Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-29T23:27:53.078Z Has data issue: false hasContentIssue false
  • English
  • Français

Texture and structural refinement using neutron diffraction data from molybdite (MoO3) and calcite (CaCO3) powders and a Ni-rich Ni50.7Ti49.30 alloy

Published online by Cambridge University Press:  29 February 2012

Husin Sitepu
Husin Sitepu*
Affiliation:
Crystallography Laboratory, Virginia Tech, Blacksburg, Virginia 24061
*
a)Also at Research and Development Center, Saudi Aramco, P.O. Box 62, Dhahran 31311, KSA. Electronic mail: sitepu@vt.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Preferred orientation or texture is a common feature of experimental powder patterns. The mathematics of two commonly used models for preferred orientation—the March-Dollase and the generalized spherical-harmonic models—is reviewed. Both models were applied individually to neutron powder data from uniaxially pressed molybdite (MoO3) and calcite (CaCO3) powders in Rietveld analyses, as well as the as-received powders. The structural refinement results are compared to single-crystal structures. The results indicate that reasonable refinement of crystal structures can be obtained using either the March model or generalized spherical-harmonic description. However, the generalized spherical-harmonic description provided better Rietveld fits than the March model for the molybdite and calcite. Therefore, the generalized spherical-harmonic description is recommended for correction of preferred orientation in neutron diffraction analysis for both crystal structure refinement and phase composition analysis. Subsequently, the generalized spherical-harmonic description is extended to crystal structure refinement of annealed and the aged polycrystalline Ni-rich Ni50.7Ti49.30 shape memory alloys.

Keywords

preferred orientationtextureneutron powder diffractionMarch modelgeneralized spherical harmonicsmolybditecalciteTi50.70Ni49.30 shape memory alloy
Type
Technical Articles
Information
Powder Diffraction , Volume 24 , Issue 4 , December 2009 , pp. 315 - 326
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

