Commensurate Modulated Structure Research Articles

Modes vs. modulations: Symmetry-mode analysis of commensurate modulated structures compared with the superspace method

We know from Landau theory that the natural language to deal with distorted structures is the one of symmetry-adapted modes. A symmetry-mode decomposition is both useful for investigating the mechanisms responsible of these phases and for pure crystallographic purposes. Some symmetry-mode components are usually dominant, introducing a parameter hierarchy or reducing in practice the crystallographic degrees of freedom. Several computer tools are now freely available allowing structure refinements directly using symmetry-mode collective coordinates. Alternatively, the superspace formalism is a very efficient method for similar purposes. By means of several examples we compare the two approaches.

The commensurate modulated structure of the metastable state in spin crossover complex [Fe(abpt)2(NCS)2

Two new polymorphs (C and D) of [t-Fe(abpt)(2)(NCS)(2)] are characterized, a commensurate modulated structure with the c axis tripled in the thermally quenched metastable high spin state at 25 K is found in polymorph C.

Commensurate and incommensurate “5M” modulated crystal structures in Ni–Mn–Ga martensitic phases

It is well known that the composition of ferromagnetic shape memory Ni–Mn–Ga Heusler alloys determines both temperature of martensitic transformations and the structure type of the product phase. In the present work we focused our attention on the structural study of the so-called “5M” modulated structure. In particular, the structure of Ni 1.95Mn 1.19Ga 0.86 martensitic phase is analysed by powder X-ray diffraction (PXRD) and compared with that of the stoichiometric Ni 2MnGa martensite. The study of the diffraction data reveals the occurrence of commensurate (C) structural modulation in Ni 1.95Mn 1.19Ga 0.86; this contrasts with Ni 2MnGa, where an incommensurate (IC) structural modulation was evident. The two phases also differ in the symmetry of the fundamental martensitic lattice. In fact, the incommensurate modulation is related to an orthorhombic basic structure, while the commensurate variant presents a monoclinic symmetry. The commensurate modulated structure has been investigated by using the superspace approach already adopted to solve the structure of Ni 2MnGa martensite. The structure has been determined by Rietveld refinement of PXRD data.

Structural characterization of the hollandite host lattice for the confinement of radioactive cesium: Quantification of the amorphous phase taking into account the incommensurate modulated character of the crystallized part

X-ray patterns of the Ba 1Cs 0.28Fe 0.82Al 1.46Ti 5.72O 16 compound evidence two wide peaks at low angle in addition to the well defined peaks of the I4/ m hollandite structure type. Two hypotheses have been explored to account for these features: the coexistence of the hollandite phase with an amorphous phase and the appearance of a commensurate or incommensurate modulated structure associated with a cationic ordering, as proposed in the literature. Actually, even if the amorphous phase quantification by the Rietveld method reveals about 15 wt% of non-crystalline phase in some of the powdered sample, the origin of the two wide peaks was found to stem from the incommensurate modulated character of the hollandite structure type (super space group I4/ m(0 0 γ)0 0) with a distribution of the modulation wavevectors presumably related to slight chemical composition changes.

Structure of the C-terminal domain of the catalase-peroxidase KatG from Escherichia coli.

Catalase-peroxidases or KatGs, the apparent in vivo activators of the anti-tubercular pro-drug isoniazid, are active as homodimers, each subunit having two distinct but sequence- and structure-related domains. The N-terminal domain contains the haem group and is catalytically active, while the C-terminal domain lacks the cofactor. The C-terminal domain of KatG from Escherichia coli is expressed as a soluble protein which has been crystallized in triclinic, orthorhombic and tetragonal crystal forms. Packing in the orthorhombic crystals, with eight molecules in the asymmetric unit, follows the pattern of commensurate modulated structures, which explains the diversity of pseudo-origin peaks observed in the native Patterson map. The different crystal forms arise from variations in the length and sequence of the N-terminal extensions in the different constructs. Despite the variability in the N-terminal region, the overall domain conformations beginning with Pro437 are very similar both to each other and to the C-terminal domains within the native structures of the KatGs from Haloarcula marismortui and Burkholderia pseudomallei. Some structural reorganization in the C-terminal domain relative to the N-terminal domain has evolved to compensate for the absence of the haem group. A high percentage of the residues in the C-terminal domains of KatG proteins from different sources are highly conserved and these residues are spread uniformly throughout the domain. The easily folded nature and retention of structure in the C-terminal domain suggests that it may serve as a platform for the folding of the N-terminal domain and for stabilization of the molecular dimer.

