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Applications of Rietveld Analysis to Materials Characterization in Solid-State Chemistry, Physics and Mineralogy

Published online by Cambridge University Press:  06 March 2019

R.J. Hill
R.J. Hill*
Affiliation:
CSIRO Division of Mineral Products PO Box 124, Port Melbourne VIC 3207, Australia
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The utilization and optimization of the properties of materials follows most effectively from a detailed knowledge and understanding of the positions and energetics of their constituent atoms, generally obtained from scattering/diffraction experiments involving electrons, neutrons or electromagnetic radiation. For the most part, these experiments are undertaken on individual crystals of the material, thereby preserving the resolution (and information content) of the three-dimensional reciprocal lattice. However, many of the substances of greatest academic and technical importance either do not crystallize with dimensions large enough for single-crystal studies, or display the properties of maximal interest only when present in finely-divided (powdered) form. In a diffraction experiment, the reciprocal lattice is then collapsed on to the single dimension of the 2θ scale.

Type
I. Whole Pattern Fitting, Rietveld Analysis and Calculated Diffraction Patterns
Information
Advances in X-Ray Analysis , Volume 35 , Issue A: First Pacific-International Congress on X-ray Analytical Methods (PICXAM). Fortieth Annual Conference on Applications of X-ray Analysis, August 7-16, 1991 , 1991 , pp. 25 - 38
Copyright
Copyright © International Centre for Diffraction Data 1991

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References

Ahtee, M., Nurmela, M., Suortti, P., and Jarvinen, M., 1989, Correction for preferred orientation in Rietveld refinement, J. Appl. Cryst., 22: 261.Google Scholar
Albinati, A., and Willis, B.T.M., 1982, The Rietveld method in neutron and X-ray powder diffraction, J. Appl. Cryst,, 15: 361.Google Scholar
Antoniadis, A., Berruyer, J., and Filhol, A” 1990, Maximum-likelihood methods in powder diffraction refinements, Acta Cryst., A46: 692.Google Scholar
Baerlocher, Ch., 1982, “The X-ray Rietveld System,” Institut flir Kristallographie und Petrogiaphie, Zurich, Switzerland.Google Scholar
Baerlocher, Ch., 1984, The possibilities and the limitations of the powder method in zeolite structure analysis; the refinement of the silica end-member of TPA-ZSM-5, Proc. 6th Int. Zeolite Conf., Reno, USA, Butterworth, London.Google Scholar
Baharie, E., and Pawley, G.S., 1982, The temperature dependence of the anharmonic properties of crystalline naphthalene-dg, Acta Cryst., A38: 803.Google Scholar
Benedetti, A., Fagherazzi, G., Enzo, S., and Battagliarin, M., 1988, A profile-fitting procedure for analysis of broadened X-ray diffraction peaks. II, Application and discussion of the methodology, J. Appl. Cryst., 21: 543.Google Scholar
Bish, D.L., and Howard, S.A., 1988, Quantitative phase analysis using the Rietveld method, 7. Appl Cryst., 21: 86.Google Scholar
Bish, D.L., and Von Dreele, R.B., 1989, Rietveld refinement of non-hydrogen atomic positions in kaolinite, Clays and Clay Minerals, 37: 289.Google Scholar
Boysen, H. 1985, Analysis of diffuse scattering in neutron powder diagrams. Application to glassy carbon, J. Appl. Cryst., 18: 320.Google Scholar
Boysen, H., 1990, Anharmonic temperature factors from powder diagrams. Application to ionic conductors, PS-08.03.14, Collected Abstracts, XVfh Congress and General Assembly, Internat Union of Crystallogr., Bordeaux, France.Google Scholar
