scholarly journals Crystal structure solution from experimentally determined atomic pair distribution functions

2010 ◽  
Vol 43 (3) ◽  
pp. 623-629 ◽  
Author(s):  
P. Juhás ◽  
L. Granlund ◽  
S. R. Gujarathi ◽  
P. M. Duxbury ◽  
S. J. L. Billinge
Keyword(s):  
Crystal Structure ◽  
Distribution Functions ◽  
Unit Cell ◽  
Second Step ◽  
X Ray ◽  
Atomic Pair ◽  
Structure Solution ◽  
Pair Distribution Functions ◽  
Atomic Radii ◽  
Periodic Crystal

An extension of the Liga algorithm for structure solution from atomic pair distribution functions (PDFs), to handle periodic crystal structures with multiple elements in the unit cell, is described. The procedure is performed in three separate steps. First, pair distances are extracted from the experimental PDF. In the second step the Liga algorithm is used to find unit-cell sites consistent with these pair distances. Finally, the atom species are assigned over the cell sites by minimizing the overlap of their empirical atomic radii. The procedure has been demonstrated on synchrotron X-ray PDF data from 16 test samples. The structure solution was successful for 14 samples, including cases with enlarged supercells. The algorithm success rate and the reasons for the failed cases are discussed, together with enhancements that should improve its convergence and usability.

Algorithm for systematic peak extraction from atomic pair distribution functions

2015 ◽  
Vol 71 (4) ◽  
pp. 392-409 ◽  
Author(s):  
L. Granlund ◽  
S. J. L. Billinge ◽  
P. M. Duxbury
Keyword(s):  
Structural Model ◽  
Information Criterion ◽  
Distribution Functions ◽  
Theory And Practice ◽  
Chi Square ◽  
Information Theoretic ◽  
Atomic Pair ◽  
Structure Solution ◽  
The Impact ◽  
Pair Distribution Functions

The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python programSrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.

Crystal structure of the (REE)-uranyl carbonate mineral kamotoite-(Y)

2017 ◽  
Vol 81 (3) ◽  
pp. 653-660 ◽  
Author(s):  
Jakub Plášil ◽  
Václav Petříček
Keyword(s):  
Crystal Structure ◽  
Cell Transformation ◽  
Unit Cell ◽  
Original Structure ◽  
Carbonate Mineral ◽  
X Ray Diffraction ◽  
X Ray ◽  
Uranyl Carbonate ◽  
Structure Solution ◽  
Super Cell

AbstractKamotoite-(Y) is a rare supergene product of uraninite hydration–oxidation weathering and its structure is unknown. Based on single-crystal X-ray diffraction data collected with high-redundancy using a microfocus source, kamotoite-(Y) is monoclinic, has space group P21/n,with a = 12.3525(5), b = 12.9432(5), c = 19.4409(7) Å, β = 99.857(3)°, V = 3069.8(2) Å3 and Z = 4. Crystals are pervasively twinned (two-fold rotation around [0.75 0 0.75]), giving a strongly pseudo-orthorhombic diffractionpattern. The pseudoorthorhombic pattern can be described with an orthorhombic super-cell (transformation matrix 0,1,0/1,0,1/3,0,1), approximately four times larger in volume then a true monoclinic unit cell. This unit-cell is the same as the cell given elsewhere for the structure of bijvoetite-(Y),another (REE)-containing uranyl carbonate. The successful structure solution and refinement (R = 0.044 for 6294 unique observed reflections), carried out using our choice of unit cell, as well as the superstructure refinement and comparison of the original structure data forbijvoetite-(Y) reveal that these two crystal structures are identical. The crystal structure of kamotoite-(Y) consists of electroneutral sheets of the bijvoetite-(Y) uranylanion topology and an interlayer with H2O molecules not-coordinated directly to any metal cation. Despite determinationof the kamotoite-(Y) structure and demonstration that bijvoetite-(Y) has the same structure, the identity of these two minerals cannot be proved without additional study of the holotype material.