Domain structures in rutile in ultrahigh-pressure metamorphic rocks from Dabie Mountains, China

According to the HRTEM study, the UHP jadeite–quartzite mineral (Rutile, TiO 2) in Anhui Province, Dabie Mountains, China, has ultrastructures such as 〈011〉 two-dimensional commensurable modulated structures or superstructures, {011} twin domain structures, dislocations and crystal deformations. The SAED patterns and HRTEM images indicate the existence of the deformations and stacking faults on the interface of {011} twin crystal of rutile and its two-dimensional commensurate modulated structures with repetition period 0.753 nm (3 d 011) has tetragonal symmetry, cell parameters a=3a 0=1.377 nm ( a 0=0.459 nm ), c=c 0=0.3 nm. The modulated structures of rutile were probably caused by the isomorphic replacement of Ti 4+ and position modulation or occupation modulation of oxygen atoms in different degree; the deformation structures reveal that during the process of crystallization and mineralization, this mineral may be affected by the geological environment (such as temperature, pressure and stress), metamorphism and deformation.

Diffuse scattering and short-range order in uranium iodine phthalocyanine [U1-xPc(2)]I2-y and the X-ray structure analysis of crystals with diffuse superstructure reflections.

Crystals of uranium iodine phthalocyanine present an example of a disordered commensurate modulated structure of the intergrowth type. The short-range order of both uranium ions and iodine chains [I(3)(-)](n) has been analysed by Reverse Monte Carlo (RMC) simulation of X-ray diffuse scattering. The diffraction pattern of uranium iodine phthalocyanine contains diffuse superstructure reflections. In the routine crystal structure analysis diffuse superstructure reflections may be either omitted or measured and classified along with other Bragg reflections. The crystal structure of uranium iodine phthalocyanine is an example of such ambiguity. The crystal structures of two specimens of [U(1-x)Pc(2)]I(2-y) with slightly different composition have been published in the literature with different space groups and unit cells. We have shown that the structure of both specimens differs only in the degree of short-range order and is isostructural with [YbPc(2)]I(2). We have also shown that while the omission of diffuse reflections results in the average crystal structure, the treatment of these reflections as normal Bragg reflections is incorrect and produces the structure averaged over a limited small range.

New Compounds In3Ti2AO10, In6Ti6BO22, and Their Solid Solutions (A: Al, Cr, Mn, Fe, or Ga; B: Mg, Mn, Co, Ni, Cu, or Zn): Synthesis and Crystal Structures

New compounds, In3Ti2AO10 (A: Al, Cr, Mn, Fe, or Ga) and In6Ti6BO22 (B: Mg, Mn, Co, Ni, Cu, or Zn) were synthesized at and above 1000°C in air through solid-state reactions among the constituent cation oxide powders. They are isostructural with the monoclinic and/or orthorhombic In3Ti2FeO10 having a pyrochlore-related crystal structure with a commensurate or incommensurate modulated structure. The high-temperature phase is orthorhombic, and the low-temperature phase is monoclinic. The lattice constants of In3Ti2AO10 are as follows: In3Ti2AlO10 (1200°C): a(Å)=5.833(2), b(Å)=3.371(2), and c(Å)=12.060(6); In3Ti2AlO10 (1100°C): a(Å)=5.8368(7), b(Å)=3.3721(4), c(Å)=6.3402(8), and β(°)=107.87(1); In3Ti2CrO10 (1200°C): a(Å)=5.9246(8), b(Å)=3.3562(5), c(Å)=6.3546(9), and β(°)=108.10(1); In3Ti2GaO10 (1200°C): a(Å)=5.861(2), b(Å)=3.385(1), and c(Å)=12.094(4); In3Ti2GaO10 (1000°C): a(Å)=5.8742(9), b(Å)=3.3828(5), c(Å)=6.353(1), and β(°)=107.87(1). In3Ti2AlO10 and In3Ti2GaO10 are polymorphic. The lattice constants of In6Ti6BO22 are as follows: In6Ti6MgO22 (1200°C): a(Å)=5.9236(7), b(Å)=3.3862(4), c(Å)=6.3609(7), and β(°)=108.15(1); In6Ti6MnO22 (1200°C): a(Å)=5.9361(9), b(Å)=3.4031(5), c(Å)=6.3435(10), and β(°)=108.26(1); In6Ti6CoO22 (1200°C): a(Å)=5.9243(5), b(Å)=3.3841(3), c(Å)=6.3495(6), and β(°)=108.18(1); In6Ti6NiO22 (1200°C): a(Å)=5.9191(6), b(Å)=3.3729(3), c(Å)=6.3568(6), and β(°)=108.13(1); In6Ti6CuO22 (1000°C): a(Å)=5.916(2), b(Å)=3.379(1), and c(Å)=12.029(4); In6Ti6ZnO22 (1200°C): a(Å)=5.9223(6), b(Å)=3.3830(3), c(Å)=6.3576(6), and β(°)=108.16(1). In6Ti6BO22 (B: Mg, Mn, Co, Ni, or Zn) are monoclinic and In6Ti6CuO22 is orthorhombic. Solid solutions were synthesized in between In3Ti2AO10 (A: Al, Cr, Mn, Fe, or Ga) and In6Ti6BO22 (B: Mg, Mn, Co, Ni, Cu or Zn), and their lattice constants were determined. Temperature in the parenthesis means synthesis temperature, and all the lattice constants were measured at room temperature. The relationship between the unit cells of In3Ti2AO10, In6Ti6BO22, their solid solutions, and the constituent cation elements of A and B are discussed in terms of their tendency for site preference.

