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Thermal expansion of anatase and rutile between 300 and 575 K using synchrotron powder X-ray diffraction

Published online by Cambridge University Press:  01 March 2012

D. R. Hummer ,
P. J. Heaney  and
J. E. Post
D. R. Hummer
Affiliation:
Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16082
P. J. Heaney
Affiliation:
Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16082
J. E. Post
Affiliation:
Department of Mineral Sciences, Smithsonian Institution, Washington, DC 20560-0119
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Abstract

High-precision unit-cell parameters for the TiO2 polymorphs anatase and rutile at temperatures between 300 and 575 K have been determined using Rietveld analysis of synchrotron powder XRD data. Polynomial models were used to express the tetragonal unit-cell parameters as a function of absolute temperature, with a (anatase)=1.759 37×10−8×T2+6.418 16×10−6×T+3.779 84, c (anatase)=6.6545×10−8×T2+4.0464×10−5×T+9.4910, V (anatase)=2.237 58×10−6×T2+1.027 77×10−3×T+135.602, a (rutile)=−6.636 42×10−11×T3+1.005 01×10−7×T2−1.009 9310−5×T+4.586 34, c (rutile)=−4.115 50×10−11×T3+6.405 94×10−8×T2+4.675 61×10−7T+2.951 81, and V (rutile)=−2.7790×10−9×T3+4.2386×10−6×T2−3.3551×10−4×T+62.100. The polynomial expressions were used to calculate linear (α) and volume (β) thermal expansion coefficients of anatase and rutile between 300 and 575 K. At 298.15 K, these values were αa=4.46943×10−6 K−1, αc=8.4283×10−6 K−1, and β=17.3542×10−6 K−1 for anatase, and αa=6.99953×10−6 K−1, αc=9.36625×10−6 K−1, and β=28.680×10−6 K−1 for rutile.

Keywords

anataserutilethermal expansionsynchrotronpowder diffraction
Type
Technical Articles
Information
Powder Diffraction , Volume 22 , Issue 4 , December 2007 , pp. 352 - 357
Copyright
Copyright © Cambridge University Press 2007

