scholarly journals An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films

2020 ◽  
Vol 76 (3) ◽  
pp. 345-357 ◽  
Author(s):  
Josef Simbrunner ◽  
Benedikt Schrode ◽  
Jari Domke ◽  
Torsten Fritz ◽  
Ingo Salzmann ◽  
...  
Keyword(s):  
Rotational Symmetry ◽  
Grazing Incidence ◽  
Unit Cell ◽  
Structure Identification ◽  
X Ray Diffraction ◽  
Cell Parameters ◽  
Lattice Constants ◽  
The Matrix ◽  
Unit Cells ◽  
Complex Scenario

Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.

Unit cell dimensions of the hydrated aluminium phosphate–sulphate minerals sanjuanite, kribergite, and hotsonite

1989 ◽  
Vol 53 (371) ◽  
pp. 385-386 ◽  
Author(s):  
H. De Bruiyn ◽  
G. J. Beukes ◽  
W. A. Van Der Westhuizen ◽  
E. A. W. Tordiffe
Keyword(s):  
Unit Cell ◽  
X Ray Diffraction ◽  
Aluminium Phosphate ◽  
Powder Diffraction File ◽  
Cell Parameters ◽  
Cell Dimensions ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Unit Cell Dimensions ◽  
Hydrated Aluminium

AT the time when the hydrated aluminium phosphate-sulphate hotsonite (Beukes et al., 1984a) and its equally rare relative zaherite (Beukes et al., 1984b; De Bruiyn et al., 1985) were discovered near Pofadder, South Africa, very little was known about the unit cells of the other two hydrated aluminium phosphate-sulphate minerals sanjuanite and kribergite, originally described by De Abeledo et al. (1968) from Argentina and Sweden, respectively. Although the Powder Diffraction file (PDF) contains the X-ray diffraction patterns for sanjuanite and kribergite (PDF 20-47 and 20-48 respectively), they had not been indexed nor have their unit cell parameters been calculated thus far.

scholarly journals Indexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin films

2018 ◽  
Vol 74 (4) ◽  
pp. 373-387 ◽  
Author(s):  
Josef Simbrunner ◽  
Clemens Simbrunner ◽  
Benedikt Schrode ◽  
Christian Röthel ◽  
Natalia Bedoya-Martinez ◽  
...  
Keyword(s):  
Substrate Surface ◽  
Grazing Incidence ◽  
Diffraction Peak ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
X Ray ◽  
Lattice Constants ◽  
Mathematical Expressions ◽  
Rotation Parameters ◽  
Diffraction Patterns

Crystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacenequinone are determined.

Ternary gradient metal–organic frameworks

2017 ◽  
Vol 201 ◽  
pp. 163-174 ◽  
Author(s):  
Chong Liu ◽  
Nathaniel L. Rosi
Keyword(s):  
Ligand Exchange ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Exchange Reactions ◽  
Reaction Conditions ◽  
Gradient Distribution ◽  
X Ray ◽  
Cell Parameters ◽  
Unit Cells ◽  
Metal Organic

Gradient MOFs contain directional gradients of either structure or functionality. We have successfully prepared two ternary gradient MOFs based on bMOF-100 analogues, namely bMOF-100/102/106 and bMOF-110/100/102, via cascade ligand exchange reactions. The cubic unit cell parameter discrepancy within an individual ternary gradient MOF crystal is as large as ∼1 nm, demonstrating the impressive compatibility and flexibility of the component MOF materials. Because of the presence of a continuum of unit cells, the pore diameters within individual crystals also change in a gradient fashion from ∼2.5 nm to ∼3.0 nm for bMOF-100/102/106, and from ∼2.2 nm to ∼2.7 nm for bMOF-110/100/102, indicating significant porosity gradients. Like previously reported binary gradient MOFs, the composition of the ternary gradient MOFs can be easily controlled by adjusting the reaction conditions. Finally, X-ray diffraction and microspectrophotometry were used to analyse fractured gradient MOF crystals by comparing unit cell parameters and absorbance spectra at different locations, thus revealing the profile of heterogeneity (i.e. gradient distribution of properties) and further confirming the formation of ternary gradient MOFs.

scholarly journals GIDInd: an automated indexing software for grazing-incidence X-ray diffraction data

2021 ◽  
Vol 54 (4) ◽  
Author(s):  
Manuel Peter Kainz ◽  
Lukas Legenstein ◽  
Valentin Holzer ◽  
Sebastian Hofer ◽  
Martin Kaltenegger ◽  
...  
Keyword(s):  
Substrate Surface ◽  
Grazing Incidence ◽  
Unit Cell ◽  
Successful Implementation ◽  
Mathematical Framework ◽  
X Ray Diffraction ◽  
Unknown Parameters ◽  
X Ray ◽  
Fitting Procedure ◽  
Unit Cells