The An+2BnB′O3n+3 Family (B=B′=Co): Ordered Intergrowth between 2H–BaCoO3 and Ca3Co2O6 Structures

The n integer members of the An+2BnB′O3n+3 homologous series keeping B=B′=Co the same have been characterized by selected area electron diffraction and high resolution electron microscopy. Its commensurate modulated structure is made up of chains, separated by A atoms, running along the c direction containing a succession of one Co atom (B′) in prismatic trigonal sites and n Co atoms octahedrally coordinated sharing faces. All of them can be described as ordered intergrowths of two structures of the end members of the family, 2H–BaCoO3 (n=∞) and Ca3Co2O6 (n=1). The modulation observed in all terms can be described as a function of the difference between the c-axis of the Co sublattice with respect to the 2H structure. Members of the series can be obtained by modifying the distance between layers keeping B=Co the same, as shown in (Sr1−xBax)6Co5O15 (n=4), Sr5Co4O12 (n=3), and (Sr0.5Ca0.5)4Co3O9 (n=2).

Reinvestigation and Structural Approach of the Ba–Pt–O System for[formula omitted]

A reinvestigation of the Ba-rich region of the Ba–Pt–O system has been undertaken. The existence of a solid solution, already mentioned, has been confirmed, and its true formulation has been determined: Ba12[BaxPt3−x]Pt6O27with 0≤x≤3. The structure of these phases can be schematically considered as being built up from the periodic stacking along thecdirection of one close-packing [Ba3O9] layer, similar to those of the hexagonal perovskite, and three [Ba3A′O6] layers, withA′=Ba, Pt. The stacking of these mixed layers is of hexagonal type, and then columns parallel tocare formed. They consist of octahedra and trigonal prisms, sharing faces, which are occupied byA′ cations. For 0≤x≤1, the structure appears to be incommensurate and should be described as a composite crystal based on two subsystems: [Ba] and [(Ba, Pt)O3]. Forx>1, the X-ray diffraction pattern can be explained using a three-dimensional cell, but the structure refinement attempts as well as the electron diffraction patterns seem to indicate these phases are commensurate modulated structures.

Modulated charge ordering process in Sm0.5Ca0.5Mn1−xCrxO3 manganites

The oxides Sm0.5Ca0.5Mn1–xCrxO3 , with 0≤x≤0.07, have been studied by electron diffraction and electron microscopy versustemperature from 90 K to 300 K, in connection with their magnetic and transport properties. An incommensurate charge ordering appears atTCO=275 K for the undoped compound, then a progressive transition from an incommensurate to a commensurate modulated structure is observed as Tdecreases from 275 K to 170 K. But the most important point is that chromium doping enhances the incommensurability of the structure: theq vector of the low temperature form decreases and TCO decreases abruptly as the chromium content x increases, so that the charge ordering process is weakened and finally disappears for x=0.05. The structure of the low temperature form of these manganites is characterized by a double supercell, 2ap √2×2ap ×ap √2, similar to that observed for other Ln0.5Ca0.5MnO3 manganites with Ln=La, Pr, Nd, Tb. However, in these series, one observes similar space groups (P2mmorPmmm) for Ln=Nd, Sm, different from those observed for Ln=La, Tb.

Electron crystallographic study of superconducting oxides and related compounds

A review on crystal structure determination of high temperature superconductors using electron diffraction or the combination of electron diffraction and high resolution electron microscopy is given. The two-stage image processing technique and the multi-dimensional direct method are employed. Four examples including the determination of commensurate and incommensurate modulated structures are reported.

