaking for 60 min at 300 ◦C) to cure microcracks induced by thequenching process [5]. The CTE and Young’s modulus of the sinteredsamples were measured using the TMA with the heating and cool-ing rates of 3 ◦C/min in an argon gas environment. Three samplesproduced for each material were tested for CTE and Young’s modu-lus. The CTE variation is less than 5% and the maximum discrepancyin the Young’s modulus data is 6% in the three samples. There-fore, we considered that the CTE and Young’s modulus test resultsfor each material are consistent. The sintered samples were thenpolished (Abramin, Denmark) and thermal etched in the furnaceat 600 ◦C for the microstructure observation. The microstructureof each sample was observed using Scanning Electron Microscopy(JEOL 6400 V, Japan).

4. Results and discussion

4.1. Synthesis of ZrW2O8 substrate and its CTE

The in situ reaction is utilized to produce pure ZrW2O8 from a2:1 stoichiometric ratio of WO3 and ZrO2 powder mixture (massratio is mWO3 : mZrO2 = 1 : 0.266). The heating rate is 5 ◦C/minand the soaking temperature and duration were 1190 ◦C and 6 h,respectively, and a quenching step is necessary to prevent thedecomposition of ZrW2O8. After quenching in open air, the surfacesof the samples featured small cracks. These microcracks disap-peared completely after the cure treatment cycle mentioned above.The XRD pattern of the reaction product was compared to thestandard powder diffraction file of ZrW2O8. The similarity of thetwo patterns verifies that the produced compound is pure ZrW2O8[22].

The sintered ZrW2O8 samples maintained their cylindricalshape with a final diameter of 7.51 mm and height of 5.68 mm andthe final relative density of the samples was 90%. The microstruc-ture of the resulting ZrW2O8 is shown in Fig. 1.

The temperature dependence of the ZrW2O8 substrate’s CTE wasmeasured, and the relationship is shown in Fig. 2. Also shown isthe CTE–temperature relationship of partially sintered CERAC-2003utilizing the same ramp/soak path to produce pure ZrW2O8. Thesetwo ceramics are the components of the composites presented inthis paper. As expected, the CTE of ZrW2O8 is negative and uni-form for a wide range of temperature except around 160 ◦C, wherea sharp change occurs due to �-to-� phase transition [1]. The CTE of

the ZrW2O8 at room temperature was found to be −8.1 × 10−6 K−1,a result that matches the report of Mary et al. [1]. The CTE of thepartially sintered CEREAC-2003 is 8.6 × 10−6 K−1 at room temper-ature.

L. Sun, P. Kwon / Materials Science and Engineering A 527 (2009) 93–97 95

Fig. 1. The microstructure of the ZrW2O8 substrate.

Fb

4r

ZitZuvZsZw

TTZ

to �-ZrW2O8 (high pressure phase) [23] due to the thermal stressinduced by the CTE mismatch between ZrO2 and ZrW2O8.

ig. 2. The temperature dependence of CTEs of ZrW2O8 and CERAC-2003 sinteredy the ramp/soak path to produce pure ZrW2O8.

.2. ZrW2O8/ZrO2 composites and the CTE–temperatureelationship

Utilizing the same ramp/soak path in the production of purerW2O8, a ZrW2O8/ZrO2 composite can be fabricated by simplyncreasing the proportion of ZrO2. Thus, by varying the ratio of WO3o ZrO2, the resulting composites feature varying ratio betweenrW2O8 and ZrO2. Table 2 shows several WO3/ZrO2 mass ratiossed in this study and the corresponding calculated ZrW2O8/ZrO2olume ratios in the sintered samples. The volume fraction of

rW2O8 determined from the micrograph of each sample is con-istent to the corresponding reported value in Table 2. All of therW2O8/ZrO2 composites maintained their initial cylindrical shape,ith final diameter and height around 7.35 and 5.57 mm, respec-

able 2he WO3/ZrO2 mass ratios of various green samples and the corresponding resultantrW2O8/ZrO2 volume ratios in the sintered samples.

