Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-25T00:55:41.728Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of the X-ray diffraction line profile analysis method on the structural and microstructural parameters determination of sol-gel TiO2 powders

Published online by Cambridge University Press:  29 February 2012

Serge Vives  and
Cathy Meunier
Serge Vives*
Affiliation:
FEMTO-ST, ENISYS, Université de Franche-Comté, UMR 6174-CNRS, 4 place Tharradin, BP 71427, 25211 Montbéliard Cedex, France
Cathy Meunier
Affiliation:
FEMTO-ST, ENISYS, Université de Franche-Comté, UMR 6174-CNRS, 4 place Tharradin, BP 71427, 25211 Montbéliard Cedex, France
*
a)Author to whom correspondence should be addressed. Electronic mail: serge.vives@pu-pm.univ-fcomte.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Four sol-gel TiO2 powders have been prepared from titanium tetraisopropoxide. The calcined powders are then characterized by X-ray diffraction. Cell parameters are extracted using two Rietveld refinement programs (FULLPROF and MAUD) leading to close values and indicating a contraction of the a (or b) cell parameter and an expansion of the c cell parameter of the anatase phase with temperature. Crystallite size and microstrain are highly dependent not only on the sol synthesis but also on the diffraction line profile analysis (LPA) models (i.e., Williamson-Hall, Thomson-Cox-Hastings, Dehlez et al., and log-normal size distribution) employed. Discrepancies are then observed for the phase transformation critical size, the activation energy of grain growth, and the microstrain stored potential energy according to the LPA approach used to calculate the microstructural parameters.

Keywords

X-ray diffractionline profile analysismicrostructurenanocrystalline materialssol-gel
Type
Technical Articles
Information
Powder Diffraction , Volume 24 , Issue 3 , September 2009 , pp. 205 - 220
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adler, T. and Houska, C. R. (1979). “Simplifications in the X-ray line shape analysis,” J. Appl. Phys. JAPIAU 50, 3282–3287. 10.1063/1.326368CrossRefGoogle Scholar
Alivisatos, A. P. (2000). “Naturally aligned nanocrystals,” Science SCIEAS 289, 736–737. 10.1126/science.289.5480.736CrossRefGoogle ScholarPubMed
Babonneau, F., Doeuff, S., Leaustic, A., Sanchez, C., Cartier, C., and Verdaguer, M. (1988). “XANES and EXAFS study of titanium alkoxides,” Inorg. Chem. INOCAJ 27, 3166–3172. 10.1021/ic00291a024CrossRefGoogle Scholar
Balzar, D. (1995). “breadth—a program for analyzing diffraction line broadening,” J. Appl. Crystallogr. JACGAR 28, 244–245. 10.1107/S0021889894014172CrossRefGoogle Scholar
Balzar, D. (1999). “Voigt function model in diffraction-line broadening analysis” in Defect and Microstructure Analysis by Diffraction, edited by Snyder, R. L., Fiala, J., and Bunge, H.J. (IUCr/OUP, Oxford), pp. 94–126.Google Scholar
Balzar, D., Audebrand, N., Daymond, M. R., Fitch, A., Hewat, A., Langford, J. I., Le Bail, A., Louër, D., Masson, O., McCowan, C. N., Popa, N. C., Stephens, P. W., and Toby, B. H. (2004). “Size-strain line-broadening analysis of the ceria round-robin sample,” J. Appl. Crystallogr. JACGAR 37, 911–924. 10.1107/S0021889804022551CrossRefGoogle Scholar
Bartlett, J. R. and Woolfrey, J. L. (1996). “Preparation of multicomponent powders by alkoxide hydrolysis. I. Chemical processing,” Chem. Mater. CMATEX 8, 1167–1174. 10.1021/cm950270uCrossRefGoogle Scholar
