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  • 1
    Electronic Resource
    Electronic Resource
    Crystal structure and charge distribution of YbFeMnO4 (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 805-810 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure of synthetic YbFeMnO4 has been refined by single-crystal X-ray diffraction. Space group R\bar 3m, a = 3.4580 (1), c = 25.647 (3) Å, V = 265.59 (3) Å3, Z = 3. Yb is in octahedral coordination, whereas Fe and Mn are disordered on a single crystallographic type of trigonal bipyramid, in which the cation is off-centred from the basal plane. Assuming perfect stoichiometry, R1 = 0.0195, but the charge distribution (CD) analysis suggests incomplete occupation of the Yb site. Refinement of the occupancy lowers R1 to 0.0175, resulting in s.o.f.(Yb) = 0.963 (3), with a significant improvement of the Fourier difference. The electroneutrality is likely preserved through incomplete occupancy of one of the two oxygen sites: the compound is thus non-stoichiometric, with the formula Yb0.963FeMnO3.945. Another mechanism for preserving the electroneutrality is the oxidation of a small amount of Mn2+ to Mn3+, which is, however, less probable because of the reduction conditions in which the sample was synthesized. Both models give a satisfactorily CD result, but they cannot be definitively distinguished by X-ray data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768100005383
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  • 2
    Electronic Resource
    Electronic Resource
    A TEM study of long-period mica polytypes: determination of the stacking sequence of oxybiotite by means of atomic resolution images and Periodic Intensity Distribution (PID) (1999)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 507-516 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In this study it is shown that the stacking sequences in long-period mica polytypes (including a rare example of a mixed-rotation polytype, with a 36-layer long periodicity) can be unambiguously determined using atomic resolution images recorded down two zone axes separated by 30° (e.g. [100] and [31¯0]) at the same area. Uniformity of these stacking sequences in a large area is further confirmed by the correspondence between computed and observed Periodic Intensity Distributions (PIDs) in electron diffraction patterns. The appearance of long-period polytypes containing layers with different orientation parity may be explained by the coalescence of two small crystals during crystal growth.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768199003845
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  • 3
    Electronic Resource
    Electronic Resource
    Charge distribution as a tool to investigate structural details. II. Extension to hydrogen bonds, distorted and hetero-ligand polyhedra (2001)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 652-664 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that one of the main reasons for most failures of the methods for calculating distance-dependent bond strengths is related to the distortion of the coordination polyhedra. The charge distribution (CD) method which depends on only one universal empirical parameter (contraction parameter) is modified to include: (i) an iterative calculation of the effective coordination number (ECoN), to deal with structures containing very distorted coordination polyhedra; (ii) a specific contraction parameter to treat structures containing any type of hydrogen bond; (iii) scale factors for coordination subshells, to treat structures with hetero-ligand polyhedra. The contraction parameter for the hydrogen bonds was obtained from 119 well refined structures based on neutron diffraction data. Examples of the application of the iterative charge distribution (CD-IT) are presented to show the efficiency of the new method in dealing with distorted (including hydrogen bonding) and hetero-ligand polyhedra. In particular, analysis of a series of 74 structures with pentacoordinated cations shows that deviations from overall trends are related to structure instability. The possible failure of the method with polyionic structures and `dynamic' structures is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768101009879
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  • 4
    Electronic Resource
    Electronic Resource
    Charge distribution as a tool to investigate structural details: meaning and application to pyroxenes (1999)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 902-916 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The charge distribution (CD) method, previously introduced as a development of the bond-valence (BV) approach, is applied for the first time to mineral structures, and specifically to pyroxenes. CD essentially involves the distribution of the Effective Coordination Number (ECoN) of a cation among all the neighboring anions. This distribution is then interpreted in terms of distribution of `charges', where `charge' represents the formal oxidation state. Differently from BV, the CD description depends upon the geometry of each coordination polyhedron, which is characterized through ECoN (a non-integer number). The contribution of each cation–oxygen bond to ECoN, labelled `bond weight', corresponds to the bond strength in the BV method, but it is defined in terms of bond-length ratio in each polyhedron and not as a function of the cation–oxygen pair. The ratio q/Q of the formal oxidation number to the computed charge can be interpreted as a measure of the correctness of the structure (cation ratio) and of the degree of over- or under-bonding (anion ratio). A similar interpretation is not possible for the analogous quantities obtained through the BV approach. The analysis in terms of CD of the pyroxene chains (from 101 structures) shows different trends as a function of composition, temperature and pressure; in particular it shows a different behaviour of the two crystallographically independent chains of orthopyroxenes and of P21/c clinopyroxenes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768199008708
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  • 5
    Electronic Resource
    Electronic Resource
    Identification of two allotwins of mica polytypes in reciprocal space through the minimal rhombus unit (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 639-647 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The X-ray investigation (precession method) of the Ruiz Peak oxybiotite, which is well known for the occurrence of a large number of polytypes and twins, revealed two complex diffraction patterns, which cannot be identified as long-period polytypes. These patterns are analysed in terms of the minimal rhombus, a geometrical asymmetric unit in reciprocal space which permits the decomposition of the composite reciprocal lattice of a twin or allotwin into the reciprocal lattices of the individuals. Both the recorded patterns correspond to a 1M–2M1 allotwin: the relative rotation between the individuals is 120° in one case and 60° in the other. The geometrical criteria for evaluating the presence of twinning or allotwinning are analysed through these two natural examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768100002044
