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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 964-974 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A distribution of crystallite size reduces the width of a powder diffraction line profile, relative to that for a single crystallite, and lengthens its tails. It is shown that estimates of size from the integral breadth or Fourier methods differ from the arithmetic mean of the distribution by an amount which depends on its dispersion. It is also shown that the form of `size' line profiles for a unimodal distribution is generally not Lorentzian. A powder pattern can be simulated for a given distribution of sizes, if it is assumed that on average the crystallites have a regular shape, and this can then be compared with experimental data to give refined parameters defining the distribution. Unlike `traditional' methods of line-profile analysis, this entirely physical approach can be applied to powder patterns with severe overlap of reflections, as is demonstrated by using data for nanocrystalline ceria. The procedure is compared with alternative powder-pattern fitting methods, by using pseudo-Voigt and Pearson VII functions to model individual line profiles, and with transmission electron microscopy (TEM) data.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 184-189 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: MarqX is a computer program for the modelling of powder diffraction data. It can be used for an unconstrained profile fitting (pattern decomposition, PD) or constrained modelling of the whole powder pattern (Pawley method, PM), for single- as well as multiple-phase samples. The program output includes: lattice parameters or peak positions (for PM and PD, respectively), width and shape of the diffraction peak (in terms of half width at half-maximum and mixing parameter of a pseudo-Voigt function), corrected for the instrumental broadening component, intensity, peak area and profile asymmetry. In addition, errors on the goniometer zero and shift in sample position with respect to the goniometric axis can also be modelled, together with distance and relative intensity of the spectral components of the X-ray beam (e.g. Kα1 and Kα2). Specific output files are provided for line-profile analysis, including the Williamson–Hall plot and Warren–Averbach method.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 32 (1999), S. 36-50 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A set of general guidelines for structure refinement using the Rietveld (whole-profile) method has been formulated by the International Union of Crystallography Commission on Powder Diffraction. The practical rather than the theoretical aspects of each step in a typical Rietveld refinement are discussed with a view to guiding newcomers in the field. The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features specific to data from neutron (both constant-wavelength and time-of-flight) and synchrotron radiation sources are also addressed. The topics covered include (i) data collection, (ii) background contribution, (iii) peak-shape function, (iv) refinement of profile parameters, (v) Fourier analysis with powder diffraction data, (vi) refinement of structural parameters, (vii) use of geometric restraints, (viii) calculation of e.s.d.'s, (ix) interpretation of R values and (x) some common problems and possible solutions.
    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. 246-252 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new procedure for simultaneous refinement of structural and microstructural disorder parameters for polycrystalline materials is proposed. It is based on the Rietveld method combined with Fourier analysis for broadened peaks. Crystallite size and shape and r.m.s. microstrain are regarded as fitting parameters, replacing the well known formula of Caglioti, Paoletti & Ricci [Nucl. Instrum. Methods (1958), 3, 223–228] for the angular dependence of the peak width. In particular, from these microstructural disorder parameters, by inverting the Warren–Averbach procedure [Warren & Averbach (1950). J. Appl. Phys. 21, 595–599; (1952), 23, 1059] for a single peak, it is possible to obtain the parameters of the pseudo-Voigt (pV) functions employed to fit the experimental data. The anisotropy of the crystallite size and microstrain is also taken into account. The method has been tested on three materials with different degrees of crystallization: tetragonal ZrO2 (P42/nmc, a = 3.5961, c = 5.1770 Å, Vc = 66.95 Å3, Z = 2, Rwp = 0.077, M ∼100 Å, 〈ε2〉1/2 ∼ 3 × 10−3); tetragonal Zr0.82Ce0.18O2 (P42/nmc, a = 3.6419, c = 5.2440 Å, Vc = 69.556 Å3, Z = 2, Rwp = 0.0654, M ∼1000 Å, 〈ε2〉1/2 ∼8 × 10−4); α-Al2O3 (R{\bar 3}c, a = 4.7605, c = 12.9956 Å, Vc = 255.05 Å3, Z = 6, Rwp = 0.0684, M ∼ 1400 Å, 〈ε2〉1/2 ∼7 × 10−4).
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 25 (1992), S. 459-462 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A computer program has been written to introduce profile analysis into the Rietveld method. The devised algorithm simultaneously refines both structural and microstructural parameters, also accounting for anisotropy in crystallite size and microstrain. Instead of using phenomenological relations to describe the trend of profile width and shape as a function of diffraction angle, a model based on the Warren–Averbach approach has been developed that permits extraction of more information from data, also achieving faster convergence.
    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. 290-295 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Anisotropic strain broadening in X-ray or neutron powder diffraction can cause severe difficulties in whole powder-pattern fitting and Rietveld structure refinement. Several phenomenological models have been proposed to deal with this problem. These, however, lack physically sound bases. In the present work the dislocation-based model of strain anisotropy is applied in the Fourier formalism of profile fitting. It is shown that the anisotropic contrast of dislocations can fully account for strain anisotropy. A few physically sound parameters, namely the average dislocation density, the average coherent domain size, the dislocation arrangement parameter and the dislocation contrast factors, enable a perfect profile fitting to the powder pattern of a cubic Li–Mn spinel obtained at the Daresbury synchrotron storage ring.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 32 (1999), S. 1186-1189 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The structural evolution of LiMn2O4 spinel was followed from 320 K down to 10 K. The structural transformation, recently studied down to 230 K [Rodriguez-Carvajal, Rousse, Masquelier & Hervieu (1998). Phys. Rev. Lett. 81, 4660–4663], takes place near room temperature with a significant hysteresis: the high-temperature cubic phase transforms to a superstructure orthorhombic cell. The present study indicates that the nuclear structure is stable down to 10 K, while neutron diffraction patterns below 80 K show the rise of a magnetic ordering in the spinel phase. From Mn—O bond-length analysis of the MnO6 octahedra, a temperature-independent charge ordering in the structure can be deduced.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Surface & Coatings Technology 68-69 (1994), S. 106-112 
    ISSN: 0257-8972
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Surface & Coatings Technology 48 (1991), S. 131-135 
    ISSN: 0257-8972
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Surface & Coatings Technology 61 (1993), S. 52-59 
    ISSN: 0257-8972
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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