Brindley, G.W., 1945, The effect of grain or particle size on X-ray reflections from mixed powders and alloys, considered in relation to the quantitative determination of crystalline substances by X-ray methods, Philos. Mag., 36: 347.Google Scholar
Brückner, S., Meille, S.V., Malpezzi, L., Cesaro, A., Navarim, L., and Tombolini, R., 1988, The structure of poly(D-(-)-β-hydroxybutyrate). A refinement based on the Rietveld method, Macromolecules, 21: 967.Google Scholar
Cheetham, A.K., David, W.I.F., Eddy, M.M., Jakeman, R.T.B., Johnson, M.W., and Torardi, C.C., 1986, Crystal structure determination by powder neutron diffraction at the spallation neutron source, ISIS, Nature, 320: 46.Google Scholar
Cheetham, A.K., and Taylor, J.C., 1977, Profile analysis of powder neuuon diffraction data: its scope, limitations, and applications in solid state chemistry, J. Solid State Chemistry, 21: 253.Google Scholar
Cockcroft, J. X., and Fitch, A.N., 1990, The solid phases of deuterium sulphide by powder neutron diffraction, Zeit. Kristallogr., 193: 1.Google Scholar
Cox, D.E., Hastings, J.B., Thomlinson, W., and Prewitt, C.T., 1983, Application of synchrotron radiation to high resolution powder diffraction and Rietveld refinement, Nucl. Inst, and Methods, 208: 573.Google Scholar
Cox, D.E., Hastings, J.B., Cardoso, L.P., and Finger, L.W., 1986, Synchrotron X-ray powder diffraction at X13A: a dedicated powder diffractometer at the National Synchrotron Light Source, Mater. Sci. Forum., 9: 1.Google Scholar
David, W.I.F., 1986, Powder diffraction peak shapes. Parameterization of the pseudo-Voigt as a Voigt function, J. Appl. Cryst, 19: 63.Google Scholar
David, W.I.F., 1987, The probabilistic determination of intensities of completely overlapping reflections in powder diffraction patterns, J. Appl. Cryst., 20: 316.Google Scholar
David, W.I.F., Harrison, W.T.A., and Johnson, M.W., 1986, High resolution powder diffraction at ISIS, Mater. Sci. Forum., 9: 89.Google Scholar
David, W.I.F., Hull, S., and Ibberson, R.M., 1990, High pressure neutron powder diffraction studies of ferroelastic LaNbO4, Abstr. A48, ISIS Annual Report RAL-90-050, Rutherford Appleton Lab., Chilton, Didcot, Oxon, England.Google Scholar
David, W.I.F., and Matthewman, J.C., 1985, Profile refinement of powder patterns using the Voigt function, J. Appl. Cryst., 18: 461.Google Scholar
DeHaven, P.W., and Jacobson, R,A., 1979, Profile refinement of multiple-wavelength neutron powder data, J. Appl. Cryst… 12: 601.Google Scholar
Dollase, W.A., 1986, Correction of intensities for preferred orientation in powder diffractometry: application of the March model, J. Appl. Cryst., 19: 267.Google Scholar
Dove, M., Palmer, D., and Swainson, I., 1990, Detailed study of the phase transition in leucite, Abstr. A8, ISIS Annual Report RAL-90-050, Rutherford Appleton Lab., Chilton, Didcot, Oxon, England.Google Scholar
Eriksson, L., Louef, D., and Werner, P.-E., 1989, Crystal structure determination and Rietveld refinement of Zn(OH)(NO3).H2O, J. Solid State Chem., 81: 9.Google Scholar
Fitch, A.N., 1986, Some disordered systems studied by high resolution neutron powder diffraction, Mat. Sci. Forum, 9: 113.Google Scholar
Fitch, A.N., Wright, A.F., and Fender, B” 1982, The structure of UO2DAsO4.4D2O by powder neutron diffraction, Acta Cryst., B38: 2546.Google Scholar
Fitch, A.N., Jobic, H., and Renouprez, A., 1985, The localization of benzene in Y-zeolite, J. Chem. Soc, Chem. Commun., 1985: 284.Google Scholar
