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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 30 (1974), S. 607-616 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: 14 of the 17 sets of structure factor data for D( + )-tartaric acid collected on the initiative of the Commission on Crystallographic Apparatus of the IUCr have been compared without making explicit assumptions concerning either the nature of the interaction of X-rays with a crystal or of the statistical distributions of the measurement errors. It is shown that the greater part of the differences between the 14 sets of structure factors derived from the different single crystals depends systematically on the intensity and wavelength in a manner strongly suggesting extinction as the cause. These differences are apparent even for medium intensities and the largest structure factors may be underestimated by as much as a factor of two. When the major systematic intensity-dependent differences are removed the statistics of the residuals show an excess of both large and small values as compared with a normal (Gaussian) distribution. The effects of different weighting schemes on various R values are considered and it is shown that while the ordinary R value is fairly robust, weighted R values with weights that correspond to assuming σ(F) ∝ F or σ(F) = const, grossly overemphasize respectively either the low or the high intensities.
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 4 (1971), S. 402-403 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 81-85 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The error in the temperature factor arising from the use of anharmonic perturbation theory is investigated for a one-dimensional one-particle potential by comparison with an exact evaluation of the Fourier transform of the Boltzmann probability density. Results are presented for a range of values of cubic and quartic coefficients for temperature factors derived from moment or cumulant expansions about the harmonic probability density function. It is found that either expansion provides an adequate approximation to the anharmonic temperature factor for moderately small anharmonicity but that both expansions become increasingly Inadequate as the anharmonicity gets larger.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 304-304 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The parts of Fig. 1 in Mackenzie & Mair [Acta Cryst. (1985). A41, 81-85] have been wrongly labelled, so that (a) to (d) and (e) to (h) run vertically. The correct labelling has parts (a) and (b) on the top line, (c) and (d) on the second line, (e) and (f) on the third line and (g) and (h) at the bottom. References to Scheringer (1984a, b) should read Scheringer (1985a, b).
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 10 (1957), S. 61-62 
    ISSN: 0001-5520
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 15 (1962), S. 979-982 
    ISSN: 0001-5520
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 24 (1968), S. 628-639 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The seven sets of X-ray intensity data for CaF2 obtained in the ACA project are compared. The data are graded so as to reduce statistical errors in mean values, and deviations from these means are plotted against angle of reflection and measured intensity. The plots reveal systematic errors depending on both of these variables; this dependence was partly obscured in the ACA analysis. A rank correlation method is used both to confirm the significance of this systematic dependence and also to search for any dominant dependence on unsuspected and unspecified variables; none is found. The data for the important reflections 111, 002, 022 are grossly discordant and low-angle reflections must receive prime attention in any future development of experimental techniques. Further guidance is provided by the results of the present analysis. The deviations for the other reflections are everywhere large for the device using a fixed crystal and fixed detector, but while they are large at the lower angles for that using an ω-scan without monochromator, they are reasonably small for the other ω-scan and ω/2θ-scan devices. It is suggested that particular systematic errors are associated with incorrect calibration of attenuator factors, with change of filters and with counting statistics.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 29 (1973), S. 201-204 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For a given total counting time in a diffractometer experiment the variance (or square of the standard deviation) of the estimated integrated intensity of a reflexion is least when the counting time at each point is proportional to the square root of the intensity at that point. If the ratio of the peak to background intensity does not exceed 10 and data points are equidistant, a constant counting time at each point gives a variance not more than 1.4 times the minimum possible value. For greater peak/background ratios a further improvement in variance is achieved. The effect of subtracting off the background intensity is equivalent to regarding the line as extended, at background intensity, over a further range equal to the range over which measurements are made. Full advantage of the optimum choice can be obtained by computer control of the diffractometer, and then less time is required for collection of data of the same accuracy.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 231-236 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Rather than an uncritical comparison of experimental and theoretical values, the various sets of structure-factor values of copper metal derived from experimental diffraction procedures are mutally compared as also are the various sets of theoretical values derived from band-structure calculations. This approach reveals the presence of outlier sets in each group and allows recognition of their condition before any attempt is made to intercompare the groups. Within the experimental group, the γ-ray values do not appear to sustain the absolute status originally claimed for them. Within the theoretical group, an inadequacy in defining the core contribution is indicated. The latter conclusion suggests that it is an inappropriate operation to make direct comparison between diffraction-sourced experimental values of structure factors and theoretical values from band-structure calculations. Instead, the latter should be used on a complementary basis with the full (sin θ)/λ range of experimental values to establish the best core contribution. The minor valence-bond contribution to scattering, which is largely restricted to the low (sin θ)/λ region, is most sensitively defined by reference to band-structure prediction of photoemission spectral distribution. Attention is drawn to the possible significance of the form-factor curve versus (sin θ)/λ being dependent on the unit-cell dimension.
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 45-50 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method of deriving an extinction-free estimate of an X-ray structure-factor value is outlined. The method is based on the availability of experimental estimates of the level of extinction from the mosaic distribution of the crystal. A plot of the diffracted intensity or its corresponding structure factor (uncorrected or nominally corrected for extinction) against the percentage extinction effect yields an extinction-free value in the limit on extrapolation to zero level. Such a procedure can also reveal any inadequacy in the correction procedures by lack of internal consistency. An illustration of the potential of this procedure is given using the set of 11 experimental values of f for the 220 reflexion of Cu derived by Schneider [Acta Cryst. (1977), A33, 235- 243] from γ-ray diffractometry. Use of the experimental estimates of the level of extinction together with the nominally corrected f data indicates the presence of systematic residual error. Linear extrapolation of these f values to zero extinction yields an estimate of f (220) in the region of 16.77. A value in this region is more in accord with a Hartree-Fock value than with the band-structure value, which was favoured by Schneider's original estimate of 16.46.
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