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Journal articles on the topic 'Aristotype'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2025

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1

HAUCK, J., and K. MIKA. "INTERACTIONS FROM SELF-COORDINATION NUMBERS – A PHYSICAL RELATION WITHOUT FORMULA." International Journal of Modern Physics B 20, no. 14 (2006): 2065–84. http://dx.doi.org/10.1142/s0217979206034315.

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A large number of homogeneous particles A with different A–A interactions like carbon atoms in diamond, CO 3 ions in CaCO 3, S 6 molecules in rhombic sulphur, colloid or micelle particles are ordered in such a way that the bulk structure can be characterized by the self-coordination numbers Ti, i =1-3 of nearest, second and third neighbors. There are about 500 sets with increased Ti values (aristotypes) and about 500 sets with reduced Ti values, which are obtained from characteristic lattice complexes. The number k=1,2,3, etc. of the (T1 T2 T3) aristotype is added to the Wyckoff letters of sta

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2

Girgsdies, Frank, and Malte Behrens. "On the structural relations of malachite. I. The rosasite and ludwigite structure families." Acta Crystallographica Section B Structural Science 68, no. 2 (2012): 107–17. http://dx.doi.org/10.1107/s0108768112005125.

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The crystal structures of malachite Cu2(OH)2CO3 and rosasite (Cu,Zn)2(OH)2CO3, though not isotypic, are closely related. A previously proposed approach explaining this relation via a common hypothetical parent structure is elaborated upon on the basis of group–subgroup considerations, leading to the conclusion that the aristotype of malachite and rosasite should crystallize in the space group Pbam (No. 55). An ICSD database search for actual representatives of this aristotype leads to the interesting observation that the structure type of ludwigite (Mg,Fe)2FeO2BO3, which is adopted by several

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3

Cochrane, Amber K., Michael Telfer, Charlotte A. L. Dixon, et al. "NdBaScO4: aristotype of a new family of geometric ferroelectrics?" Chemical Communications 52, no. 73 (2016): 10980–83. http://dx.doi.org/10.1039/c6cc05940f.

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4

Le Bail, A. "Crystal structure of NaAlF4, a new aristotype." Powder Diffraction 24, no. 4 (2009): 301–5. http://dx.doi.org/10.1154/1.3257603.

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A model for the long awaited crystal structure of metastable NaAlF4 is established from the powder diffraction pattern of a partly disproportionated sample. Orthorhombic, Cmcm, a=3.6121(3), b=14.952(1), c=5.2692(4) Å, Z=4, V=284.58(4) Å3. Sodium atoms are in NaF6 trigonal prisms interconnected by edges in compact layers. AlF6 octahedra are both cis- and trans-corner connected forming a layer structure similar to that observed in the NaNbO2F2 (P21/c) and BaZnF4 (Cmc21) structure types. NaAlF4 is ideally simple and symmetrical, isostructural with BiReO4 (Cmcm), representing the aristotype of the

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5

Abrahams, S. C. "Atomic displacements at and order of all phase transitions in multiferroic YMnO3 and BaTiO3." Acta Crystallographica Section B Structural Science 65, no. 4 (2009): 450–57. http://dx.doi.org/10.1107/s0108768109021144.

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Coordinate analysis of the multiple phase transitions in hexagonal YMnO3 leads to the prediction of a previously unknown aristotype phase, with the resulting phase-transition sequence: P63′cm′(e.g.) ↔ P63 cm ↔ P63/mcm ↔ P63/mmc ↔ P6/mmm. Below the Néel temperature T N ≃ 75 K, the structure is antiferromagnetic with the magnetic symmetry not yet determined. Above T N the P63 cm phase is ferroelectric with Curie temperature T C ≃ 1105 K. The nonpolar paramagnetic phase stable between T C and ∼ 1360 K transforms to a second nonpolar paramagnetic phase stable to ∼ 1600 K, with unit-cell volume one

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6

PROTS, Yurii, Micha DEPPE, Raul CARDOSO-GIL, et al. "Yb2Al15Pt6 - the most ordered variety of the Sc1.2Fe4Si9.8 aristotype." Chemistry of Metals and Alloys 7, no. 1/2 (2014): 85–99. http://dx.doi.org/10.30970/cma7.0276.

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7

Stein, Sebastian, and Rainer Pöttgen. "Rows of corner- and face-sharing Mg4 tetrahedra arranged as hexagonal rod packing in the hexagonal Laves phases REMg2 and the rare earth-rich phases RE9CoMg4 (RE=Y, Dy-Tm, Lu)." Zeitschrift für Kristallographie - Crystalline Materials 233, no. 9-10 (2018): 607–13. http://dx.doi.org/10.1515/zkri-2017-2124.

