Space Group Theoretical Analysis of Grain Boundaries in Ordered Alloys

1986 ◽  
Vol 93 (1) ◽  
pp. 45-55 ◽  
Author(s):  
D. Farkas ◽  
A. Ran
Keyword(s):  
Theoretical Analysis ◽  
Grain Boundaries ◽  
Space Group ◽  
Ordered Alloys ◽  
Group Theoretical Analysis

scholarly journals Group-theoretical analysis of 1:3 A-site-ordered perovskite formation

2019 ◽  
Vol 75 (2) ◽  
pp. 379-397 ◽  
Author(s):  
Mikhail V. Talanov
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Perovskite Structure ◽  
Functional Materials ◽  
Order Parameters ◽  
Space Group ◽  
Symmetry Phase ◽  
Structural Mechanisms ◽  
Low Symmetry ◽  
Group Theoretical Analysis

The quadruple perovskites AA′3 B 4 X 12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.

Structures of the ordered double perovskites Sr2YTaO6 and Sr2YNbO6

2005 ◽  
Vol 61 (3) ◽  
pp. 258-262 ◽  
Author(s):  
Christopher J. Howard ◽  
Paris W. Barnes ◽  
Brendan J. Kennedy ◽  
Patrick M. Woodward
Keyword(s):  
Theoretical Analysis ◽  
Group Symmetry ◽  
Double Perovskites ◽  
Monoclinic Structure ◽  
Space Group Symmetry ◽  
Space Group ◽  
Recent Group ◽  
Triclinic Structure ◽  
Group Theoretical Analysis

The ordered perovskite Sr2YTaO6, distrontium yttrium tantalum hexaoxide, has been reported as showing an unusual triclinic structure, at odds with the results from a recent group-theoretical analysis. A new investigation establishes that Sr2YTaO6 and the isostructural Sr2YNbO6, distrontium yttrium niobium hexaoxide, in fact both adopt the commonly occurring monoclinic structure, with the space-group symmetry P21/n.

Group-theoretical analysis of octahedral tilting in ferroelectric perovskites

2002 ◽  
Vol 58 (6) ◽  
pp. 934-938 ◽  
Author(s):  
Harold T. Stokes ◽  
Erich H. Kisi ◽  
Dorian M. Hatch ◽  
Christopher J. Howard
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Landau Theory ◽  
Group Symmetry ◽  
Theoretical Methods ◽  
Space Group Symmetry ◽  
Space Group ◽  
First Order ◽  
Octahedral Tilting ◽  
Group Theoretical Analysis

Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolomé [Phase Transit. (2001), 74, 255–335] and a number of differences are found. The group–subgroup relationships between the structures are also determined, along with an indication of those phase transitions that must be first order by Landau theory.

Symmetry properties of the normal modes of vibration of calcite and α-corundum

1969 ◽  
Vol 47 (13) ◽  
pp. 1381-1391 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Theoretical Analysis ◽  
Normal Modes ◽  
Dispersion Curves ◽  
Dynamical Matrix ◽  
Space Group ◽  
Symmetry Properties ◽  
Modes Of Vibration ◽  
Symmetry Species ◽  
Group Theoretical Analysis

A group theoretical analysis is carried out on the symmetry properties of the normal modes of vibration of crystals with the calcite and α-corundum structures. Both of these structures have the space group [Formula: see text]. The symmetry species present in the dispersion curves are determined for important wave vectors, and a transformation to block-diagonalize the dynamical matrix at the zone center is given.

Ordered double perovskites – a group-theoretical analysis

2003 ◽  
Vol 59 (4) ◽  
pp. 463-471 ◽  
Author(s):  
Christopher J. Howard ◽  
Brendan J. Kennedy ◽  
Patrick M. Woodward
Keyword(s):  
Irreducible Representation ◽  
Theoretical Analysis ◽  
Irreducible Representations ◽  
Cation Ordering ◽  
Double Perovskites ◽  
Cation Site ◽  
Theoretical Methods ◽  
Space Group ◽  
Octahedral Tilting ◽  
Group Theoretical Analysis

Group-theoretical methods are used to enumerate the structures of ordered double perovskites, A 2 BB′X 6, in which the ordering of cations B and B′ into alternate octahedra is considered in combination with the ubiquitous BX 6 (or B′X 6) octahedral tilting. The cation ordering on the B-cation site is described by the irreducible representation R_1^+ of the Pm \overline 3 m space group of the cubic aristotype, while the octahedral tilting is mediated by irreducible representations M_3^+ and R_4^+. There are 12 different structures identified, and the corresponding group–subgroup relationships are displayed. Known structures are briefly reviewed.

