Preferred crystallographic orientation, i.e. texture in crystalline materials powder diffraction data, can cause serious systematic errors in phase composition analysis and also in crystal structure determination. The March model [Dollase (1986). J. Appl. Cryst. 19, 267-272] has been used widely in Rietveld refinement for correcting powder diffraction intensities with respect to the effects of preferred orientation. In the present study, a comparative evaluation of the March model and the generalized spherical harmonic [Von Dreele (1997). J. Appl. Cryst. 30, 517-525] description for preferred orientation was performed with X-ray powder diffraction data for molybdite (MoO 3 ) and calcite (CaCO 3 ) powders uniaxially pressed at five different pressures. Additional molybdite and calcite powders, to which 50% by weight silica gel had been added, were prepared to extend the range of preferred orientations considered. The patterns were analyzed initially assuming random orientation of the crystallites and subsequently the March model was used to correct the preferred orientation. The refinement results were compared with parallel refinements conducted with the generalized spherical harmonic [Sitepu (2002). J. Appl. Cryst. 35,[274][275][276][277]. The results obtained show that the generalized spherical harmonic description generally provided superior figures-of-merit compared with the March model results. ‡ Present address:

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 ͑MoO 3 ͒ and calcite ͑CaCO 3 ͒ 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 Ni 50.7 Ti 49.30 shape memory alloys. © 2009 International Centre for Diffraction Data.

Crystallographic texture (or preferred orientation) characterization of uniaxially pressed molybdite (MoO 3 ) and calcite (CaCO 3 ) powders has been carried out using the BT-1 high-resolution ®xed-wavelength 32-detector powder diffractometer at the NIST Center for Neutron Research. Initially, each pattern was analysed assuming a random orientation of the crystallites. Subsequently, the March model and the generalized spherical harmonic description were used independently to extract the texture description directly from a re®nement with neutron diffraction data of molybdite and calcite. The results indicate that the generalized spherical harmonic description provided a better Rietveld ®t than the March model for the molybdite sample that had been subjected to the highest pressure.

2002b). Texture and quantitative phase analysis of aged Ni-rich NiTi using X-ray and neutron diffractions. Materials Science Forum, 394-395, 237-240.) showed that Rietveld refinement with generalized spherical harmonic (GSH) description for neutron powder diffraction (ND) data of the aged (673 K, 20 h) Ni-rich NiTi shape memory alloy (Sitepu H. (2002). Assessment of preferred orientation with neutron powder diffraction data. J. Appl. Cryst, 35, 274-277); of nominal composition 50.7 at.% Ni at 294 K consists of four phases: precipitate (Ni 4 Ti 3 ), R-phase, monoclinic (B19 0 ) and some residual cubic (B2). Therefore, they concluded that the differential scanning calorimetry (DSC) first peak, on cooling, (321 K) is not due to the formation of the R-phase alone. The second, lower DSC peak (271 K) is due to the transformation of R-phase and residual B2 phase to B19 0 phase. The structural refinement of R-phase problem, which was neglected in the previous study, was undertaken with great care in this study. The objective of the present article is to use the third generation synchrotron X-ray source at the European Synchrotron Research Facility (ESRF) in Grenoble, which make available X-ray beams of higher energy and much higher intensity than laboratory X-ray sources, for describing crystal structure of the R-phase in 50.75 at.% Ti-47.75 at.% Ni-1.50 at.% Fe ternary alloy. The synchrotron diffraction data of R-phase were analyzed using the Rietveld refinement with GSH description. The results showed that no significant improvement in fit is found when the inversion center is removed from the P3 model, suggesting that the space group is indeed P3 and not P3.