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Abstract Six new rare earth metal-rich intermetallic compounds RE9CoMg4 with RE=Y, Dy, Ho, Er, Tm and Lu were synthesized by induction-melting the elements in sealed niobium ampoules followed by annealing in muffle furnaces. The structures of Y9CoMg4 and Tm8.56CoMg4.44 were refined from single-crystal X-ray diffraction data: P63/mmc, a=965.65(6), c=971.07(5) pm, wR2=0.0599, 614 F2 values, 20 variables for Y9CoMg4 and a=945.20(4), c=953.11(5) pm, wR2=0.0358, 585 F2 values, 21 variables for Tm8.56CoMg4.44 (a small homogeneity range results from Tm/Mg mixing). The RE9CoMg4 phases crystallize with

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8

Morita, Kazuki, Daniel W. Davies, Keith T. Butler, and Aron Walsh. "Breaking the Aristotype: Featurization of Polyhedral Distortions in Perovskite Crystals." Chemistry of Materials 34, no. 2 (2022): 562–73. http://dx.doi.org/10.1021/acs.chemmater.1c02959.

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9

Howard, C. J., and H. T. Stokes. "Group-Theoretical Analysis of Octahedral Tilting in Perovskites." Acta Crystallographica Section B Structural Science 54, no. 6 (1998): 782–89. http://dx.doi.org/10.1107/s0108768198004200.

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A group-theoretical analysis is made of the structures derived from the aristotype cubic perovskite (Pm3¯m) by the simple tilting of rigid octahedral units. The tilting is mediated by the irreducible representations R^+_4 and M^+_3 or the two in combination. These result in 15 possible structures, compared with the 23 possibilities suggested previously by Glazer [Acta Cryst. (1972), B28, 3384–3392]. The analysis makes the group–subgroup relationships apparent.

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10

Knight, Kevin S. "Crystallographic parameterisation of distortions in the SOD framework in the sodalite and helvine groups: An analysis in condensed normal modes of an aristotype phase." Mineralogical Magazine 86, no. 1 (2022): 87–102. http://dx.doi.org/10.1180/mgm.2022.4.

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AbstractCrystallographic distortions in the alternating aluminium and silicon tetrahedral framework of sodalite (Na8Al6Si6O24Cl2), and beryllium and silicon in helvine (Mn8Be6Si6O24S2), (framework designated SOD) are described in terms of a set of condensed normal mode amplitudes and phases derived from an ideal tetrahedron of a theoretical aristotype phase. For a sodalite-structured hettotype phase in space group $P{\overline 4} 3n$, these normal modes transform as the irreducible representations A1, E(α) and T1(z) of point-group ${\overline 4} 3m$, where to a good approximation A1 acts as a

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11

Howard, Christopher J., Brendan J. Kennedy, and Patrick M. Woodward. "Ordered double perovskites – a group-theoretical analysis." Acta Crystallographica Section B Structural Science 59, no. 4 (2003): 463–71. http://dx.doi.org/10.1107/s0108768103010073.

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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 a

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12

Haines, J., C. Chateau, J. M. Léger, et al. "Crystal structure of moganite-type phosphorus oxynitride: relationship to other twinned-quartz-based structures." Acta Crystallographica Section B Structural Science 55, no. 5 (1999): 677–82. http://dx.doi.org/10.1107/s010876819900347x.

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The structure of moganite-type phosphorus oxynitride quenched from high-pressure high-temperature conditions has been refined using neutron powder diffraction data. This moganite-type structure, space group I2/a, Z = 12, is slightly less distorted with respect to the Imab aristotype than is moganite (a monoclinic form of silica). A close topological relationship has been identified between the moganite-type and orthorhombic BeH2 structures indicating that SiO2, PON and BeH2 all adopt structures belonging to the twinned-quartz-based group. This group represents another possible structure type f

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13

Schultz-Coulon, Verena, and Wolfgang Schnick. "CaMg2N2 – ein gemischtes Erdalkalimetallnitrid mit anti-La2O3-Struktur / CaMg2N2 – a Mixed Alkaline-Earth Metal Nitride with anti-La2O3 Structure." Zeitschrift für Naturforschung B 50, no. 4 (1995): 619–22. http://dx.doi.org/10.1515/znb-1995-0425.

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CaMg2N2 (trigonal, P3̄ m 1 (Nr. 164); a = 354.046(1), c = 609.079(2) pm; Z = 1) is isotypic to the anti-La2O3 structure with octahedral and tetrahedral coordination for Ca2+ and Mg2+ ions, respectively. The compound has been prepared by the reaction o f the binary nitrides Ca3N2 and Mg3N2 (molar ratio 1:2) in a tungsten crucible under a pure nitrogen atmosphere at 1050 °C. The formation of the solid CaMg2N2 may be interpreted in analogy to reactions o f related oxides as an acid-base reaction between the binary nitrides with different coordination tendencies of Ca2+ and Mg2+ ions. An analysis

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14

Torgashev, V., Yu Yuzyuk, L. Latush, et al. "Infrared and Raman spectroscopy of Li2Ge7O15single crystals: spectra of the paraelectric and aristotype phases." Journal of Physics: Condensed Matter 7, no. 28 (1995): 5681–700. http://dx.doi.org/10.1088/0953-8984/7/28/021.

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15

Dixon, Charlotte A. L., Jason A. McNulty, Steven Huband, Pamela A. Thomas, and Philip Lightfoot. "Unprecedented phase transition sequence in the perovskite Li0.2Na0.8NbO3." IUCrJ 4, no. 3 (2017): 215–22. http://dx.doi.org/10.1107/s2052252517002226.

