scholarly journals From space group to space groupoid: the partial symmetry of low-temperature E-vanillyl oxime

2019 ◽  
Vol 75 (4) ◽  
pp. 733-741
Author(s):  
Katharina Ehrmann ◽  
Stefan Baudis ◽  
Berthold Stöger
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Low Temperature ◽  
Euclidean Space ◽  
Single Crystal ◽  
Connected Components ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Full Symmetry

The phase transition of E-vanillyl oxime {1-[(E)-(hydroxyimino)methyl]-4-hydroxy-3-methoxybenzene, C8H9NO3} has been analysed by single-crystal and powder X-ray diffraction. The high-temperature (HT) phase (P21/a, Z′ = 1) transforms into the low-temperature (LT) phase (threefold superstructure, P\overline{1}, Z′ = 6) at ca 190 K. The point operations lost on cooling, {m [010], 2[010]}, are retained as twin operations and constitute the twin law. The screw rotations and glide reflections are retained in the LT phase as partial operations acting on a subset of Euclidean space {\bb E}^3. The full symmetry of the LT phase, including partial operations, is described by a disconnected space groupoid which is built of three connected components.

Structural chemistry of NaCoPO4

1996 ◽  
Vol 52 (3) ◽  
pp. 440-449 ◽  
Author(s):  
R. Hammond ◽  
J. Barbier
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Large Family ◽  
X Ray Diffraction ◽  
Tetrahedral Framework ◽  
Space Group ◽  
X Ray ◽  
Cell Parameters ◽  
Tetrahedral Sites ◽  
Bond Valence Analysis

Sodium cobalt phosphate, NaCoPO4, occurs as two different polymorphs which transform reversibly at 998 K. The crystal structures of both polymorphs have been determined by single-crystal X-ray diffraction. The low-temperature form α-NaCoPO4 crystallizes in the space group Pnma with cell parameters: a = 8.871 (3), b = 6.780 (3), c = 5.023 (1) Å, and Z = 4 [wR(F 2) = 0.0653 for all 945 independent reflections]. The α-phase contains octahedrally coordinated Co and Na atoms and tetrahedrally coordinated P atoms, and is isostructural with maracite, NaMnPO4. The structure of high-temperature β-NaCoPO4 is hexagonal with space group P65 and cell parameters: a = 10.166 (1), c = 23.881 (5) Å, and Z = 24 [wR(F 2) = 0.0867 for 4343 unique reflections]. The β-phase belongs to the large family of stuffed tridymites, with the P and Co atoms occupying tetrahedral sites and the Na atoms located in the cavities of the tetrahedral framework. The long c axis corresponds to a 3 × superstructure of the basic tridymite framework (c ≃ 8 Å) and is caused by the displacement of the Na atoms, tetrahedral tilts and strong distortions of the CoO4 tetrahedra. A bond-valence analysis of these phases reveals that the polymorphism in NaCoPO4 is due in part to over-/underbonding of the Na atom in the low-/high-temperature structures, respectively.

High-pressure syntheses and crystal structures of orthorhombic DyGaO3 and trigonal GaBO3

2015 ◽  
Vol 70 (4) ◽  
pp. 207-214 ◽  
Author(s):  
Daniela Vitzthum ◽  
Stefanie A. Hering ◽  
Lukas Perfler ◽  
Hubert Huppertz
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Single Crystal ◽  
Crystal Structures ◽  
Diffraction Data ◽  
Room Temperature ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
High Pressure High Temperature

AbstractOrthorhombic dysprosium orthogallate DyGaO3 and trigonal gallium orthoborate GaBO3 were synthesized in a Walker-type multianvil apparatus under high-pressure/high-temperature conditions of 8.5 GPa/1350 °C and 8 GPa/700 °C, respectively. Both crystal structures could be determined by single-crystal X-ray diffraction data collected at room temperature. The orthorhombic dysprosium orthogallate crystallizes in the space group Pnma (Z = 4) with the parameters a = 552.6(2), b = 754.5(2), c = 527.7(2) pm, V = 0.22002(8) nm3, R1 = 0.0309, and wR2 = 0.0662 (all data) and the trigonal compound GaBO3 in the space group R3̅c (Z = 6) with the parameters a = 457.10(6), c = 1419.2(3) pm, V = 0.25681(7) nm3, R1 = 0.0147, and wR2 = 0.0356 (all data).

Space-Group Determination of the Orthorhombic Form of NaV6O11

1995 ◽  
Vol 28 (5) ◽  
pp. 599-603 ◽  
Author(s):  
Y. Kanke ◽  
H. Shigematsu ◽  
K. Ohshima ◽  
K. Kato
Keyword(s):  
Phase Transition ◽  
Low Temperature ◽  
Single Crystal ◽  
Diffraction Study ◽  
Structural Phase ◽  
Unit Cell ◽  
Single Crystal Diffraction ◽  
Space Group ◽  
X Ray

The unit cell and space group of orthorhombic NaV6O11 (low-temperature form) are found by an X-ray single-crystal diffraction study at 300 K (hexagonal, P63/mmc), 100 K (hexagonal, P63 mc) and 20 K (orthorhombic). The orthorhombic form (o) shows no superstructure and its unit cell is related to the hexagonal one (h): a o ≃ a h + b h , a o ≃ −a h + b h and c o ≃ c h . Bijvoet-pair examination confirms that it crystallizes in the noncentrosymmetric space group Cmc21. The hexagonal (P63 mc)-orthorhombic (Cmc21) structural phase transition is proved to be of second order.

