scholarly journals The Fedorov–Groth law revisited: complexity analysis using mineralogical data

2020 ◽  
Vol 76 (3) ◽  
pp. 429-431 ◽  
Author(s):  
Sergey V. Krivovichev ◽  
Vladimir G. Krivovichev
Keyword(s):  
Complexity Analysis ◽  
Point Group ◽  
Complex Compounds ◽  
Chemical Information ◽  
Higher Symmetry ◽  
Chemical Complexity ◽  
Lower Symmetry

The Fedorov–Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov–Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.

scholarly journals Systems chemical analytics: introduction to the challenges of chemical complexity analysis

2019 ◽  
Vol 218 ◽  
pp. 9-28 ◽  
Author(s):  
Philippe Schmitt-Kopplin ◽  
Daniel Hemmler ◽  
Franco Moritz ◽  
Régis D. Gougeon ◽  
Marianna Lucio ◽  
...  
Keyword(s):  
Complexity Analysis ◽  
Integrated Approach ◽  
Chemical Complexity ◽  
Complex Chemistry

We present concepts of complexity, and complex chemistry in systems subjected to biotic and abiotic transformations, and introduce analytical possibilities to disentangle chemical complexity into its elementary parts as a global integrated approach termed systems chemical analytics.

Retention of -4 Symmetry in Compounds Containing MAr4 Molecules and Ions

1997 ◽  
Vol 53 (5) ◽  
pp. 780-786 ◽  
Author(s):  
M. A. Lloyd ◽  
C. P. Brock
Keyword(s):  
Cross Sections ◽  
Low Energy ◽  
Cambridge Structural Database ◽  
Higher Symmetry ◽  
Lower Symmetry ◽  
Structural Database

A search of the Cambridge Structural Database shows that MAr4 molecules usually retain the low-energy \overline 4 conformation in the crystal. MAr^{q}_{4} ions also usually occupy sites if the counterion can conform to \overline 4 (or higher) symmetry. The ability of the aryl groups to fit well around an empty \overline 4 site is crucial to the symmetry retention. Molecules (and ions) in the tetragonal structures pack in columns that parallel the c axis; the columnar cross sections are approximately square. Aryl groups in adjacent columns can interleave to form a sort of herringbone arrangement. The tetragonal packing of columns is sufficiently favorable that it sometimes occurs even if the molecules must be disordered. The columnar motif is also found in some lower-symmetry structures of MAr4 molecules and MAr^{q}_{4} ions; these structures may be pseudosymmetric.

Crystal Structure Analysis of Cu-Zr Alloys by Convergent Beam Diffraction

1981 ◽  
Vol 39 ◽  
pp. 354-355
Author(s):  
A. F. Marshall ◽  
J. W. Steeds ◽  
D. Bouchet ◽  
S. L. Shinde ◽  
R. G. Walmsley
Keyword(s):  
Crystal Structure ◽  
Point Group ◽  
Intermetallic Phase ◽  
Three Dimensional ◽  
Crystal Structure Analysis ◽  
Ion Milling ◽  
Composition And Structure ◽  
Unit Cells ◽  
Sputter Deposited ◽  
Convergent Beam

Convergent beam electron diffraction is a powerful technique for determining the crystal structure of a material in TEM. In this paper we have applied it to the study of the intermetallic phases in the Cu-rich end of the Cu-Zr system. These phases are highly ordered. Their composition and structure has been previously studied by microprobe and x-ray diffraction with sometimes conflicting results.The crystalline phases were obtained by annealing amorphous sputter-deposited Cu-Zr. Specimens were thinned for TEM by ion milling and observed in a Philips EM 400. Due to the large unit cells involved, a small convergence angle of diffraction was used; however, the three-dimensional lattice and symmetry information of convergent beam microdiffraction patterns is still present. The results are as follows:1) 21 at% Zr in Cu: annealed at 500°C for 5 hours. An intermetallic phase, Cu3.6Zr (21.7% Zr), space group P6/m has been proposed near this composition (2). The major phase of our annealed material was hexagonal with a point group determined as 6/m.