Grazing-incidence X-ray diffraction (GIXD) is a widely used technique for the crystallographic characterization of thin films. The identification of a specific phase or the discovery of an unknown polymorph always requires indexing of the associated diffraction pattern. However, despite the importance of this procedure, only a few approaches have been developed so far. Recently, an advanced mathematical framework for indexing of these specific diffraction patterns has been developed. Here, the successful implementation of this framework in the form of an automated indexing software, named GIDInd, is introduced. GIDInd is based on the assumption of a triclinic unit cell with six lattice constants and a distinct contact plane parallel to the substrate surface. Two approaches are chosen: (i) using only diffraction peaks of the GIXD pattern and (ii) combining the GIXD pattern with a specular diffraction peak. In the first approach the six unknown lattice parameters have to be determined by a single fitting procedure, while in the second approach two successive fitting procedures are used with three unknown parameters each. The output unit cells are reduced cells according to approved crystallographic conventions. Unit-cell solutions are additionally numerically optimized. The computational toolkit is compiled in the form of a MATLAB executable and presented within a user-friendly graphical user interface. The program is demonstrated by application on two independent examples of thin organic films.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals Crystal Structure Refinements of Four Monazite Samples from Different Localities

Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1028 ◽  
Author(s):  
M. Mashrur Zaman ◽  
Sytle M. Antao
Keyword(s):  
Crystal Structure ◽  
Electron Probe ◽  
Unit Cell Volume ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Large Unit Cell ◽  
A Site

This study investigates the crystal chemistry of monazite (APO4, where A = Lanthanides = Ln, as well as Y, Th, U, Ca, and Pb) based on four samples from different localities using single-crystal X-ray diffraction and electron-probe microanalysis. The crystal structure of all four samples are well refined, as indicated by their refinement statistics. Relatively large unit-cell parameters (a = 6.7640(5), b = 6.9850(4), c = 6.4500(3) Å, β = 103.584(2)°, and V = 296.22(3) Å3) are obtained for a detrital monazite-Ce from Cox’s Bazar, Bangladesh. Sm-rich monazite from Gunnison County, Colorado, USA, has smaller unit-cell parameters (a = 6.7010(4), b = 6.9080(4), c = 6.4300(4) Å, β = 103.817(3)°, and V = 289.04(3) Å3). The a, b, and c unit-cell parameters vary linearly with the unit-cell volume, V. The change in the a parameter is large (0.2 Å) and is related to the type of cations occupying the A site. The average <A-O> distances vary linearly with V, whereas the average <P-O> distances are nearly constant because the PO4 group is a rigid tetrahedron.

Compressibility of β-As4S4: an in situ high-pressure single-crystal X-ray study

2012 ◽  
Vol 76 (4) ◽  
pp. 963-973 ◽  
Author(s):  
G. O. Lepore ◽  
T. Boffa Ballaran ◽  
F. Nestola ◽  
L. Bindi ◽  
D. Pasqual ◽  
...  
Keyword(s):  
Pressure Range ◽  
Substantial Reduction ◽  
Structural Data ◽  
Unit Cell ◽  
Van Der Waals Interactions ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Intermolecular Distances

AbstractAmbient temperature X-ray diffraction data were collected at different pressures from two crystals of β-As4S4, which were made by heating realgar under vacuum at 295ºC for 24 h. These data were used to calculate the unit-cell parameters at pressures up to 6.86 GPa. Above 2.86 GPa, it was only possible to make an approximate measurement of the unit-cell parameters. As expected for a crystal structure that contains molecular units held together by weak van der Waals interactions, β-As4S4 has an exceptionally high compressibility. The compressibility data were fitted to a third-order Birch–Murnaghan equation of state with a resulting volume V0 = 808.2(2) Å3, bulk modulus K0 = 10.9(2) GPa and K' = 8.9(3). These values are extremely close to those reported for the low-temperature polymorph of As4S4, realgar, which contains the same As4S4 cage-molecule. Structural analysis showed that the unit-cell contraction is due mainly to the reduction in intermolecular distances, which causes a substantial reduction in the unit-cell volume (∼21% at 6.86 GPa). The cage-like As4S4 molecules are only slightly affected. No phase transitions occur in the pressure range investigated.Micro-Raman spectra, collected across the entire pressure range, show that the peaks associated with As–As stretching have the greatest pressure dependence; the S–As–S bending frequency and the As–S stretching have a much weaker dependence or no variation at all as the pressure increases; this is in excellent agreement with the structural data.