# WO3/ZrO2 mass ratio inreactant powder

ZrW2O8/ZrO2 volume ratiosin the sintered sample

Final relativedensity

1 0.159:1 20:80 77%2 0.264:1 30:70 79%3 0.38:1 39:61 80%4 0.593:1 52:48 82%5 1.096:1 70:30 83%6 2.307:1 90:10 84%

Fig. 3. The microstructure of representative ZrW2O8/ZrO2 composite (sample 3).

tively, and they featured final relative densities in the 77–84% range(see Table 2). This low density persists mainly because ZrO2 has notbeen fully sintered by the ramp/soak path to produce pure ZrW2O8.The micrograph of representative ZrW2O8/ZrO2 composite in Fig. 3shows the large particles surrounded by small ZrO2 particles, whichare ZrW2O8. The abundance of pores remaining between the ZrO2particles is due to the fact that ZrO2 is far from fully sintered. Inaddition, cracks are observed to exist between ZrO2 and ZrW2O8grains, resulting from the considerable difference in CTEs for thesetwo component materials. These cracks also contribute to the lowfinal density.

The temperature-dependent CTE value of each sintered sampleis shown in Fig. 4. As shown, both samples 1 and 2 feature positiveCTEs, samples 4–6 exhibit negative CTEs, and the CTE of sample3 is nearly zero. Fig. 4 shows that the CTE–temperature curves ofthe composites feature a shape that is very similar to that of pureZrW2O8. However, the peak caused by phase transition occurs at alower temperature for the composites. This “peak shift” is possiblya result of phase transition from �-ZrW2O8 (low pressure phase)

Fig. 4. The temperature-dependent CTEs of the various ZrW2O8/ZrO2 compositesamples.

96 L. Sun, P. Kwon / Materials Science and Engineering A 527 (2009) 93–97

ulated

4c

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creopirdbTittZ

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TT

reacts and forms a composite made of mainly ZrW2O8, ZrO2 andtrace of Al2(WO4)3. Due to the melting point of Al2(WO4)3 at1135 ◦C [28], a liquid phase exists if the soaking temperature is1190 ◦C. The presence of liquid will promote the densificationkinetics, resulting in the improved final relative density.

Fig. 5. The CTEs of the ZrW2O8/ZrO2 composite samples and corresponding calc

.3. CTE–phase volume ratio relationship of ZrW2O8/ZrO2omposites

The relationship between the CTEs of various samples and theorresponding volume fractions of ZrW2O8 at both room temper-ture and 500 ◦C is plotted in Fig. 5(a) and (b), respectively. It cane observed that the CTE values continuously decrease as the vol-me fraction of ZrW2O8 increases in the composites. For the zeroTE ZrW2O8/ZrO2 composite, the volume fraction of ZrW2O8 in thenal product is about 39% (sample 3).

As mentioned in Section 2, the ROM is the simplest method toalculate the effective CTE of a composite. The experimental CTEesults of ZrW2O8 and ZrO2 shown in Fig. 2 provide the CTE ofach constituent, which were used to calculate the effective CTEsf ZrW2O8/ZrO2 composites based on the ROM. The result is alsoresented in Fig. 5. Large discrepancy exists between the exper-

mental results and the calculated values from the ROM for bothoom temperature and 500 ◦C test conditions. In fact, the ROM pre-icts that sample 4 has a room temperature CTE of nearly zero,ut the experimental data showed its CTE to be −2.14 × 10−6 K−1.his discrepancy is due to the interfacial gaps between matrix andnclusion phases of the resulting composites (see Fig. 3). At the sameime, the ROM to predict affective CTE does not include the elas-ic constants that account for the thermal stress influence betweenrO2 and ZrW2O8.

The calculated CTE as a function of V% of ZrW2O8 results fromqs. (5) to (8) also are shown in Fig. 5, which takes into accounthe elastic constants into the calculation of CTEs. The correspond-ng effective Young’s modulus data were measured with the TMAnit using the three-point bending method, which are presented inable 3. After sintering and polishing, the samples used in Young’sodulus test are rectangular parallelepipeds (cuboids) whose edge

engths were 12.6, 4.2 and 2.5 mm, respectively. The effectiveoung’s modulus of pure ZrW2O8 at room temperature was foundo be 4.31 ± 0.01 GPa, which nearly matches the value of 4.22 GPaeported by Chen et al. [5]. However, these values are quite lower

able 3he measured Young’s moduli (E) of samples at room temperature and 500 ◦C.

