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  • Articles: DFG German National Licenses  (5)
  • 1985-1989  (5)
Source
  • Articles: DFG German National Licenses  (5)
Material
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Parameterizations of scattering intensities and values of the angularities and of the interphase surfaces for three-component amorphous samples (1985)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 18 (1985), S. 219-229 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Different functional parameterizations of the radiation intensity scattered by an N-component amorphous sample are considered. Each parameterization is such that (i) it depends only on the areas and on the angularities of the samples' interphase surfaces, (ii) it fulfils all the known physical constraints and (iii) it yields a rather simple algebraic expression both for the correlation function and for the scattered intensity. The parameterizations have been used for analysing the scattering data relevant to some three-component catalysts. Provided the volume fraction of the metal is not very small, the best fit yields satisfactory results only for some of the considered parameterizations. In this way, the determination of both the areas and the angularities of catalysts appears possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889885010184
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Oscillatory deviations from Porod's law in the intensities scattered by some glasses (1986)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 19 (1986), S. 195-197 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The oscillatory deviations with respect to the Porod asymptote, observed in the small-angle X-ray intensities scattered by some selenium ruby glasses, are explained in terms of a finite discontinuity of the second-order derivative of the correlation function. The best fit of the intensity allows the value of the discontinuity to be determined as well as the point at which it occurs. The physical implications of these results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889886089677
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the Porod law (1988)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 21 (1988), S. 117-128 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The Porod law states that i(h), the intensity of X-radiation scattered by an ideal multiphase noncrystalline system, for `large' momentum transfer values (≡ h) approaches lh−4 and that l is linearly related to the interphase surface areas. A more general expression is obtained which relates the value of the correlation-function derivative at the origin to the integral of the discontinuity of the electron density fluctuation along the discontinuity surface. Debye's assumption, by which the continuous electron density of the sample is approximated by a discrete-valued one, is critically discussed. The validity of the approximation results in the presence of a Porod plateau [h4i(h) = constant]. The momentum transfer range where the plateau is observed is related to the scale of lengths where the sharp-boundary idealization remains essentially unchanged. It is argued that the scattered intensity can show more than one Porod plateau and some examples of correlation functions with this behaviour are reported. The problem of the background subtraction is discussed and the corresponding coefficients are related to the electron densities relevant to the real and to the associated sharp-boundary sample.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889887010409
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Deviations from the Porod law due to parallel equidistant interfaces (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 560-568 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is proved that the second-order derivative of the correlation function, relevant to an amorphous N-component sample, can have a first-order discontinuity at a point r0 (≠ 0) only when the interfaces have the following geometrical property: there exists a finite-area subset of one phase boundary, say Si, such that any point P1 of this is far away, r0, from a point P2, belonging to another boundary, say Sj, and moreover the segment P1P2 is orthogonal both to Si and to Sj. The explicit integral expression of the discontinuity is obtained. The relevance of this result to the analysis of scattered intensities showing a systematic deviation from the Porod-Debye law is pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385001222
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Particle shapes and oscillatory deviations from the Porod law: the hyperbolic contact point case (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 86-99 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The leading term in the asymptotic expansion of the isotropic component of the X-ray intensity scattered by a homogeneous right circular cylindrical particle (of height H and diameter D) can be written as: {\cal ch-4[ST-2SB cos (hH)- SL sin (hD)]. Here SL, SB and ST denote respectively the lateral, the base and the total surface area of the cylinder, while {\cal c is a normalization factor. From this expression one is led to conjecture that the oscillatory deviations from the Porod law, originated by the two interface subsets which have the same normal and are separated by δ, are proportional to cos (hδ) or to sin (hδ) depending on whether the tangency points between one of the interphase subsets and the spheres of radius δ centred on the opposite subset are elliptical or hyperbolic respectively. It is proved that the conjecture is true and general expressions for the coefficients in front of the two oscillatory functions are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009286
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    Paper (German National Licenses)
    Fulltext
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