The crystal chemistry of the uranyl carbonate mineral grimselite, (K, Na)3Na[(UO2)(CO3)3](H2O), from Jáchymov, Czech Republic

2012 ◽  
Vol 76 (3) ◽  
pp. 443-453 ◽  
Author(s):  
J. Plášil ◽  
K. Fejfarová ◽  
R. Skála ◽  
R. Škoda ◽  
N. Meisser ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Czech Republic ◽  
Structure Refinement ◽  
Unit Cell ◽  
Carbonate Mineral ◽  
X Ray Diffraction ◽  
The Czech Republic ◽  
Cell Parameters ◽  
Uranyl Carbonate ◽  
Diffraction Peaks

AbstractTwo crystals of the uranyl carbonate mineral grimselite, ideally K3Na[(UO2)(CO3)3](H2O), from Jáchymov in the Czech Republic were studied by single-crystal X-ray diffraction and electron-probe microanalysis. One crystal has considerably more Na than the ideal chemical composition due to substitution of Na into KO8 polyhedra; the composition of the other crystal is nearer to ideal, and similar to synthetic grimselite. The presence of Na atoms in KO8 polyhedra, which are located in channels in the crystal structure, reduces their volume, and as a result the unit-cell volume also decreases. Structure refinement shows that the formula for the sample with the anomalously high Na content is (K2.43Na0.57)Σ3.00Na[(UO2)(CO3)3](H2O). The unit-cell parameters, refined in space group P2c, are a = 9.2507(1), c = 8.1788(1) Å, V = 606.14(3) Å3 and Z = 2. The crystal structure was refined to R1 = 0.0082 and wR1 = 0.0185 with a GOF = 1.33, based on 626 observed diffraction peaks [Iobs>3σ(I)].

High-temperature diffraction experiments and phase diagram of ZrO2 and ZrSiO4

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Akira Yoshiasa ◽  
Tsubasa Tobase ◽  
Hiroshi Arima-Osonoi ◽  
Ken-Ichi Funakoshi ◽  
Osamu Ohtaka ◽  
...  
Keyword(s):  
High Temperature ◽  
Unit Cell ◽  
Cubic Phase ◽  
Imaging Plate ◽  
X Ray Diffraction ◽  
Space Group ◽  
Cell Parameters ◽  
Time Observation ◽  
Short Time ◽  
Clear Change

Abstract High-temperature X-ray diffraction (XRD) experiments up to T = 2710 °C have been performed on ZrSiO4 and ZrO2 powders, using the container-less levitation technique. A two-dimensional imaging plate (IP) detector was used for short-time observation. The diffraction data in a wide area was projected in one dimension. The unit cell parameters, thermal expansions, and c/a ratios for ZrSiO4 (space group I41/amd and Z = 4), tetragonal ZrO2 (space group P42/nmc and Z = 2) and cubic ZrO2 (space group  F m 3   ‾ m $Fm3&#x203e;{}m$ and Z = 4) were measured to understand the high-temperature behaviors. The transition temperature between tetragonal and cubic ZrO2 was specified to be between 2430 and 2540 °C. The pre-transitional behavior was observed around 2200 °C. As no clear change in unit cell volume is evident, the phase boundary between the tetragonal and the cubic phase has been shown to be a positive slope. The ZrO2 and ZrO2–SiO2 phase diagrams are proposed based on the chemical composition and the crystal structure.

scholarly journals Crystallization and X-ray diffraction analysis of native and selenomethionine-substituted PhyH-DI fromBacillussp. HJB17

2017 ◽  
Vol 73 (11) ◽  
pp. 607-611
Author(s):  
Fang Lu ◽  
Bei Zhang ◽  
Yong Liu ◽  
Ying Song ◽  
Gangxing Guo ◽  
...  
Keyword(s):  
Unit Cell ◽  
Diffusion Method ◽  
Data Sets ◽  
Asymmetric Unit ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
Solvent Content ◽  
Space Group ◽  
X Ray ◽  
Cell Parameters

Phytases are phosphatases that hydrolyze phytates to less phosphorylatedmyo-inositol derivatives and inorganic phosphate. β-Propeller phytases, which are very diverse phytases with improved thermostability that are active at neutral and alkaline pH and have absolute substrate specificity, are ideal substitutes for other commercial phytases. PhyH-DI, a β-propeller phytase fromBacillussp. HJB17, was found to act synergistically with other single-domain phytases and can increase their efficiency in the hydrolysis of phytate. Crystals of native and selenomethionine-substituted PhyH-DI were obtained using the vapour-diffusion method in a condition consisting of 0.2 Msodium chloride, 0.1 MTris pH 8.5, 25%(w/v) PEG 3350 at 289 K. X-ray diffraction data were collected to 3.00 and 2.70 Å resolution, respectively, at 100 K. Native PhyH-DI crystals belonged to space groupC121, with unit-cell parametersa = 156.84,b = 45.54,c = 97.64 Å, α = 90.00, β = 125.86, γ = 90.00°. The asymmetric unit contained two molecules of PhyH-DI, with a corresponding Matthews coefficient of 2.17 Å3 Da−1and a solvent content of 43.26%. Crystals of selenomethionine-substituted PhyH-DI belonged to space groupC2221, with unit-cell parametersa = 94.71,b= 97.03,c= 69.16 Å, α = β = γ = 90.00°. The asymmetric unit contained one molecule of the protein, with a corresponding Matthews coefficient of 2.44 Å3 Da−1and a solvent content of 49.64%. Initial phases for PhyH-DI were obtained from SeMet SAD data sets. These data will be useful for further studies of the structure–function relationship of PhyH-DI.

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