Octahedral tilting in cation-ordered perovskites – a group-theoretical analysis

2004 ◽  
Vol 60 (6) ◽  
pp. 674-684 ◽  
Author(s):  
Christopher J. Howard ◽  
Harold T. Stokes
Keyword(s):  
Theoretical Analysis ◽  
Irreducible Representations ◽  
Cation Ordering ◽  
Cation Site ◽  
Theoretical Methods ◽  
Space Group ◽  
Octahedral Tilting ◽  
Group Theoretical Analysis

Group-theoretical methods are used to enumerate the structures of ordered perovskites, in which 1:2 and 1:3 ordering of B and B′ cations is considered in combination with the ubiquitous BX 6 (or B′X 6) octahedral tilting. The cation ordering on the B-cation site is described by irreducible representations of the Pm\bar 3m space group of the cubic aristotype: Λ1 ( k = 1/3,1/3,1/3) for the cation ordering pattern in the 1:2 compound A 3 BB_2^{\prime}X 9 and M_1^ + ( k = 1/2,1/2,0) for the cation ordering in the 1:3 compound A 4 BB_3^{\prime}X 12. The octahedral tilting is mediated by the irreducible representations M_3^ + and R_4^ +. Ten distinct structures have been identified in the 1:2 case and 11 structures for 1:3.

scholarly journals Phonons in Short-Period GaN/AlN Superlattices: Group-Theoretical Analysis, Ab initio Calculations, and Raman Spectra

Nanomaterials ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 286
Author(s):  
Valery Davydov ◽  
Evgenii Roginskii ◽  
Yuri Kitaev ◽  
Alexander Smirnov ◽  
Ilya Eliseyev ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Ab Initio Calculations ◽  
Ab Initio ◽  
Raman Spectra ◽  
Density Functional ◽  
Structural Characteristics ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
Short Period ◽  
Group Theoretical Analysis

We report the results of experimental and theoretical studies of phonon modes in GaN/AlN superlattices (SLs) with a period of several atomic layers, grown by submonolayer digital plasma-assisted molecular-beam epitaxy, which have a great potential for use in quantum and stress engineering. Using detailed group-theoretical analysis, the genesis of the SL vibrational modes from the modes of bulk AlN and GaN crystals is established. Ab initio calculations in the framework of the density functional theory, aimed at studying the phonon states, are performed for SLs with both equal and unequal layer thicknesses. The frequencies of the vibrational modes are calculated, and atomic displacement patterns are obtained. Raman spectra are calculated and compared with the experimental ones. The results of the ab initio calculations are in good agreement with the experimental Raman spectra and the results of the group-theoretical analysis. As a result of comprehensive studies, the correlations between the parameters of acoustic and optical phonons and the structure of SLs are obtained. This opens up new possibilities for the analysis of the structural characteristics of short-period GaN/AlN SLs using Raman spectroscopy. The results obtained can be used to optimize the growth technologies aimed to form structurally perfect short-period GaN/AlN SLs.

Group theoretical analysis of a rotating shallow liquid in a rigid container

1989 ◽  
Vol 22 (22) ◽  
pp. 4743-4767 ◽  
Author(s):  
D Levi ◽  
M C Nicci ◽  
C Rogers ◽  
P Winternitz
Keyword(s):  
Theoretical Analysis ◽  
Group Theoretical Analysis

Group Theoretical Analysis of Lattice Vibrations in GaSe Polytypes

1974 ◽  
Vol 52 (24) ◽  
pp. 2454-2458 ◽  
Author(s):  
S. Jandl ◽  
J. L. Brebner
Keyword(s):  
Theoretical Analysis ◽  
Raman Scattering ◽  
Brillouin Zone ◽  
Wave Vector ◽  
Lattice Vibrations ◽  
Group Theoretical Analysis

We present here a group theoretical analysis of the lattice vibrations of the ε and γ polytypes of GaSe for different directions of the wave vector in the Brillouin zone. The effect of the interlayer interactions and the assignment of the modes observed in Raman scattering is discussed.

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