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The perovskite Li0.2Na0.8NbO3is shown, by powder neutron diffraction, to display a unique sequence of phase transitions at elevated temperature. The ambient temperature polar phase (rhombohedral, space groupR3c) transformsviaa first-order transition to a polar tetragonal phase (space groupP42mc) in the region 150–300°C; these two phases correspond to Glazer tilt systemsa−a−a−anda+a+c−, respectively. At 500°C a ferroelectric–paraelectric transition takes place fromP42mctoP42/nmc, retaining thea+a+c−tilt. Transformation to a single-tilt system,a0a0c+(space groupP4/mbm), occurs at 750°C, with the

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16

Gulay, Nataliya L., Yaroslav M. Kalychak, Maximilian K. Reimann, Christian Paulsen, Jutta Kösters, and Rainer Pöttgen. "Scandium-rich ternary coloring variants of the cubic Ag7+xMg26–x type." Monatshefte für Chemie - Chemical Monthly 151, no. 11 (2020): 1673–79. http://dx.doi.org/10.1007/s00706-020-02701-7.

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Abstract The scandium-rich intermetallic compounds Sc50T13In3 (T = Ni, Ru, Pd) were synthesized from the elements in sealed tantalum crucibles in an induction furnace. The samples were studied through Guinier powder patterns and their structures were refined from single-crystal X-ray diffractometer data. The Sc50T13In3 phases are site occupancy (coloring) variants of the aristotype Ag7+xMg26–x (Fm$$ \bar{3} $$ 3 ¯ , cF264). Refinements of the occupancy parameters indicated one mixed occupied site for each crystal, leading to the refined compositions Sc50Ni13.16(1)In2.84(1), Sc49.59(1)Ru13In3.4

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17

Zagorac, Jelena, Dejan Zagorac, Aleksandra Zarubica, J. Christian Schön, Katarina Djuris, and Branko Matovic. "Prediction of possible CaMnO3modifications using anab initiominimization data-mining approach." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 70, no. 5 (2014): 809–19. http://dx.doi.org/10.1107/s2052520614013122.

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We have performed a crystal structure prediction study of CaMnO3focusing on structures generated by octahedral tilting according to group–subgroup relations from the ideal perovskite type (Pm\overline 3 m), which is the aristotype of the experimentally known CaMnO3compound in thePnmaspace group. Furthermore, additional structure candidates have been obtained using data mining. For each of the structure candidates, a local optimization on theab initiolevel using density-functional theory (LDA, hybrid B3LYP) and the Hartree-–Fock (HF) method was performed, and we find that several of the modific

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18

Umayahara, Akihiro, and Massimo Nespolo. "Derivative structures based on the sphere packing." Zeitschrift für Kristallographie - Crystalline Materials 233, no. 3-4 (2018): 179–203. http://dx.doi.org/10.1515/zkri-2017-2125.

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Abstract A significant number of non-molecular crystal structures can be described as derivative structures of sphere packings, with variable degrees of distortion. The undistorted sphere packing model with all the cavities completely occupied is the aristotype, from which an idealized model of the real structure can be obtained as a substitution, undistorted hettotype. The real structure can then be seen as a distorted derivative of the substitution hettotype. In this article we revive the symbolism introduced by Zoltai and Stout to describe the substitution hettotypes and compare these with

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19

Engelbert, Simon, Rolf-Dieter Hoffmann, Jutta Kösters, Steffen Klenner, and Rainer Pöttgen. "Temperature-induced structural phase transitions in RERhSn (RE = Y, Gd-Tm, Lu)." Zeitschrift für Kristallographie - Crystalline Materials 236, no. 3-4 (2021): 93–104. http://dx.doi.org/10.1515/zkri-2021-2008.

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Abstract The structures of the equiatomic stannides RERhSn with the smaller rare earth elements Y, Gd-Tm and Lu were reinvestigated on the basis of temperature-dependent single crystal X-ray diffraction data. GdRhSn crystallizes with the aristotype ZrNiAl at 293 and 90 K. For RE = Y, Tb, Ho and Er the HP-CeRuSn type (approximant with space group R3m) is already formed at room temperature, while DyRhSn adopts the HP-CeRuSn type below 280 K. TmRhSn and LuRhSn show incommensurate modulated variants with superspace groups P31m(1/3; 1/3; γ) 000 (No. 157.1.23.1) (γ = 3/8 for TmRhSn and γ = 2/5 for L

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20

Hahn, Friedemann, and Werner Massa. "Topotaktische Entwässerung von Cs2MnF5 · H2O zu Cs2MnF5 und die Kristallstrukturen beider Verbindungen / Topotactical Dehydration of Cs2MnF5 · H2O to Cs2MnF5 and the Crystal Structures of Both Compounds." Zeitschrift für Naturforschung B 45, no. 10 (1990): 1341–48. http://dx.doi.org/10.1515/znb-1990-1001.

