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  • 1970-1974  (4)
Materialart
Erscheinungszeitraum
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  • 1
    Digitale Medien
    Digitale Medien
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 4 (1971), S. 37-43 
    ISSN: 1600-5767
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Geologie und Paläontologie , Physik
    Notizen: The effects of axial and equatorial divergences, of beam penetration, and of misalignment on the integrated Bragg reflections as well as on diffuse scattering and specimen fluorescence are calculated for the reflection and transmission methods of powder diffractometry. The formulation encompasses both the &thgr;0–2&thgr; case with stationary specimen and (wide) receiving slit and the usual &thgr;–2&thgr; scan with a narrow receiving slit. To a good approximation, the effects of the various aberrations may be separated and simple formulas which allow the corrections to be calculated to an accuracy of 0.1% are presented. Although almost all practical cases are included, the formulation is illustrated in detail for the important case of Bragg scattering in reflection geometry. The largest effects are in the low angle region where, for the &thgr;–2&thgr; scan, all the aberrations increase the observed intensity. For a realistic case of a low density sample near 20° 2&thgr;, the total correction may be well above 5%, but the results depend strongly on absorption coefficient and on scattering angle. The effects of the most serious aberrations are considerably reduced in the &thgr;0–2&thgr; case; for the above example the total is less than 2%. In the transmission method, within the useful range, the only significant aberrations arise from the deviation of the specimen center from the diffractometer axis and from axial divergences. In the case of diffuse scattering or specimen fluorescence, in either transmission or reflection geometries, the intensity is affected by the equatorial aberrations even more than in the Bragg case, but the effects of axial aberrations are usually negligible.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 613-622 
    ISSN: 1600-5724
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: The thermal diffuse scattering (TDS) contribution to X-ray Bragg peaks is discussed in terms of its two experimental components, the included and the background parts. The discussion is primarily directed toward situations where detailed elastic constant information and a large computer are not available. Graphs are displayed which, in the spherical average approximation, allow an accurate assessment of the influence of all the experimental variables on the TDS contribution. It is shown that, even in the general case where spherical averaging is a poor approximation, the included TDS varies linearly with length of scan for small scans. A technique for determining the constant of proportionality is suggested. Thus the included TDS may be evaluated even though the elastic constants are not known.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    facet.materialart.
    Unbekannt
    Syracuse, N.Y. : Periodicals Archive Online (PAO)
    Symposium. 25:2 (1971:Summer) 123 
    ISSN: 0039-7709
    Thema: Allgemeine und vergleichende Sprach- und Literaturwissenschaft. Indogermanistik. Außereuropäische Sprachen und Literaturen
    Notizen: MYTH
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 22 (1974), S. 325-332 
    ISSN: 0945-3245
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A direct error analysis is given for orthogonal factorization methods for calculating the least squares solution of an overdetermined system of linear equations. The direct method has the interesting advantage in that it permits the separation of errors occurring in the transformation and back-substitution phases of solution. This shows the partial elimination of potentially significant terms occurring in different stages of the algorithm. Presumably it is prudent to minimize the error at each stage of the algorithm, so it is significant that numerical evidence shows column pivoting can reduce the magnitude of these terms. This is offered as an explanation for the common observation that column pivoting is beneficial in least squares calculations. We also summarize the corresponding error analysis for the calculation of the minimum norm solution of an underdetermined system using orthogonal transformations.
    Materialart: Digitale Medien
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