Macroprobe Mode for the Study of Segregation in Steels

1990 ◽  
Vol 48 (2) ◽  
pp. 260-261
Author(s):  
Auclair Gilles ◽  
Benoit Danièle
Keyword(s):  
Mechanical Properties ◽  
Spatial Distribution ◽  
High Performance ◽  
Volume Fraction ◽  
Sheet Steel ◽  
Acquisition Time ◽  
Chemical Information ◽  
X Ray ◽  
Accurate Quantitative Analysis ◽  
Optical Micrographs

During these last 10 years, high performance correction procedures have been developed for classical EPMA, and it is nowadays possible to obtain accurate quantitative analysis even for soft X-ray radiations. It is also possible to perform EPMA by adapting this accurate quantitative procedures to unusual applications such as the measurement of the segregation on wide areas in as-cast and sheet steel products.The main objection for analysis of segregation in steel by means of a line-scan mode is that it requires a very heavy sampling plan to make sure that the most significant points are analyzed. Moreover only local chemical information is obtained whereas mechanical properties are also dependant on the volume fraction and the spatial distribution of highly segregated zones. For these reasons we have chosen to systematically acquire X-ray calibrated mappings which give pictures similar to optical micrographs. Although mapping requires lengthy acquisition time there is a corresponding increase in the information given by image anlysis.

Friedel'S law breakdown and interpretation of stacking fault images in tetrahedral semiconductors

1987 ◽  
Vol 45 ◽  
pp. 318-319
Author(s):  
Rob. W. Glaisher ◽  
A.E.C. Spargo
Keyword(s):  
Relative Phase ◽  
Point Group ◽  
Binary Compound ◽  
Stacking Fault ◽  
Fold Axis ◽  
Atom Pair ◽  
Tetrahedral Semiconductors ◽  
Group Symmetries ◽  
Thin Crystal ◽  
Phase Differences

Images of <11> oriented crystals with diamond structure (i.e. C,Si,Ge) are dominated by white spot contrast which, depending on thickness and defocus, can correspond to either atom-pair columns or tunnel sites. Olsen and Spence have demonstrated a method for identifying the correspondence which involves the assumed structure of a stacking fault and the preservation of point-group symmetries by correctly aligned and stigmated images. For an intrinsic stacking fault, a two-fold axis lies on a row of atoms (not tunnels) and the contrast (black/white) of the atoms is that of the {111} fringe containing the two-fold axis. The breakdown of Friedel's law renders this technique unsuitable for the related, but non-centrosymmetric binary compound sphalerite materials (e.g. GaAs, InP, CdTe). Under dynamical scattering conditions, Bijvoet related reflections (e.g. (111)/(111)) rapidly acquire relative phase differences deviating markedly from thin-crystal (kinematic) values, which alter the apparent location of the symmetry elements needed to identify the defect.

High Resolution Electron Microscopy of internal interfaces in layered materials

1990 ◽  
Vol 48 (4) ◽  
pp. 320-321
Author(s):  
Yoichi Ishida ◽  
Hideki Ichinose ◽  
Yutaka Takahashi ◽  
Jin-yeh Wang
Keyword(s):  
Grain Boundaries ◽  
Mirror Symmetry ◽  
Functional Materials ◽  
High Resolution Electron Microscopy ◽  
Layered Materials ◽  
Plane Boundary ◽  
Chemical Information ◽  
Layer Plane ◽  
High Tc ◽  
Cubic Metals

Layered materials draw attention in recent years in response to the world-wide drive to discover new functional materials. High-Tc superconducting oxide is one example. Internal interfaces in such layered materials differ significantly from those of cubic metals. They are often parallel to the layer of the neighboring crystals in sintered samples(layer plane boundary), while periodically ordered interfaces with the two neighboring crystals in mirror symmetry to each other are relatively rare. Consequently, the atomistic features of the interface differ significantly from those of cubic metals. In this paper grain boundaries in sintered high-Tc superconducting oxides, joined interfaces between engineering ceramics with metals, and polytype interfaces in vapor-deposited bicrystal are examined to collect atomic information of the interfaces in layered materials. The analysis proved that they are not neccessarily more complicated than that of simple grain boundaries in cubic metals. The interfaces are majorly layer plane type which is parallel to the compound layer. Secondly, chemical information is often available, which helps the interpretation of the interface atomic structure.