Imaging of interstitial atoms in Ga1−xMnxAs layers by means of X-ray diffuse scattering

2008 ◽  
Vol 41 (3) ◽  
pp. 544-547 ◽  
Author(s):  
Miloš Kopecký ◽  
Edoardo Busetto ◽  
Andrea Lausi ◽  
Zbyněk Šourek ◽  
Jiří Kub ◽  
...  
Keyword(s):  
Atomic Structure ◽  
Diffuse Scattering ◽  
Annealing Process ◽  
Distribution Functions ◽  
Unit Cell ◽  
X Ray ◽  
Interstitial Atoms ◽  
Before And After ◽  
The Difference ◽  
Pair Distribution Functions

The local atomic structure of a Ga1−xMnxAs (x= 0.07) layer during the annealing process was studied by means of X-ray diffuse scattering. The difference between the pair-distribution functions before and after annealing indicated the fraction of atoms that changed concentration and identified them to be exclusively interstitial atoms at the centres of gallium and/or arsenic tetrahedra in the GaMnAs unit cell.

Atomic ordering in nanosized PtxAu1–x(x= 0, 0.51, 1) by resonant X-ray diffraction and differential atomic pair distribution functions

2012 ◽  
Vol 227 (5) ◽  
pp. 262-267 ◽  
Author(s):  
Valeri Petkov ◽  
Sarvjit Shastri ◽  
Bridgid Wanjala ◽  
Rameshiwori Loukrakpam ◽  
Jin Luo ◽  
...  
Keyword(s):  
Distribution Functions ◽  
X Ray Diffraction ◽  
Atomic Ordering ◽  
X Ray ◽  
Atomic Pair ◽  
Pair Distribution Functions

scholarly journals The structure of kaliophilite KAlSiO4, a long-lasting crystallographic problem

IUCrJ ◽  
2020 ◽  
Vol 7 (6) ◽  
pp. 1070-1083 ◽  
Author(s):  
Enrico Mugnaioli ◽  
Elena Bonaccorsi ◽  
Arianna E. Lanza ◽  
Erik Elkaim ◽  
Virginia Diez-Gómez ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Rietveld Method ◽  
Structural Features ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Channel System ◽  
X Ray ◽  
Cell Parameters ◽  
Peak Broadening ◽  
Structure Solution

Kaliophilite is a feldspathoid mineral found in two Italian magmatic provinces and represents one of the 12 known phases with composition close to KAlSiO4. Despite its apparently simple formula, the structure of this mineral revealed extremely complex and resisted structure solution for more than a century. Samples from the Vesuvius–Monte Somma and Alban Hills volcanic areas were analyzed through a multi-technique approach, and finally the crystal structure of kaliophilite was solved using 3D electron diffraction and refined against X-ray diffraction data of a twinned crystal. Results were also ascertained by the Rietveld method using synchrotron powder intensities. It was found that kaliophilite crystallizes in space group P3 with unit-cell parameters a = 27.0597 (16), c = 8.5587 (6) Å, V = 5427.3 (7) Å3 and Z = 54. The kaliophilite framework is a variant of the tridymite topology, with alternating SiO4 and AlO4 tetrahedra forming sheets of six-membered rings (63 nets), which are connected along [001] by sharing the apical oxygen atoms. Considering the up (U) and down (D) orientations of the linking vertex, kaliophilite is the first framework that contains three different ring topologies: nine (1-3-5) (UDUDUD) rings, six (1-2-3) (UUUDDD) rings and twelve (1-2-4) (UUDUDD) rings. This results in a relatively open (19.9 tetrahedra nm−3) channel system with multiple connections between the double six-ring cavities. Such a framework requires a surprisingly large unit cell, 27 times larger than the cell of kalsilite, the simplest phase with the same composition. The occurrence of some Na for K substitution (3–10%) may be related to the characteristic structural features of kaliophilite. Micro-twinning, pseudo-symmetries and anisotropic hkl-dependent peak broadening were also detected, and they may account for the elusive character of the kaliophilite crystal structure.

scholarly journals Natural Nanomaterials: Reappraising the Elusive Structure of the Nano-Sized Mineral Ferrihydrite through X-Ray Absorption Spectroscopy at the Iron K-Edge

