Modular crystals as modulated structures: the case of the lillianite homologous series

2008 ◽  
Vol 64 (6) ◽  
pp. 684-701 ◽  
Author(s):  
Luis Elcoro ◽  
J. M. Perez-Mato ◽  
Karen Friese ◽  
Václav Petříček ◽  
Tonči Balić-Žunić ◽  
...  
Keyword(s):  
Homologous Series ◽  
Robust Method ◽  
Composite Approach ◽  
Modulated Structures ◽  
Superspace Formalism ◽  
Study Case ◽  
Starting Model ◽  
Modular Structures ◽  
Composite Description

The use of the superspace formalism is extended to the description and refinement of the homologous series of modular structures with two symmetry-related modules with different orientations. The lillianite homologous series has been taken as a study case. Starting from a commensurate modulated composite description with two basic subsystems corresponding to the two different modules, it is shown how a more efficient description can be achieved using so-called zigzag modulation functions. These linear zigzag modulations, newly implemented in the program JANA2006, have very large fixed amplitudes and introduce in the starting model the two orientations of the underlying module sublattices. We show that a composite approach with this type of function, which treats the cations and anions as two separate subsystems forming a misfit compound, is the most appropriate and robust method for the refinements.

Structure of (Ga2O3)2(ZnO)13 and a unified description of the homologous series (Ga2O3)2(ZnO)2 n + 1

2012 ◽  
Vol 68 (3) ◽  
pp. 250-260 ◽  
Author(s):  
Yuichi Michiue ◽  
Noboru Kimizuka ◽  
Yasushi Kanke ◽  
Takao Mori
Keyword(s):  
Homologous Series ◽  
Unit Cell ◽  
Dimensional Model ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
Modulated Structures ◽  
Superspace Formalism ◽  
Complex Phenomena ◽  
Unified Description

The structure of (Ga2O3)2(ZnO)13 has been determined by a single-crystal X-ray diffraction technique. In the monoclinic structure of the space group C2/m with cell parameters a = 19.66 (4), b = 3.2487 (5), c = 27.31 (2) Å, and β = 105.9 (1)°, a unit cell is constructed by combining the halves of the unit cell of Ga2O3(ZnO)6 and Ga2O3(ZnO)7 in the homologous series Ga2O3(ZnO) m . The homologous series (Ga2O3)2(ZnO)2n + 1 is derived and a unified description for structures in the series is presented using the (3+1)-dimensional superspace formalism. The phases are treated as compositely modulated structures consisting of two subsystems. One is constructed by metal ions and another is by O ions. In the (3 + 1)-dimensional model, displacive modulations of ions are described by the asymmetric zigzag function with large amplitudes, which was replaced by a combination of the sawtooth function in refinements. Similarities and differences between the two homologous series (Ga2O3)2(ZnO)2n + 1 and Ga2O3(ZnO) m are clarified in (3 + 1)-dimensional superspace. The validity of the (3 + 1)-dimensional model is confirmed by the refinements of (Ga2O3)2(ZnO)13, while a few complex phenomena in the real structure are taken into account by modifying the model.

Superspace description of the crystal structures of Ca n (Nb,Ti) n O3n + 2 (n = 5 and 6)

2007 ◽  
Vol 63 (2) ◽  
pp. 183-189 ◽  
Author(s):  
Jonathan Guevarra ◽  
Andreas Schönleber ◽  
Sander van Smaalen ◽  
Frank Lichtenberg
Keyword(s):  
Crystal Structures ◽  
Homologous Series ◽  
Three Dimensional ◽  
Natural Explanation ◽  
Modulated Structures ◽  
Superspace Formalism ◽  
Superspace Description

The crystal structures of two members of the homologous series Ca n (Nb,Ti) n O3n + 2, with n = 5 and 6, are presented within the superspace formalism. A common (3 + 1)-dimensional superspace model is used to describe the crystal structures of both compositions within a particular homologous series, where the primary modulation wavevector and the width of the atomic domains vary systematically with composition. The two crystal structures are characterized as commensurately modulated structures consisting of discontinuous atomic domains described by occupational crenel functions. The displacive modulation functions for the two compounds exhibit similarities, but they also show that the idea of a unified superspace model does not extend toward the precise atomic positions. For n = 6, the centrosymmetric (3 + 1)-dimensional superspace symmetry provides a natural explanation for the pseudo-symmetries that are present in the non-centrosymmetric (three-dimensional) superstructure of this compound. The efficiency of the superspace approach is demonstrated by structure refinements in (3 + 1)-dimensional superspace and by comparing these results with the refinements in their three-dimensional superstructures.