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Redetermination of the crystal structure of Cs2MnF5 · H2O (space group Cmm 2, Z = 2, a = 974.0(2), b = 867.4(1), c = 426.0(1) pm, R = 0.026 for 478 reflections) revealed ordered instead of disordered positions of water molecules indicating ferroelectric properties. The dehydration of a twinned crystal gave an untwinned single crystal of Cs2MnF5 by a topotactical reaction. The crystal structure of Cs2MnF5 (space group P4/mmm, Z = 1, a = 642.0(1), c = 422.9(1) pm, R = 0.034 for 175 reflections) shows trans-connected octahedral chains [MnF5]∞2- with 180° Mn-F-Mn bridge angles like in the monohydr

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21

Guo, Yuan-Yuan, Alexandra S. Gibbs, J. Manuel Perez-Mato, and Philip Lightfoot. "Unexpected phase transition sequence in the ferroelectric Bi4Ti3O12." IUCrJ 6, no. 3 (2019): 438–46. http://dx.doi.org/10.1107/s2052252519003804.

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The high-temperature phase behaviour of the ferroelectric layered perovskite Bi4Ti3O12 has been re-examined by high-resolution powder neutron diffraction. Previous studies, both experimental and theoretical, had suggested conflicting structural models and phase transition sequences, exacerbated by the complex interplay of several competing structural instabilities. This study confirms that Bi4Ti3O12 undergoes two separate structural transitions from the aristotype tetragonal phase (space group I4/mmm) to the ambient-temperature ferroelectric phase (confirmed as monoclinic, B1a1). An unusual, a

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22

Seidel, Stefan, Wolfgang G. Zeier, and Rainer Pöttgen. "The polymorphs of the Na+ ion conductor Na3PS4 viewed from the perspective of a group-subgroup scheme." Zeitschrift für Kristallographie - Crystalline Materials 235, no. 1-2 (2020): 1–6. http://dx.doi.org/10.1515/zkri-2019-0053.

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AbstractThe Na+ solid state electrolyte Na3PS4 is currently being investigated due to its high ionic conductivity and its synthesis-dependent crystal structure. Na3PS4 adopts a tetragonal low-temperature modification with space group P 4̅21c that transforms to a cubic high-temperature modification with space group I 4̅3m (Tl3VS4 type). These two modifications are related by a group-subgroup scheme. The symmetry reduction proceeds via a translationengleiche transition from I 4̅3m to I 4̅2m and subsequently via a klassengleiche transition to P 4̅21c. The tetragonal phase with space group I 4̅2m

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23

Howard, Christopher J., and Harold T. Stokes. "Octahedral tilting in cation-ordered perovskites – a group-theoretical analysis." Acta Crystallographica Section B Structural Science 60, no. 6 (2004): 674–84. http://dx.doi.org/10.1107/s0108768104019901.

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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 irreduc

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24

Hlukhyy, Viktor, Ute Ch Rodewald, Rolf-Dieter Hoffmann, and Rainer Pöttgen. "Synthesis and Structure of RhMg3 and Ir3Mg13." Zeitschrift für Naturforschung B 59, no. 3 (2004): 251–55. http://dx.doi.org/10.1515/znb-2004-0301.

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The binary transition metal magnesium compounds RhMg3 and Ir3Mg13 have been synthesized from the elements in sealed niobium tubes and investigated on the basis of X-ray powder and single crystal data: Cu3P type, P63cm, a = 790.5(4), c = 825.6(3) pm, wR2 = 0.0244, 344 F2 values, 27 variable parameters for RhMg3, and R3̅c, a = 1607.0(2), c = 844.88(9) pm, wR2 = 0.0535, 656 F2 values, 29 variable parameters for Ir3Mg13. The rhodium atoms in RhMg3 have coordination number 11. These polyhedra show an AB AB stacking sequence like in the hexagonal close-packed structure. The crystal chemical relation

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25

Le Bail, A., та A. M. Mercier. "Distorted chiolite crystal structures of α-Na5M3F14 (M=Cr,Fe,Ga) studied by X-ray powder diffraction". Powder Diffraction 18, № 2 (2003): 128–34. http://dx.doi.org/10.1154/1.1556990.

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The crystal structures of the chiolite-related room temperature phases α-Na5M3F14 (MIII=Cr,Fe,Ga) are determined. For all of them, the space group is P21/n, Z=2; a=10.5096(3) Å, b=7.2253(2) Å, c=7.2713(2) Å, β=90.6753(7)° (M=Cr); a=10.4342(7) Å, b=7.3418(6) Å, c=7.4023(6) Å, β=90.799(5)° (M=Fe), and a=10.4052(1) Å, b=7.2251(1) Å, c=7.2689(1), β=90.6640(4)° (M=Ga). Rietveld refinements produce final RF factors 0.036, 0.033, and 0.035, and RWP factors, 0.125, 0.116, and 0.096, for MIII=Cr, Fe, and Ga, respectively. The MF6 polyhedra in the defective isolated perovskite-like layers deviate very f

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26

Benndorf, Christopher, Hellmut Eckert, Jutta Kösters, and Rainer Pöttgen. "Equiatomic transition metal (T) silicides TT′Si: systematics of ²⁹Si NMR Knight shifts." Zeitschrift für Naturforschung B 79, no. 12 (2024): 583–94. https://doi.org/10.1515/znb-2024-0015.

