Subscribe: Acta Crystallographica Section A
Preview: Acta Crystallographica Section A

Acta Crystallographica Section A

Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination

Published: 2016-10-18


Towards atomistic understanding of polymorphism in the solvothermal synthesis of ZrO2 nanoparticles


Varying atomic short-range order is correlated with the ratio of the monoclinic (m) to tetragonal (t) phase in ZrO2 nanoparticle formation by solvothermal methods. Reactions from Zr oxynitrate in supercritical methanol and Zr acetate in water (hydrothermal route) were studied in situ by X-ray total scattering. Irrespective of the Zr source and solvent, the structure of the precursor in solution consists of edge-shared tetramer chains. Upon heating, the nearest-neighbor Zr—O and Zr—Zr distances shorten initially while the medium-range connectivity is broken. Depending on the reaction conditions, the disordered intermediate transforms either rapidly into m-ZrO2, or more gradually into mixed m- and t-ZrO2 with a concurrent increase of the shortest Zr—Zr distance. In the hydrothermal case, the structural similarity of the amorphous intermediate and m-ZrO2 favors the formation of almost phase-pure m-ZrO2 nanoparticles with a size of 5 nm, considerably smaller than the often-cited critical size below which the tetragonal is assumed to be favoured. Pair distribution function analysis thus unravels ZrO2 phase formation on the atomic scale and in this way provides a major step towards understanding polymorphism of ZrO2 beyond empirical approaches.

Observing structural reorientations at solvent–nanoparticle interfaces by X-ray diffraction – putting water in the spotlight


Nanoparticles are attractive in a wide range of research genres due to their size-dependent properties, which can be in contrast to those of micrometre-sized colloids or bulk materials. This may be attributed, in part, to their large surface-to-volume ratio and quantum confinement effects. There is a growing awareness that stress and strain at the particle surface contribute to their behaviour and this has been included in the structural models of nanoparticles for some time. One significant oversight in this field, however, has been the fact that the particle surface affects its surroundings in an equally important manner. It should be emphasized here that the surface areas involved are huge and, therefore, a significant proportion of solvent molecules are affected. Experimental evidence of this is emerging, where suitable techniques to probe the structural correlations of liquids at nanoparticle surfaces have only recently been developed. The recent validation of solvation shells around nanoparticles has been a significant milestone in advancing this concept. Restructured ordering of solvent molecules at the surfaces of nanoparticles has an influence on the entire panoply of solvent–particle interactions during, for example, particle formation and growth, adhesion forces in industrial filtration, and activities of nanoparticle–enzyme complexes. This article gives an overview of the advances made in solvent–nanoparticle interface research in recent years: from description of the structure of bulk solids and liquids via macroscopic planar surfaces, to the detection of nanoscopic restructuring effects. Water–nanoparticle interfaces are given specific attention to illustrate and highlight their similarity to biological systems.

The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices


This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.

Quantitative theory of diffraction by ordered coaxial nanotubes: reciprocal-lattice and diffraction pattern indexing


A quantitative theory of diffraction by right- and left-handed coaxial nanotubes with an ordered structure is developed. Their reciprocal lattices, including pseudo-orthogonal nodes, are studied. The explicit formulas that govern relations between direct and reciprocal lattices of a nanotube are achieved and a simple descriptive tool for diffraction pattern indexing is proposed.

Residue-based scattering factors


A glob is defined as a group of atoms in the crystal which can be chosen in various ways. Globs themselves can be used as scattering elements in the theory of structure determination, just as atoms are used at present. In this paper, amino-acid residues are chosen to form globs and empirical formulas for residue-based scattering factors have been developed.

Direct observation of incommensurate structure in Mo3Si


Z-contrast imaging, electron diffraction, atom-probe tomography (APT) and density functional theory calculations were used to study the crystal structure of the Mo3Si phase which was previously reported to have an A15 crystal structure. The results showed that Mo3Si has an incommensurate crystal structure with a non-cubic unit cell. The small off-stoichiometry in composition of the sample which was revealed by APT and atomic resolution Z-contrast imaging suggested that site substitution caused the development of split atomic positions, disorder and vacancies.

An alternative to the goodness of fit


An alternative measure to the goodness of fit (GoF) is developed and applied to experimental data. The alternative goodness of fit squared (aGoFs) demonstrates that the GoF regularly fails to provide evidence for the presence of systematic errors, because certain requirements are not met. These requirements are briefly discussed. It is shown that in many experimental data sets a correlation between the squared residuals and the variance of observed intensities exists. These correlations corrupt the GoF and lead to artificially reduced values in the GoF and in the numerical value of the wR(F2). Remaining systematic errors in the data sets are veiled by this mechanism. In data sets where these correlations do not appear for the entire data set, they often appear for the decile of largest variances of observed intensities. Additionally, statistical errors for the squared goodness of fit, GoFs, and the aGoFs are developed and applied to experimental data. This measure shows how significantly the GoFs and aGoFs deviate from the ideal value one.