Search results for "Reciprocal lattice"

On the lattice of J-subnormal subgroups

1992

From Lattice Valued Theories to Lattice Valued Analysis

2015

We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.

Exact Coulomb cutoff technique for supercell calculations in two dimensions

2009

We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in cutting off the long-range part of the interaction by modifying the expression for the Coulomb operator in reciprocal space. The physical result amounts in an effective screening of the spurious interactions originated by the presence of ghost periodic replicas of the system. This work extends a previous report [C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006)], where three-dimensional systems were considered. We show that the use of the cutoffs dramatic…

Automated Electron Diffraction Tomography

2012

Ab-initio structure analysis by electron diffraction is hampered by two major problems: insufficient number of reflections sampled and an intensity alteration by dynamical scattering contribution or beam damage. Thus, in recent years the principles of automated diffraction tomography (ADT) allowing systematic reciprocal space sampling and automated data analysis were developed. Here the basic ideas of ADT and its general applicability will be discussed along with some examples of solved structures.

Automated diffraction tomography combined with electron precession: a new tool forab initionanostructure analysis

2009

AbstractThree-dimensional electron diffraction data was collected with our recently developed module for automated diffraction tomography and used to solve inorganic as well as organic crystal structuresab initio. The diffraction data, which covers nearly the full relevant reciprocal space, was collected in the standard nano electron diffraction mode as well as in combination with the precession technique and was subsequently processed with a newly developed automated diffraction analysis and processing software package. Non-precessed data turned out to be sufficient forab initiostructure solution by direct methods for simple crystal structures only, while precessed data allowed structure s…

Structure solution with automated electron diffraction tomography data: different instrumental approaches

2011

Summary Over the past few years automated electron diffraction tomography has become an established technique for structure solution of nano-crystalline material. The intentional choice of an arbitrary tilt axis and thus, the use of nonoriented diffraction patterns (off-zone acquisition) together with fine equidistant sampling of the reciprocal space result in high quality intensity data sets. Coupling automated electron diffraction tomography with electron beam precession (Vincent & Midgley, 1994) enables sampling of intensities between the static slices of reciprocal space and therefore enhances the quality of intensity data further; relatively complex structures have been solved using 3D…

128-Channel Silicon Strip Detector Installed at a Powder Diffractometer

2004

Silicon strip detectors represent a new class of one-dimensional position-sensitive single photon counting devices. They allow a reduction of measurement time at the powder diffractometers by a factor up to 100 compared to instruments with a single counter, while maintaining comparable count statistics. Present work describes a 128-channel detector working with a standard diffractometer. The detector is 12.8 mm long and covers the angular range of 3.2 deg. We discuss the diffraction geometry in real and reciprocal space, the FWHM of diffraction peaks, and the background level. Measurements were made on standard samples and on complex samples of industrial importance (e. g., portland clinker…

Towards automated diffraction tomography. Part II--Cell parameter determination.

2008

Automated diffraction tomography (ADT) allows the collection of three-dimensional (3d) diffraction data sets from crystals down to a size of only few nanometres. Imaging is done in STEM mode, and diffraction data are collected with quasi-parallel beam nanoelectron diffraction (NED). Here, we present a set of developed processing steps necessary for automatic unit-cell parameter determination from the collected 3d diffraction data. Cell parameter determination is done via extraction of peak positions from a recorded data set (called the data reduction path) followed by subsequent cluster analysis of difference vectors. The procedure of lattice parameter determination is presented in detail f…

Automated electron diffraction tomography - a new tool for nano crystal structure analysis

2011

Automated electron Diffraction Tomography (ADT) comprises an upcoming method for “ab intio” structure analysis of nano crystals. ADT allows fine sampling of the reciprocal space by sequential collection of electron diffraction patterns while tilting a nano crystal in fixed tilt steps around an arbitrary axis. Electron diffraction is collected in nano diffraction mode (NED) with a semi-parallel beam with a diameter down to 50 nm. For crystal tracking micro-probe STEM imaging is used. Full automation of the acquisition procedure allowed optimisation of the electron dose distribution and therefore analysis of highly beam sensitive samples. Cell parameters, space group and reflection intensitie…

Structural analysis of CdO layers grown on r-plane sapphire (011¯2) by metalorganic vapor-phase epitaxy

2004

Abstract High-quality fully relaxed CdO layers have been grown directly on r -plane sapphire by metalorganic vapor-phase epitaxy. The crystalline structure has been analyzed by high-resolution X-ray diffraction. The structural quality of the (0 0 1) oriented layers degrades as the growth temperature decreases, process which is accompanied by the appearance of pyramidal grains as revealed by scanning force microscopy. The lattice parameters, perpendicular and parallel to the sample surface, have been determined by means of reciprocal space maps taken on asymmetrical reflections and measurements of symmetrical reflections at different azimuths. The epitaxial relationships between the CdO laye…