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Abstract A series of 64 ternary equiatomic tetrelides TT′Tt (T = electron-poor transition metal; T′ = electron-rich transition metal; Tt = Si, Ge) was synthesized by arc-melting and subsequent annealing. The samples were characterized by powder X-ray diffraction and 20 structures were refined from single-crystal X-ray diffractometer data. These tetrelides (mostly silicides) crystallize with TiNiSi-related structures, orthorhombic space groups Pnma. They are ternary ordered, orthorhombically distorted superstructure variants of the aristotype AlB2. The precise single-crystal data show distinct

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27

Malchus, M., and M. Jansen. "Structural Investigations of the Phase Transitions of Tetramethylammonium Sulfate." Acta Crystallographica Section B Structural Science 54, no. 4 (1998): 494–502. http://dx.doi.org/10.1107/s0108768197018351.

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Tetramethylammonium sulfate, [N(CH3)4]2SO4, was prepared in high purity via ion exchange. Two reversible first-order phase transitions at 263 ± 3 and 462 ± 3 K have been established by differential thermal analysis and temperature-dependent X-ray powder diffraction. Crystal structure determinations at 223 and 293 K reveal completely ordered sulfate and tetramethylammonium tetrahedra for the low-temperature modification, while at room temperature half of the sulfate groups are orientationally disordered. The space groups are P42/nmc with a = 7.5355 (9), c = 10.9910 (14) Å and Z = 2 [wR(F 2) = 0

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Berger, Patric, Clemens Schmetterer, Herta Silvia Effenberger, and Hans Flandorfer. "Crystal structure relations in the binary system Li–Sn including the compound c-Li3Sb." Zeitschrift für Kristallographie - Crystalline Materials 235, no. 12 (2020): 581–90. http://dx.doi.org/10.1515/zkri-2020-0036.

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AbstractA topological analysis of the crystal structures of Li, Li–Sn compounds, Li8Sn3−xSbx and metastable c-Li3Sb showed that these structures can be described by a hierarchical scheme of building blocks based on atom blocks and polyhedra blocks, respectively. These blocks are linked in distinct ways to form the individual 3D atom arrangement. A common model was established for the construction of the mentioned structures from bespoke building blocks, for which bcc-Li is the aristotype. This latter structure can be described on the basis of hexa-capped cubes from which variants are derived t

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Rafailov, Gennady, Isaac Dahan, and Louisa Meshi. "New ordered phase in the quasi-binary UAl3–USi3system." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 70, no. 3 (2014): 580–85. http://dx.doi.org/10.1107/s2052520614003801.

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The industrial importance of the U–Al–Si system stems from the fact that during processing the Al-based alloy (containing Si as impurity), used for the cladding of U (fuel in nuclear reactors), undergoes heat treatment which stimulates diffusion between the fuel and the cladding. One of the possible ways to represent the ternary U–Al–Si phase diagram is the construction of an UAl3–USi3quasi-binary phase diagram. On the one hand, since the UAl3and USi3phases are isostructural, an isomorphous phase diagram is expected; on the other hand, some researchers observed a miscibility gap at lower tempe

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Falkowski, Viktoria, Alexander Zeugner, Stefan Seidel, et al. "Syntheses and crystal structures of the manganese hydroxide halides Mn5(OH)6Cl4, Mn5(OH)7I3, and Mn7(OH)10I4." Zeitschrift für Kristallographie - Crystalline Materials 235, no. 8-9 (2020): 375–89. http://dx.doi.org/10.1515/zkri-2020-0040.

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AbstractSingle-crystals of the new manganese hydroxide halides Mn5(OH)6Cl4, Mn5(OH)7I3, and Mn7(OH)10I4 were obtained by means of high-pressure/high-temperature synthesis in a Walker-type multianvil apparatus. The chloride crystallizes in the monoclinic space group P21/c (no. 14) with the lattice parameters (single-crystal data) a = 592.55(8), b = 1699.7(2), c = 597.33(8) pm, and β = 112.58(1)°. The iodides crystallize in the triclinic space group P$\bar{1}$ (no. 2) with a = 653.16(2), b = 905.98(3), c = 1242.98(4) pm, α = 114.21(1)°, β = 99.91(1)°, and γ = 94.37(1)° for Mn5(OH)7I3 and a = 656

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31

Knight, K. S. "PARAMETERIZATION OF CENTROSYMMETRIC ELPASOLITE-TYPE CRYSTAL STRUCTURES IN TERMS OF SYMMETRY-ADAPTED BASIS-VECTORS OF THE PRIMITIVE CUBIC ARISTOTYPE PHASE." Canadian Mineralogist 47, no. 2 (2009): 401–20. http://dx.doi.org/10.3749/canmin.47.2.401.

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Hoffmann, Rolf-Dieter, Daniel Voßwinkel, Samir F. Matar, and Rainer Pöttgen. "Quaternary Germanides RE 3 T Rh4 Ge4 (RE = Ce, Pr, Nd; T = Nb, Ta) - A New Coloring Variant of the Aristotype AlB2." Zeitschrift für anorganische und allgemeine Chemie 642, no. 18 (2016): 979–86. http://dx.doi.org/10.1002/zaac.201600225.

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Barnes, Paris W., Michael W. Lufaso, and Patrick M. Woodward. "Structure determination of A 2 M 3+TaO6 and A 2 M 3+NbO6 ordered perovskites: octahedral tilting and pseudosymmetry." Acta Crystallographica Section B Structural Science 62, no. 3 (2006): 384–96. http://dx.doi.org/10.1107/s0108768106002448.