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References

Cromer, D. T. and Herrington, K. (1955). “The structures of anatase and rutile,” J. Am. Chem. Soc.JACSAT10.1021/ja01623a004 77, 4708–4709.CrossRefGoogle Scholar
Dolcater, D. L., Syers, J. K., and Jackson, M. L. (1970). “Titanium as free oxide and substituted forms in kaolinites and other soil minerals,” Clays Clay Miner.CLCMAB10.1346/CCMN.1970.0180202 18, 71–79.CrossRefGoogle Scholar
Filyukov, D. V., Brodskaya, E. N., Piotrovskaya, E. M., and Leeuw, S. W. (2006). “Molecular-dynamics simulation of nanoclusters of crystal modifications of titanium dioxide,” Russ. J. Gen. Chem. 77, 10–16.CrossRefGoogle Scholar
Finger, L. W., Cox, D. E., and Jephcoat, A. P. (1994). “A correction for powder diffraction peak asymmetry due to axial divergence,” J. Appl. Crystallogr.JACGAR10.1107/S0021889894004218 27, 892–900.CrossRefGoogle Scholar
Gratzel, M. (2004). “Conversion of sunlight to electric power by nanocrystalline dye-sensitized solar cells,” J. Photochem. Photobiol., AJPPCEJ10.1016/j.jphotochem.2004.02.023 164, 3–14.CrossRefGoogle Scholar
Gribb, A. A. and Banfield, J. F. (1997). “Particle size effects on transformation kinetics and phase stability in nanocrystalline TiO2,” Am. Mineral.AMMIAY 82, 717–728.CrossRefGoogle Scholar
Hammersley, A. P., Svensson, S. O., Hanfland, M., Fitch, A. N., and Hausermann, D. (1996). “Titanium two-dimensional detector software: From real detector to idealised image or two-theta scan,” High Press. Res.HPRSEL10.1080/08957959608201408 14, 235–248.CrossRefGoogle Scholar
Horn, M., Schwerdtfeger, C. F., and Meagher, E. P. (1972). “Refinement of the structure of anatase at several temperatures,” Z. Kristallogr.ZEKRDZ 136, 273–281.CrossRefGoogle Scholar
Howard, C. J., Sabine, T. M., and Dickson, F. (1991). “Structural and thermal parameters for rutile and anatase,” Acta Crystallogr., Sect. B: Struct. Sci.ASBSDK10.1107/S010876819100335X 47, 462–468.CrossRefGoogle Scholar
Huang, C., Hsu, Y., Chen, J., Suryanarayanan, V., Lee, K., and Ho, K. (2006). “The effects of hydrothermal temperature and thickness of TiO2 film on the performance of a dye-sensitized solar cell,” Sol. Energy Mater. Sol. CellsSEMCEQ10.1016/j.solmat.2006.03.012 90, 2391–2397.CrossRefGoogle Scholar
Hummer, D. R., Heaney, P. J., and Post, J. E. (2006). “Aqueous nucleation and growth of titanium oxides using time-resolved synchrotron X-ray diffraction,” Abstracts of the American Geophysical Union, Joint Assembly, Session V06.Google Scholar
Jagtap, N., Bhagwat, M., Awati, P., and Ramaswamy, V. (2005). “Characterization of nanocrystalline anatase titania: an in situ HTXRD study,” Thermochim. ActaTHACAS 427, 37–41.CrossRefGoogle Scholar
Karunagaran, B., Rajendra Kumar, R. T., Mangalaraj, D., Narayandass, Sa. K., and Mohan Rao, G. (2002). “Influence of thermal annealing on the composition and structural parameters of DC magnetron sputtered titanium dioxide thin films,” Cryst. Res. Technol.CRTEDF10.1002/crat.200290004 37, 1285–1292.CrossRefGoogle Scholar
Larson, A. C. and Von Dreele, R. B. (2000). General Structure Analysis System (GSAS), Report LAUR 86-748, Los Alamos National Laboratory, Los Alamos, NM.Google Scholar
Li, W., Ni, C., Lin, H., Huang, C. P., and Ismat Shah, S. (2004). “Size dependence of thermal stability of TiO2 nanoparticles,” J. Appl. Phys.JAPIAU10.1063/1.1807520 96, 6663–6668.CrossRefGoogle Scholar
Lindsley, D. H. (1976). “Experimental studies of oxide minerals,” Rev. Mineral.RMINDF 3, L-61–L-88.Google Scholar
Meagher, E. P. and Lager, G. A. (1979). “Polyhedral thermal expansion in the TiO2 polymorphs: refinement of the crystal structures of rutile and brookite at high temperature,” Can. Mineral.CAMIA6 17, 77–85.Google Scholar
O’Regan, B. C. and Durrant, J. R. (2006). “Calculation of activation energies for transport and recombination in mesoporous TiO2/dye/electrolyte films—taking into account surface charge shifts with temperature,” J. Phys. Chem. BJPCBFK10.1021/jp060979w 110, 8544–8547.CrossRefGoogle ScholarPubMed
Ranade, M. R., Navrotsky, A., Zhang, H. Z., Banfield, J. F., Elder, S. H., Zaban, A., Borse, P. H., Kulkarni, S. K., Doran, G. S., and Whitfield, H. J. (2002). “Energetics of nanocrystalline TiO2,” Proc. Natl. Acad. Sci. U.S.A.PNASA610.1073/pnas.251534898 99, 6476–6481.CrossRefGoogle ScholarPubMed
Rao, K. V. K., Naidu, S. V. N., and Iyengar, L. (1970). “Thermal expansion of rutile and anatase,” J. Am. Ceram. Soc.JACTAW10.1111/j.1151-2916.1970.tb12051.x 53, 124–126.CrossRefGoogle Scholar
Richards, B. S., Richards, S. R., Boreland, M. B., and Jamieson, D. N. (2004). “High temperature processing of TiO2 thin films for application in silicon solar cells,” J. Vac. Sci. Technol. AJVTAD610.1116/1.1647594 22, 339–348.CrossRefGoogle Scholar
Rincon, C., Wasim, S. M., and Marin, G. (1998). “Effect of thermal expansion coefficient on the temperature dependence of the band gap in CuInTe 2,” Mater. Lett.MLETDJ10.1016/S0167-577X(98)00041-X 36, 245–248.CrossRefGoogle Scholar
Santa-Nokki, H., Kallioinen, J., Kololuoma, T., Tuboltsev, V., and Korppi-Tommola, J. (2006). “Dynamic preparation of TiO2 films for fabrication of dye-sensitized solar cells,” J. Photochem. Photobiol., AJPPCEJ10.1016/j.jphotochem.2006.02.011 182, 187–191.CrossRefGoogle Scholar
Sebastian, P. J., Olea, A., Campos, J., Toledo, J. A., and Gamboa, S. A. (2004). “Temperature dependence and the oscillatory behavior of the opto-electronic properties of a dye-sensitized nanocrystalline TiO2 solar cell,” Sol. Energy Mater. Sol. CellsSEMCEQ10.1016/j.solmat.2003.11.011 81, 349–361.CrossRefGoogle Scholar
Stephens, P. W. (1999). “Phenomenological model of anisotropic peak broadening in powder diffraction,” J. Appl. Crystallogr.JACGAR10.1107/S0021889898006001 32, 281–289.CrossRefGoogle Scholar
Sugiyama, K. and Takeuchi, Y. (1991). “The crystal structure of rutile as a function of temperature up to 1600°C,” Z. Kristallogr.ZEKRDZ 194, 305–313.Google Scholar
Swamy, V., Menzies, D., Muddle, B. C., Kuznetsov, A., Dubrovinsky, L. S., Dai, Q., and Dmitriev, V. (2006). “Nonlinear size dependence of anatase TiO2 lattice parameters,” Appl. Phys. Lett.APPLAB10.1063/1.2213956 88, 243103-1–243103-3.CrossRefGoogle Scholar
Takeshita, K., Sasaki, Y., Kobashi, M., Tanaka, Y., Maeda, S., Yamakata, A., Ishibashi, T., and Onishi, H. (2004). “Effect of annealing temperature on back electron transfer and distribution of deep trap sites in dye-sensitized TiO2, studied by time-resolved infrared spectroscopy,” J. Phys. Chem. BJPCBFK10.1021/jp035416o 108, 2963–2969.CrossRefGoogle Scholar
Van Laar, B. and Yelon, W. B. (1984). “The peak in neutron powder diffraction,” J. Appl. Crystallogr.JACGAR10.1107/S0021889884011006 17, 47–54.CrossRefGoogle Scholar
Zhang, H. and Banfield, J. F. (1998). “Thermodynamic analysis of phase stability of nanocrystalline titania,” J. Mater. Chem.JMACEP10.1039/a802619j 8, 2073–2076.CrossRefGoogle Scholar
Zhang, H. and Banfield, J. F. (2000). “Understanding polymorphic phase transformation behavior during growth of nanocrystalline aggregates: Insights from TiO2,” J. Phys. Chem. BJPCBFK10.1021/jp000499j 104, 3481–3487.CrossRefGoogle Scholar