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Publications Influence

Multiplicative congruential generators, their lattice structure, its relation to lattice-sublattice transformations and applications in crystallography.

- Wolfgang Hornfeck, B. Harbrecht
- Mathematics, Medicine
- Acta crystallographica. Section A, Foundations of…
- 1 November 2009

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 the… Expand

7- PDF

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.

- Wolfgang Hornfeck, Dirk Menke, +6 authors D. Herlach
- Materials Science, Medicine
- The Journal of chemical physics
- 5 December 2014

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-angle… Expand

6- PDF

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 the… Expand

5

Structural chemistry and number theory amalgamized: crystal structure of Na11Hg52.

- Wolfgang Hornfeck, C. Hoch
- Chemistry, Medicine
- Acta crystallographica Section B, Structural…
- 1 December 2015

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 modular… Expand

6- PDF

Ir7Zn19 and IrZn3, two new γ-brass-related Phases Classified as AlB2-type Derivatives with Ordered Vacancies

- Wolfgang Hornfeck, Samuel Freistein, B. Harbrecht
- Chemistry
- 1 September 2004

6

Diaphony, a measure of uniform distribution, and the Patterson function.

- Wolfgang Hornfeck, P. Kuhn
- Mathematics, Medicine
- Acta crystallographica. Section A, Foundations…
- 1 July 2015

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 to… Expand

3

Octagonal symmetry in low-discrepancy β-manganese.

- Wolfgang Hornfeck, P. Kuhn
- Mathematics, Medicine
- Acta crystallographica. Section A, Foundations…
- 1 September 2014

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 are… Expand

3

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 structure… Expand

1

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 geometric… Expand

Number-theoretic Approaches to the Description of Crystal Structures

- Wolfgang Hornfeck
- Mathematics
- 7 August 2012

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 formation… Expand