Frey, F., Boysen, H., and Vogt, T., 1990, Neutron powder investigation of the monoclinic to tetragonal phase transformation in undoped zirconia, Acta Cryst., B46: 724,Google Scholar
Gibaud, A., Le Bail, A., and Bulou, A., 1986, A re-investigation of the room-temperature phase of KAlF4: evidence of antiphase domains, J. Phys. C: Sol. St. Phys., 19: 4623.Google Scholar
Goldstone, J.A., Lawson, A.C., and Cort, B., 1989, Investigation of vacancies in high-purity a-plutonium, LANSCE Experimental Report LA-11933-PR, Los Alamos National Lab., Los Alamos, NM, USA, p. 88.Google Scholar
Haile, S.M., Wuensch, B.J., and Prince, E., 1990, Neutron Rietveld analysis of anion and cation disorder in the fast-ion conducting pyrochlore system yttrium zirconium titanium oxide (Y2(ZrxTi1-x)2O7), Mater. Pes. Soc. Symp. Proc, 166: 81.Google Scholar
Hatton, P.D., 1986, Powder diffraction at very high pressures, Mat. Sci. Forum, 9: 21.Google Scholar
Hepp, A., and Baerlocher, Ch., 1988, Learned peak shape functions for powder diffraction data, Aust. J. Phys., 41: 229.Google Scholar
Hewat, A.W., 1986, High-resolution neutron and synchrotron powder diffraction, Chemica Scripta, 26A:119.Google Scholar
Hewat, A.W., 1990, Neutron powder diffraction and oxide superconductors, Neutron News, 1[1]:28.Google Scholar
Hill, R.J., 1985, Structure of Pb3O2(OH)2 by Rietveld analysis of neutron powder diffraction data, Acta Cryst., C41:998.Google Scholar
Hill, R.J., 1991a, Data collection strategies: fitting the experiment to the need, in: “The Rietveld Method,” R.A. Young, ed., Oxford University Press, Oxford.Google Scholar
Hill, R.J., 1991b, Expanded use of the Rietveld method in studies of phase abundance in multiphase mixtures, Powder Diffraction, 6: 74.Google Scholar
Hill, R.J., Hartshorn, A.J., and Houchin, M.R., 1988, A new method for the determination of yttrium distribution in yttria-doped tetragonal zirconia, Mat. Sci. Forum, 34-36: 153.Google Scholar
Hill, R.J., and Howard, C.J., 1987, Quantitative phase analysis from neutron powder diffraction data using the Rietveld method, J. Appl. Cryst., 20: 467.Google Scholar
Hill, R.J., and Jackson, I., 1990, The thermal expansion of ScAlO3 - a silicate perovskite analogue, Phys. Chem. Minerals, 17: 89.Google Scholar
Hili, R.J., and Madsen, I.C., 1984, Structural parameters of [β-Pb02 and their relationship to the hydrogen-loss concept of lead-acid battery failure, J. Electrochem. Soc, 131: 1486.Google Scholar
Hill, R.J., and Madsen, I.C., 1987, Data collection strategies for constant wavelength RieWeld analysis, Powder Diffraction, 2: 146.Google Scholar
Hill, R.J., and Madsen, I.C., 1991, Rietveld analysis using para-focusing and Debye Scherrer geometry data collected with a Bragg-Brentano diffractometer, Ze.it. fur Kristallogr., 194:(in press).Google Scholar
Hill, R.J., and Reichert, B.E., 1990, Measurement of phase abundance in magnesia-parti allystabilized zirconia by Rietveld analysis of X-ray diffraction data, J. Am. Ceram. Soc, 73: 2822.Google Scholar
Howard, C.J., Kisi, E.H., Roberts, R.B., and Hill, R.J., 1990, Neutron diffraction studies of phase transformations between tetragonal and orthorhombic zirconia in magnesiaparti ally-stabilized zirconia, J. Am. Ceram. Soc, 73: 2828.Google Scholar
Howard, S.A., and Snyder, 1989, The use of direct convolution products in profile and pattern fitting algorithms. I. Development of the algorithms, J. Appl Cryst., 22: 238.Google Scholar
Iannelli, P., and Immirzi, A., 1989, Structure analysis of polyisobutylene based on the whole-pattern fibre diffraction method. 2. Refinement of structure based on several constrained models, Macromolecules, 22: 200.Google Scholar