Barnard, A. S. and Zapol, P. (2004). “Effects of particle morphology and surface hydrogenation on the phase stability of TiO2,” Phys. Rev. B PRBMDO 70, 235403. 10.1103/PhysRevB.70.235403CrossRefGoogle Scholar
Barringer, E. A. and Bowen, H. K. (1985). “High-Purity, monodisperse TiO2 powders by hydrolysis of titanium tetraethoxide. I. Synthesis and physical properties,” Langmuir LANGD5 1, 414–420. 10.1021/la00064a005CrossRefGoogle Scholar
Bertaut, E. F. (1950). “Raies de Debye-Scherrer et répartition des dimensions des domaines de Bragg dans les poudres polycristallines,” Acta Crystallogr. ABCRE6 3, 14–18. 10.1107/S0365110X50000045CrossRefGoogle Scholar
Birnie, D. P. III and Bendzko, N. J. (1999). “1H and 13C and NMR observation of the reaction of acetic acid with titanium isopropoxide,” Mat. Chem. Phys. 59, 26–35. 10.1016/S0254-0584(99)00021-8CrossRefGoogle Scholar
Caglioti, G., Paoletti, A., and Ricci, F. P. (1958). “Choice of collimators for a crystal spectrometer: For neutron diffraction,” Nucl. Instrum. NUINAO 3, 223–228. 10.1016/0369-643X(58)90029-XCrossRefGoogle Scholar
Cheary, R. W. and Coelho, A. A. (1996). Programs XFIT and FOURYA, deposited in CCP14 Powder Diffraction Library, Engineering and Physical Sciences Research Council, Daresbury Laboratory, Warrington, England (http://www.ccp14.ac.uk/tutorial/xfit-95/xfit.htm).Google Scholar
De Keijser, Th. H., Langford, J. I., Mittemeijer, E. J., and Vogels, B. P. (1982). “Use of the Voigt function in a single-line method for the analysis of X-ray diffraction line broadening,” J. Appl. Crystallogr. JACGAR 15, 309–314. 10.1107/S0021889882012035CrossRefGoogle Scholar
De Keijser, Th. H., Mittemeijer, E. J., and Rozendaal, H. C. F. (1983). “The determination of for crystallite-size and lattice-strain parameters in conjunction with the profile-refinement method for the determination of crystal structures,” J. Appl. Crystallogr. JACGAR 16, 309–314. 10.1107/S0021889883010493CrossRefGoogle Scholar
Debeila, M. A., Raphulu, M. C., Mokoena, E., Avalos, M., Petranovskii, V., Coville, N. J., and Scurrell, M. S. (2005). “The effect of gold on the phase transitions of titania,” Mater. Sci. Eng., A MSAPE3 396, 61–69. 10.1016/j.msea.2004.12.047CrossRefGoogle Scholar
Delhez, R., De Keijser, T. H., Langford, J. I., Loüer, D., Mittemeijer, E., and Sonneveld, E. J. (1995). “Crystal imperfection broadening and peak shape in the Rietveld method” in The Rietveld Method, edited by Young, R. A. (IUCr/OUP, Oxford), pp. 132–166.Google Scholar
Djerdj, I. and Tonejc, A. M. (2006). “Structural investigations of nanocrystalline samples,” J. Alloys Compd. JALCEU 413, 159–174. 10.1016/j.jallcom.2005.02.105CrossRefGoogle Scholar
Doeuff, S., Henry, M., and Sanchez, C. (1990). “Sol-gel synthesis and characterization of titanium oxo-acetate polymers,” Mater. Res. Bull. MRBUAC 25, 1519–1529. 10.1016/0025-5408(90)90129-PCrossRefGoogle Scholar
Doeuff, S., Henry, M., Sanchez, C., and Livage, J. (1987). “Hydrolysis of titanium alkoxides: Modification of molecular precursor by acetic acid,” J. Non-Cryst. Solids JNCSBJ 89, 206–216. 10.1016/S0022-3093(87)80333-2CrossRefGoogle Scholar
Enzo, S., Fagherazzi, G., Benedetti, A., and Polizzi, S. (1988). “A profile-fitting procedure for analysis of broadened X-ray diffraction peaks. I. Methodology,” J. Appl. Crystallogr. JACGAR 21, 536–542. 10.1107/S0021889888006612CrossRefGoogle Scholar
