Rietveld analysis of powder neutron diffraction data displaying anisotropic crystallite size broadening

Abstract

48SHORT COMMUNICATIONS the direction of the streaking caused by the thinness of the precipitates. Except for the few cases indicated in our table of observed and calculated structure factors (Auld & Cousland, 1974), the reflections were sufficiently well separated to allow true integrated intensities to be measured for each reflection. For the above reasons, our recorded M' reflections were not chains of diffuse reflections and the comparison of observed intensities with those calculated by the usual structure factor method is appropriate.(ii) As to the second objection, the chief disagreement between R6gnier et al. and ourselves concerns the intensities of the 007, 113, 034 and 125 reflections of M'. R6gnier et al. did not observe any of these reflections whereas we observed all four; furthermore, the intensities of these four reflections, calculated for our proposed M' structure, were reasonably high. In the discussion that follows, the positions of M' and M reflections are given by coordinates referred to the (100)* axes of the aluminium reciprocal lattice, taking d*00Ai as one unit. The 007 M, reflection is found at positions of the type 1.17, 1.17, 1.17. As stated in our original Table 2, it was impossible to measure its intensity reliably, as it lies close to the 004M reflection at 1"09, 1.09, 1.09 and also to the very strong l llA~ reflection, Fig. 1. (Note that exposure times of about 100 h, used to record reflections from the M' phase, cause each aluminium reflection to be highly overexposed and so visible diffuse scattering extends a considerable distance from each node of the aluminium reciprocal lattice.) However, although the intensities of 007M, and of 004M could not be reliably measured by the microdensitometer, both were definitely detectable by eye, with 007M, fading and 004M strengthening as aging progressed. Similarly, the 113M, reflections occur at positions of the type 1-17, Again, these 125~r reflections were present. The intensity data for precipitates of this size and morphology are necessarily very poor compared with those required for precise crystal-structure determinations but, bearing this in mind, a fairly satisfactory fit to the data was found for the structure proposed. Hence we contend that the proposed M' structure is basically correct. S. McK. (1974). J. Aust. Inst. Met. 19, 194-199. GRAF, R. (1957 1.17, 0.83, also fairly close to 111AI and to 112M at 1.19, 1-19, 0.73, Fig. l; these l l3M, reflections are nevertheless sufficiently AbstractIn order to accommodate anisotropic crystallite-size broadening effects in the Rietveld refinement of constantwavelength powder neutron diffraction data, a modified function for the peak full width at half maximum has been evaluated for polycrystalline Ni(OD)2. The function resulted in significantly better agreement between observed and calculated profiles (the weighted residual R,,.p decreased from 14.1 to 8.5%), and structural standard deviations were reduced by an average of 43%.

Data Collection Strategies for Constant Wavelength Rietveld Analysis

“…The deleterious effects of all of these factors can be minimized either by careful alignment of the instrument or by application of appropriate analytical or numerical functions during Rietveld refinement (Wilson, 1973;Cooper & Glasspool, 1976;Howard, 1982;Thompson & Wood, 1983;Greaves, 1985;Retief, ad., 1985). Unfortunately, attention is rarely given to aberrations of this sort in data obtained from medium-and low-resolution instruments since their effect is usually lost in the relatively broad instrumental diffraction peak profiles.…”

Refinement of the structure of deuterated nickel hydroxide, Ni(OD)2, by powder neutron diffraction and evidence for structural disorder in samples with high surface area

“…Maximum correlations between structural parameters Consequently the refinement was unsatisfactory (weighted profile index Rwp =0.141 compared with the statistically expected value Rexp = 0"025), and a modified function for FWHM was introduced which has been described elsewhere (Greaves, 1985). Much better agreement was obtained (Rwp = 0"085) and further improvements resulted from the use of a pseudo-Voigt peak-shape function (see, for example, Young & Wiles, 1982 ) rather than a pure Gaussian.…”

Size-broadening anisotropy in whole powder pattern fitting. Application to zinc oxide and interpretation of the apparent crystallites in terms of physical models

“…Two models of size-broadening anisotropy are currently used in Rietveld programs. A model of infinite plates and needles, originally proposed by Greaves (1985), is implemented in GSAS (Larson & Von Dreele, 1986). The crystal rotation axis is normal to the plate or parallel to the needle axis.…”