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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 78-81 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The geometric parameters related to the point in the coordination polyhedron having the minimum variation of distances to the vertices (`the centroid of the coordination polyhedron') are proposed as a measure of polyhedral irregularity or deformation. The numerical method for the determination of the centroid coordinates is described. Knowing these coordinates, the radius of the sphere circumscribed to the coordination polyhedron, the degree of sphericity of coordination, the principal axes of the ellipsoid fitted to the polyhedron and the displacement of the central atom from the centroid are calculated. These quantities are measures for various aspects of irregularity in the coordination polyhedron. The centroid calculation has been applied to the family of ABS2-type sulfides with cations in slightly to highly deformed octahedral coordinations.
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 16 (1983), S. 505-507 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A specific case of the doping method [Popovic & Grzeta-Plenkovic (1979). J. Appl. Cryst. 12, 205–208] is elaborated, in which the weight fraction of a crystalline component in the multicomponent system can be determined from the measurement of diffraction line intensities of that component only. Optimum conditions to attain maximum accuracy of the doping method are discussed.
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  • 3
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 29 (1996), S. 305-306 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 766-773 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new global measure of distortion for coordination polyhedra is proposed, based on a comparison of the ratios Vs(circumscribed sphere)/Vp(polyhedron) calculated, respectively, for the real and ideal polyhedra of the same number of coordinated atoms which have the same circumscribed sphere. This formula can be simplified to υ (%) = 100[Vi(ideal) − Vr(real)]/Vi, where Vi and Vr are the volumes of the above-defined polyhedra. The global distortion can be combined with other polyhedral characteristics, e.g. with the eccentricity of the central atom in the polyhedron or with the degree of sphericity of the coordination sphere [Balic Zõunic & Makovicky (1996). Acta Cryst. B52, 78–81].Vs/Vp ratios are given for a number of ideal polyhedra, including several types of trigonal coordination prisms, with the aim of facilitating the distortion calculations. The application examples included in the paper are: complex sulfides based on PbS and SnS archetypes, coordination polyhedra of large cations in feldspars, a phase transformation in a monoclinic amphibole and the subdivision of structures isopointal to ilmenite.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Mineralogy and petrology 53 (1995), S. 265-276 
    ISSN: 1438-1168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Description / Table of Contents: Zusammenfassung Die synthetische Phase TlPbSbS3 ist ein seltenes Beispiel von einem Sulfosalz mit der statistischen Verteilung von TI, Pb und Sb in der Struktur. In der TlSbS2-PbS Phasensystem, ist TlPbSbS3 das Endmitglied der Mischkristallreihe, die sich im Richtung TlSbS2 ausstreckt. Weitere Ausdehnung der Mischkristallreihe in der Richtung SbS konnte nicht bewiesen werden. Die Hochtemperaturβ-TlPbSbS3 ist rhombisch und wird beim 620 K in die Tieftemperaturα Modifikation umgewandelt. Die Tieftemperaturphase ist mit der Röntgenpulverdiffraktion und Rietveld Methode strukturell untersucht worden. Die ist monoklin, mit den Gitterkonstanten: a = 4.1707(4) Å, b = 4.2856(4) Å, c = 12.157(1) Å,β = 105.49(1)°, Raumgruppe P21/c. Die statistische Verteilung von Kationen ist auch hier vorhanden. Die zwischenatomare Abstande (Tl, Pb, Sb)-S sind: 2.71, 2.72, 2.88, 3.14, 3.28, 3.51 (Å). Es besteht eine enge Verwandschaft zwischen den polymorphen Modifikationen von TlPbSbS3 und denα undβ Polymorphen von SnS, was die atomare Koordinationen und den generellen Strukturtypus betrifft, wobei ein ähnlicher Mechanismus der Phasenumwandlung für die beiden Fälle vermutet werden könnte. Die Differenzen in der Struktur und Symmetrie zwischen der Tieftemperaturmodifikationen von SnS und TlPbSbS3 sind wahrscheinlich durch die bedeutende Metall-Metall Wirkungen in der zweiten verursacht. Die Phase TlPbSbS3 ist ein “substitution-derivative” von der SnS Struktur, was durch die starke “lone-electron-pair” Aktivität von Kationen zu erklären ist. Die Ersetzung von Tl durch Ag und Sb durch Bi vermindert diese Aktivität und die entstandenen Strukturen sind in dem Fall dem PbS-Typus verwandt.
    Notes: Summary The synthetic TlPbSbS3 represents a rare example of a sulphosalt with statistical distribution of Tl, Pb and Sb in the structure. Within the TlSbS2-PbS system, TlPbSbS3 is the end member of the solid solution series with TlSbS2, but no solubility with PbS is detected. The high temperatureβ-TlPbSbS3 is orthorhombic and inverts at about 620 K to the low-temperatureα phase. The low-temperature modification of TlPbSbS3 was structurally investigated by X-ray powder diffraction and by the Rietveld analysis of the data. The structure is monoclinic, with a = 4.1707(4) Å, b = 4.2856(4) Å, c = 12.157(1) Å,β = 105.49(1)°, space group P21/c. Like in the high-temperature form, there is a cation disorder over the equivalent positions in the structure. The interatomic distances of (Tl, Ph, Sb) to S are 2.71, 2.72, 2.88, 3.15, 3.29, 3.51 (Å). There is a close similarity between the TlPbSbS3 polymorphs and theα andβ forms of SnS, as regards the atomic coordinations and the general structure types and the same type of phase transformation is supposed for both cases. The small differences in the structure type and symmetry, between the low temperature forms of SnS and TlPbSbS3, result probably from stronger metal-metal interactions in the latter. A substitution-derivative relation to SnS type is established owing to the strong structural effect of the lone electron pairs of Tl and Sb. The substitution of Ag for Tl and Bi for Sb in ABCS3 type compounds diminishes this effect and PbS type structures are produced.