Ahtee, M., Nurmela, M., Suortti, P., and Jarvinen, M. (1989). “Correction for preferred orientation in Rietveld refinement,” J. Appl. Crystallogr.JACGAR 22, 261–268.10.1107/S0021889889000725CrossRefGoogle Scholar
Bergmann, J., Monecke, T., and Kleeberg, R. (2001). “Alternative algorithm for the correction of preferred orientation in Rietveld analysis,” J. Appl. Crystallogr.JACGAR 34, 16–19.10.1107/S002188980001623XCrossRefGoogle Scholar
Bunge, H. J. (1982). Texture Analysis in Materials Science: Mathematical Methods (Butterworths-Heinemann, London).Google Scholar
Calvert, L. D., Sirianni, A. F., Gainsford, G. J., and Hubbard, C. R. (1983). “A comparison of methods for reducing preferred orientation,” Adv. X-Ray Anal.AXRAAA 26, 105–110.Google Scholar
Chen, T. (1991). Ph.D. thesis, University of California.Google Scholar
Dollase, W. A. (1986). “Correction of intensities for preferred orientation in powder diffractometry: Application of the March model,” J. Appl. Crystallogr.JACGAR 19, 267–272.10.1107/S0021889886089458CrossRefGoogle Scholar
Järvinen, M. (1993). “Application of symmetrized harmonics expansion to correction of the preferred orientation effect,” J. Appl. Crystallogr.JACGAR 26, 525–531.10.1107/S0021889893001219CrossRefGoogle Scholar
Kihlborg, L. (1963). “Least squares refinement of the crystal structure of molybdenum trioxide,” Ark. KemiARKEAD 21, 357–364.Google Scholar
Kudoh, Y., Tokonami, M., Miyazaki, S., and Otsuka, K. (1985). “Crystal structure of the martensite in Ti50.8Ni49.2 alloy analyzed by the single crystal X-ray diffraction method,” Acta Metall.AMETAR 33, 2049–2056.10.1016/0001-6160(85)90128-2CrossRefGoogle 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
Lutterotti, L., Chateigner, D., Ferrari, S., and Ricote, J. (2004). “Texture, residual stress and structural analysis of thin films using a combined X-ray analysis,” Thin Solid FilmsTHSFAP 450, 34–41.10.1016/j.tsf.2003.10.150CrossRefGoogle Scholar
March, A. (1932). “Mathematische theorie der regelung nach der korngestalt bei affiner deformation,” Z. Kristallogr.ZEKRDZ 81, 285–297.CrossRefGoogle Scholar
Maslen, E. N., Streltsov, V. A., Streltsova, N. R., and Ishizawa, N. (1995). “Electron density and optical anisotropy in rhombohedral carbonates. III. Synchrotron X-ray studies of CaCO3, MgCO3, and MnCO3,” Acta Crystallogr., Sect. B: Struct. Sci.ASBSDK 51, 929–939.10.1107/S0108768195006434CrossRefGoogle Scholar
Matthies, S., Lutterotti, L., and Wenk, H. -R. (1997). “Advances in texture analysis from diffraction spectra,” J. Appl. Crystallogr.JACGAR 30, 31–42.10.1107/S0021889896006851CrossRefGoogle Scholar
Matthies, S., Wenk, H. -R., and Vinel, G. W. (1988). “Some basic concepts of texture analysis and comparison of three methods to calculate orientation distributions from pole figures,” J. Appl. Crystallogr.JACGAR 21, 285–304.10.1107/S0021889888000275CrossRefGoogle Scholar
NIST Center for Neutron Research. 〈http://webster.ncnr.nist.gov/xtal/〉.Google Scholar
O’Connor, B. H., Li, D. Y., and Sitepu, H. (1991). “Strategies for preferred orientation corrections in X-ray powder diffraction using line intensity ratios,” Adv. X-Ray Anal.AXRAAA 34, 409–415.Google Scholar
O’Connor, B. H., Li, D. Y., and Sitepu, H. (1992). “Texture characterization in X-ray powder diffraction using the March formula,” Adv. X-Ray Anal.AXRAAA 35, 277–283.Google Scholar
Otsuka, K. and Ren, X. (2005). “Physical metallurgy of Ti-Ni-based shape memory alloys,” Prog. Mater. Sci.PRMSAQ 50, 511–678.10.1016/j.pmatsci.2004.10.001CrossRefGoogle Scholar
Owens, W. H. (1973). “Strain modification of angular density distributions,” TectonophysicsTCTOAM 16, 249–261.10.1016/0040-1951(73)90014-0CrossRefGoogle Scholar
Popa, N. C. (1992). “Texture in Rietveld refinement,” J. Appl. Crystallogr.JACGAR 25, 611–616.10.1107/S0021889892004795CrossRefGoogle Scholar
Popa, N. C. (1998). “The (h k l) dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement,” J. Appl. Crystallogr.JACGAR 31, 176–180.10.1107/S0021889897009795CrossRefGoogle 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
Schryver, D. and Potavop, P. L. (2002) “R-phase structure refinement using electron diffraction data,” Mater. Trans. 43, 774–779.CrossRefGoogle Scholar
