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Multiplicative congruential generators, their lattice structure, its relation to lattice-sublattice transformations and applications in crystallography.
An analysis of certain types of multiplicative congruential generators--otherwise known for their application to the sequential generation of pseudo-random numbers--reveals their relation to theExpand
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Nucleation and crystal growth in a suspension of charged colloidal silica spheres with bi-modal size distribution studied by time-resolved ultra-small-angle X-ray scattering.
A suspension of charged colloidal silica spheres exhibiting a bi-modal size distribution of particles, thereby mimicking a binary mixture, was studied using time-resolved ultra-small-angleExpand
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Quantitative crystal structure descriptors from multiplicative congruential generators.
  • Wolfgang Hornfeck
  • Mathematics, Medicine
  • Acta crystallographica. Section A, Foundations of…
  • 1 March 2012
Special types of number-theoretic relations, termed multiplicative congruential generators (MCGs), exhibit an intrinsic sublattice structure. This has considerable implications within theExpand
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Structural chemistry and number theory amalgamized: crystal structure of Na11Hg52.
The recently elucidated crystal structure of the technologically important amalgam Na11Hg52 is described by means of a method employing some fundamental concept of number theory, namely modularExpand
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Diaphony, a measure of uniform distribution, and the Patterson function.
This paper reviews the number-theoretic concept of diaphony, a measure of uniform distribution for number sequences and point sets based on a Fourier theory approach, and its relation toExpand
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Octagonal symmetry in low-discrepancy β-manganese.
A low-discrepancy cubic variant of β-Mn is presented exhibiting local octagonal symmetry upon projection along any of the three mutually perpendicular 〈100〉 axes. Ideal structural parameters areExpand
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On an extension of Krivovichev's complexity measures.
  • Wolfgang Hornfeck
  • Mathematics, Medicine
  • Acta crystallographica. Section A, Foundations…
  • 1 July 2020
An extension is proposed of the Shannon entropy-based structural complexity measure introduced by Krivovichev, taking into account the geometric coordinational degrees of freedom a crystal structureExpand
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A tenfold twin of the CrB structure type.
  • Wolfgang Hornfeck
  • Materials Science, Medicine
  • Acta crystallographica. Section A, Foundations…
  • 1 November 2018
NiZr crystallized from an amorphous matrix or solidified from an undercooled melt exhibits a tenfold twinned microstructure, which is explained by an ideal twin model utilizing special geometricExpand
Number-theoretic Approaches to the Description of Crystal Structures
Crystallographic group theory is commonly regarded as the method of choice for the description of crystal structures and related phenomena such as phase transformations, antiphase domain formationExpand