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  • 6
    ISSN: 1662-9752
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 7
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 228-231 (July 1996), p. 43-48 
    ISSN: 1662-9752
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 8
    Publication Date: 2009-05-15
    Print ISSN: 0013-936X
    Electronic ISSN: 1520-5851
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
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  • 9
    Publication Date: 2011-07-01
    Description: The first single-crystal structure refinement of Ag- and Cu-free heyrovsk[y]ite was performed in this study. Crystals investigated were sampled from the high-temperature fumaroles of La Fossa crater of Vulcano, Aeolian Islands, Italy. Electron microprobe analyses gave the average chemical formula (Pb5.86Cd0.03){sum}5.89Bi2.04(S8.52Se0.53Cl0.03){sum}9.08, which is very close to the ideal composition of heyrovsk[y]ite, Pb6Bi2S9. Lattice parameters are a = 13.7498(4), b = 31.5053(8), c = 4.1475(1) A, V = 1796.7(1) A3, space group Bbmm. The structure refinement converges to R = 4.17% for 1312 reflections with Fo 〉 4{sigma}(Fo). In Ag-free heyrovsk[y]ite from Vulcano, as well as in the synthetic Pb6Bi2S9, the trigonal prismatic coordinated position Me1, as well as the octahedrally coordinated position Me3 are occupied only by Pb. Me2, also octahedrally coordinated, is dominated by Pb, whereas the octahedra situated at the edges of the octahedral layers (Me4 and Me5) are centered around mixed (Pb,Bi) positions, with almost equal occupancy. The octahedrally coordinated site Me3 was found to incorporate vacancies ({square}), created by the substitution 3Pb2+ [-〉] 2Bi3++{square}, which allows for the observed deviations from the ideal composition, Pb6Bi2S9. Selenium is preferentially ordered at the fivefold-coordinated anionic sites. Taking into account vacancies, as well as Se for S substitutions the structural formula of Ag-free heyrovsk[y]ite from Vulcano is Pb5.82Bi2.12{square}0.06S8.70Se0.30. Comparison with the Ag-bearing heyrovsk[y]ite structures shows that during the 2 Pb [-〉] Ag(Cu)+Bi substitution the increased content of Bi is incorporated preferentially in the Me5 site until 2/3 Bi occupancy and thereafter in the two central octahedrally coordinated sites (Me2 and Me3). Silver occupies exclusively marginal octahedrally coordinated Me4 site like in the other members of the lillianite homologous series. The observed crystal chemical characteristics of the Ag-free heyrovsk[y]ite are in accordance with a model suggested by Callegari and Boiocchi, which describes the monoclinic form, aschamalmite, as an ordered polymorph of Pb6Bi2S9, and heyrovsk[y]ite as a fully disordered polymorph of the same compound. Ag incorporation is expected to increase the Pb/Bi disorder and to stabilize the orthorhombic heyrovsk[y]ite form.
    Print ISSN: 0003-004X
    Electronic ISSN: 1945-3027
    Topics: Geosciences
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  • 10
    Publication Date: 2012-10-01
    Description: A synthetic single crystal of pure orthoenstatite (MgSiO 3 , space group Pbca ) has been investigated at high pressure for structural determinations by in situ single-crystal X-ray diffraction using a diamond-anvil cell. Ten complete intensity data collections were performed up to 9.36 GPa. This study significantly improved the accuracy of structural parameters in comparison to a previous high-pressure structural study, allowing a more detailed examination of structural behavior of orthoenstatite at high pressures and a comparison to other more recent structural studies performed on orthopyroxenes with different compositions. The structural evolution determined in this work confirms the high-pressure evolution found previously for other orthopyroxenes and removes some ambiguities originating from the less accurate published data on the MgSiO 3 structure at high pressure. The structural compression is mostly governed by significant volume decrease of the Mg1 and Mg2 octahedra, affecting in turn the kink of the tetrahedral chains, especially the TB chain of larger SiO 4 tetrahedra. The Mg2 polyhedron undergoes the largest volume variation, 8.7%, due especially to the strong contraction of the longest bond distance (Mg2-O3B), whereas Mg1 polyhedral volume decreases by about 7.4%. The compressional behavior of the tetrahedral sites is quite different from previously published data. The TA and TB tetrahedral volumes decrease by about 2.8 and 1.8%, respectively, and no discontinuities can be observed in the pressure range investigated. Using the data on the pure orthoenstatite as reference, we can confirm the basic influences of element substitutions on the evolution of the crystal structure with pressure.
    Print ISSN: 0003-004X
    Electronic ISSN: 1945-3027
    Topics: Geosciences
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