Journal of Applied Crystallography
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Study of colloidal nature of petroleum with an automated Bonse–Hart X-ray small-angle scattering unit
Journal of Applied Crystallography - Tập 11 Số 5 - Trang 615-619 - 1978
Derivation of infinite-slit-smeared small-angle scattering from porous surface and porous mass fractals Small-angle X-ray scattering (SAXS) is often used to study porous and aggregated fractal materials. Typically whenq is small or when large primary-beam intensities are required, the small-angle geometry employed introduces infinite-slit-height smearing into the experimental data. Herein, simple derivations for infinite-slit-height-smeared SAXS from porous surface and mass fractals are presented, including an approximation for aggregated mass fractals. The models allow rapid analysis of background-subtracted data without the need for deconvolution. An equation is derived that allows analysis of normalization from deconvolution routines applied to porous-fractal data. This model is tested using simulated and experimental SAXS data.
Journal of Applied Crystallography - Tập 32 Số 5 - Trang 956-962 - 1999
Rietveld refinement of site-occupancy parameters of Mg<sub>2−<i>x</i></sub>Mn<sub><i>x</i></sub>SiO<sub>4</sub>using a new weight function in least-squares fitting The crystal structures of olivine-type Mg_{2-x}Mnx 4 (x = 0, 1, 1.4 and 2) were refined using high-resolution synchrotron radiation data and the Rietveld method, adopting the new weight function with the form 1/Y_o^e\;(e\simeq 2) (Y o J. Appl. Cryst. 31 , 333–343]. Positional parameters were accurately determined by optimizinge in 1/Y_o^e. Derived structures were in accordance with observations on olivine structures, having a constant tetrahedral Si–O distance and octahedral metal–oxygen distances which increase linearly on substitution of octahedral atoms with those having larger atomic radii. Site-occupancy parameters of octahedral atoms were refined under various refinement conditions and could be determined within ±1.2% under the constraint of chemical composition. Deviations ofx from assumed chemical compositions, when the site-occupancy parameters were refined without the constraint, were 1.0–3.5% using the new weight function; they are comparable with values obtained in single-crystal studies on Mg–Fe olivine (0.5–2.7%). The use of atomic scattering factors for fully ionized atoms gave better site-occupancy parameters, by 0.1–2.5%, than those for neutral atoms in the present analysis.
Journal of Applied Crystallography - Tập 32 Số 1 - Trang 51-59 - 1999
Estimation of statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern decomposition method Formulae for estimating statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern decomposition method have been derived. The relative magnitude of statistical uncertainty for a derived weight fraction of a component in a mixture is given by σ(W m W m W m 1/2 F (D \textstyle\sum_{i = 1}^NY oi −1/2 , whereW m m th component,F is the goodness-of-fit index,D (≤1) is a factor depending on the degree of peak overlap, and ∑Y oi Y oi Y oi T . Therefore, σ(W m W m T )1/2 . Extension of the 2θ range for whole-powder-pattern fitting towards the high-angle region is not effective for improving the precision of the derived weight fractions if the profile intensities in that region are weak. The formulae provide guidelines for optimizing experimental parameters in order to obtain a required precision.
Journal of Applied Crystallography - Tập 33 Số 6 - Trang 1324-1328 - 2000
Preparation and microstructure characterization of ball-milled ZrO<sub>2</sub>powder by the Rietveld method: monoclinic to cubic phase transformation without any additive The phase transformation kinetics of high-energy ball-milled monoclinic ZrO2 have been studied in detail by Rietveld powder structure refinement analysis. In the present study, no stabilizing compound was required to obtain the cubic phase. The fine-grain powder was milled in a planetary ball mill for up to several hours at different BPMRs (ball to powder mass ratios): 10:1, 20:1, 35:1 and 40:1. During the process of ball milling, the monoclinic phase is gradually transformed to the cubic phase. The relative phase abundances of the respective phases, the particle sizes, the r.m.s. strains, the lattice parameter changes,etc. , have been estimated from Rietveld analysis of X-ray powder diffraction data. It has been found that a higher BPMR exerts more influence on rapid phase transformation. In them - toc -ZrO2 phase transformation, no formation of an intermediate tetragonal ZrO2 phase has been found. The small change in the lattice volume ofm -ZrO2 , which is very close to the lattice volume ofc -ZrO2 , caused by ball milling may be attributed to this phase change. The formation of thec phase is noticed, in general, after just 1 h of ball milling, and the particle size of them phase is reduced to a large extent at the first stage of milling and remains almost unchanged with increasing milling time. However, the particle size of thec phase increases with increasing milling time for the samples milled with higher BPMRs (35:1 and 40:1), suggesting that quenching caused by a high impact energy followed by an annealing effect may play a vital role, which is further manifested in the agglomeration of small particles.
Journal of Applied Crystallography - Tập 35 Số 5 - Trang 517-525 - 2002
A profile-fitting procedure for analysis of broadened X-ray diffraction peaks. I. Methodology
Journal of Applied Crystallography - Tập 21 Số 5 - Trang 536-542 - 1988
Profile shape functions in Rietveld refinements
Journal of Applied Crystallography - Tập 15 Số 4 - Trang 430-438 - 1982
Weighting Scheme for the Minimization Function in Rietveld Refinement
Journal of Applied Crystallography - Tập 31 Số 3 - Trang 333-343 - 1998
Phase transformation kinetic study and microstructure characterization of ball-milled<i>m</i>-ZrO<sub>2</sub>–10 mol%<i>a</i>-TiO<sub>2</sub>by Rietveld method High-energy ball milling of a monoclinic ZrO2 –10 mol% anatase TiO2 mixture results in the formation of a nanocrystalline cubic ZrO2 polymorphic phase with equimolar fraction of the starting materials. The cubic phase is presumed to have formed from them -ZrO2 solid solution based on the (001) plane of them -ZrO2 phase. In the course of milling, the most dense (111) plane of the cubic lattice became parallel to the most dense (\bar{1}11) plane of the monoclinic lattice due to an orientation effect. Annealing of a 12 h milled sample at 773, 873 and 973 K for 1 h results in almost complete transformation of them -ZrO2 to thec -ZrO2 phase. At 1273 K annealing temperature (1 h), the nanocrystalline sample decomposed into individual starting phases. This suggests that the cubic phase is a metastable one and its stability depends on particle size as well as the working temperature. Formation of the cubic phase at such a low temperature using anatase TiO2 as a phase stabilizer has not been reported previously. The microstructures of the unmilled, all the ball-milled and the annealed samples have been characterized by employing Rietveld's X-ray powder structure refinement methodology. The particle size, root mean square (r.m.s.) lattice strain, lattice parameters, molar fraction,etc ., of individual phases have been estimated from Rietveld analysis and are utilized to interpret the results.
Journal of Applied Crystallography - Tập 36 Số 2 - Trang 260-268 - 2003
<i>LSI</i>- a computer program for simultaneous refinement of material structure and microstructure
Journal of Applied Crystallography - Tập 25 Số 3 - Trang 459-462 - 1992
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