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1.
2.
An intensity enhancement obtained from asymmetric diffraction with a fixed incident angle α has been studied. Parallel-beam synchrotron radiation with λ = 1.54 Å (Stanford Synchrotron Radiation Laboratory) and λ = 1.53 Å (Photon Factory) was used to collect powder diffraction patterns of Si, CeO2 (α = 5 and 10°) and monoclinic ZrO2 (α = 10°). The synchrotron-radiation data were analyzed using single-reflection profile fitting and whole-powder-pattern fitting techniques. The integrated intensities in the asymmetric diffraction were compared with those of symmetric diffraction obtained by the conventional θ–2θ scanning technique. An intensity, after correction for a limited height of counter aperture, was enhanced by factors of 1.8 (α = 5°) and 1.7 (α = 10°) at the maximum in asymmetric diffraction and its magnitudes agreed well with those calculated from theory. 相似文献
3.
A new procedure for quantitative phase analysis using the whole-powder-pattern decomposition method is proposed. The procedure consists of two steps. In the first, the whole powder patterns of single-component materials are decomposed separately. The refined parameters of integrated intensity, unit cell and profile shape for respective phases are stored in computer data files. In the second step, the whole powder pattern of a mixture sample is fitted, where the parameters refined in the previous step are used to calculate the profile intensity. The integrated intensity parameters are, however, not varied during the least-squares fitting, while the scale factors for the profile intensities of individual phases are adjusted instead. Weight fractions are obtained by solving simultaneous equations, coefficients of which include the scale factors and the mass-absorption coefficients calculated from chemical formulas of respective phases. The procedure can be applied to all mixture samples, including those containing an amorphous material, if single-component samples with known chemical compositions and their approximate unit-cell parameters are provided. The procedure has been tested by using two- to five-component samples, giving average deviations of 1 to 1.5%. Optimum refinement conditions are discussed in connection with the accuracy of the procedure. 相似文献
4.
Hideo Toraya 《Journal of Applied Crystallography》2016,49(5):1508-1516
A new method for the quantitative phase analysis of multi‐component polycrystalline materials using the X‐ray powder diffraction technique is proposed. A formula for calculating weight fractions of individual crystalline phases has been derived from the intensity formula for powder diffraction in Bragg–Brentano geometry. The integrated intensity of a diffraction line is proportional to the volume fraction of a relevant crystalline phase in an irradiated sample, and the volume fraction, when it is multiplied with the chemical formula weight, can be related to the weight fraction. The structure‐factor‐related quantity in the intensity formula, when it is summed in an adequate 2θ range, can be replaced with the sum of squared numbers of electrons belonging to composing atoms in the chemical formula. Unit‐cell volumes and the number of chemical formula units are all cancelled out in the formula. Therefore, the formula requires only single‐measurement integrated intensity datasets for the individual phases and their chemical compositions. No standard reference material, reference intensity ratio or crystal structure parameter is required. A new procedure for partitioning the intensities of unresolved overlapped diffraction lines has also been proposed. It is an iterative procedure which starts from derived weight fractions, converts the weight fractions to volume fractions by utilizing additional information on material densities, and then partitions the intensities in proportion to the volume fractions. Use of the Pawley pattern decomposition method provides more accurate intensity datasets than the individual profile fitting technique, and it expands the applicability of the present method to more complex powder diffraction patterns. Test results using weighed mixture samples showed that the accuracy, evaluated by the root‐mean‐square error, is comparable to that obtained by Rietveld quantitative phase analysis. 相似文献
5.
6.
H. Toraya 《Journal of Applied Crystallography》1999,32(4):704-715
Errors in the quantitative phase analysis (QPA) of α- and β-silicon nitrides (Si3N4) using the mean normalized intensity (MNI) method and the Rietveld method have been estimated by theory and experiments. A total error for a weight fraction (w) in a binary system can be expressed in the form E(w) = w(1 −w)S, where S is the quadratic sum of statistical and systematic errors. Random errors associated with counting statistics for integrated intensities in the MNI method are below 0.1∼0.2 wt% if the studied reflections have average peak heights of more than ∼1000 counts. Such errors will become approximately twice as large if peak-height intensities are used. The error associated with particle statistics in the studied samples was smaller than the counting-statistics error. Among various sources of systematic errors examined, incorrect choice of constrained/unconstrained full width at half-maximum (FWHM) parameters gave the largest error. The choice of the background function had little influence on the QPA, whereas the choice of the profile function had a large influence. Truncation errors in profile function calculations and the 2θ range of the observed data are below ±0.1 wt% when appropriate criteria are applied. Systematic errors in the measurement of peak-height intensity arise primarily from the overestimation of intensities of weak peaks that overlap the tails of strong peaks, as well as from line broadening of β-phase reflections in the studied samples. Errors caused by ignoring the difference in density between the two phases were negligibly small. Estimated errors of the methods followed the order: the MNI method using peak-height intensities < the MNI method using integrated intensities ≃ the Rietveld method. 相似文献
7.
