Group actions as applied to symmetry breaking in hexagonal crystals with space group P63/m

1984 ◽  
Vol 62 (11) ◽  
pp. 1152-1173
Author(s):  
Rose M. Morra ◽  
Robin L. Armstrong
Keyword(s):  
Phase Transition ◽  
Structural Phase ◽  
Group Actions ◽  
Order Parameters ◽  
High Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Space ◽  
Low Symmetry ◽  
Symmetry Space Group

A procedure is outlined that allows one to predict the possible low-symmetry space groups for a commensurate phase transition associated with a broken symmetry. By considering each irreducible representation of the high-symmetry space group and using a subduction procedure involving the theory of group actions, one may determine a complete set of representative order parameters and their little groups. Each little group can be identified as a possible space group for the low-symmetry phase. The method is used to deduce all possible broken symmetries of space group P63/m that can result from a phase transition associated with one of the symmetry points in the Brillouin zone. As a specific application of the resulting tables of possible order parameters and associated low-symmetry space groups, changes in the X nuclear quadrupole resonance spectrum due to structural phase transitions in hexagonal AX3 crystals with the high-symmetry space group P63/m are considered.

Space groups of the diamond polytypes

1993 ◽  
Vol 8 (11) ◽  
pp. 2835-2839 ◽  
Author(s):  
A.W. Phelps ◽  
W. Howard ◽  
D.K. Smith
Keyword(s):  
Systematic Method ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Space ◽  
Atomic Coordinates ◽  
Symmetry Space Group

Space groups and atomic coordinates for the 4H, 6H, 8H, 10H, 15R, and 21R polytypes of diamond are presented. The systematic method used to determine the highest symmetry space group for diamond polytypes is described.

scholarly journals Investigation of the structural and electronic properties of CdS under high pressure: an ab initio study

2018 ◽  
Vol 96 (2) ◽  
pp. 216-224 ◽  
Author(s):  
C. Yamcicier ◽  
Z. Merdan ◽  
C. Kurkcu
Keyword(s):  
Phase Transition ◽  
Ab Initio ◽  
Density Functional ◽  
Structural Phase ◽  
Type Structure ◽  
Ambient Conditions ◽  
Space Group ◽  
Space Groups ◽  
Intermediate States ◽  
Calculation Results

An ab initio constant pressure study is carried out to explore the behaviour of cadmium sulfide (CdS) under high hydrostatic pressure. We have studied the structural properties of CdS using density functional theory (DFT) under pressure up to 200 GPa. CdS crystallizes in a wurtzite (WZ)-type structure under ambient conditions. CdS undergoes a structural phase transition from the hexagonal WZ-type structure with space group P63mc to cubic NaCl-type structure with space group [Formula: see text]. Another phase transition is obtained from NaCl-type structure to the orthorhombic CdS-III-type structure with space group Pmmn. The first transformation proceeds via seven intermediate states with space group Cmc21, P21, Pmn21, P21/m, Pmmn, I4/mmm, and Cmcm. The latter transformation is based on two intermediate states with space groups Immm and P21/m. These phase transitions are also studied by total energy and enthalpy calculations. According to these calculations, the phase transformations occur at about 3 and 51 GPa, respectively. Calculation results on the other basic properties, such as lattice constant, volume, and bulk modulus are also compared with those of other recent theoretical and experimental data, and generally, good agreement with the available data are obtained.

scholarly journals Use of software to search for higher symmetry: space group C2

2001 ◽  
Vol 57 (6) ◽  
pp. 800-805 ◽  
Author(s):  
Richard E. Marsh ◽  
Anthony L. Spek
Keyword(s):  
Cambridge Structural Database ◽  
Higher Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Bond Lengths ◽  
Structural Database ◽  
Symmetry Space ◽  
Coordinate Data ◽  
Symmetry Space Group

From a search of the October 2000 release of the Cambridge Structural Database we find coordinate data for approximately 1500 entries under space group No. 5: C2 or, occasionally, A2, I2 or B112. Software designed to detect cases of missed higher symmetry identified 144 entries for detailed inspection. Of these, 50 should, we believe, be revised to space groups of higher symmetry. The most common revision is to space group C2/m, which entails adding a center of inversion and usually results in important changes in bond lengths and angles.

scholarly journals The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Đorđe Dangić ◽  
Olle Hellman ◽  
Stephen Fahy ◽  
Ivana Savić
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Phase Transitions ◽  
Thermoelectric Materials ◽  
Ferroelectric Phase Transition ◽  
Lattice Thermal Conductivity ◽  
Ferroelectric Phase ◽  
Structural Phase ◽  
High Symmetry ◽  
Structural Phase Transitions

AbstractThe proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.