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The room-temperature crystal structures of six A 2 M 3+ M 5+O6 ordered perovskites have been determined from neutron and X-ray powder diffraction data. Ba2YNbO6 adopts the aristotype high-symmetry cubic structure (space group Fm\overline 3m, Z = 4). The symmetries of the remaining five compounds were lowered by octahedral tilting distortions. Out-of-phase rotations of the octahedra about the c axis were observed in Sr2CrTaO6 and Sr2GaTaO6, which lowers the symmetry to tetragonal (space group = I4/m, Z = 2, Glazer tilt system = a 0 a 0 c −). Octahedral tilting analogous to that seen in GdFeO3 o

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Stein, Sebastian, Lukas Heletta, and Rainer Pöttgen. "Ternary indides RE3T2In4 (RE=Dy–Tm; T=Pd, Ir)." Zeitschrift für Naturforschung B 73, no. 11 (2018): 765–72. http://dx.doi.org/10.1515/znb-2018-0091.

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AbstractThe ternary rare earth transition metal-indides RE3T2In4 (RE=Dy–Tm; T=Pd, Ir) were obtained from high-temperature reactions in sealed niobium ampoules. These indides adopt a hexagonal structure of the Lu3Co1.87In4 type (space group P6̅), a ternary ordered superstructure of the aristotype Fe2P. The structures of three different compounds were refined from single-crystal X-ray diffractometer data: a=768.20(6), c=381.97(3) pm, 1441 F2 values, 24 parameters, wR2=0.0338 (Ho3Pd1.90In4); a=774.98(3), c=378.51(2) pm, 577 F2 values, 23 parameters, wR2=0.0742 (Ho3Ir1.69In4.31) and a=780.3(1), c=

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Matar, Samir F., and Rainer Pöttgen. "Coloring in the ZrBeSi-type structure." Zeitschrift für Naturforschung B 74, no. 4 (2019): 307–18. http://dx.doi.org/10.1515/znb-2019-0010.

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AbstractThe ZrBeSi type is a superstructure variant of the aristotype AlB2 with an ordering of the beryllium and silicon atoms on the boron network. Every other layer of Be3Si3 hexagons is rotated by 60°, leading to an ABAB stacking sequence and a sandwich-like coordination of zirconium by two Be3Si3 hexagons. The ZrBeSi type shows a pronounced coloring on its three crystallographic sites. Among the numerous compounds are electron-precise Zintl phases in the field of tetrelides, pnictides and chalcogenides, selenide hydrides and fluorides as well as intermetallic compounds. A variety of elemen

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36

Knoll, Manuel. "La giustizia distributiva tra Platone e Aristotele = Distributive Justice in Plato and Aristotle." ΠΗΓΗ/FONS 3, no. 1 (2019): 21. http://dx.doi.org/10.20318/fons.2019.4550.

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Riassunto: Secondo l’opinione prevalente tra gli studiosi di lingua tedesca, bisogna considerare Aristotele come colui che ha “scoperto” la giustizia particolare. Questo articolo dimostra che quest’opinione è errata, innanzitutto perché Platone aveva già precedentemente sviluppato, nella Repubblica e nelle Leggi, la dottrina della giustizia distributiva e il suo principio di uguaglianza geometrica o proporzionale. In un primo momento, l’articolo interpreta la dottrina della giustizia distributiva esposta da Aristotele nell’Etica Nicomachea e nella Politica. In un secondo momento, si mostra che

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37

Jin, Lei, Dimitrios Koulialias, Michael Schnedler, et al. "Atomic-Scale Characterization of Commensurate and Incommensurate Vacancy Superstructures in Natural Pyrrhotites." American Mineralogist 106, no. 1 (2021): 82–96. http://dx.doi.org/10.2138/am-2020-7479ccby.

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Abstract Pyrrhotites, characterized by the chemical formula Fe1–δS (0 &lt; δ ≤ 1/8), represent an extended group of minerals that are derived from the NiAs-type FeS aristotype. They contain layered arrangements of ordered Fe vacancies, which are at the origin of the various magnetic signals registered from certain natural rocks and can act as efficient electrocatalysts in oxygen evolution reactions in ultrathin form. Despite extensive studies over the past century, the local structural details of pyrrhotite superstructures formed by different arrangements of Fe vacancies remain unclear, in

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38

Knight, Kevin S., and C. Michael B. Henderson. "Defining an aristotype crystal structure and crystallographic distortions in leucite/pollucite-structured phases with space group $$Ia\overline {3} d$$ I a 3 ¯ d." Physics and Chemistry of Minerals 46, no. 6 (2019): 595–605. http://dx.doi.org/10.1007/s00269-019-01025-1.

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Knight, K. S. "PARAMETERIZATION OF THE CRYSTAL STRUCTURES OF CENTROSYMMETRIC ZONE-BOUNDARY-TILTED PEROVSKITES: AN ANALYSIS IN TERMS OF SYMMETRY-ADAPTED BASIS-VECTORS OF THE CUBIC ARISTOTYPE PHASE." Canadian Mineralogist 47, no. 2 (2009): 381–400. http://dx.doi.org/10.3749/canmin.47.2.381.

