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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 1311-1316 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The formula of the pseudo-Voigt function expressed by a weighted sum of Gaussian and Lorentzian functions is extended by adding two other types of peak functions in order to improve the accuracy when approximating the Voigt profile. The full width at half-maximum (FWHM) values and mixing parameters of the Gaussian, the Lorentzian and the other two component functions in the extended formula can be approximated by polynomials of a parameter ρ = ΓL/(ΓG + ΓL), where ΓG and ΓL are the FWHM values of the deconvoluted Gaussian and Lorentzian functions, respectively. The maximum deviation of the extended pseudo-Voigt function from the Voigt profile is within 0.12% relative to the peak height when sixth-order polynomial expansions are used. The systematic errors of the integrated intensity ΓG and ΓL, estimated by fitting the extended formula to Voigt profiles, are typically less than 1/10 of the errors arising from the application of the original formula of the pseudo-Voigt approximation proposed by Thompson et al. [J. Appl. Cryst. (1987), 20, 79–83], while the time required for computation of the extended formula is only about 2.5 relative to the computation time required for the original formula.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 16 (1983), S. 653-657 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 23 (1990), S. 526-534 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Following the profile decomposition of CeO2 X-ray powder data into individual structure factors, the maximum-entropy method (MEM) has been used to obtain an electron-density-distribution map. In the profile decomposition process, it is impossible to avoid the problems of overlapping peaks which have the same magnitude of reciprocal vectors, such as d*(511) and d*(333), for a cubic crystal, or very severely overlapping reflections. The formalism to treat such overlapping reflections in the MEM analysis is to introduce combined structure factors. The maximum value of the scattering vector, 4π(sinθ)/λ, which was used in the present analysis is small (about 7.8 Å−1) but the resulting electron-density-distribution map is of a high quality and much superior to the conventional map. As a consequence, the ionic charge of Ce and O ions can be obtained with reasonable accuracy from the MEM density map. Furthermore, the map reveals the existence of electrons around the supposedly vacant site surrounded by eight O atoms, which is probably related to the high ionic conductivity of this substance.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 23 (1990), S. 282-285 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A straightforward method for the systematic peak-shift correction using the standard reference material is proposed for the least-squares determination of unit-cell parameters. It requires no pre-determined angle-calibration curve, and the peak-shift correction can be applied simultaneously during the least squares. The procedure, programmed with Fortran 77 statements, has been tested with powder diffractometer data of an α-SiO2 + Si mixture. Advantages of the procedure are: (i) all reflection data from both sample and standard reference material contribute to determining the angle-dependent calibration curve, and (ii) one reflection from the standard reference material suffices for the correction of systematic errors.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 29 (1996), S. 37-41 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A series of oxides of the composition Sr2LnTaCu2O8, Ln = Nd, Sm, Eu, Gd has been prepared and characterized by X-ray powder diffraction. Samples are tetragonal, space group P4/mmm and isostructural with a perovskite-like phase Ba2LaTaCu2O8. The unit-cell parameters have been determined using Mo or Si as internal standard. The structure of Sr2SmTaCu2O8 has been refined by the Rietveld method. X-ray diffraction patterns of the samples and the crystal structure of Sr2SmTaCu2O8 showed ordering of Ta and Cu ions: the octahedrally coordinated Ta ion is on the Cu(1) site, while Cu ions remain on the Cu(2) sites of the Ba2YCu3O7−δ-type structure. (Powder Diffraction File Nos. 46–1490 for Sr/NdTaCu2O8, 46-1489 for Sr2SmTaCu2O8, 46-1488 for Sr2EuTaCu2O8 and 46-1487 for Sr2CdTaCu2O8.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 32 (1999), S. 716-729 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Two round robins (RRs) of the quantitative phase analysis (QPA) of silicon nitrides (Si3N4) using the mean normalized intensity (MNI) method and the Rietveld method were conducted as one of the projects for establishing standard methods of characterizing advanced ceramic materials. Accuracy and precision of three techniques, namely the MNI method using peak-height intensity (MNI+P), the MNI method using integrated intensity (MNI+I) and the Rietveld method (R), were tested. Precision of the methods was found to follow the order R 〈 MNI+I 〈 MNI+P in the first RR and MNI+I 〈 R 〈 MNI+P in the second RR. Resulting accuracy of the methods was ranked R ∼ MNI+P 〈 MNI+I in the first RR and MNI+P 〈 R ∼ MNI+I in the second. The MNI+P method, which relies upon a simple and routine procedure for measuring peak-height intensities, gave the best precision in both RRs. Both the accuracy and the precision of the Rietveld method were the worst among the three techniques in the first RR. They were, however, significantly improved in the second RR. Although the precision of the MNI+I method was the worst in the second RR, it was better than that in the first, and the accuracy was the best in both the first and the second RR. The degree of improvement from the first to the second RR, in both precision and accuracy, was MNI+P 〈 MNI+I 〈 R, coinciding with the ease of these three techniques in reverse order. This result is largely due to (i) a new protocol for experimental and analytical parameters and (ii) improved skill of the participants in data analysis in the second RR. Magnitudes and signs of the observed errors could be interpreted through results of the theoretical studies.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 95-102 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The crystal structure of α-silicon nitride (Si3N4) was refined by the Rietveld method using synchrotron radiation powder diffraction data (wavelength = 1.2 Å) collected at station BL-4B2 in the Photon Factory. A refinement procedure that adopted a new weight function, w = 1/Y_o^e (Yo is the observed profile intensity and e ∼ 2), for the least-squares fitting [Toraya (1998). J. Appl. Cryst. 31, 333–343] was studied. The most reasonable structural parameters were obtained with e = 1.7. Crystal data of α-Si3N4: trigonal, P31c, a = 7.75193 (3), c = 5.61949 (4) Å, V = 292.447 (3) Å3, Z = 4; Rp = 5.08, Rwp = 6.50, RB = 3.36, RF = 2.26%. The following five factors are considered equally important for deriving accurate structural parameters from powder diffraction data: (i) sufficiently large sin θ/λ range of 〉0.8 Å−1; (ii) adequate counting statistics; (iii) correct profile model; (iv) proper weighting on observations to give a uniform distribution of the mean weighted squared residuals; (v) high-angular-resolution powder diffraction data.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 1317-1323 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Line shapes of the Kα1–Kα2 doublet beam reflected from a parabolic graded multilayer (PGM) were analysed by ray tracing and rocking-curve measurements using an Si(400) flat single crystal. The integrated intensity and the intensity ratio of Kα2 to Kα1 of the reflected beam vary with the angle of incidence at the PGM. The rates of these variations are considered to increase with increasing spectral resolution of the PGM. The Kα1 and Kα2 beams are reflected from the PGM in slightly different directions. Therefore, the angular separation between the Kα1 and Kα2 peaks of the observed diffraction profile of a sample becomes smaller than that calculated from the two wavelengths for Kα1 and Kα2 when the PGM and the sample are arranged in the (+−) setting, and vice versa when they are in the (++) setting. The magnitude of the shift of the angular separation is close to the experimental uncertainty in the determination of the peak positions when the PGM consists of W/Si bilayers, whereas it is estimated to be three times as large when a PGM of high spectral resolution is used.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 18 (1985), S. 351-358 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
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