Fernandez-Garcia, M., Wang, X., Belver, C., Hanson, J. C., and Rodriguez, J. A. (2007). “Anatase- nanomaterials: Morphological/size dependence of the crystallization and phase behavior phenomena,” J. Phys. Chem. C JPCCCK 111, 674–682. 10.1021/jp065661iCrossRefGoogle Scholar
Finnie, K. S., Luca, V., Moran, P. D., Barlett, J. R., and Woolfrey, L. (2000). “Vibrational spectroscopy and EXAFS study of Ti(OC2H5)4 and alcohol exchange in Ti(iso-OC3H7)4,” J. Mater. Chem. JMACEP 10, 409–418. 10.1039/a906662dCrossRefGoogle Scholar
Grey, I. E. and Wilson, N. C. (2007). “Titanium vacancy defects in sol-gel prepared anatase,” J. Solid State Chem. JSSCBI 180, 670–678. 10.1016/j.jssc.2006.11.028CrossRefGoogle Scholar
Hill, R. J. and Howard, C. J. (1987). “Quantitative phase analysis from neutron powder diffraction data using the Rietveld method,” J. Appl. Crystallogr. JACGAR 20, 467–474. 10.1107/S0021889887086199CrossRefGoogle Scholar
Houska, C. R. and Kužel, R. (1999). “Classical treatment of line profiles influenced by strain, small size, and stacking faults,” in Defect and Microstructure Analysis by Diffraction, edited by Snyder, R. L., Fiala, J., Bunge, H. J. (IUCr/OUP, Oxford), pp. 82–93.Google Scholar
Hsiang, H. I. and Lin, S. C. (2006). “Effects of aging on the kinetics of nanocrystalline anatase crystallite growth,” Mater. Chem. Phys. MCHPDR 95, 275–279. 10.1016/j.matchemphys.2005.06.019CrossRefGoogle Scholar
Hsu, J. P. and Nacu, A. (2003). “On the factors influencing the preparation of nanosized titania sols,” Langmuir LANGD5 19, 4448–4454. 10.1021/la0270587CrossRefGoogle Scholar
Kallala, M., Sanchez, C., and Cabanne, B. (1993). “Structures of inorganic polymers in sol-gel processes based on titanium oxide,” Phys. Rev. B PRBMDO 48, 3692–3703.CrossRefGoogle ScholarPubMed
Klug, H. P. and Alexander, L. E. (1974). X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials (Wiley, New York).Google Scholar
Krill, C. E. and Birringer, R. (1998). “Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis,” Philos. Mag. PMHABF 77, 621–640.CrossRefGoogle Scholar
Kumar, N. -P. P. (1995). “Growth of rutile crystallites during the initial stage of anatase to rutile transformation in pure titania and in titania-alumina nanocomposites,” Scr. Metall. Mater. SCRMEX 32, 873–877. 10.1016/0956-716X(95)93217-RCrossRefGoogle Scholar
Langford, J. I. (1978). “A rapid method for analysing the breadths of diffraction and spectral lines using the Voigt function,” J. Appl. Crystallogr. JACGAR 11, 10–14. 10.1107/S0021889878012601CrossRefGoogle Scholar
Langford, J. I., Louër, D., and Scardi, P. (2000). “Effect of a crystallite size distribution on X-ray: Diffraction line profiles and whole-powder-pattern fitting,” J. Appl. Crystallogr. JACGAR 33, 964–974. 10.1107/S002188980000460XCrossRefGoogle Scholar
Larbot, A., Laaziz, I., Marignan, J., and Quinson, J. F. (1992). “Porous texture of titanium oxide gels: Evolution as a function of medium used,” J. Non-Cryst. Solids JNCSBJ 147–148, 157–161. 10.1016/S0022-3093(05)80610-6CrossRefGoogle Scholar
Lazzeri, M., Vittadini, A., and Selloni, A. (2001). “Structure and energetics of stoichiometric anatase surfaces,” Phys. Rev. B PRBMDO 63, 155409. 10.1103/PhysRevB.63.155409CrossRefGoogle Scholar