High-temperature single-crystal X-ray diffraction study of tetragonal and cubic perovskite-type PbTiO3phases

2016 ◽  
Vol 72 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Akira Yoshiasa ◽  
Tomotaka Nakatani ◽  
Akihiko Nakatsuka ◽  
Maki Okube ◽  
Kazumasa Sugiyama ◽  
...  
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Single Crystal ◽  
Diffraction Study ◽  
Relative Displacement ◽  
High Temperature Phase ◽  
Cubic Phase ◽  
Temperature Phase ◽  
X Ray Diffraction ◽  
X Ray

A high-temperature single-crystal X-ray diffraction study of a synthetic PbTiO3perovskite was carried out over the wide temperature range 298–928 K. A transition from a tetragonal (P4mm) to a cubic (Pm \bar 3 m) phase has been revealed near 753 K. In the non-centrosymmetricP4mmsymmetry group, the difference in relative displacement between Pb and O along thec-axis is much larger than that between Ti and O. The Pb and Ti cations contribute sufficiently to polarization being shifted in the opposite direction compared with the shift of O atoms. Deviation from the linear changes in Debye–Waller factors and bonding distances in the tetragonal phases can be interpreted as a precursor phenomenon before the phase transition. Disturbance of the temperature factorUeqfor O is observed in the vicinity of the transition point, whileUeqvalues for Pb and Ti are continuously changing with increasing temperature. The O site includes the clear configurational disorder in the cubic phase. The polar local positional distortions remain in the cubic phase and are regarded as the cause of the paraelectricity. Estimated values of the Debye temperature ΘDfor Pb and Ti are 154 and 467 K in the tetragonal phase and decrease 22% in the high-temperature phase. Effective potentials for Pb and Ti change significantly and become soft after the phase transition.

The low-temperature form of calcium gold stannide, CaAuSn

2014 ◽  
Vol 70 (8) ◽  
pp. 773-775 ◽  
Author(s):  
Qisheng Lin ◽  
John D. Corbett
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Single Crystal ◽  
Diffraction Analysis ◽  
Orthorhombic Symmetry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Symmetry Space ◽  
High Temperature Polymorph ◽  
Symmetry Space Group

The EuAuGe-type CaAuSn phase has been synthesized and single-crystal X-ray diffraction analysis reveals that it has an orthorhombic symmetry (space groupImm2), witha= 4.5261 (7) Å,b= 7.1356 (11) Å andc= 7.8147 (11) Å. The structure features puckered layers that are connected by homoatomic Au—Au and Sn—Sn interlayer bonds. This structure is one of the two parent structures of its high-temperature polymorph (ca873 K), which is an intergrowth structure of the EuAuGe- and SrMgSi-type structures in a 2:3 ratio.

Kristallstrukturen, Schwingungsspektren und Normalkoordinatenanalyse von cis-(n-Bu4N)2[ReBr4(NCS)(SCN)], trans-(n-Bu4N)2[ReBr4(NCS)(SCN)] und trans-(n-Bu4N)2[ReBr4(NCSe)(SeCN)]

1999 ◽  
Vol 54 (8) ◽  
pp. 1009-1014 ◽  
Author(s):  
L. Homolya ◽  
W. Preetz
Keyword(s):  
Low Temperature ◽  
Single Crystal ◽  
Diffraction Analysis ◽  
Raman Spectra ◽  
Monoclinic Space Group ◽  
X Ray Diffraction ◽  
Normal Coordinate ◽  
Space Group ◽  
X Ray ◽  
Ir And Raman

The crystal structures of cis-(n-Bu4N)2[ReBr4(NCS)(SCN)] (1) (monoclinic, space group P21/n, a = 11.203(3), b = 11.738(5), c = 35.218(7) Å, β = 93.434(4)°, Z = 4), trans-(n-Bu4N)2[ReBr4(NCS)(SCN)] (2) (monoclinic, space group P21/n, a = 11.644(7), b = 13.695(3), c = 29.028(8) Å, β = 95.96(4)° Z = 4) and trans-(n-Bu4N)2[ReBr4(NCSe)(SeCN)] (3) (monoclinic, space group P21/n, a = 11.894(2), b = 13.737(2), c = 28.869(7) Å, β = 96.98(10)° Z = 4) have been determined by single crystal X-ray diffraction analysis. Based on these molecular parameters the low temperature (10 K) IR and Raman spectra of the (n-Bu4N) salts have been assigned by normal coordinate analysis. The valence force constants are fd(ReN) = 1.70 (1), 1.75 (2) and 1.75 (3), fd(ReS) = 1.32 (1) and 1.37 (2) and fd(ReSe) = 1.20 mdyn/Å (3).

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