Superspace description of the homologous series Ga2O3(ZnO) m

2010 ◽  
Vol 66 (2) ◽  
pp. 117-129 ◽  
Author(s):  
Yuichi Michiue ◽  
Noboru Kimizuka
Keyword(s):  
Homologous Series ◽  
Ideal Model ◽  
Modulated Structure ◽  
Superspace Formalism ◽  
Alternative Settings ◽  
Complex Phenomena ◽  
Modular Structures ◽  
Unified Description ◽  
Superspace Description ◽  
The Ideal

A unified description for the structures of the homologous series Ga2O3(ZnO) m , gallium zinc oxide, is presented using the superspace formalism. The structures were treated as a compositely modulated structure consisting of two subsystems. One is constructed with metal ions and the other with O ions. The ideal model is given, in which the displacive modulations of ions are well described by the zigzag function with large amplitudes. Alternative settings are also proposed which are analogous to the so-called modular structures. The validity of the model has been confirmed by refinements for phases with m = 6 and m = 9 in the homologous series. A few complex phenomena in real structures are taken into account by modifying the ideal model.

Incommensurate structure of InAl1 − x Ti x O3 + x/2 [x = 0.701 (1)]: comparison between modulated and composite models

2008 ◽  
Vol 64 (4) ◽  
pp. 405-416 ◽  
Author(s):  
P. J. Bereciartua ◽  
F. J. Zuñiga ◽  
T. Breczewski
Keyword(s):  
Monoclinic Phase ◽  
Composite Approach ◽  
Incommensurate Structure ◽  
Structure Relation ◽  
Composite Models ◽  
Superspace Formalism ◽  
Composition Structure

The structure of the monoclinic phase of the compound InAl1 − x Ti x O3 + x/2 with x = 0.701 (1) has been analyzed within the (3 + 1)-dimensional superspace formalism. Two different models were refined describing the structure as an incommensurate modulated layer and modulated composite, respectively. Both models include the same composition–structure relation. In the composite approach it is derived from the mismatching between the two subsystems. In the incommensurate modulated system, it is derived from a closeness condition between O atomic domains. The distribution and coordination of the cations is discussed and compared with previously proposed models for similar compounds.

Monophosphate tungsten bronzes with pentagonal tunnels: reinvestigation through the peephole of the superspace

2013 ◽  
Vol 69 (2) ◽  
pp. 122-136 ◽  
Author(s):  
Olivier Pérez ◽  
Luis Elcoro ◽  
J. M. Pérez-Mato ◽  
Václav Petříček
Keyword(s):  
Experimental Data ◽  
Structural Analysis ◽  
Homologous Series ◽  
Large Family ◽  
Symmetry Operation ◽  
Dimensional Model ◽  
Modular Structures

The large family of monophosphate tungsten bronzes with pentagonal tunnels (MPTBp), (PO2)4(WO3)2mwithmranging from 4 to 14, can be considered as modular structuresviaa description with (PO2)2(WO3)mmodules related together by a symmetry operation and alternating along thezaxis. Following the success of the application of the superspace for the description of the lillianites homologous series, a (3 + 1)-dimensional superspace model is efficiently defined to unify the structural analysis of the MPTBp. The (3 + 1)-dimensional model reveals hidden common characteristics such as the symmetry. An evaluation of the model for six well known members of the series was carried out from experimental data collected to this aim.