X-ray microprobe for materials science

1994 ◽  
Vol 52 ◽  
pp. 56-57
Author(s):  
G.E. Ice
Keyword(s):  
Crystallographic Orientation ◽  
Local Structure ◽  
Materials Science ◽  
Chemical Information ◽  
X Ray Diffraction ◽  
Ray Optics ◽  
X Ray ◽  
Novel Materials ◽  
New Information ◽  
Elemental Sensitivity

The increasing availability of synchrotron x-ray sources has stimulated the development of advanced hard x-ray (E≥5 keV) microprobes. With new x-ray optics these microprobes can achieve micron and submicron spatial resolutions. The inherent elemental and crystallographic sensitivity of an x-ray microprobe and its inherently nondestructive and penetrating nature will have important applications to materials science. For example, x-ray fluorescent microanalysis of materials can reveal elemental distributions with greater sensitivity than alternative nondestructive probes. In materials, segregation and nonuniform distributions are the rule rather than the exception. Common interfaces to whichsegregation occurs are surfaces, grain and precipitate boundaries, dislocations, and surfaces formed by defects such as vacancy and interstitial configurations. In addition to chemical information, an x-ray diffraction microprobe can reveal the local structure of a material by detecting its phase, crystallographic orientation and strain.Demonstration experiments have already exploited the penetrating nature of an x-ray microprobe and its inherent elemental sensitivity to provide new information about elemental distributions in novel materials.

Symmetry breaking in convergent-beam diffraction

1989 ◽  
Vol 47 ◽  
pp. 480-481
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Space Groups ◽  
Atomic Displacements ◽  
Small Probe ◽  
Phase Sensitive ◽  
Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

The Possibilities for Analytical Methods in Photoemission and Low-Energy Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 348-349
Author(s):  
Ernst Bauer
Keyword(s):  
Chemical Characterization ◽  
Emission Angle ◽  
Relative Energy ◽  
Objective Lens ◽  
Chemical Information ◽  
Magnetic Lens ◽  
Incident Intensity ◽  
X Ray ◽  
Leed Pattern ◽  
Image Position

One of the major shortcomings of conventional PEEM and of LEEM is the lack of chemical information about the surface. Although the imaging of the LEED pattern in the back focal plane of the objective lens of a LEEM instrument allows chemical characterization via the crystalline structure derived from the LEED pattern, this method fails in the absence of a characteristic LEED pattern. Direct information about the atomic composition of the surface is then needed which can be best obtained from inner shell electrons either directly by x-ray-induced photoemission (XPEEM) or by x-ray- or electron-induced Auger electron emission (AEEM). These modes of excitation and imaging can be combined with conventional PEEM and LEEM in one instrument which is presently being developed. Thus a complete structural and chemical characterization becomes possible in one instrument, with parallel detection and high resolution.In contrast to LEEM, in which up to more than 50% of the incident intensity is available for image formation, the intensity of the emitted electrons is much lower in XPEEM and AEEM and the signal is much lower than the background in AEEM. Therefore, intensity I and resolution d have to be optimized simultaneously which is best done by maximizing Q = I/d2 with respect to maximum emission angle α and relative energy distribution ε = ΔVo/V accepted by the instrument. For a well-designed magnetic lens section of the cathode lens its aberrations are determined by the accelerating field F in front of the specimen. For a homogeneous accelerating field F and a cosine emission distribution one obtains for the optimum α and ε values αo,εo a radius of the minimum disc of confusion of

TEM study of lanthanum aluminate

1990 ◽  
Vol 48 (4) ◽  
pp. 1060-1061
Author(s):  
C.Y. Yang ◽  
Z.R. Huang ◽  
Y.Q. Zhou ◽  
C.Z. Li ◽  
W.H. Yang ◽  
...  
Keyword(s):  
Domain Boundary ◽  
Point Group ◽  
Optical Microscope ◽  
Dark Field ◽  
Zone Axis ◽  
Superconducting Film ◽  
Ion Milling ◽  
Lanthanum Aluminate ◽  
Ring Diameter ◽  
Diffraction Patterns

Lanthanum aluminate(LaAlO3) single crystal as a substrate for high Tc superconducting film has attracted attention recently. We report here a transmission electron microscopy(TEM) study of the crystal structure and phase transformation of LaAlO3 by using Philips EM420 and EM430 microscopes. Single crystals of LaAlO3 were investigated first by optical microscope. Stripe-shaped domains of mm size are clearly seen(Fig.1a), and 90° domain boundary is also obvious. TEM specimens were prepared by mechanical grinding and polishing followed by ion-milling.Fig.lb shows μm size stripe domains of LaAlO3. Convergent beam electron diffraction patterns (CBED) from single domain were taken.Fig. 2a and Fig. 2c are [001] zone axis patterns which show a 4mm symmetry, and the (200) dark field of this zone axis gives 2mm symmetry(fig.2b). Therefore the point group of this crystal is either 4/mmm or m3m. The projection of the first order Laue zone(FOLZ) reflections on zero layer (fig. 2c) shows that the unit cell is face centered. A tetragonal unit ceil is chosen, with a=0.532nm and c=0.753nm, c being determined from the FOLZ ring diameter.

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