scholarly journals Incommensurately modulated twin structure of nyerereite Na1.64K0.36Ca(CO3)2

2017 ◽  
Vol 73 (2) ◽  
pp. 276-284 ◽  
Author(s):  
Nadezhda B. Bolotina ◽  
Pavel N. Gavryushkin ◽  
Andrey V. Korsakov ◽  
Sergey V. Rashchenko ◽  
Yurii V. Seryotkin ◽  
...  
Keyword(s):  
Symmetry Group ◽  
Harmonic Functions ◽  
Unit Cell ◽  
Twin Structure ◽  
Modulated Structure ◽  
Modulation Vector

The incommensurately modulated twin structure of nyerereite Na1.64K0.36Ca(CO3)2has been first determined in the (3 + 1)-dimensional symmetry groupCmcm(α00)00swith modulation vectorq= 0.383a*. Unit-cell values area= 5.062 (1),b= 8.790 (1),c= 12.744 (1) Å. Three orthorhombic components are related by threefold rotation about [001]. Discontinuous crenel functions are used to describe the occupation modulation of Ca and some CO3groups. The strong displacive modulation of the O atoms in vertexes of such CO3groups is described using x-harmonics in crenel intervals. The Na, K atoms occupy mixed sites whose occupation modulation is described in two ways using either complementary harmonic functions or crenels. The nyerereite structure has been compared both with the commensurately modulated structure of K-free Na2Ca(CO3)2and with the widely known incommensurately modulated structure of γ-Na2CO3.

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.

scholarly journals News from the world of modulated intermetallics

2014 ◽  
Vol 70 (a1) ◽  
pp. C167-C167
Author(s):  
Sven Lidin ◽  
Partha Jana ◽  
Carola Müller ◽  
Shuying Piao ◽  
Simeon Ponou
Keyword(s):  
Higher Order ◽  
Ordered Structures ◽  
Modulated Structure ◽  
Formal Modelling ◽  
Modulated Structures ◽  
The World ◽  
Cubic Structure ◽  
Modulation Vector

The number of modulated structures with more than one modulation vector is small, and such structures often pose special problems in solving and refining. This talk will be concentrated on three such cases; The 3+4 dimensionally modulated cubic structure of digenite, the 3+2 dimensionally modulated structure of Cu3In2, the 3+2 dimensionally modulated structure of AuZn3 and the 3+2 dimensionally modulated structure of Se(Sn4)2K10. The three former cases are interesting because they are relatively weakly ordered structures where modelling is straight-forward, but the model itself is less than obvious to understand while the latter case appears highly ordered, but presents formal modelling difficulties. From these and previously known multi dimensional cases it would appear that higher order modulations are very prone to disorder. The image shows the hk0 layer from Se(Sn4)2K10.

scholarly journals Growth-induced incommensurability observed in the organic co-crystal hexamethylenetetramine resorcinol

2006 ◽  
Vol 62 (6) ◽  
pp. 1043-1050 ◽  
Author(s):  
Soraya Maria Belluga Rodriguez ◽  
Lukáš Palatinus ◽  
Václav Petříček ◽  
Gervais Chapuis
Keyword(s):  
Phase Transition ◽  
Poor Quality ◽  
Temperature Phase ◽  
X Ray Diffraction ◽  
Modulated Structure ◽  
Main Effect ◽  
Harmonic Modulation ◽  
Low Temperature Phase ◽  
Modulation Vector

Co-crystals of hexamethylenetetramine and resorcinol were investigated by X-ray diffraction. The structure was refined in the superspace group Xmcm(0\beta 0)s0s, X = (\,{{1}\over{2}} {{1}\over{2}} 0 {{1}\over{2}}\,). In the average structure the resorcinol molecules are disordered between two orientations. The main effect of the modulation in the structure is a harmonic modulation of the occupation probabilities of the two orientations of the resorcinol molecule. However, the modulated order is not perfect and the resorcinol molecules remain partially disordered. Below 270 K the crystal undergoes a phase transition to a commensurately modulated structure with modulation vector {\bf q} = (0 {{1}\over{2}} {{1}\over{4}}\,) and superspace group X2/m(0\beta \gamma)0s. The structure of the low-temperature phase could not be determined owing to the poor quality of the crystals affected by the reconstructive phase transition.

RICICLE: A FORTRAN program to refine unit cell parameters of incommensurate structures

1993 ◽  
Vol 8 (3) ◽  
pp. 168-172 ◽  
Author(s):  
R. I. Smith
Keyword(s):  
Least Squares ◽  
Powder Diffraction ◽  
Fortran Program ◽  
Unit Cell ◽  
Unit Cell Parameters ◽  
Full Matrix ◽  
Cell Parameters ◽  
Incommensurate Structures ◽  
Diffraction Patterns ◽  
Modulation Vector

A FORTRAN 77 program to perform full matrix least-squares refinement of unit cell parameters from powder diffraction patterns showing incommensurate supercell reflections is described. The code is completely general, being applicable to any crystal system, and can refine all three unit cell edges and angles and, in the presence of an incommensurate supercell, can refine the components of the modulation vector along all three reciprocal axes. Estimated standard deviations on all the refined parameters are calculated analytically.

