Cayron, Cyril
Published in
Acta crystallographica. Section A, Foundations of crystallography

Multiple twinning in cubic crystals is represented geometrically by a three-dimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the Sigma3(n) operators are the different types of operations (expressed by sets of equivalent opera...

Bodner, Mark Patera, Jiří Szajewska, Marzena
Published in
Acta crystallographica. Section A, Foundations of crystallography

The icosahedral symmetry group H3 of order 120 and its dihedral subgroup H2 of order 10 are used for exact geometric construction of polytopes that are known to exist in nature. The branching rule for the H3 orbit of the fullerene C60 to the subgroup H2 yields a union of eight orbits of H2: four of them are regular pentagons and four are regular de...

Henn, Julian Schönleber, Andreas
Published in
Acta crystallographica. Section A, Foundations of crystallography

The usual residual values are complemented by expectation values based solely on the experimental data and the number of model parameters. These theoretical R values serve as benchmark values when all of the basic assumptions for a least-squares refinement, i.e. no systematic errors and a fully adequate model capable of describing the data, are ful...

Billinge, Simon J L Miao, Jianwei
Published in
Acta crystallographica. Section A, Foundations of crystallography

Kocian, Philippe
Published in
Acta crystallographica. Section A, Foundations of crystallography

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn t...

Beanland, Richard Thomas, Paul J Woodward, David I Thomas, Pamela A Roemer, Rudolf A
Published in
Acta crystallographica. Section A, Foundations of crystallography

The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident b...

Staic, Mihai D Petrescu-Nita, Alina
Published in
Acta crystallographica. Section A, Foundations of crystallography

This paper studies the symmetry group of two special types of carbon nanotori. The construction is motivated by a group-theoretical result.

Liu, Haiguang Poon, Billy K Saldin, Dilano K Spence, John C H Zwart, Peter H
Published in
Acta crystallographica. Section A, Foundations of crystallography

Femtosecond X-ray pulses from X-ray free-electron laser sources make it feasible to conduct room-temperature solution scattering experiments far below molecular rotational diffusion timescales. Owing to the ultra-short duration of each snapshot in these fluctuation scattering experiments, the particles are effectively frozen in space during the X-r...

Stokes, Harold T Campbell, Branton J Cordes, Ryan
Published in
Acta crystallographica. Section A, Foundations of crystallography

New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a...

Rius, Jordi Mugnaioli, Enrico Vallcorba, Oriol Kolb, Ute
Published in
Acta crystallographica. Section A, Foundations of crystallography

δ Recycling is a simple procedure for directly extracting phase information from Patterson-type functions [Rius (2012). Acta Cryst. A68, 399-400]. This new phasing method has a clear theoretical basis and was developed with ideal single-crystal X-ray diffraction data. On the other hand, introduction of the automated diffraction tomography (ADT) tec...