Immirzi, A., 1980, Constrained powder-profile refinement based on generalized coordinates. Application to X-ray data of isotactic polypropylene, Acta Cryst., B36: 2378.Google Scholar
Izumi, F., 1989, New Rietveld refinement programs and their applications, Invited paper 115, International Workshop on the Rietveld Method, Petten, The Netherlands.Google Scholar
Jorgensen, J.D., 1978, Compression mechanisms in a-quartz structures - SiO2 and GeO2, J. Appl. Phys., 49: 5473.Google Scholar
Jorgensen, J.D., and Hinks, D.G., 1990, Defects in oxide superconductors: the key to synthesis and superconductivity, Neutron News, 1 [2] :24.Google Scholar
Jorgensen, J.D., Veal, B.W., Paulikas, A.P., Nowicki, L.J., Crabtree, G.W., Claus, H., and Kwok, W.K., 1990, Structural properties of oxygen-deficient YBa2Cu3O7-δ, Phys. Rev.B,4lA86Z. Google Scholar
Kisi, E.H., Howard, C.J., and Hill, R.J., 1989, Crystal structure of orthorhombic zirconia in partially stabilized zirconia,J. Am. Ceram. Soc, 72: 1757.Google Scholar
Klug, H.P., and Alexander, L.E., 1974, “X-ray Diffraction Procedures for Poly crystalline and Amorphous Materials,” Wiley-Interscience, New York.Google Scholar
Lager, G.A., Th., Annbruster, and Faber, J., 1987, Neutron and X-ray diffraction study of hydrogarnet Ca3Al2(O4H4)3, Amer. Mineral., 72: 756.Google Scholar
Larsen, A.C., and Von Dreele, R.B., 1988, “GSAS Generalized Structure Analysis System,” LAUR 86-748, Los Alamos, National Laboratory, Los Alamos, NM 87545, USA.Google Scholar
Lartigue, C., Le Bail, A.,and Percheron-Guegan, A., 1987, A new study of the structure of LaNitDg-j using a modified Rietveld method for the refinement of neutron powder diffraction data, J. Less-Common Metals, 129: 65.Google Scholar
Le Bail, A., Ferey, G., Amoros, P., Beltran-Porter, D” and Villeneuve, G., 1989, Crystal structure of β-VO(HPO4).2H2O solved from X-ray powder diffraction, J. Solid State Chem., 79: 169.Google Scholar
Loiier, D., and Langford, J.I., 1988, Peak shape and resolution in conventional diffractometry with monochromatic X-rays, J. Appl. Cryst., 21: 430.Google Scholar
Loveday, J., Nelmes, R.J., Besson, J.M., Hamel, G. Weil, G., Hull, S., Mayers, 1990, The development of high pressure neutron diffraction above 50 kbar, Abstr. ASS, ISIS Ann. Rep. RAL-90-050, Rutherford Appleton Lab., Chilton, Didcot, Oxon. England.Google Scholar
Luttorotti, L., and Scardi, P., 1990, Simultaneous structure and size-strain refinement by the Rietveld method, J. Appl. Cryst., 23: 246.Google Scholar
Madsen, I.C., Finney, R.J., Flann, R.C.A., Frost, M.T., and Wilson, B.W., 1991, Quantitative analysis of high-alumina refractories using X-ray powder diffraction data and the Rietveld method, J. Am. Ceram. Soc, 74: 619.Google Scholar
Madsen, I.C., and Hill, R.J., 1990, QPDA - A user-friendly, interactive program for quantitative phase and crystal size/strain analysis of powder diffraction data, Powder Diffraction, 5: 195.Google Scholar
Maichle, J.K., Ihringer, J., and Prandl, W., 1988, Simultaneous structure refinement of neutron, synchrotron and X-ray powder diffraction patterns, J. Appl. Cryst., 21: 22.Google Scholar
McCusker, L., 1988, The ab initio structure determination of sigma-2 (a new clathrasil phase) from synchrotron powder diffraction data, J. Appl. Cryst., 21: 305.Google Scholar
Mentzen, B.F., 1987, Characterization of guest molecules adsorbed on zeolites of known structure by combined X-ray powder profile refinements and conventional Fourier techniques. Part II - Localization of the n-hexane, TPA and p-xylene guests in a pentasil type zeolite, Mat. Res. Bull., 22: 489.Google Scholar
