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  • 11
    Electronic Resource
    Electronic Resource
    Determination of quasicrystalline structures: a refinement program using symmetry-adapted parameters (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 182-193 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general program for the refinement of quasicrystalline structures using diffraction data is presented. The program can be used for both icosahedral and polygonal quasicrystals. The refinement process is based on the fitting of the structural model to experimental diffraction data and observed density and chemical composition. Superspace formalism is used for the structure description and the hypersurfaces in superspace describing the atomic positions are assumed to be parallel to the internal space. No additional a priori assumption on the form of the atomic hypersurfaces is necessary except that the deviations of the atomic surface contours from a spherical shape do not contain very short wave components in a significant amount. The contours of each symmetry-independent atomic hypersurface in internal space are parametrized in terms of linear combinations of radial functions (surface harmonic) invariant for the hypersurface point group in internal space. This allows a continuous refinement of the structure in terms of symmetry-adapted parameters consistent with the symmetry restrictions resulting from the postulated superspace symmetry. The program requires an initial very approximate guess of the structure in terms of `spherical' hypersurfaces of which only the symmetry centres are known with confidence. The continuous parametrization of the hypersurfaces does not a priori restrict their form, except in its degree of complexity or fine detail, which is limited by the number of terms considered in the linear expansion of the surface contours. In general, the number of surface harmonics considered should be consistent with the accuracy allowed by the experimental data set. The refinement process can be performed either by a full least-squares method or by means of a simplex algorithm. The physical consistency of the refined hypersurfaces with respect to the predicted density, chemical composition and interatomic distances is controlled by including additional `penalty functions' in the parameter to be minimized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767393008189
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  • 12
    Electronic Resource
    Electronic Resource
    Determination of quasicrystalline structures: a refinement program using symmetry-adapted parameters. Erratum (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 550-550 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A typesetting error in equation (28) of Elcoro, Perez-Mato & Madariaga [Acta Cryst. (1994), A50, 182–193] is corrected. The correct equation is TeX where a = \sum_{i} a_{i}^{\mu,{\rm in}}Z_{i}(\varphi_{1}, \dots, \varphi_{n - 4})b = \sum_{i} a_{i}^{\mu,{\rm ex}}Z_{i}(\varphi_{1}, \dots ,\varphi_{n - 4}).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767394004836
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  • 13
    Electronic Resource
    Electronic Resource
    Time Relaxation of the Low-Temperature Modulated Structure of Thiourea (1996)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 203-211 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A conspicuous time variation of the diffraction diagram of thiourea in its incommensurate phase at 170 K is observed and characterized. The phenomenon is systematic and reproducible. Satellite intensities decrease according to linear laws, reaching in the case of third-order satellites up to a 28% reduction. Main reflections decrease or increase depending on the particular reflection. Sample degradation could be discarded as a possible cause. Through a rather complex procedure, which makes use of the structural data determined in previous studies, the kinetic process observed is shown to be fully consistent with a slow time relaxation of the soliton density of the incommensurate structural modulation from a value of 0.62 at the beginning of the measurement to 0.69 at the end of the main experiment, after 166 h. This variation represents a correlated decrease in the amplitudes of the harmonics of the modulation, with a reduction of its anharmonicity. Clearly, the structural modulation evolves with time towards a more sinusoidal regime. The origin of the phenomenon is unclear and its possible existence in other incommensurate materials is to be ascertained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767395012864
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  • 14
    Electronic Resource
    Electronic Resource
    Nomenclature of magnetic, incommensurate, composition-changed morphotropic, polytype, transient-structural and quasicrystalline phases undergoing phase transitions. II. Report of an IUCr Working Group on Phase Transition NomenclatureEstablished 15 February 1994 by the IUCr Commission on Crystallographic Nomenclature; following the resignation of two members upon acceptance of the first Report, three new members were appointed 18 July 1998. This second Report was received by the Commission 26 February 2001 and accepted 19 April 2001. The present Report, as all other Reports of the Commission, is available online at the Commission's webpage: http://www.iucr.org/iucr-top/comm/cnom.html. (2001)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 614-626 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general nomenclature applicable to the phases that form in any sequence of transitions in the solid state has been recommended by an IUCr Working Group [Acta Cryst. (1998). A54, 1028–1033]. The six-field notation of the first Report, hereafter I, was applied to the case of structural phase transitions, i.e. to transformations resulting from temperature and/or pressure changes between two crystalline (strictly periodic) phases involving modifications to the atomic arrangement. Extensive examples that illustrate the recommendations were provided. This second Report considers, within the framework of a similar six-field notation, the more complex nomenclature of transitions involving magnetic phases, incommensurate phases and transitions that occur as a function of composition change. Extension of the nomenclature to the case of phases with less clearly established relevance to standard schemes of transition in equilibrium systems, namely polytype phases, radiation-induced and other transient phases, quasicrystalline phases and their transitions is recommended more tentatively. A uniform notation for the translational periodicity, propagation vector or wavevector for magnetic and/or incommensurate substances is specified. The notation adopted for incommensurate phases, relying partly on the existence of an average structure, is also consistent with that for commensurate phases in a sequence. The sixth field of the nomenclature is used to emphasize the special features of polytypes and transient phases. As in I, illustrative examples are provided for each category of phase sequence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767301006821
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  • 15
    Electronic Resource
    Electronic Resource
