Acta Crystallographica Section A
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.enCopyright (c) 2015 International Union of Crystallography2015-03-25International Union of CrystallographyInternational Union of Crystallographyhttp://journals.iucr.orgurn:issn:2053-2733Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlActa Crystallographica Section A: Foundations and Advances, Volume 71, Part 3, 2015textyearly62002-01-01T00:00+00:003712015-03-25Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances255urn:issn:2053-2733med@iucr.orgMarch 20152015-03-25Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2015/03/00/isscontsbdy.html
Still imageX-ray investigation of lateral hetero-structures of inversion domains in LiNbO3, KTiOPO4 and KTiOAsO4
http://scripts.iucr.org/cgi-bin/paper?wo5016
In this paper periodically domain-inverted (PDI) ferroelectric crystals are studied using high-resolution X-ray diffraction. Rocking curves and reciprocal-space maps of the principal symmetric Bragg reflections in LiNbO3 (LN) (Λ = 5 µm), KTiOPO4 (KTP) (Λ = 9 µm) and KTiOAsO4 (KTA) (Λ = 39 µm) are presented. For all the samples strong satellite reflections were observed as a consequence of the PDI structure. Analysis of the satellites showed that they were caused by a combination of coherent and incoherent scattering between the adjacent domains. Whilst the satellites contained phase information regarding the structure of the domain wall, this information could not be rigorously extracted without a priori knowledge of the twinning mechanism. Analysis of the profiles reveals strain distributions of Δd/d = 1.6 × 10−4 and 2.0 × 10−4 perpendicular to domain walls in KTP and LN samples, respectively, and lateral correlation lengths of 63 µm (KTP), 194 µm (KTA) and 10 µm (LN). The decay of crystal truncation rods in LN and KTP was found to support the occurrence of surface corrugations.Copyright (c) 2015 Thomas S. Lyford et al.urn:issn:2053-2733Lyford, T.S.Collins, S.P.Fewster, P.F.Thomas, P.A.2015-03-13doi:10.1107/S2053273315001503International Union of CrystallographyPeriodically-poled ferroelectric crystals are studied by observing their superlattice (grating) diffraction profiles with high-resolution X-ray diffraction. In order to successfully model the data, the effects of strain, and sample and beam coherence, must be taken into account.ENferroelectricsdiffractioncoherencesynchrotron radiationgratingIn this paper periodically domain-inverted (PDI) ferroelectric crystals are studied using high-resolution X-ray diffraction. Rocking curves and reciprocal-space maps of the principal symmetric Bragg reflections in LiNbO3 (LN) (Λ = 5 µm), KTiOPO4 (KTP) (Λ = 9 µm) and KTiOAsO4 (KTA) (Λ = 39 µm) are presented. For all the samples strong satellite reflections were observed as a consequence of the PDI structure. Analysis of the satellites showed that they were caused by a combination of coherent and incoherent scattering between the adjacent domains. Whilst the satellites contained phase information regarding the structure of the domain wall, this information could not be rigorously extracted without a priori knowledge of the twinning mechanism. Analysis of the profiles reveals strain distributions of Δd/d = 1.6 × 10−4 and 2.0 × 10−4 perpendicular to domain walls in KTP and LN samples, respectively, and lateral correlation lengths of 63 µm (KTP), 194 µm (KTA) and 10 µm (LN). The decay of crystal truncation rods in LN and KTP was found to support the occurrence of surface corrugations.text/htmlX-ray investigation of lateral hetero-structures of inversion domains in LiNbO3, KTiOPO4 and KTiOAsO4text3712015-03-13Copyright (c) 2015 Thomas S. Lyford et al.Acta Crystallographica Section Aresearch papers00Symmetry of semi-reduced lattices
http://scripts.iucr.org/cgi-bin/paper?sc5085
The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M−1 are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\bb M}(p,q,r), where {\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375–384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255–259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421–429] and (iii) from fixed cell transformations to transformations derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view – the combinatorial set {\bb V} of matrices, their semi-reduced lattice context and their geometric properties.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Stróż, K.2015-03-12doi:10.1107/S2053273315001096International Union of CrystallographyThe characterization of Bravais types is extended according to metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions. There are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new point of view – the combinatorial set of 960 matrices, their semi-reduced lattice context and their geometric properties.ENreduced cellmetric symmetrysymmetry matrixThe main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M−1 are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\bb M}(p,q,r), where {\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375–384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255–259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421–429] and (iii) from fixed cell transformations to transformations derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view – the combinatorial set {\bb V} of matrices, their semi-reduced lattice context and their geometric properties.text/htmlSymmetry of semi-reduced latticestext3712015-03-12Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Structure factor for an icosahedral quasicrystal within a statistical approach