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Lufaso, Michael W., Paris W. Barnes, and Patrick M. Woodward. "Structure prediction of ordered and disordered multiple octahedral cation perovskites using SPuDS." Acta Crystallographica Section B Structural Science 62, no. 3 (2006): 397–410. http://dx.doi.org/10.1107/s010876810600262x.

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The software package SPuDS has previously been shown to accurately predict crystal structures of AMX 3 and A 1 − x A′ x MX 3 perovskites that have undergone octahedral tilting distortions. This paper describes the extension of this technique and its accuracy for A 2 MM′X 6 ordered double perovskites with the aristotype Fm\overline 3m cubic structure, as well as those that have undergone octahedral tilting distortions. A survey of the literature shows that roughly 70% of all ordered double perovskites undergo octahedral tilting distortions. Of the 11 distinct types of octahedral tilting that ca

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Eustermann, Fabian, Frank Stegemann, Simon Gausebeck, and Oliver Janka. "Structural and magnetic investigations of the pseudo-ternary RE2TAl3 series (RE=Sc, Y, La–Nd, Sm, Gd–Lu; T=Ru, Rh, Ir) – size dependent formation of two different structure types." Zeitschrift für Naturforschung B 73, no. 11 (2018): 819–30. http://dx.doi.org/10.1515/znb-2018-0124.

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AbstractSeveral rare earth metal containing pseudo-ternary compounds in the RE2TAl3 series (RE=Sc, Y, La–Nd, Sm, Gd–Lu; T=Ru, Rh, Ir) have been synthesized from the elements by arc-melting or in tantalum capsules. Within the Rh series, the compounds with RE=La–Nd crystallize in the cubic MgCu2-type (Fd3̅m) structure. For Sm besides the cubic Laves phase also the hexagonal Laves phase (MgZn2 type, P63/mmc) is found. For the remaining compounds of both series, also the hexagonal MgZn2-type structure is observed. The structures of Ho2Ru0.96(1)Al3.04(1) (a=547.4(1), c=875.7(1) pm, wR=0.0397, 201 F

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Abbate, Michele. "La Repubblica di Platone nell’esegesi simbolica, e metafisico-teologica di Proclo." ΠΗΓΗ/FONS 2, no. 1 (2017): 153. http://dx.doi.org/10.20318/fons.2017.3853.

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Riassunto: Delle diverse tematiche affrontate da Proclo nella sua articolata interpretazione della Repubblica di Platone, il saggio propone una disamina di alcune fra quelle che appaiono particolarmente significative per comprendere in quale direzione proceda complessivamente l’esegesi procliana del dialogo platonico: lo σκοπός (ossia l’argomento principale) e l’impianto simbolico della Repubblica (dissertazione I); la natura, la funzione e il ruolo della giustizia secondo l’esegesi procliana (dissertazioni III e VII-VIII); l’esame e la critica delle obiezioni mosse da Aristotele alla Repubbli

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Flores-Sanchez, Nelly, Ivonne Rosales, and Lauro Bucio. "Symmetry Relations Between Space Groups in Layered Germanate Structures: Modeling Crystal Structures." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1763. http://dx.doi.org/10.1107/s2053273314082369.

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Structural models for the new layered germanates ScInGe2O7 and ScFeGe2O7 were analyzed within the framework of symmetry relations between space groups. These compounds were supposed to be hettotypes of the thortveitite mineral, (Sc,Y)2Si2O7, which was considered as the aristotype. Thortveitite crystallizes in the monoclinic system, and the symmetry is described by the space group type C2/m. Other monoclinic hettotypes for the thortveitite are FeInGe2O7 (PDF 01-070-8447, ICSD - 94487), space group C2/m (No. 12); TbInGe2O7 (PDF 01-072-6515, ICSD - 96360), space group C2/c (No. 15); and FeYGe2O7

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44

Seidel, Stefan, Oliver Niehaus, Samir F. Matar, et al. "The Gallium Intermetallics REPdGa3 (RE=La, Ce, Pr, Nd, Sm, Eu) with SrPdGa3-type Structure." Zeitschrift für Naturforschung B 69, no. 11-12 (2014): 1105–18. http://dx.doi.org/10.5560/znb.2014-4119.

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Abstract The gallium-rich intermetallic phases REPdGa3 (RE=La, Ce, Pr, Nd, Sm, Eu) were obtained by arc-melting of the elements and subsequent annealing for crystal growth. The samples were studied by X-ray diffraction on powders and single crystals. The structures of three crystals were refined from X-ray diffractometer data: SrPdGa3 type, Cmcm, a=634.3(1), b=1027.2(1), c=593.5(1) pm, wR=0.0621, 380 F2 values, 20 variables for CePd0:80(4)Ga3:20(4), a=635.9(1), b=1027.5(1), c=592.0(1) pm, wR=0.1035, 457 F2 values, 19 variables for CePdGa3, and a=640.7(1), b=1038.2(1), c=593.7(1) pm, wR=0.0854,

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Yusupov, R. G., C. J. Stanley, M. D. Welch, et al. "Mavlyanovite, Mn5Si3: a new mineral species from a lamproite diatreme, Chatkal Ridge, Uzbekistan." Mineralogical Magazine 73, no. 1 (2009): 43–50. http://dx.doi.org/10.1180/minmag.2009.073.1.43.