Superspace description of the modulated structure of the metal-salt-hybrid Bi7 − δNi2Br5 − 2δ (δ = 1/9)

2009 ◽  
Vol 65 (5) ◽  
pp. 593-599 ◽  
Author(s):  
B. Wahl ◽  
M. Ruck
Keyword(s):  
Crystal Structure ◽  
Metal Salt ◽  
Intermetallic Phase ◽  
Structure Model ◽  
Orthorhombic Space Group ◽  
Modulated Structure ◽  
Edge Sharing Octahedra ◽  
Strong Resemblance ◽  
Superspace Description ◽  
Modulation Vector

The compound Bi7 − δNi2Br5 − 2δ = (Bi3Ni)2[Bi1 − δBr4]Br1 −2δ (δ = 1/9) is a sub-bromide of the intermetallic phase Bi3Ni. Its crystal structure contains metallic rods, ^1_{\infty}[Bi3Ni], which are embedded in a salt-like matrix of bromido-bismuthate(III) and bromide anions. The non-stoichiometry originates from the variation of the number n of trans edge-sharing octahedra in the [Bi n Br4n + 2](n + 2)− oligomers (3 ≤ n ≤ 5), as well as from vacancies on the sites of the isolated Br atoms. The simplified structure is described in the orthorhombic space group Cmcm with a = 4.0660 (4), b = 23.305 (3), c = 17.130 (2) Å. It shows a statistical distribution of vacancies and orientational disorder of the concatenated octahedra. By choosing the modulation vector q = a*/9 + b*/2, the additional weak reflections of the diffraction pattern can be indexed. In the [3 + 1]-dimensional superspace group Pmnm(α½0)000, an ordered structure model is achieved. The modulated crystal structure bears a strong resemblance to the somewhat higher oxidized sub-bromide Bi7 − δNi2Br5 (δ = 1/9).

scholarly journals Could incommensurability in sulfosalts be more common than thought? The case of meneghinite, CuPb13Sb7S24

2017 ◽  
Vol 73 (3) ◽  
pp. 369-376 ◽  
Author(s):  
Luca Bindi ◽  
Václav Petříček ◽  
Cristian Biagioni ◽  
Jakub Plášil ◽  
Yves Moëlo
Keyword(s):  
Driving Forces ◽  
Bimodal Distribution ◽  
Modulated Structure ◽  
Cell Parameters ◽  
Incommensurate Structure ◽  
Incommensurate Modulation ◽  
Coupled Substitution ◽  
Modulation Vector ◽  
Different Parts ◽  
Apuan Alps

The structure of meneghinite (CuPb13Sb7S24), from the Bottino mine in the Apuan Alps (Italy), has been solved and refined as an incommensurate structure in four-dimensional superspace. The structure is orthorhombic, superspace groupPnma(0β0)00s, cell parametersa =24.0549 (3),b =4.1291 (6),c =11.3361 (16) Å, modulation vectorq= 0.5433 (4)b*. The structure was refined from 6604 reflections to a finalR= 0.0479. The model includes modulation of both atomic positions and displacement parameters, as well as occupational waves. The driving forces stabilizing the modulated structure of meneghinite are linked to the occupation modulation of Cu and some of the Pb atoms. As a consequence of the Cu/[] and Pb/Sb modulations, three- to sevenfold coordinations of theMcations (Pb/Sb) occur in different parts of the structure. The almost bimodal distribution of the occupation of Cu/[] and Pb/Sb atM5 conforms with the coupled substitution Sb3++ [] → Pb2++ Cu+, thus corroborating the hypothesis deduced previously for the incorporation of copper in the meneghinite structure. The very small departure (∼0.54versus0.50) from the commensurate value of the modulation raises the question of whether other sulfosalts considered superstructures have been properly described, and, in this light, if incommensurate modulation in sulfosalts could be much more common than thought.

scholarly journals Capabilities and limitations of a (3 + d)-dimensional incommensurately modulated structure as a model for the derivation of an extended family of compounds: example of the scheelite-like structures

2008 ◽  
Vol 64 (1) ◽  
pp. 12-25 ◽  
Author(s):  
Alla Arakcheeva ◽  
Gervais Chapuis
Keyword(s):  
Extended Family ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Unit Cell ◽  
Group Symmetry ◽  
Dimensional Structure ◽  
Basic Unit ◽  
Modulated Structure ◽  
Three Dimensional Structure ◽  
Cell Parameters