Eine synthetische Spezies zum Mineral Howardevansit mit Eisen anstelle von Kupfer: NaFe3V3O12 / A Synthetic Species of the Mineral Howardevansite with Copper Displacing Iron: NaFe3V3O12

1995 ◽  
Vol 50 (1) ◽  
pp. 51-55 ◽  
Author(s):  
F.-D. Martin ◽  
Hk. Müller-Buschbaum
Keyword(s):  
Solid State ◽  
Melting Point ◽  
Single Crystals ◽  
Crystal Chemistry ◽  
Solid State Reaction ◽  
Space Group ◽  
Triclinic Symmetry ◽  
Symmetry Space ◽  
Symmetry Space Group

Single crystals of NaFe3V3O12 have been prepared by solid state reaction below the melting point of the reaction mixture. This compound is isotypic to the mineral Howardevansite but shows lower triclinic symmetry, space group C11–P1, a = 6.757(2), b = 8.155(2), c = 9.816(3) Å, α = 106.05(2), β = 104.401(9), γ = 102.09(2)°, Z = 2. The acentric space group is caused by the sodium positions, all other atoms comply with the space group P̄ of Howardevansite. The different ions are coordinated by O2- forming VO4 tetrahedra, FeO6 octahedra, trigonal FeO5 bipyramids and irregular NaO5 and NaO7 polyhedra, respectively. The crystal chemistry is discussed with respect to Howardevansite.

scholarly journals Low-Temperature Ordering in the Cluster Compound (Bi8)Tl[AlCl4]3

Inorganics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 45 ◽  
Author(s):  
Maximilian Knies ◽  
Martin Kaiser ◽  
Mai Lê Anh ◽  
Anastasia Efimova ◽  
Thomas Doert ◽  
...  
Keyword(s):  
Cluster Compound ◽  
Structure Model ◽  
X Ray Diffraction ◽  
Hexagonal Symmetry ◽  
Threefold Axis ◽  
Space Group ◽  
X Ray ◽  
A Chain ◽  
Symmetry Space ◽  
Symmetry Space Group

The reaction of Bi, BiCl3, and TlCl in the ionic liquid [BMIm]Cl·4AlCl3 (BMIm = 1-n-butyl-3-methylimidazolium) at 180 °C yielded air-sensitive black crystals of (Bi8)Tl[AlCl4]3. X-ray diffraction on single crystals at room temperature revealed a structure containing [ Tl ( AlCl 4 ) 3 ] ∞ 1 2 − strands separated by isolated Bi82+ square antiprisms. The thallium(I) ion is coordinated by twelve Cl− ions of six [AlCl4]− groups, resulting in a chain of face-sharing [TlCl12]11− icosahedra. The Bi82+ polycation is disordered, simulating a threefold axis through its center and overall hexagonal symmetry (space group P63/m). Slowly cooling the crystals to 170 K resulted in increased order in the Bi8 cluster orientations. An ordered structure model in a supercell with a’ = 2a, b’ = 2b, c’ = 3c and the space group P65 was refined. The structure resembles a hexagonal perovskite, with complex groups in place of simple ions.

Geordnete Metallverteilung in KBaVO4 und KSrVO4 mit β-K2SO4-Struktur / Ordered Metal Distribution in KBaVO4and KSrVO4 Showing β -K2SO4 Structure

1996 ◽  
Vol 51 (4) ◽  
pp. 477-480 ◽  
Author(s):  
O. Schrandt ◽  
Hk. Müller-Buschbaum
Keyword(s):  
Single Crystals ◽  
Lattice Energy ◽  
Metal Distribution ◽  
Orthorhombic Symmetry ◽  
Space Group ◽  
Group D ◽  
Symmetry Space ◽  
Symmetry Space Group

Abstract Single crystals of KBaVO4(I) and KSrVO4(II) have been prepared by crystallization from V2O5 flux. The yellowish crystals show orthorhombic symmetry, space group D162h-Pnma with (I): a = 7.774(2), b = 5.899(1), c = 10.375(2) Å , (II): a = 7.400(2), b = 5.812(1), c -9.961(1), Z = 4. Both compounds show an ordered distribution of K+ and Ba2+ and Sr2+ respectively. The different sizes of the KO10 and BaO9 (SrO9) polyhedra are discussed with respect to those of the β-K2SO4 structure, considering the calculations of the Coulomb terms of lattice energy.