Vacancy-ordering effects in AlB2-type ErGe2 − x (0.4 < x ≤ 0.5)

2008 ◽  
Vol 64 (3) ◽  
pp. 272-280 ◽  
Author(s):  
Jeppe Christensen ◽  
Sven Lidin ◽  
Bernard Malaman ◽  
Gerard Venturini
Keyword(s):  
Powder Diffraction ◽  
Homologous Series ◽  
Composition Range ◽  
Direct Measure ◽  
X Ray ◽  
Arc Melting ◽  
Ordering Effects ◽  
Vacancy Ordering ◽  
Superspace Formalism ◽  
Modulation Vector

In the Er–Ge system, the compostion range ErGe2 to Er2Ge3 has been investigated. Eight samples were produced by arc melting of the elements, and analyzed using X-ray powder diffraction. Nine crystal structures were found to be present in the samples. The structures are described as a homologous series and presented within the superspace formalism using the superspace group X2/m(α0γ)0s, X representing the centring vector (½, ½, 0, ½). In this description the modulation vector q = (αa* + γc*) is shown to be a direct measure of the Ge content as ErGe2 − α (α falls in the range 1\over 3 to ½). The large composition range is achieved by extended vacancy ordering in the planar 63 net of Ge with subsequent relaxation.

scholarly journals Modulated order in ionic conductors: a fine line between helping and hindering

2014 ◽  
Vol 70 (a1) ◽  
pp. C228-C228
Author(s):  
Chris Ling
Keyword(s):  
Ionic Conduction ◽  
Proton Conductor ◽  
Neutron Diffraction Pattern ◽  
Ionic Conductors ◽  
Ion Conductor ◽  
Oxide Ion Conductor ◽  
3 Dimensional ◽  
Modulated Structures ◽  
Superspace Formalism ◽  
The Relationship

"Solid-state ionic conduction relies on essentially conflicting structural properties: long-range crystalline order, to provide structural stability (as fuel cell membranes, battery cathodes etc.); and short-range disorder, to provide smooth conduction pathways without deep local energy minima that could trap the conducting species. Materials that combine these features are generally metastable, and prone to ordering into complex modulated structured that can only be described in (3+n) dimensions using the superspace formalism. Such ordering would normally be expected to seriously compromise conduction properties. However, low-temperature modulated structures can be effective and stable precursors to high-temperature ionic conductors - and, in some cases, can coexist with regions of local disorder that actually enhance conduction. The relationship between modulated order and ionic conduction is relatively little studied, but some of our recent work points to its potential importance. This presentation will focus on two examples: the (3+3)-dimensional commensurately modulated proton conductor Ba4Nb2O9.1/3H2O; [1,2] and the (3+3)-dimensional incommensurately modulated oxide ion conductor ""Type II"" Bi2O3.xNb2O5 (for which a single-crystal neutron diffraction pattern and the refined structure are shown below). [3] The aim is to show how modulated structures can be designed and manipulated to optimise technological performance by striking a balance between stabilising the overall framework while destabilising the conduction pathways."

Incommensurate modulations made visible by the Maximum Entropy Method in superspace

2004 ◽  
Vol 219 (11) ◽  
Author(s):  
Lukás Palatinus ◽  
Sander van Smaalen
Keyword(s):  
Missing Data ◽  
Maximum Entropy ◽  
Electron Density ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Basic Principles ◽  
Layer Compound ◽  
Modulated Structures ◽  
Structure Solution ◽  
Superspace Formalism

AbstractThis paper presents the application of the Maximum Entropy Method (MEM) to structure solution of incommensurately modulated structures within the superspace formalism. The basic principles of the MEM are outlined, and its generalization toward superspace is discussed. Possible problems in MEM reconstructions and their solutions are summarized. They include series-termination errors in the reconstructed electron density, the effect of insufficient constraints, and the effect of missing data. The use of the MEM in superspace is illustrated by three examples: the structure of the misfit-layer compound (LaS)

Intergrowth of modulated structures in high Tc Bi-Sr-Ca-Cu-O superconductors

1990 ◽  
Vol 48 (4) ◽  
pp. 76-77
Author(s):  
A.Q. He ◽  
G.W. Qiao ◽  
J. Zhu ◽  
H.Q. Ye
Keyword(s):  
Twin Structure ◽  
Modulated Structure ◽  
High Tc ◽  
One Dimensional ◽  
Lattice Constants ◽  
Superconducting Phases ◽  
Modulated Structures ◽  
Layer Structures

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.

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