Magnetic modes compatible with the symmetry of crystals

2021 ◽  
Vol 77 (4) ◽  
Author(s):  
Piotr Fabrykiewicz ◽  
Radosław Przeniosło ◽  
Izabela Sosnowska
Keyword(s):  
Space Group ◽  
Ferromagnetic Component ◽  
Magnetic Mode ◽  
Magnetic Symmetry ◽  
Point Groups

A classification of magnetic point groups is presented which gives an answer to the question: which magnetic groups can describe a given magnetic mode? There are 32 categories of magnetic point groups which describe 64 unique magnetic modes: 16 with a ferromagnetic component and 48 without. This classification focused on magnetic modes is helpful for finding the magnetic space group which can describe the magnetic symmetry of the material.

scholarly journals Symmetrical Analysis Phonon Modes of Crystal -Ag8SnSe6

2015 ◽  
Vol 16 (2) ◽  
pp. 257-260
Author(s):  
І.V. Semkiv ◽  
А.І. Kashuba ◽  
H.A. Ilchuk ◽  
M.V. Chekaylo
Keyword(s):  
Raman Spectra ◽  
Infrared Spectra ◽  
Room Temperature ◽  
Group Symmetry ◽  
Phonon Modes ◽  
Orthorhombic System ◽  
Space Group Symmetry ◽  
Space Group ◽  
Phonon Spectra

Symmetrical analysis of the phonon spectra of  lowtemperature b¢-phase of crystal Ag8SnSe6 carried out. At the room temperature argyrodite Ag8SnSe6 belong to orthorhombic system with space group symmetry Pmn21. Classification of the main phonon modes of crystal carried out. Clarified selection rules for Raman spectra and infrared spectra.

2. Symmetry

2016 ◽  
pp. 24-38
Author(s):  
A. M. Glazer
Keyword(s):  
Crystal Structure ◽  
Reflection Point ◽  
Notation System ◽  
Space Group ◽  
Space Groups ◽  
Different Types ◽  
Point Groups

In order to explain what crystals are and how their structures are described, we need to understand the role of symmetry, for this lies at the heart of crystallography. ‘Symmetry’ explains the different types of symmetry: rotational, mirror or reflection, point, chiral, and translation. There are thirty-two point groups and seven crystal systems, according to which symmetries are present. These are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Miller indices, lattices, crystal structure, and space groups are described in more detail. Any normal crystal belongs to one of the 230 space group types. Crystallographers generally use the International Notation system to denote these space groups.

Crystal chemistry and nomenclature of rhodonite-group minerals

2019 ◽  
Vol 83 (6) ◽  
pp. 829-835 ◽  
Author(s):  
Nadezhda V. Shchipalkina ◽  
Igor V. Pekov ◽  
Nikita V. Chukanov ◽  
Cristian Biagioni ◽  
Marco Pasero
Keyword(s):  
Crystal Chemistry ◽  
Structural Formula ◽  
Structure Type ◽  
Mineral Species ◽  
Triclinic Space Group ◽  
Space Group ◽  
International Mineralogical Association ◽  
Mineralogical Association ◽  
General Chemical

AbstractThis paper presents the nomenclature of the rhodonite group accepted by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA). An overview of the previous studies of triclinic (space group P$\bar{1}$) pyroxenoids belonging to the rhodonite structure type, with a focus on their crystal chemistry, is given. These minerals have the general structural formula VIIM(5)VIM(1)VIM(2)VIM(3)VIM(4)[Si5O15]. The following dominant cations at the M sites are known at present: M(5) = Ca or Mn2+, M(1–3) = Mn2+; and M(4) = Mn2+ or Fe2+. In accordance with the nomenclature, the rhodonite group consists of three IMA-approved mineral species having the following the general chemical formulae: M(5)AM(1–3)B3M(4)C[Si5O15], where A = Ca or Mn2+; B = Mn2+; and C = Mn2+ or Fe2+. The end-member formulae of approved rhodonite-group minerals are as follows: rhodonite CaMn3Mn[Si5O15]; ferrorhodonite CaMn3Fe[Si5O15]; and vittinkiite MnMn3Mn[Si5O15].

3D Braided Geometry Structures Based on Space Group

2010 ◽  
Vol 152-153 ◽  
pp. 1156-1161 ◽  
Author(s):  
Wen Suo Ma ◽  
Bin Qian Yang ◽  
Xiao Zhong Ren
Keyword(s):  
Group Theory ◽  
Symmetry Groups ◽  
The Novel ◽  
Geometrical Structures ◽  
Braided Group ◽  
Space Group ◽  
Space Groups ◽  
Geometry Structure ◽  
Point Groups ◽  
Space Point

3D braided group theory is dissertated. The analysis procedure is described from the existing braided geometry structure to the braided space group; 3D braided geometrical structures are finally described by means of group theory. Some of novel 3D braided structures are deduced from the braided space groups. By describing the 3D braided materials with braided space point and braided space groups, the braided space groups are not always the same as symmetry groups of crystallographic because novel lattices can be produced and the reflection operation cannot exist in braided space point groups. Braided point and space groups are theoretical basis for deriving the novel braided geometry structure.

scholarly journals Classification of crystal structure using a convolutional neural network

IUCrJ ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 486-494 ◽  
Author(s):  
Woon Bae Park ◽  
Jiyong Chung ◽  
Jaeyoung Jung ◽  
Keemin Sohn ◽  
Satendra Pal Singh ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Inorganic Compounds ◽  
Powder Xrd ◽  
Xrd Pattern ◽  
Extinction Group ◽  
Space Group ◽  
Crystal System ◽  
Xrd Patterns

A deep machine-learning technique based on a convolutional neural network (CNN) is introduced. It has been used for the classification of powder X-ray diffraction (XRD) patterns in terms of crystal system, extinction group and space group. About 150 000 powder XRD patterns were collected and used as input for the CNN with no handcrafted engineering involved, and thereby an appropriate CNN architecture was obtained that allowed determination of the crystal system, extinction group and space group. In sharp contrast with the traditional use of powder XRD pattern analysis, the CNN never treats powder XRD patterns as a deconvoluted and discrete peak position or as intensity data, but instead the XRD patterns are regarded as nothing but a pattern similar to a picture. The CNN interprets features that humans cannot recognize in a powder XRD pattern. As a result, accuracy levels of 81.14, 83.83 and 94.99% were achieved for the space-group, extinction-group and crystal-system classifications, respectively. The well trained CNN was then used for symmetry identification of unknown novel inorganic compounds.

Molecular Rovibronic Symmetries in Electric and Magnetic Fields

1975 ◽  
Vol 53 (19) ◽  
pp. 2210-2220 ◽  
Author(s):  
James K. G. Watson
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Symmetry Groups ◽  
Nuclear Spins ◽  
Symmetry Classification ◽  
Electric And Magnetic Fields ◽  
Field Symmetry ◽  
Point Groups

The structures of the symmetry groups for the rovibronic levels of a molecule in a homogeneous electric or magnetic field are derived, and the symmetry classification of the levels in terms of the representations and corepresentations of these groups is discussed. Specific results are given for molecules of the point groups C3, C2v, C3v, D2d, and Td in an electric field. Symmetry in combined electric and magnetic fields and the inclusion of nuclear spins are considered briefly.

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