Sitepu, H. (1991). MSc thesis, Curtin University of Technology.Google Scholar
Sitepu, H. (1998). Ph.D. thesis, Curtin University of Technology.Google Scholar
Sitepu, H. (2002). “Assessment of preferred orientation with neutron powder diffraction data,” J. Appl. Crystallogr.JACGAR 35, 274–277.10.1107/S0021889801021537CrossRefGoogle Scholar
Sitepu, H. (2003). “Use of synchrotron diffraction data for describing crystal structure and crystallographic phase analysis of R-phase NiTi shape memory alloy,” Textures Microstruct.TEMIDK 35, 185–195.10.1080/07303300310001634961CrossRefGoogle Scholar
Sitepu, H. (2007). “Structural refinement of neutron powder diffraction data of two-stage martensitic phase transformations in Ti50.75Ni47.75Fe1.50 shape memory alloy,” Powder Diffr.PODIE2 22, 209–318.10.1154/1.2754715CrossRefGoogle Scholar
Sitepu, H. (2008). “In situ structural and texture analyses of monoclinic phase for polycrystalline Ni-rich Ti49.86Ni50.14 alloy from neutron diffraction data,” Powder Diffr.PODIE2 23, 35–40.10.1154/1.2839141CrossRefGoogle Scholar
Sitepu, H., O’Connor, B. H., Benmarouane, A., Hansen, T., Ritter, C., and Brokmeier, H. -G. (2004). “Texture correction in neutron powder diffraction data of molybdite using the generalized spherical harmonic model,” Physica BPHYBE3 350, e573–e576.10.1016/j.physb.2004.03.154CrossRefGoogle Scholar
Sitepu, H., O’Connor, B. H., and Li, D. Y. (2004). “Deriving the bulk modulus of a single-phase powder from the March preferred orientation parameters,” Physica BPHYBE3 350, e577–e580.10.1016/j.physb.2004.03.155CrossRefGoogle Scholar
Sitepu, H., O’Connor, B. H., and Li, D. Y. (2005). “Comparative evaluation of the March and generalized spherical harmonic preferred orientation models using X-ray diffraction data for molybdite and calcite powders,” J. Appl. Crystallogr.JACGAR 38, 158–167.10.1107/S0021889804031231CrossRefGoogle Scholar
Sitepu, H., Prask, H. J., and Vaudin, M. D. (2001). “Texture characterization in X-ray and neutron powder diffraction data using the generalized spherical-harmonic,” Adv. X-Ray Anal.AXRAAA 44, 241–246.Google Scholar
Sitepu, H., Schmahl, W. W., Allafi, J. K., Eggeler, G., Dlouhy, A., Toebbens, D. M., and Tovar, M. (2002). “Neutron diffraction phase analysis during thermal cycling of a Ni-rich NiTi shape memory alloy using the Rietveld method,” Scr. Mater.SCMAF7 46, 543–548.10.1016/S1359-6462(02)00032-5CrossRefGoogle Scholar
Sitepu, H., Schmahl, W. W., and Stalick, J. K. (2002). “Correction of intensities for preferred orientation in neutron-diffraction data of NiTi shape-memory alloy using the generalized spherical-harmonic description,” Appl. Phys. A: Mater. Sci. Process.APAMFC 74, S1719–S1721.10.1007/s003390201840Google Scholar
Sitepu, H., Schmahl, W. W., and Von Dreele, R. B. (2002). “Use of the generalized spherical harmonic model for describing crystallographic texture in polycrystalline NiTi shape-memory alloy with time-of-flight neutron powder diffraction data,” Appl. Phys. A: Mater. Sci. Process.APAMFC 74, S1676–S1678.10.1007/s003390201934Google Scholar
Stephens, P. W. (1999). “Phenomenological model of anisotropic peak broadening in powder diffraction,” J. Appl. Crystallogr.JACGAR 32, 281–289.10.1107/S0021889898006001CrossRefGoogle Scholar
Tirry, W., Schryvers, D., Jorissen, K., and Lamoen, D. (2006). “Electron-diffraction structure refinement of Ni4Ti3 precipitates in Ni52Ti48,” Acta Crystallogr., Sect. B: Struct. Sci.ASBSDK 62, 966–971.10.1107/S0108768106036457CrossRefGoogle ScholarPubMed
Von Dreele, R. B. (1997). “Quantitative texture analysis by Rietveld refinement,” J. Appl. Crystallogr.JACGAR 30, 517–525.10.1107/S0021889897005918CrossRefGoogle Scholar
Von Dreele, R. B. and Vogel, S. C. (2009). Personal communication.10.1107/S0021889897005918Google Scholar
Wang, F. E., Buehler, W. J., and Pickart, S. J. (1965). “Crystal structure and a unique “martensitic” transition of TiNi,” J. Appl. Phys.JAPIAU 36, 3232–3239.10.1063/1.1702955CrossRefGoogle Scholar
Wenk, H. R. (1985). Preferred Orientation in Deformed Metals and Rocks, edited by Wenk, H. -R. (Academic Press, Orlando), pp. 11–47.CrossRefGoogle Scholar