A parallel-slit analyzer (PSA) has been developed for the purpose of lowering tails in diffraction profiles from powders and thin films. In the present work, four different materials were used for the foils: sintered and hot-pressed tungsten (W), cold-worked stainless steel (SUS), beryllium bronze (Cu98Be2) and chemically surface-processed beryllium bronze (CuOx). The PSAs were tested in a parallel-beam geometry using Cu Kα radiation collimated with a graded d-spacing parabolic multilayer mirror. The W and CuOx PSAs gave pseudo-Voigt profiles of ∼80% Gaussian in the direct-beam case. Textured and roughened surfaces of W and CuOx foils are considered effective for depressing total-reflection effects from the surfaces of the foil materials, and consequently for lowering the tails of diffraction peaks. 相似文献
8.
A computer program for the deconvolution of X-ray diffraction profiles has been written in Fortran IV. The deconvolution procedure is based on the minimization of the difference between the observed data function and a calculated function, where the latter is the convolution of the instrumental function and the true data function approximated with an analytical expression. The composite of two asymmetric Pearson type VII functions was assumed to represent the true data function, and the simplex method was used for the minimization. The stability of convergence and the influences of the truncation effect and the step width of intensity data on the deconvoluted profile were examined. The computer program can deconvolute the X-ray diffraction profile in moderate computation time without generating spurious oscillations due to the truncation effect. 相似文献
9.
H. Toraya 《Journal of Applied Crystallography》1985,18(5):351-358
Computer-synthesized reflection profiles were used to analyze the effects of truncation of the profile functions in X-ray whole-powder-pattern fitting. The effects of truncation on the deduced integrated intensity and background were first elucidated for singlet, doublet and triplet profiles. It was found that weak reflections suffer large truncation errors in their integrated intensities when they overlap with strong reflections. Truncation also influenced the results for both positional and thermal parameters in whole-pattern-fitting structure refinement through its effects on the deduced integrated intensities and background levels in the powder pattern. The intensity variations of individual reflections during structure refinement are, however, constrained by the structure. Truncation errors in positional parameters are larger in structures with lower symmetry and more freedom for variations of the atomic positions in the model being refined because more variation is possible in individual reflections, particularly the weak ones. It is shown that truncation errors in the refined parameters can be substantially suppressed by a simple strategem: extending the definition range of the profile function (DRPF) for the strong reflections to include > 99% of the profile area while leaving the DRPF for the other reflections at the smaller values customarily used. 相似文献
10.
Hideo Toraya 《Journal of Applied Crystallography》2019,52(3):520-531
The direct‐derivation (DD) method for quantitative phase analysis (QPA) can be used to derive weight fractions of individual phases in a mixture from the sums of observed intensities along with the chemical composition data [ Toraya (2016). J. Appl. Cryst. 49 , 1508–1516 ]. The whole‐powder‐pattern fitting (WPPF) technique can be used as one of the tools for deriving the observed intensities of individual phases. In WPPF, the observed powder pattern of a single‐phase sample after background (BG) subtraction can be used as the fitting function in combination with the fitting functions widely used in Pawley and Rietveld refinements. The direct fitting of the observed pattern is a very useful technique when the target component is a low‐crystallinity or amorphous material [ Toraya (2018). J. Appl. Cryst. 51 , 446–455 ]. Technical problems in utilizing the BG‐subtracted pattern are the uncertainty associated with the determination of BG height and the parameter interaction between the BG function (BGF) and the BG‐subtracted pattern in the least‐squares fit. In this study, a practical approach in which single‐phase observed patterns are used for the direct fitting without subtracting their BG intensities is proposed. In QPA, the contribution of BG intensities can be neutralized by converting the sum of BG‐included intensities into the sum of BG‐subtracted intensities by multiplying by a conversion factor. When the magnitudes of the conversion factors are almost identical for all components, they can be canceled out under the normalization condition in deriving weight fractions, and they are not required in QPA. The magnitude of the conversion factor for each component can be determined by one of two experimental techniques: using a single‐phase powder of the target component or a mixture containing the target component in a known weight ratio. The theoretical basis of the present procedure is given, and the procedure is experimentally verified. In this procedure, the interaction between the BGF and the BG‐included observed pattern is negligibly small. Least‐squares fitting with a few adjustable parameters is very fast and stable. Accurate QPA could be conducted, as indicated by the average deviation of 0.05% from weighed values in QPA of α‐Al2O3 + γ‐Al2O3 mixtures with five different weight ratios and 0.4% in QPA of an α‐SiO2 + SiO2 glass mixture 相似文献