Crystal structure determination for crystals with twinning by hemihedry or pseudohemihedry

1991 ◽  
Vol 194 (3-4) ◽  
Author(s):  
Takaharu Araki
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Structure Determination ◽  
Difficult Case ◽  
Proper Selection ◽  
Space Group ◽  
Geometrical Symmetry ◽  
Symmetry Space ◽  
Symmetry Space Group ◽  
Selection Of

AbstractAn approach to structure determination for a crystal from component crystals in equal volume fractions, the most difficult case to the solution, is outlined with precautions for stepwise initialization. Proper selection of a crystal geometrical symmetry space group from a corresponding twin anti-symmetry space group and interpretation of a Patterson space are indispensable prerequisite for the solution. Observations unique to the case are briefly described in a sequence of Patterson synthesis, Fourier approach and least-squares refinement for efficient interpretation and processing.

A New Copper (II) Complex with the N,N'-Bis(antipyryl-4-methyl)-piperazine (BAMP) Ligand: [Cu(BAMP)](ClO4)2

2002 ◽  
Vol 57 (12) ◽  
pp. 1454-1460 ◽  
Author(s):  
Otilia Costișor ◽  
Ramona Tudose ◽  
Ingo Pantenburg ◽  
Gerd Meyer
Keyword(s):  
Crystal Structure ◽  
Copper Complex ◽  
Structural Parameters ◽  
Complex Molecule ◽  
Lattice Parameters ◽  
Tetragonal Symmetry ◽  
Apical Position ◽  
Space Group ◽  
Symmetry Space ◽  
Symmetry Space Group

The synthesis of the Mannich base N,N’-bis(antipyryl-4-methyl)-piperazine (BAMP) (1), its crystal structure as well as the synthesis and the crystal structure of the copper complex Cu(BAMP)(ClO4)2 (2) are reported. C28H34N6O2 ∙ 4H2O (BAMP ∙ 4H2O) crystallizes with triclinic symmetry, space group P1̄, lattice parameters: a = 704,9(2), b = 983,4(2), c = 1198,9(3) pm, α = 68,72°, β = 73,62°, γ = 78,49°. The copper-complex Cu(BAMP)(ClO4)2 crystallizes with tetragonal symmetry, space group P42/n, lattice parameters: a = 2295,1(3), c = 1412,2(2) pm. The copper(II) atom is five-coordinate by the two nitrogen atoms belonging to the piperazine ring and the oxygen atoms of the antipyrinemoieties. The geometry of the copper(II) atom can be described as a square-based pyramid with the N2O2 donor atoms of BAMP forming the basal plane and an oxygen atom of the neighbouring complex molecule occupying the apical position. BAMP acts as a tetradentate ligand, which incorporates a piperazine-fused ring. The structural parameters illustrate well the reinforcing effect exerted by the double “straps” of the piperazine molecule.

Über das Oxomolybdat AgKCu3Mo4O16 mit Silber in siebenfacher Koordination / About the Oxomolybdate AgKCu3Mo4O16 with Silver in Seven-Fold Coordination

1995 ◽  
Vol 50 (2) ◽  
pp. 252-256 ◽  
Author(s):  
H. Szillat ◽  
Hk. Müller-Buschbaum
Keyword(s):  
Crystal Structure ◽  
Single Crystals ◽  
Monoclinic Symmetry ◽  
Space Group ◽  
X Ray ◽  
Silver Copper ◽  
Symmetry Space ◽  
Symmetry Space Group

Single crystals of AgKCu3Mo4O16 have been prepared by crystallization from melts and investigated by X-ray diffractometer techniques. This compound crystallizes with monoclinic symmetry, space group C2h5 - P21/c, a = 5.056(1), b = 14.546(4), c = 19.858(9) Å, β = 86.64(5)°, Z = 4. The crystal structure of AgKCu3Mo4O16 is closely related to K2Cu3Mo4O16 showing ribbons of edge-sharing CuO6 and AgO7 polyhedra. The ribbons are linked by tetrahedrally coordinated molybdenum and K2O10 groups. Another kind of MoO4 tetrahedra occupies the cavities inside the ribbons. The crystal structure and the coordination of silver, copper, potassium and molybdenum by oxygen are discussed with respect to K2Cu3Mo4O16.

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