2012 ◽  
Vol 730-732 ◽  
pp. 931-935 ◽  
Author(s):  
Maria Ondina Figueiredo ◽  
Teresa P. Silva ◽  
Joao P. Veiga
Keyword(s):  
Distribution Functions ◽  
Mine Wastes ◽  
X Ray Diffraction ◽  
X Ray ◽  
Ferric Oxyhydroxide ◽  
Atomic Pair ◽  
Icosahedral Clusters ◽  
X Ray Absorption ◽  
Pair Distribution Functions ◽  
Tetrahedral Iron

Ferrihydrite is natural ferric oxyhydroxide occurring exclusively nanocrystalline. With ideal formula 5 Fe2 O3 . 9 H2 O, ferrihydrite is quite abundant in sediments, weathering crusts and mine wastes, being characteristic of red pre-soils formed by loose weathered rock plus mineral debris (regoliths) and commonly designated as “2-line” or “6-line” on the basis of the broadened maxima observed in the X-ray diffraction pattern. Synthetic nanocrystalline “6-line” ferrihydrite was recently studied through methods based on atomic-pair distribution functions disclosing the possible occurrence of icosahedral clusters formed by twelve octahedra centred by an inner tetrahedron, all filled by Fe 3+ ions. However, Mössbauer studies were inconclusive about the existence of 4-coordinated iron, thus suggesting that the tetrahedral cation may well be Si4+. In view of such structural uncertainty, a XANES study at the Fe K-edge was undertaken on ferrihydrite from a regolith to ascertain the occurrence of tetrahedral iron. Comparison with data collected from well crystallized iron oxide and hydroxide minerals where Fe 3+/2+ ions occur in octahedral and tetrahedral coordination is described and the results so far obtained are discussed, showing that supplementary study is needed on the elusive structure of ferrihydrite.

Structure and thermal expansion of sulfuric acid octahydrate

2012 ◽  
Vol 45 (6) ◽  
pp. 1198-1207 ◽  
Author(s):  
Helen E. Maynard-Casely ◽  
Helen E. A. Brand ◽  
Kia S. Wallwork
Keyword(s):  
Crystal Structure ◽  
Thermal Expansion ◽  
Sulfuric Acid ◽  
Powder Diffraction ◽  
Unit Cell ◽  
Acid Solutions ◽  
X Ray ◽  
Structure Solution ◽  
Sulfuric Acid Solutions

Synchrotron X-ray powder diffraction has been used to structurally characterize crystallization products from 37.8 and 40.5 wt% aqueous sulfuric acid solutions. It is confirmed that, despite speculation in the literature, the structure that predominately crystallized from these solutions is sulfuric acid octahydrate (SAO). The existence of an uncharacterized phase is also noted. It was found that existing models proposed for the crystal structure of SAO did not satisfactorily fit to the data acquired here, and hence a new structure solution was sought. It is reported here that the structure of SAO is contained within a unit cell withI2 symmetry witha= 7.44247 (11),b= 7.4450 (1),c= 26.1168 (3) Å, β = 125.0428 (7)°,V= 1184.78 (3) Å3at 80 K. Data were collected at temperatures between 80 and 198 K, which enabled determination of the thermal expansion of SAO.

Structure of crystallographically challenged materials by profile analysis of atomic pair distribution functions: study of LiMoS2 and mesostructured MnGe4S10.

2001 ◽  
Vol 678 ◽  
Author(s):  
V. Petkov ◽  
K. K. Rangan ◽  
M. G. Kanatzidis ◽  
S.J.L. Billinge
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Profile Analysis ◽  
Three Dimensional ◽  
Distribution Functions ◽  
Unit Cell ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair ◽  
Pair Distribution Functions ◽  
Triclinic Unit Cell

AbstractThe approach of the atomic pair distribution function (PDF) technique to study the structure of materials with significant disorder is considered and successfully applied to LiMoS2 and mesostructured MnGe4S10. We find that LiMoS2 is built of layers of distorted MoS6 octahedra stacked along the c axis of a triclinic unit cell with well-defined Mo-Mo bonding. Mesostructured MnGe4S10 is a three-dimensional framework of “adamantane-like” [Ge4S10] units bridged by Mn atoms.

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