Material E at room temperature (GPa) E at 500 ◦C (GPa)

ZrO2a 1.50 ± 0.01 1.51 ± 0.01

#1 1.85 ± 0.01 1.83 ± 0.01#2 2.05 ± 0.01 2.02 ± 0.01#3 2.26 ± 0.01 2.21 ± 0.01#4 2.59 ± 0.02 2.53 ± 0.01#5 3.19 ± 0.01 3.08 ± 0.01#6 3.90 ± 0.01 3.74 ± 0.02ZrW2O8 4.31 ± 0.01 4.12 ± 0.01

a Sintered by the ramp/soak path to produce pure ZrW2O8.

values from several prediction models at (a) room temperature and (b) 500 ◦C.

than the single crystal value of 88.3 GPa reported by Drymiotis etal. [24]. This difference is due to the porosity in the bulk ZrW2O8.Since the ZrO2 sample was only partially sintered by the ramp/soakpath to produce ZrW2O8 and contains microcracks caused by thequenching process, its Young’s modulus is also much lower thanthat of a fully sintered sample (∼200 GPa) [25]. From the reports ofDrymiotis et al. [24] and Holcome et al. [26], the Poisson’s ratio wastaken to be 0.3 for both ZrO2 and ZrW2O8.

Clearly, Eqs. (5)–(8) result in better predictions than the ROM.Among those, the Levin model produces CTE values that are mostsimilar to the experimental data. The maximum error of Levinmodel was found to be less than 8%. By studying the series ofAl2O3/NiAl composites, Hsieh and Tuan [27] concluded “the Kernerand Turner models can be used as the upper and lower boundsfor the CTE of two-phase materials, respectively.” This conclusionalso matches the results of our ZrW2O8/ZrO2 composites. Anotherinteresting finding is that the upper boundary predicted by theRosen–Hashin Bounds model [13] almost superimposes on thecurve form Kerner model [12] for the ZrW2O8/ZrO2 composites.

4.4. Final density improvement

At temperature above 1100 ◦C, ZrO2, WO3 and trace of Al2O3

Fig. 6. The micrograph of sample 3 with 0.07 wt% alumina.

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L. Sun, P. Kwon / Materials Scienc

The 0.07 wt% Al2O3 (TMDAR) was added into our ZrO2 + WO3owder system, which caused the final relative density to increaserom 80 to 90%. Furthermore, the minute amount of TMDARllowed the samples to maintain their cylindrical shape. Theicrostructure of these improved-density composites remains

ery similar to that of Fig. 3, with the exception that far fewer poresxist between ZrO2 grains (Fig. 6), a result which can be attributedo the presence of the liquid Al2(WO4)3 phase during sintering.

This small additional amount of Al2O3 did not change the CTEsf various samples. However, due to the decreased porosity, theoung’s moduli of samples with Al2O3 are higher than samplesithout Al2O3. For example, the Young’s modulus increases to

1.19 GPa for sample 3 and 15.22 GPa for pure ZrW2O8.

. Conclusion

By the in situ synthesis of WO3 and ZrO2 in a mass ratio of:0.266, a ZrW2O8 substrate was fabricated. By increasing the ratiof ZrO2 in the reactants, the product was found to be ZrW2O8/ZrO2omposites. The CTEs of various samples were measured, and thoseata were compared with several model predictions, including theule of mixture (ROM), the Turner model, the Kerner model, theosen–Hashin bounds model, and the Levin model. Among theodel predictions, the Levin model shows best correlation to the

TE test values. To the knowledge of the authors, this research is therst time to apply CTE prediction models to composites contain-

ng negative CTE materials. Adding a small amount of Al2O3 intohe WO3 + ZrO2 reaction system was found to effectively increasehe final densities and Young’s moduli of the sintered composites.he controllable CTE characteristics formulated in this study can besed to fabricate a specific ZrW2O8/ZrO2 composite in order to meetiven requirements for thermal expansion in an industrial process.

cknowledgement

The authors would like to acknowledge Dr. Les Lee at AFOSRor supporting this work under the Contract Number F49620-02-

[

[[[

Engineering A 527 (2009) 93–97 97

1-0025. We also thank Adam Sneller and Sam Baldauf for thepreparation of some samples.

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