Munekawa, S., and Toraya, H., 1988, Development of a high resolution X-ray powder diffractometer and its evaluation, 37th Denver Conf. on Applic. of X-ray Anal. Google Scholar
Pannetier, J., 1986, Time-resolved neutron powder diffraction, Chemica Scripta, 26A: 131.Google Scholar
Pannetier, J., Chabre, Y., and Poinsignon, C., 1990, Structural study of the electrochemical reduction of manganese dioxide with proton intercalation, ISSI Letters, 1: 5.Google Scholar
Parrish, W.B., 1987, Advances in synchrotron X-ray polycrystalline diffraction, Aust. J. Phys., 41: 101.Google Scholar
Parrish, W.B., and Hart, M., 1989, Parallel beam and focusing X-ray powder diffractometry, Adv. X-ray Anal. 32: 481.Google Scholar
Pawley, G.S., 1980, EDINP, the Edinburgh powder profile refinement program, J. Appl. Cryst., 13: 630.Google Scholar
Post, J.E., and Bish, D.L., 1988, Rietveld refinement of the todorokite structure, Amer. Mineral., 73: 861.Google Scholar
Post, J.E., and Bish, D.L., 1989, Rietveld refinement of crystal structures using powder Xray diffraction data, in: “Modern Powder Diffraction,” D.L, Bish and J.E. Post, eds, Mineial. Soc. Amer., Washington.Google Scholar
Post, J.E., and Veblen, D.R., 1990, Crystal structure determinations of synthetic sodium, magnesium, and potassium birnessite using TEM and the Rietveld method, Amer. Mineral., 75: 477.Google Scholar
Raudsepp, M. Hawthorne, F.C., and Turnock, A.C., 1990, Evaluation of the Rietveld method for the characterization of fine-grained products of mineral synthesis: the diopside-hedenbergite join, Can. Mineral., 28: 93.Google Scholar
Raudsepp, M., Turnock, A.C., and Hawthorne, F.C., 1987, Characterization of cation ordering in synthetic scandium-fiuor-eckermannite, indium-flu or-eckermannite, and scandium-fluor-nybdite by Rietveld structure refinement, Amer. Mineral., 72: 959.Google Scholar
Retief, J.J., Engel, D.W., and Boonstra, E.G., 1985, X-ray powder diffractometric procedure for lattice parameter determination for long-chain molecules, J. Appl. Cryst., 18: 150.Google Scholar
Richardson, J.W. Jr., Pluth, J.J., and Smith, J.V., 1988, Rietveld profile analysis of calcined AIPO4-11 using pulsed neutron powder diffraction, Acta Cryst., B44: 367.Google Scholar
Rietveld, H.M., 1969, A profile refinement method for nuclear and magnetic structures, J. Appl. Cryst., 2: 65.Google Scholar
Rudolf, P.R., and Clearfield, A., 1985, The solution of unknown crystal structures from Xray powder diffraction data. Technique and an example, ZrNaH(PO4)2, Acta Cryst., B41: 418.Google Scholar
Rudolf, P.R., and Crowder, C.E., 1990, Structure refinement and water location in the very large-pore molecular sieve VPI-5 by X-ray Rietveld techniques, Zeolites, 10: 163.Google Scholar
Sabine, T.M., 1988, A reconciliation of extinction theories, Acta Cryst., A44: 368.Google Scholar
Sabine, T.M., Von Dreele, R.B., and JŸrgensen, J.-E., 1988, Extinction in time-of-flight neutron powder diffractometry, Acta Cryst., A44: 374.Google Scholar
Salje, E., 1986, Application of high resolution powder diffractometry to the investigation of structural phase transitions, Mat. Sci. Forum, 9: 57.Google Scholar
Santoro, A., 1983, The role of modern neutron powder diffraction techniques in the study of solid state ionics, Solid State Ionics, 9-10: 31.Google Scholar
Sato, M., Kodama, N. and Matsuda, S. 1981, An application of pattern fitting structure refinement to muscovite KAl2(Si3Al)O10(OH)2, Mineralog. J., 10: 222.Google Scholar