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Mavlyanovite, ideally Mn5Si3, is a new mineral from a lamproite diatreme close to the upper reaches of the Koshmansay river, Chatkal ridge, Uzbekistan. It occurs together with unnamed manganese siliciphosphide and manganese silicicarbide minerals in round to ovoid segregations, up to 10 cm in diameter, in volcanic glass. Segregations of hexagonal prismatic mavlyanovite up to 1–2 mm occur in interstices in the matrix and tiny inclusions (1–2 μm) of alabandite and khamrabaevite occur within mavlyanovite. It is opaque with a metallic lustre, has a dark-grey streak, is brittle with a conchoidal fr

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Boffa Ballaran, Tiziana, Kanchana Kularatne, and Reidar Trønnes. "High-pressure structural behaviour of CaIrO3polymorphs." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C267. http://dx.doi.org/10.1107/s2053273314097320.

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The two known polymorphs of CaIrO3 crystallize int the orthorhombic space groups Pbnm and Cmcm. These compounds have been the focus of much research in the Earth sciences community because they are isostructural with MgSiO3 perovskite and post-perovskite structures which are likely the most abundant minerals in the Earth's lower mantle. CaIrO3 post-perovskite is stable at ambient conditions and transforms at 1-3 GPa and at temperatures above 13500C to the CaIrO3 perovskite structure providing an ideal low pressure and low temperature analogue for the MgSiO3 perovskite to post-perovskite phase

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Stöger, Berthold. "Symmetry reduction in thortveitites: incommensurability and polytypism." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C182. http://dx.doi.org/10.1107/s2053273314098179.

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For many years periodicity was the defining property of crystalline materials. The discovery of numerous aperiodic materials like incommensurately modulated phases or quasi-crystals led to a paradigm shift and since 1992 crystallinity is defined by the IUCr via the discreteness of the diffraction pattern [1]. A different class of materials lacking periodicity in three dimensions, albeit following strict building principles, are polytypes. Polytypes are composed of modules that can be arranged in different but energetically similar ways. On the example of the thortveitite family of compounds it

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Langenmaier, Michael, Julian Brantl, and Caroline Röhr. "New sodium-rich mixed Mn/In chalcogenido metallates Na12MnIn2Q10 (Q = S, Se)." Zeitschrift für Naturforschung B 75, no. 9-10 (2020): 825–32. http://dx.doi.org/10.1515/znb-2020-0125.

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AbstractThe sodium-rich sulfido and selenido metallates Na12MnIn2Q10 (Q = S/Se) were synthesized in pure phase from melts composed of stoichiometric quantities of the manganese monochalcogenides MnQ, elemental indium and the chalcogens together with either Na2S (Q = S) or elemental sodium (Q = Se) as starting material. The samples were heated up to maximum temperatures of 1000/900 °C under an argon atmosphere; crystallization was achieved by slow cooling rates of 10 K h−1. The two isotypic compounds (monoclinic, space group P21/m, a = 678.26(2)/698.85(10), b = 2202.77(7)/2298.7(3), c = 766.39(

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Weil, Matthias, and Berthold Stöger. "Crystal chemistry of transition metal diarsenates M 2As2O7 (M = Mn, Co, Ni, Zn): variants of the thortveitite structure." Acta Crystallographica Section B Structural Science 66, no. 6 (2010): 603–14. http://dx.doi.org/10.1107/s0108768110040802.

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The structures of the 3d divalent transition-metal diarsenates M 2As2O7 (M = Mn, Co, Ni, Zn) can be considered as variants of the monoclinic (C2/m) thortveitite [Sc2Si2O7] structure type with a ≃ 6.7, b ≃ 8.5, c ≃ 4.7 Å, α ≃ 90, β ≃ 102, γ ≃ 90° and Z = 2. Co2As2O7 and Ni2As2O7 are dimorphic. Their high-temperature (β) polymorphs adopt the thortveitite aristotype structure in C2/m, whereas their low-temperature (α) polymorphs are hettotypes and crystallize with larger unit cells in the triclinic crystal system in space groups P\bar 1 and P1, respectively. Mn2As2O7 undergoes no phase transition

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Weil, Matthias, and Enrique J. Baran. "Polymorphism of the Transition Metal Oxidotellurates NiTeO4 and CuTe2O5." Crystals 15, no. 2 (2025): 183. https://doi.org/10.3390/cryst15020183.

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As part of crystal growth experiments on transition metal oxidotellurates using chemical vapor transport reactions or hydrothermal conditions, single crystals of NiIITeVIO4 and CuIITeIV2O5 were obtained for the first time in the form of new modifications, as revealed by crystal structure determinations from X-ray data. In the course of these investigations, the crystal structure model of the only phase of NiIITeVIO4 reported so far (from now on named α-) was corrected. Both α-(space group P21/c, Z = 2) and the new β-polymorph of NiIITeVIO4 (space group I41/a, Z = 8) can be considered derivativ

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