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  • 1
    Electronic Resource
    Electronic Resource
    The von Mises distribution of the phase of a structure invariant (1977)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 33 (1977), S. 873-878 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The main terms in the exponential forms of the phase probability distributions of structure invariants are von Mises distributions P(Φ = [2πI0(k)]-1 exp [k cos (Φ - φ)] (a). It is shown that in this formula k and φ are given by k exp iφ = 2 〈F〉 |F|/σ2 (b), where F, a complex variable, is identified with a structure invariant, 〈F〉 is its mean value andσ2 is its variance. From (a) and (b) are obtained, by simple algebraic calculations of 〈F〉 and σ2, the formulae for phase probability distributions of structure invariants, the derivation of which up to now required lengthy calculations via joint probability distributions of many structure factors. A new application is the calculation of the phase probability distribution of a quartet employing both the magnitudes of the cross terms and a priori structural information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739477002162
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  • 2
    Electronic Resource
    Electronic Resource
    The joint probability distribution of Eh, Eh+k and cos 2π(h/2+k).U – where U is a single Patterson vector – and related conditional averages: space group P\overline{1} (1975)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 731-737 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In order to establish a generalized form of an earlier derived algebraic relation between a structure factor, triple products and a single Patterson vector U, the joint probability distribution P(X0, X1, M) of Ek, Eh + k and cos 2π(h/2 + k). U with h fixed, is derived for space group P{\bar 1}. From this distribution the desired generalized equations are obtained. The sign probability formula for triple products is adapted to the case that cos 2π(h/2 + k). U is known. A numerical check on the expression for the conditional average (cos 2πh/2 + k). U||Ek| 〉 t, |Eh + k 〉 t )k, showed that for an artificial structure the set of signs of the structure factors obtained from this expression was better than that calculated from heavy-atom positions related by U.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739475001581
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  • 3
    Electronic Resource
    Electronic Resource
    Conditional phase probability distributions of structure factors in a Karle–Hauptman matrix (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 105-107 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: From the joint probability distribution of all structure factors in a Karle-Hauptman matrix new phase probability distributions are obtained. These calculations lead to a reformulation of the maximum-determinant rule for phase determination. In addition a new function is derived whose maximum corresponds to the most probable values for the phases of an arbitrary subset of the structure factors in a Karle-Hauptman matrix. This function accounts for the interaction among phases in a Karle-Hauptman matrix through triple products and quartets simultaneously.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479000188
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  • 4
    Electronic Resource
    Electronic Resource
    Direct phase determination of triple products from Bijvoet inequalities. II. A probabilistic approach (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 447-450 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Probability calculations confirm a recently proposed formula for the calculation of sin \bar \phihk from Bijvoet inequalities, where \bar \phihk is the average phase of the triple products FhFkF{\bf {\bar h + k}} and F{\bf {\bar h}}, F{\bf {\bar k}}F{\bf {\bar h + k}} [paper I: Kroon, Spek & Krabbendam (1977), Acta Cryst. A33, 382-3851. In paper I it was shown that {\bar \phi}hk could be calculated quite accurately without knowledge of the positions of the anomalous scatterers, provided an appropriate scaling procedure was applied. If the magnitudes of the individual structure factors are considered in addition to the magnitudes of the triple products, an improved formula is obtained which leads to even better results without any scaling procedure. The efficacy of the improved formula is demonstrated by test calculations for the same structure as in paper I (space group P1, two Br ions): (i) the phases of 5139 triple products formed from 322 reflexions (observed) with |E| 〉 1.2 are calculated with a mean error in {\bar \phi}hk of 16° (paper I: 21°), (ii) the phases of 3832 triple products formed from 258 reflexions (calculated) with |E| 〉 1.2 are calculated with a mean error in {\bar \phi}hk of 8° (paper I: 14°). 447
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478000881
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  • 5
    Electronic Resource
    Electronic Resource
    Restriction of the number of terms in the Sayre–Hughes equation connected with a criterion to establish the absence of atomic overlap in projection (1976)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 115-119 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the Sayre-Hughes equation the variable reciprocal-lattice vector ranges over the whole reciprocal net. It is shown that under the condition that a projection along a zone axis has no overlapping atoms the variable reciprocal-lattice vector can be restricted to range over a plane of the reciprocal net. A fortiori if a projection on an axis is free from overlap the variable vector can be restricted to range over a row of the reciprocal net. Criteria to determine the projections for which these conditions are best fulfilled are given. These criteria involve the absolute values of the structure factors only. The theory is illustrated by a test employing normalized structure factors calculated from atomic coordinates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739476000211
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  • 6
    Electronic Resource
    Electronic Resource
    The joint probability distribution of the structure factors in a Karle–Hauptman matrix (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 101-105 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The joint probability distribution of all structure factors Ehi - hj (i, j = 0, ..., m) in an (m + 1) × (m + 1) Karle-Hauptman matrix is derived for structures in the space group P1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479000176
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  • 7
    Electronic Resource
    Electronic Resource
    Crystallization of low-molecular-weight organic compounds for X-ray crystallography (1989)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 22 (1989), S. 340-344 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: General strategies are described to obtain crystals of low-molecular-weight compounds suitable for X-ray structure determination. A survey is given of a variety of crystallization techniques together with their advantages and drawbacks, illustrated by experiences with notoriously crystallization-resisting compounds. The methods discussed range from preliminary investigations using evaporation, batch crystallization and liquid–liquid diffusion methods, via the most frequently used methods such as sitting-drop vapor-phase diffusion and change of temperature, to methods such as gel crystallization, sublimation and solidification. The most successful method appears to be the sitting-drop vapor-phase diffusion. Complete crystallization routes are described, taking into account the results of preliminary investigations. The hard-to-crystallize vecuronium bromide is presented as a case study.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889889003894
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  • 8
    Electronic Resource
    Electronic Resource
    A - and B -type hydrogen bond modifications of potassium hydrogen tartronate (1976)
    [s.l.] : Nature Publishing Group
    Nature 260 (1976), S. 600-601 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] A reliable tool for establishing the type of hydrogen bond present in crystals of acid salts is infrared spectroscopy, which can be used to examine the region of the stretch vibration of the hydroxyl group2. Also, geometric evidence from X-ray data on a number of acid salts unambiguously reveals ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/260600a0
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  • 9
    Electronic Resource
    Electronic Resource
    X-ray evidence of temperature-dependent conformational disorder of hydrogen-bonded carboxylic acid molecules in crystal structures (1975)
    [s.l.] : Nature Publishing Group
    Nature 257 (1975), S. 625-626 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Fig. 1 Trans (a) and cis conformation (b) in a-substituted carboxylic acids. From infrared studies of unsubstituted monocarboxylic acids at different temperatures, Hayashi etal.6t* deduced that in odd-membered acids the crystal contains the cis form at lower temperatures, whereas (lower ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/257625a0
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  • 10
    Electronic Resource
    Electronic Resource
    Conformational aspects of meso-tartaric acid. IX. Structure of (+)-(R)-α-methylbenzylammonium meso-tartrate monohydrate, 2C8H12N+.C4H4O62−.H2O (1985)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 1205-1208 
    Details
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108270185007156
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