Leaustic, A., Babonneau, F., and Livage, J. (1989). “Structural investigation of the hydrolysis-condensation process of titanium alkoxides (, OEt) modified by acetylacetone, 1. Study of the alkoxide modification,” Chem. Mater. CMATEX 1, 240–247. 10.1021/cm00002a015CrossRefGoogle Scholar
Li, G., Li, L., Boerio-Goates, J., and Woodfield, B. F. (2005). “High purity anatase nanocrystals: Near room-temperature synthesis, grain growth kinetics, and surface hydration chemistry,” J. Am. Chem. Soc. JACSAT 127, 8659–8666. 10.1021/ja050517gCrossRefGoogle ScholarPubMed
Li, Y., White, T. J., and Lim, S. H. (2004). “Low-temperature synthesis and microstructural control of titania nano-particles,” J. Solid State Chem. JSSCBI 177, 1372–1381. 10.1016/j.jssc.2003.11.016CrossRefGoogle Scholar
Liao, S. C., Mayo, W. E., and Pae, K. D. (1997). “Theory of high pressure/low temperature sintering of bulk nanocrystalline TiO2,” Acta Mater. ACMAFD 45, 4027–4040. 10.1016/S1359-6454(97)00087-6CrossRefGoogle Scholar
Lutterotti, L. (2005). “Quantitative Rietveld analysis in batch mode with Maud, and new features in MAUD2.037,” CPD-IUCr NewsLetter , 32, 53–55.Google Scholar
Mändar, H., Felsche, J., Mikli, V., and Vajakas, T. (1999). “AXES1.9: New tools for estimation of crystallite size and shape by Williamson-Hall analysis,” J. Appl. Crystallogr. JACGAR 32, 345–350. 10.1107/S0021889898011170CrossRefGoogle Scholar
Matyi, R. J., Schwartz, L. H., and Butt, J. B. (1987). “Particle size, particle size distribution, and related measurements of supported metal catalysts,” Catal. Rev. - Sci. Eng. CRSEC9 29, 41–99. 10.1080/01614948708067547CrossRefGoogle Scholar
Oliver, P. M., Watson, G. W., Kelsey, E. T., and Parker, S. C. (1997). “Atomistic simulation of the. surface structure of the polymorphs rutile and anatase,” J. Mater. Chem. JMACEP 7, 563–568. 10.1039/a606353eCrossRefGoogle Scholar
Padmanabhan, S. C., Pillai, S. C., Colreavy, J., Balakrishnan, S., McCormack, D. E., Perova, T. S., Gun’ko, Y., Hinder, S. J., and Kelly, J. M. (2007). “A simple sol-gel processing for the development of high-temperature stable photoactive anatase titania,” Chem. Mater. CMATEX 19, 4474–4481. 10.1021/cm070980nCrossRefGoogle Scholar
Parra, R., Góes, M. S., Castro, M. S., Longo, E., Bueno, P. R., and Varela, J. A. (2008). “Reaction pathway to the synthesis of anatase via the chemical modification of titanium isopropoxide with acetic acid,” Chem. Mater. CMATEX 20, 143–150. 10.1021/cm702286eCrossRefGoogle Scholar
Penn, R. L. and Banfield, J. F. (1998). “Imperfect oriented attachment: Dislocation generation in defect-free nanocrystals,” Science SCIEAS 281, 969–971. 10.1126/science.281.5379.969CrossRefGoogle ScholarPubMed
Penn, R. L. and Banfield, J. F. (1999). ““Formation of rutile nuclei at anatase {112} twin interfaces and the phase transformation mechanism in nanocrystalline titania,” Am. Mineral 84, 871–876. CrossRefGoogle Scholar
Rao, S., and Houska, C. R. (1986) “X-ray particle-size broadening,” Acta Crystallogr., Sect. A: Found. Crystallogr. ACACEQ 42, 6–13. 10.1107/S0108767386099981CrossRefGoogle Scholar
Rietveld, H. M. (1969). “A profile refinement method for nuclear and magnetic structures,” J. Appl. Crystallogr. JACGAR 2, 65–71. 10.1107/S0021889869006558CrossRefGoogle Scholar
Rodriguez-Carvajal, J. (2001). “Recent developments of the program FULLPROF,” IUCr-CPD NewsLetter. 26, 12–20.Google Scholar
