Fedorov pseudosymmetry of crystals: Review

Chuprunov, E. V.

doi:10.1134/s1063774507010014

Cited by 16 publications

(32 citation statements)

References 13 publications

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“…Pseudo-symmetries of the Fedorov type [43] as well as metric and motif based pseudo-symmetries [44] will be discussed in the third and fourth sections of this paper. The basis of these discussions will be two pairs of synthetic images, whereby (i) one image of each pair is free of noise and (ii) Gaussian distributed noise of mean zero has been added to that image in order to create a more or less 2D periodic image for demonstration purposes.…”

Section: Introductionmentioning

confidence: 99%

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

Moeck

2019

IEEE Trans. Nanotechnology

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The existing types of classification approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions (2D) are reviewed. Their relative performance is evaluated in a qualitative manner. Pseudosymmetries of different kinds are discussed as they present severe challenges to most classification approaches when noise levels are moderate to high. The author's information theory based approaches utilize digital images and geometric Akaike Information Criteria. They perform well in the presence of pseudo-symmetries and turn out to be the only ones that allow for fully objective (completely researcher independent) and generalized noise level dependent classifications of the full range of crystallographic symmetries, i.e. Bravais lattice type, Laue class, and plane symmetry group, of noisy real-world images. His method's identification of the plane symmetry group that can with the highest likelihood be assigned to a noisy 2D periodic image enables the most meaningful crystallographic averaging in the spatial frequency domain. This kind of averaging suppresses generalized noise much more effectively than traditional Fourier filtering. Taking account of the fact that it is fundamentally unsound to assign an abstract mathematical concept such as a single symmetry type, class, or group with 100 % certainty to a more or less 2D periodic record of a noisy real-world imaging experiment that involved a real-world sample, the author's information theory based approaches to crystallographic symmetry classifications deliver probabilistic (rather than definitive) classifications. Recent applications of deep convolutional neural networks (DCNNs) to classifications of crystallographic translation symmetry types in 2D and crystals in three dimensions (3D) are discussed as these "correlation detection and optimization" machines deliver probabilistic classifications by other -non-analytical -means. The discussed DCNN classifications ignore the fact that many crystallographic symmetries are hierarchic, i.e. that the classification classes are often non-disjoint. They are currently also incapable of dealing with pseudo-symmetries. DCNNs for classifications of crystals in 3D are discussed separately in an appendix.

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Section: Introductionmentioning

confidence: 99%

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

Moeck

2019

IEEE Trans. Nanotechnology

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“…Thus, the analysis of the pseudo inversion of individual sublattices suggests that the reductions of pseudoinversion of structures as a whole at a transition to doped KTP compositions, which is noted in Table 2 and Figure 3(b), is related to a great extent to the higher sensitivity of the pseudoinversion of M-type sublattice to the presence of doped atoms. Note that pseudosymmetry was previously studied [58] by the atomic displacement method [1] for 11 KTP-type structures. In particular, it was established that the potassium sublattice is less centrosymmetric in comparison with the TiO 6 -PO 4 subsystem, and its pseudosymmetry relative to inversion is more sensitive to introduction of impurities.…”

Section: Analysis Of the Degree Of Invariance Of The Structure Of Ktpmentioning

confidence: 99%

“…The calculations were performed using the computer program and technique described in [54]. Within this approach the electron density function is expanded in a Fourier series in structural amplitudes ( [1], see Formulas (5) and (6)). Figure 2, the origin of coordinates is chosen on the two fold screw axis, and the coordinates of pseudoinversion peaks on the x and y axes are 0.25.…”

Section: Analysis Of the Degree Of Invariance Of The Structure Of Ktpmentioning

confidence: 99%

“…These maps were obtained with scanning steps over the unit-cell axes a, b, and c chosen to be 0.05 of the cor responding unit-cell parameters. For 118 crystals (Figure 1) with known structure, we calculated three-dimensional pseudoinversion maps using Equation (1). The calculations were performed using the computer program and technique described in [54].…”

Section: Analysis Of the Degree Of Invariance Of The Structure Of Ktpmentioning

confidence: 99%

“…The symmetric features of atomic structures of crystals can be characterized more completely taking into account the phenomenon of pseudosymmetry, which makes it possible to establish finer relationships of the structure-property type. Fedorov pseudosymmetry of crystals [1] is the phenomenon of invariance of a considerable part of the crystal atomic structure (part of electron density and (or) subsystem of atomic nuclei) with respect to some group of symmetry operations compatible with the lattice (with respect to some supergroup of the symmetry space group of crystal).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pseudosymmetric Features and Nonlinear Optical Properties of Potassium Titanyl Phosphate Crystals

Gazhulina¹,

Marychev²

2013

CSTA

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A number of publications containing structural data, characteristics of nonlinear optical properties of pure and doped crystals of potassium titanyl phosphate (KTP) family have been reviewed to analyze the structural and symmetry conditionality of nonlinear optical properties of these crystals. The pseudosymmetric features of KTP-type crystals with respect to inversion are investigated. Specifically, pseudoinversion distribution maps are calculated; pseudoinversion extrema and coordinates of pseudoinversion centres are found; and the distributions of pure and doped KTP-type structures and their individual atomic sublattices over the degree of pseudoinversion are analyzed. A correlation between the characteristics of nonlinear optical properties of a number of crystals belonging to the KTP family and the degree of pseudoinversion of their atomic structures is demonstrated.

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Three‐Dimensional FIB‐OIM of Ceramic Materials

Dillon

Rohrer

2008

Ceramic Transactions Series

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Three-dimensional characterization of materials is important for understanding and predicting their microstructural evolution and properties. Traditional serial sectioning of bulk samples is difficult, tedious, and not well suited for fined grained materials. In recent years, the dual-beam focused ion beam microscope has allowed for the prospect of three-dimensional characterization of fine grained materials to be performed more routinely. However, limited work has been performed on ceramics. Examples of three-dimensional reconstruction of orientation image maps from electron backscatter diffraction patterns are given for yttriastabilized zirconia, alumina, strontium titanate and spinel.

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Fedorov pseudosymmetry of crystals: Review

Cited by 16 publications

References 13 publications

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

Pseudosymmetric Features and Nonlinear Optical Properties of Potassium Titanyl Phosphate Crystals

Three‐Dimensional FIB‐OIM of Ceramic Materials

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