The previously reported incommensurately modulated scheelite-like structure KNd(MoO4)2 has been exploited as a natural (3 + 1)-dimensional superspace model to generate the scheelite-like three-dimensional structure family. Although each member differs in its space-group symmetry, unit-cell parameters and compositions, in (3 + 1)-dimensional space, they share a common superspace group, a common number of building units in the basic unit cell occupying Wyckoff sites with specific coordinates (x, y, z) and specific basic unit-cell axial ratios (c/a, a/b, b/c) and angles. Variations of the modulation vector q, occupation functions and t 0 are exploited for the derivation. Eight topologically and compositionally different known structures are compared with their models derived from the KNd(MoO4)2 structure in order to evaluate the capabilities and limitations of the incommensurately modulated structure to act as a superspace generating model. Applications of the KNd(MoO4)2 structure as a starting model for the refinement and prediction of some other modulated members of the family is also illustrated. The (3 + 1)-dimensional presentation of the scheelite-like structures reveals new structural relations, which remain hidden if only conventional three-dimensional structure descriptions are applied.

scholarly journals Characterization of smectite and illite by FTIR spectroscopy of interlayer NH4+ cations

Clay Minerals ◽  
2003 ◽  
Vol 38 (2) ◽  
pp. 201-211 ◽  
Author(s):  
J . Pironon ◽  
M. Pelletier ◽  
P. De Donato ◽  
R. Mosser-Ruck
Keyword(s):  
Ftir Spectroscopy ◽  
Symmetry Group ◽  
Clay Minerals ◽  
Area Ratio ◽  
Unit Cell ◽  
Tetrahedral Symmetry ◽  
Bending Vibration ◽  
Band Area ◽  
Stretching Vibration

AbstractFTIR spectroscopy has been applied to NH4+-exchanged dioctahedral clay minerals to determine the molecular environment of NH4+ and to quantify N concentration. FTIR under vapourpressure control, coupled with heating and freezing treatments has shown that NH4+ ion symmetry varies with the nature of clay minerals. NH4+ has a perfect tetrahedral symmetry in hydrated or dehydrated smectites and belongs to the Td symmetry group. The NH4+-bending vibration is centred at 1450 and 1425 cm–1.The Si4+-Al3+ substitution in dioctahedral clay minerals induces the loss of symmetry elements of the NH4+ tetrahedron which acquires a C2v symmetry. As a consequence, the Td –C2v transition can be used to characterize the smectite–illite transition. Quantification of NH4+ content per half unit cell is provided by nNH4 = k[NH4]/[OH] where [NH4]/[OH] is the band area ratio of the NH4+-bending vibration to the OH-stretching vibration. k = 1.1 for hydrated smectite, 0.9 for dehydrated smectite and 0.8 for illite or tobelite. The bending vibration of NH4+ is chosen for the calculation because it is not affected by superimposed contributions.

Incommensurate crystal structure of PbHfO3

2020 ◽  
Vol 76 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Alexei Bosak ◽  
Volodymyr Svitlyk ◽  
Alla Arakcheeva ◽  
Roman Burkovsky ◽  
Vadim Diadkin ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Amplitude Modulation ◽  
Intermediate Phase ◽  
Unit Cell ◽  
Lead Ions ◽  
Diffraction Experiment ◽  
Pure Compound ◽  
Synchrotron Diffraction ◽  
Structure Modulation ◽  
Modulation Vector

Controversy in the description/identification of so-called intermediate phase(s) in PbHfO3, stable in the range ∼420–480 K, has existed for a few decades. A synchrotron diffraction experiment on a partially detwinned crystal allowed the structure to be solved in the superspace group Imma(00γ)s00 (No. 74.2). In contrast to some previously published reports, in the pure compound only one distinct phase was observed between Pbam PbZrO3-like antiferroelectric and Pm3m paraelectric phases. The modulation vector depends only slightly on temperature. The major structure modulation is associated with the displacement of lead ions, which is accompanied by a smaller amplitude modulation for the surrounding O atoms and tilting of HfO6 octahedra. Tilting of the octahedra results in a doubling of the unit cell compared with the parent structure.

X-ray powder diffraction analysis of the incommensurate modulated structure of Bi2Sr2CaCu2O8

1994 ◽  
Vol 9 (1) ◽  
pp. 28-37 ◽  
Author(s):  
D. P. Matheis ◽  
R. L. Snyder
Keyword(s):  
Powder Diffraction ◽  
Structural Parameters ◽  
Lattice Parameter ◽  
Processing Conditions ◽  
Modulated Structure ◽  
X Ray ◽  
Modulated Structures ◽  
Sample Composition ◽  
Modulation Model ◽  
Modulation Vector

X-ray powder diffraction is a convenient tool for monitoring changes in structural parameters due to modifications in sample composition and processing conditions. Due to the complexity of incommensurate modulated structures powder diffraction techniques have not been commonly applied. Programs ALSQ and QRIET have been produced to perform lattice parameter and structure refinements on incommensurate modulated materials with a displacive modulation model. In applying these programs to the Bi2Sr2CaCu2O8 superconductor which has this type of structure, it is shown that a decrease in the lattice parameters and an increase in the modulation vector occurs as the Ca content of the Bi-2212 phase, controlled by the use of the glass ceramic process, increases.

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