http://scripts.iucr.org/cgi-bin/paper?pc5049
This paper describes a detailed derivation of a structural model for an icosahedral quasicrystal based on a primitive icosahedral tiling (three-dimensional Penrose tiling) within a statistical approach. The average unit cell concept, where all calculations are performed in three-dimensional physical space, is used as an alternative to higher-dimensional analysis. Comprehensive analytical derivation of the structure factor for a primitive icosahedral lattice with monoatomic decoration (atoms placed in the nodes of the lattice only) presents in detail the idea of the statistical approach to icosahedral quasicrystal structure modelling and confirms its full agreement with the higher-dimensional description. The arbitrary decoration scheme is also discussed. The complete structure-factor formula for arbitrarily decorated icosahedral tiling is derived and its correctness is proved. This paper shows in detail the concept of a statistical approach applied to the problem of icosahedral quasicrystal modelling.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Strzalka, R.Buganski, I.Wolny, J.2015-03-12doi:10.1107/S2053273315001473International Union of CrystallographyA structure factor for an icosahedral quasicrystal with an arbitrary decoration scheme based on a primitive icosahedral tiling model and a statistical approach is derived. The average unit cell concept is used as an alternative to the commonly used higher-dimensional description.ENicosahedral quasicrystalprimitive icosahedral tilingaverage unit cell conceptstatistical approachhigher-dimensional analysisdiffraction patternThis paper describes a detailed derivation of a structural model for an icosahedral quasicrystal based on a primitive icosahedral tiling (three-dimensional Penrose tiling) within a statistical approach. The average unit cell concept, where all calculations are performed in three-dimensional physical space, is used as an alternative to higher-dimensional analysis. Comprehensive analytical derivation of the structure factor for a primitive icosahedral lattice with monoatomic decoration (atoms placed in the nodes of the lattice only) presents in detail the idea of the statistical approach to icosahedral quasicrystal structure modelling and confirms its full agreement with the higher-dimensional description. The arbitrary decoration scheme is also discussed. The complete structure-factor formula for arbitrarily decorated icosahedral tiling is derived and its correctness is proved. This paper shows in detail the concept of a statistical approach applied to the problem of icosahedral quasicrystal modelling.text/htmlStructure factor for an icosahedral quasicrystal within a statistical approachtext3712015-03-12Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Absolute refinement of crystal structures by X-ray phase measurements
http://scripts.iucr.org/cgi-bin/paper?ae5003
A pair of enantiomer crystals is used to demonstrate how X-ray phase measurements provide reliable information for absolute identification and improvement of atomic model structures. Reliable phase measurements are possible thanks to the existence of intervals of phase values that are clearly distinguishable beyond instrumental effects. Because of the high susceptibility of phase values to structural details, accurate model structures were necessary for succeeding with this demonstration. It shows a route for exploiting physical phase measurements in the crystallography of more complex crystals.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Morelhão, S.L.Amirkhanyan, Z.G.Remédios, C.M.R.2015-03-12doi:10.1107/S2053273315002508International Union of CrystallographyThe application of X-ray phase measurements for absolute identification and improvement of atomic model structures is described.ENsingle crystalschiralityinvariant phase tripletsX-ray diffractionA pair of enantiomer crystals is used to demonstrate how X-ray phase measurements provide reliable information for absolute identification and improvement of atomic model structures. Reliable phase measurements are possible thanks to the existence of intervals of phase values that are clearly distinguishable beyond instrumental effects. Because of the high susceptibility of phase values to structural details, accurate model structures were necessary for succeeding with this demonstration. It shows a route for exploiting physical phase measurements in the crystallography of more complex crystals.text/htmlAbsolute refinement of crystal structures by X-ray phase measurementstext3712015-03-12Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Axial point groups: rank 1, 2, 3 and 4 property tensor tables
http://scripts.iucr.org/cgi-bin/paper?kx5041
The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Litvin, D.B.2015-03-26doi:10.1107/S2053273315002740International Union of CrystallographyPhysical property tensors of materials such as nanotubes or polymers are determined by the material's axial point group. Rank 1, 2, 3 and 4 property tensors are given for a wide variety of tensor types invariant under each point group in all 31 infinite series of axial point groups.ENaxial point groupsproperty tensorsnanotubesmultiferroic hexaferritesThe form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.text/htmlAxial point groups: rank 1, 2, 3 and 4 property tensor tablestext3712015-03-26Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Ashort communications00