    On the structure and symmetry of incommensurate phases. A practical formulation (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 216-226 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structural description, symmetry and diffraction properties of incommensurate modulated phases are revised using a real-space framework. The superspace formalism usually employed is reformulated using a practical description where no multidimensional geometrical constructions are needed. The incommensurate structural distortion is described in terms of 'atomic modulation functions' where the internal space is only considered as a continuous label for the cells of the non-distorted structure. Hence, no atomic positions or thermal tensors in a multidimensional space are defined. By this means and with the introduction of the concept of 'atomic modulation factors' a general expression for the structure factor is proposed which constitutes a direct generalization of the standard expression for a commensurate structure. The concept of superspace symmetry is reduced in this approach to a simple relation between the defined atomic modulation functions, which can be directly translated by means of the structure-factor expression into the symmetry and extinction rules of the diffraction diagram. The advantages of superspace formalism in the analysis of commensurate modulated phases are also discussed. The use of superspace groups for describing the symmetry of superstructures, contrary to some recent claims, does not formally reduce the number of structural parameters but may often allow some of them to be neglected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387099537
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  • 16
    Electronic Resource
    Electronic Resource
    Checklist for the Description of Incommensurate Modulated Crystal Structures. Report of the International Union of Crystallography Commission on Aperiodic Crystals (1997)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 95-100 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: One of the terms of reference published in 1992 (Acta Cryst. A48, 922–946) in the report of the (at that time) Ad Interim Commission on Aperiodic Crystals was `to co-operate with other Commissions of the IUCr in establishing adequate guidelines and standards for articles to be published in IUCr journals reporting structural investigations of aperiodic crystals and theoretical investigations of aperiodic patterns'. It was soon recognized by the Commission that the establishment of a checklist for the publication of incommensurately modulated structures was perhaps the most urgent task. One of the first attempts to address the problem of publishing incommensurate structures was presented during a discussion organized in 1991 in Leikeitio, Spain, in a workshop dedicated to methods of structural analysis of modulated structures and quasicrystals. Since this meeting, the work of the Commission progressed interactively by numerous exchanges on the occasions of international meetings and mostly by electronic correspondence. The Checklist was accepted in 1994 by the Executive Committee of the IUCr. The opinion of the Commission on Journals was also requested and, following the comments of its members, the Checklist has been completed with an example of an incommensurate crystal structure illustrating each specific item that is required in the Checklist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767396010185
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  • 17
    Electronic Resource
    Electronic Resource
    Temperature Dependence of the Static Distortion in Incommensurate Displacive Phases and its Effect on the Diffraction Pattern. I. Main Reflections (1997)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 329-333 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The effect of the temperature dependence of the structural modulation on the intensity of main reflections is analyzed. A simple expression for the atomic scattering modulation factors has been derived describing the structural distortion in terms of the amplitude and the inhomogeneous phase of the order parameter. According to this expression, some main reflections can be strongly influenced by modulation harmonics. Owing to this influence, the intensity of some main reflections can increase, decrease or even show a pronounced minimum as the temperature is lowered. These results are experimentally verified in thiourea.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397000111
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  • 18
    Electronic Resource
    Electronic Resource
    Temperature Dependence of the Static Distortion in Incommensurate Displacive Phases and its Effect on the Diffraction Pattern. II. Satellite Reflections (1997)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 334-340 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The effect on satellite reflections of the temperature variation of the static structural modulation in incommensurate phases is studied. A structural model is introduced that includes the anharmonicity described by the soliton density and follows the assumptions and predictions of the Landau theory generalized to incommensurate phases. Within these premises, a simulation of the diffraction pattern as a function of temperature of Rb2ZnCl4 has been carried out. It is shown that the intensity of satellites does not always decrease monotonically with their order and its temperature dependence varies, depending on the satellite, so that it cannot be reduced to a common effective power law. Satellites of first order, for instance, can decrease or increase near the lock-in transition, depending on the particular reflection considered. A simple method for measuring the soliton density is proposed that is based on the expected correlation of the intensities of close first-order and higher-order satellites. Finally, the effect that high-order harmonics can have in a standard refinement of an incommensurate structure near the lock-in transition is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397000123
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  • 19
    Electronic Resource
    Electronic Resource
    Symmetry-Mode Analysis of Displacive Phase Transitions using International Tables for Crystallography (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 19-30 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The symmetry-mode analysis of a structural phase transition involves the use of methods of the representation theory of space groups. The aim of the paper is to present an alternative approach for the determination of the primary and secondary symmetry modes that contribute to the structural distortion of the low-symmetry phase. It only requires the systematic use of the data from International Tables for Crystallography, Vol. A, and is based on a fact, well known to crystallographers: the fully symmetrical displacements of any orbit of atoms (i.e. the modes compatible with the symmetry of the structure) follow in a straightforward way from the coordinate triplets of the corresponding Wyckoff positions. This property, systematically used for all intermediate subgroups between the space groups of the two phases, allows the determination of the relevant symmetry modes. Their distinction into primary and secondary modes comes out directly in the process of calculation. As an example, primary and secondary modes in the ferroelectric distortion of potassium selenate are divided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397010106
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  • 20
    Electronic Resource
    Electronic Resource
    Structural analysis of the incommensurate and lock-in phases of tetramethylammonium tetrachlorozincate(II), [N(CH3)4]2[ZnCl4] (1987)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 356-368 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768187097726
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