Roisnel, T. and Rodriguez-Carvajal, J. (2001). “WINPLOTR: A windows tool for powder diffraction pattern analysis,” Mater. Sci. Forum. 378–381, 118–124. 10.4028/www.scientific.net/MSF.378-381.118CrossRefGoogle Scholar
Scherrer, P. (1918). “Bestimmung der grösse und der inneren struktur von kolloidteilchen mittels röntgenstrahlen,” Nachr. Ges. Wiss. Göttingen. Math.-Phys. NWGAAN 2, 98–101.Google Scholar
Stibitz, G. R. (1936). “Energy and lattice spacing in strained solids,” Phys. Rev. PRVAAH 49, 862–863.Google Scholar
Stokes, A. R. (1948). “A numerical Fourier-analysis method for the correction of widths and shapes of lines on X-ray powder photographs,” Proc. Phys. Soc. London PPSOAU 61, 382–391. 10.1088/0959-5309/61/4/311CrossRefGoogle Scholar
Stokes, A. R. and Wilson, A. C. J. (1944). “The diffraction of X-rays by distorted crystal aggregates-I,” Proc. Phys. Soc. London PPSOAU 56, 174–181. 10.1088/0959-5309/56/3/303CrossRefGoogle Scholar
Swamy, V., Dubrovinsky, L. S., Dubrovinskaia, N. A., Simionovici, A. S., Drakopoulos, M., Dmitriev, V., and Weber, H. P. (2003). “Compression behavior of nanocrystalline anatase TiO2,” Solid State Commun. SSCOA4 125, 111–115. 10.1016/S0038-1098(02)00601-4CrossRefGoogle Scholar
Swamy, V., Menzies, D., Muddle, B. C., Kuznetsov, A., Dubrovinsky, L. S., Dai, Q., and Dmitriev, V. (2006). “Nonlinear size dependence of anatase lattice parameters,” Appl. Phys. Lett. APPLAB 88, 243103. 10.1063/1.2213956CrossRefGoogle Scholar
Thompson, P., Cox, D. E., and Hastings, J. B. (1987). “Rietveld refinement of Debye-Scherrer synchrotron X-ray data from Al2O3,” J. Appl. Crystallogr. JACGAR 20, 79–83. 10.1107/S0021889887087090CrossRefGoogle Scholar
Ungár, T., Gubicza, J., Ribárik, G., and Borbély, A. (2001). “Crystallite size distribution and dislocation structure determined by diffraction profile analysis: Principles and practical application to cubic and hexagonal crystals,” J. Appl. Crystallogr. JACGAR 34, 298–310. 10.1107/S0021889801003715CrossRefGoogle Scholar
Vives, S., Gaffet, E., and Meunier, C. (2004). “X-ray diffraction line profile analysis of iron ball milled powders,” Mater. Sci. Eng., A MSAPE3 366, 229–238. 10.1016/S0921-5093(03)00572-0CrossRefGoogle Scholar
Warren, B. E. and Averbach, B. L. (1950). “The effect of cold-work distortion on X-ray patterns,” J. Appl. Phys. JAPIAU 21, 595–599. 10.1063/1.1699713CrossRefGoogle Scholar
Williamson, G. K. and Hall, W. H. (1953). “X-ray line broadening from filled aluminium and wolfram,” Acta Metall. AMETAR 1, 22. 10.1016/0001-6160(53)90006-6CrossRefGoogle Scholar
Yoldas, B. E. (1986). “Hydrolysis of titanium alkoxide and effects of hydrolytic polycondensation parameters,” J. Mater. Sci. JMTSAS 21, 1087–1092. 10.1007/BF01117399CrossRefGoogle Scholar
Young, R. A. (editor) (1995). The Rietveld Method (IUCr/OUP, Oxford).Google Scholar
Young, R. A. and Dessai, P. (1989). “Crystallite size and microstrain indicators in Rietveld refinement,” Archiwum Nauki o Materialach 10, 71–90.Google Scholar
Zhang, H. and Banfield, J. F. (1998). “Thermodynamic analysis of phase stability of nanocrystalline titania,” J. Mater. Chem. JMACEP 8, 2073–2076. 10.1039/a802619jCrossRefGoogle Scholar
Zhang, H. and Banfield, J. F. (2002). “Kinetics of crystallization and crystal growth of nanocrystalline anatase in nanometer-sized amorphous titania,” Chem. Mater. CMATEX 14, 4145–4154. 10.1021/cm020072kCrossRefGoogle Scholar