Schrader, H., Boysen, H. Frey, F., and Convert, P., 1990, On the phase transformation of proto- to cliiio-/orthoenstatite: neutron powder investigation, Phys. Chem. Minerals, 17: 409.Google Scholar
Shishiguchi, S., Minato, I. and Hashizume, H., 1986, Rapid collection of X-ray powder data for pattern analysis by a cylindrical position-sensitive detector, J. Appl. Cryst., 19: 420.Google Scholar
Spackman, M.A., Hill, R.J., and Gibbs, G.V., 1987, Exploration of structure and bonding in stishovite widi Fourier and pseudoatom refinement methods suing single crystal and powder X-ray diffraction data, Phys. Chem. Minerals, 14: 139.Google Scholar
Stranger, R., Grey, I.E., Madsen, I.C., and Smith, P.W., 1987, Structure systematics in A3Mo2X9, X=Cl,Br,I from Rietveld refinement of X-ray powder data, J. Solid State Chem., 69: 162.Google Scholar
Taylor, J.C. 1985, Technique and performance of powder diffraction in crystal structure studies, Aust. J. Phys., 38: 519.Google Scholar
Taylor, J.C., and Matulis, C.E., 1991, Absorption contrast effects in the quantitative XRD analysis of powders by full multi-phase profile refinement, J.Appl. Cryst., 24: 14,Google Scholar
Thompson, P., Cox, D.E., and Hastings, J.B., 1987a, Rietveld refinement of Debye-Scherrer synchrotron X-ray data from Al2O3, J. Appl. Cryst., 20: 79.Google Scholar
Thompson, P., Reilly, J.J., and Hastings, J.M., 1987b, The accommodation of strain and particle size broadening in Rietveld refinement; its application to de-deuterated LaNig alloy, J. Less-Common Metals, 129: 105.Google Scholar
Thompson, P., Reilly, J.J., and Hastings, J.M., 1989, The application of the Rietveld method to a highly strained material with microtwins: TiFeD1.9, J. Appl. Cryst., 22: 256.Google Scholar
Toraya, H., 1990, Array-type universal profile function for powder pattern fitting, J. Appl, Cryst., 23: 485.Google Scholar
Uno, R., Ozawa, H., Yamanaka, T., Morikawa, H., Ando, M., Ohsumi, K., Nukui, A., Yukino, K., and Kawasaki, T., 1987, Powder diffrac tome try at the Tsukuba Photon Factory, Aust, J. Phys., 41: 133.Google Scholar
Wiles, D.B., and Young, R.A., 1981, A new computer program for Rietveld analysis of Xray powder diffraction patterns, J. Appl. Cryst., 14: 149.Google Scholar
Will, G., 1989, Crystal structure analysis from powder diffraction data, Zeit. Krlstallogr., 188: 169.Google Scholar
Wilson, A.J.C., 1963, “Mathematical Theory of X-ray Powder Diffractometry,” Centrex, Eindhoven.Google Scholar
Williams, A., Kwei, G.H., R.B., Von Dreele, Larson, A.C., Raistrick, I.D., and Bish, D.L., 1988, Joint x-ray and neutron refinement of the structure of superconducting YBa2Cu3O7-x: precision structure, anisotropic thermal parameters, strain, and cation disorder, Phys. Rev. B, 37: 7960.Google Scholar
Wood, I.G., and Brown, G., 1988, Least-squares profile refinement of randomly interstratified clay mineral structures, J. Appl. Cryst., 21: 154,Google Scholar
Yamamoto, A., Onoda, M., Takayama-Muromachi, E., Izumi, F., Ishigaki, T., and Asano, H., 1990, Rietveld analysis of the modulated structure in the superconducting oxide Bi2(Sr,Ca)3Cu2O8+x, Phys. Rev, B, 42: 4228.Google Scholar
Yamanaka, T. and Ogata, K., 1991, Structure refinement of GeO2 polymorphs at high pressures and temperatures by energy-dispersive spectra of powder diffraction, J. Appl. Cryst., 24: 111,Google Scholar
Young, R.A., and Sakthivel, A., 1988, Bimodal distributions of profile-broadened effects in Rietveld refinement, J. Appl. Cryst., 21: 416.Google Scholar
Young, R.A. and Wiles, D.B., 1982, Profile shape functions in Rietveld refinements, J. Appl. Cryst., 15: 430.Google Scholar