Structural modulation and phase transition in a Na-rich alkali feldspar

Transmission electron microscopy (TEM) revealed a commensurate modulated structure in a Na-rich alkali feldspar (Ab660r29Ans) from a basalt from Anhui Province, China. High-resolution TEM images with wavelike (001) lattice fringes directly reveal one-dimensional modulation waves in the crystal. The average modulation period along the b axis is l4dolO (;;;; 180 A), although both larger and smaller spacings have been observed. The modulated structure can be described as periodic stacking of (010) layer domains following the albite twin law. The relationship between the extended cell (supercell) of the modulated structure and the normal alkali feldspar unit cell (subcell) is as follows: a,up ;;;; a,ub, b,up ;;;; l4boub,c,uP ;;;; C,ub,{3,up ;;;; {3,ub (subscripts sup and sub indicate the supercell and subcell, respectively). A possible space group for the modulated structure is Pm. In situ heating and cooling experiments suggestthat the phase transition in this feldspar thin foil might be a weakly first-order and displacive transformation. The transition temperature is close to 500 DCfor the crystal examined. The modulated structure formed during the phase transition of the feldspar from C2/m symmetry to Cl at a rapid cooling rate. A heuristic nonlinear dynamics model for the arrangement of triclinic domains in the feldspar at the phase transition from monoclinic to triclinic symmetry was developed on the basis of a Landau potential, a damping term accounting for the structural differences among neighboring units, and a periodic force in the crystal along the b axis. Numerical solutions indicate that periodic modulation arises during the monoclinic to triclinic transition only under special conditions relatively far from equilibrium, and a nonperiodic arrangement of triclinic domains along the b axis is the more general case. Therefore, according to this model, the modulated structure is a metastable and intermediate structure between monoclinic (C2/m) and triclinic (Cl) phases. This type of modulated structure in Na-rich alkali feldspars may indicate high-temperature growth as a monoclinic crystal, followed by very rapid cooling into the triclinic stability field.

On the structure factor for commensurate modulated structures

A superstructure may be looked upon as a commensurate modulated structure and be described through the superspace formalism. It can be studied using low- or high-symmetry superspace groups. The possibility of adopting a high-symmetry description is related to the existence of at least two independent three-dimensional sections in the supercrystal with the same space-group symmetry. The usual structure-factor formula for commensurate structures [Yamamoto (1982). Acta Cryst. A38, 87–92] includes just one of these sections, thus allowing for a low-symmetry description only. A very simple generalization of this in the superspace formalism is presented, which allows for the use of either low- or high-symmetry superspace groups in the structural analysis. The reasons for a seemingly successful refinement found in the literature, making use of the high-symmetry description, are discussed.

Connections between polytypes, modulated structures and quasicrystals

Abstract Polytypes built up of two or more different kinds of layers can be regarded as modulated structures, where the modulation means the stacking sequence of the different building units. Polytypes have a strictly periodic lattice in two dimensions, and the “modulation” is always restricted to the third dimension, and so they always have commensurate modulated structures, although the modulation itself cannot usually be described by a simple function. Aperiodic polytypes, i.e. polytypes with stacking faults can be described by Fibonacci chains. Using the well-known “A” “B” “C” notation to denote the three possible positions of the translationally equivalent double layers of hexagonal symmetry, the A and B values in the Fibonacci rule can be given by adequate sequences of “A”, “B” and “C”.

Modulated structures of (Bi1−xPbx)2Sr2CoOy examined by high-resolution transmission electron microscopy

Abstract The Pb-doped Bi-Sr-Co-O complex oxides, (Bi 1- x Pb x ) 2 Sr 2 CoO y with x =0.0 to 0.5, are examined by means of electron diffraction and high-resolution transmission electron microscopy (HRTEM) in order to clarify the effects of Pb-doping on the commensurate modulated structure of Bi 2 Sr 2 CoO y . Specimens with Pb content up to 10% ( x ≤0.1) have a commensurate modulated structure with modulation periodicity b s =4 b . At 15% substitution ( x =0.15), a stepwise increase of the value of b s is observed and the specimens with Pb content from 20 to 30% (0.2≤ x ≤0.3) have incommensurate modulations with b s ≈4.5 b . Modulated structures are absent for specimens with Pb more than 40% (0.4≤ x ). All of the modulated structures have body-centered orthorhombic symmetries (Mode I) and no transition to base-centered symmetry (Mode II) is observed even by high Pb-substitution in the present (Bi 1- x Pb x ) 2 Sr 2 CoO y system, although transition to Mode II is generally observed for superconducting Pb-doped Bi-Sr-Cu-O systems.

Commensurate and incommensurate modulated structures of Rb2ZnCl4

Abstract The commensurate and incommensurate structures of Rb2ZnCl4 have been refined using the four-dimensional formalism for modulated structures. They are characterized by a rigid body modulated rotation of the ZnCl4 tetrahedra and by a translation motion of the Rb atoms.