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  • 6
    Electronic Resource
    Electronic Resource
    Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings (1999)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 659-676 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Following a preliminary revisitation of the nomenclatures in use for mica polytypes, the properties of the periodic intensity distribution (PID) function, which represents the Fourier transform of the stacking sequence, are analysed. On the basis of the relative rotations of neighbouring layers, mica polytypes are classified into three types; for each type, the PID exists in different subspaces of the reciprocal space. A revised procedure to compute the PID, in which further restrictions on the structural model orientation are introduced, is presented. A unifying terminology based upon the most common symbols used to describe mica polytypes (RTW, Z and TS) is derived; these symbols represent the geometrical basis for the computation of the PID. Results are presented for up to four layer polytypes and are compared with the reflection conditions derived by means of Zvyagin's functions. Both the PID values and the reflection conditions are expressed in suitable axial settings and compared with previous partial reports, revealing some errors in previous analyses. A computer program to compute PID from the stacking symbols is available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767398017735
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  • 7
    Electronic Resource
    Electronic Resource
    Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal space (2000)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 132-148 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The geometry of the diffraction pattern from twins and allotwins of the four basic mica polytypes (1M, 2M1, 3T, 2M2) is analysed in terms of the `minimal rhombus', a geometrical asymmetric unit in reciprocal space defined by nine translationally independent reciprocal-lattice rows. The minimal rhombus contains the necessary information to decompose the reciprocal lattice of twins or allotwins into the reciprocal lattices of the individuals. The nine translationally independent reciprocal-lattice rows are divided into three types (S, D and X): rows of different type are not overlapped by the n × 60° rotations about c∗, which correspond to the relative rotations between pairs of twinned or allotwinned individuals. A symbolic representation of the absolute orientation of the individuals, similar to that used for layers in polytypes, is introduced. The polytypes 1M and 2M1 undergo twinning by reticular pseudo-merohedry with five pairs of twin laws: they produce twelve independent twins, of which nine can be distinguished by the minimal rhombus analysis. The 2M2 polytype has two pairs of twin laws by pseudo-merohedry, which give a single diffraction pattern geometrically indistinguishable from that of the single crystal, and three pairs of twin laws by reticular pseudo-merohedry, which give a single diffraction pattern different from that of the single crystal. The 3T polytype has three twin laws: one corresponds to complete merohedry and the other two to selective merohedry. Selective merohedry produces only partial restoration of the weighted reciprocal lattice built on the family rows and the presence of twinning can be recognized from the geometry of the diffraction pattern.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767399014907
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  • 8
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    Zero-obliquity twin lattice quasi-symmetry threefold twinning in 1-{(R)-1-[(3-oxo-2-isoindolinoyl)methyl]-2-propenyl}-5-methyl-2,3-indolinedione (2020)
    International Union of Crystallography
    Details
    Publication Date: 2020-07-15
    Description: Threefold twinning in 1-{(R)-1-[(3-oxo-2-isoindolinoyl)methyl]-2-propenyl}-5-methyl-2,3-indolinedione, C21H16N2O4, has been reported recently [Trost et al. (2020). Org. Lett. 22, 2584–2589] but the twin characterization was not published. This twinning presents several interesting features. The crystal structure is monoclinic, but its lattice is metrically strongly pseudo-orthorhombic and underpins a strongly pseudo-hexagonal sublattice. Several possible twin laws are compatible with these metric specializations, among which the one found experimentally corresponds to a trichromatic point group. Twinning is by reticular pseudo-merohedry with twin index 2 and zero obliquity but a non-zero twin misfit. The twin lattice coincides with the pseudo-hexagonal sublattice of the individual domain, which justifies the adoption of the unconventional setting B21 of the space group.
    Print ISSN: 2052-5192
    Electronic ISSN: 2052-5206
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Published by International Union of Crystallography
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  • 9
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    Fighting the wind mills: are crystallographers the successors of Don Quixote? (2019)
    International Union of Crystallography
    Details
    Publication Date: 2019-08-18
    Electronic ISSN: 2053-2733
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Published by International Union of Crystallography
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  • 10
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    A survey of hybrid twins in silicate minerals (2011)
    Schweizerbart
    Details
    Publication Date: 2011-10-01
    Description: This article is the second part of the survey presenting a systematic crystallographic analysis of hybrid twins in minerals. Here we deal with silicate minerals and in particular the hybrid twins of allanite, augite, axinite, beryl, chloritoid, clinoenstatite, clinozoisite, cordierite, cummingtonite-grunerite, diopside-hedenbergite, enstatite-ferrosilite, epidote, forsterite-fayalite, johannsenite, natrolite, piemontite, pigeonite, protoenstatite, pumpellyite, pyroxmangite, quartz, titanite, spodumene, staurolite, topaz, tourmaline, tremolite-actinolite-ferroactinolite, tridymite. The comparison with the twin analysis of non-silicate minerals shows that the number of hybrid twins for non-silicates is higher than that of the silicates. This well agrees with the fact that the twin formation is favoured by the high symmetries of the close-packing topologies, typical of many non-silicates, especially oxides and simple sulphides, whereas the silicate structures are more complex and characterized by different degrees of polymerization of Si-O tetrahedra.
    Print ISSN: 0935-1221
    Electronic ISSN: 1617-4011
    Topics: Geosciences
    Published by Schweizerbart
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