Simulated Diffraction Patterns Research Articles

Influence of the Mg and Al ratio on the restructuring of hydrotalcite

The influence of the Mg : Al ratio on the phase composition and structure of the products of hydrotalcite restructuring was studied by X-ray diffraction. At a high Mg ion content, besides hydrotalcite, Mg(OH)2 and an interstratified phase consisting of hydrotalcite and Mg(OH)2 are also present. The real structure was studied by simulation of diffraction patterns using the DIFFaX program.

Updating a software package for the simulation of diffraction patterns and the computation of the parameters of the twinning and self-accommodation of martensite crystals

An updated software package for the simulation of point diffraction pictures and the computation of several crystallographic characteristics of martensite crystals in alloys with the shape-memory effect is presented. Optimization was carried out for the procedure of the analysis of the orientation relationships between the lattices of austenite and martensite from the viewpoint of the possibility of the formation of self-accommodation complexes.

Lithium Dihydroborate: First-Principles Structure Prediction of LiBH2

We report a first-principles structure prediction of the LiBH(2), which structures are modeled by using four formula units per unit cell without symmetry restrictions. The computational methodology combines a simulated annealing approach and density functional total energy calculations for crystalline solid structures. The predicted lowest energy structure shows the formation of linear anionic chains, (∞)(1)[BH(2)], enthalpy of formation at 0 K equal to -90.07 kJ/mol. Ring structures, in particular with butterfly and planar square topologies, are found to be stable but well above the ground state by 20.26 and 12.92 kJ/mol, respectively. All convergent structures fall in the symmetry families monoclinic, tetragonal, and orthorhombic. For the representative structures of each family group, simulated X-ray diffraction patterns and infrared spectra are reported.

Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams

Condensed matter systems with topological defects in the ground states range from the Abrikosov phases in superconductors, to various blue phases and twist grain boundary phases in liquid crystals, and to phases of skyrmion lattices in chiral ferromagnets and Bose-Einstein condensates. In nematic and chiral nematic liquid crystals, which are true fluids with long-range orientational ordering of constituent molecules, point and line defects spontaneously occur as a result of symmetry-breaking phase transitions or due to flow, but they are unstable, hard to control, and typically annihilate with time. Here we describe the optical generation of two-dimensional crystalline, quasicrystalline, and arbitrary ensembles of particlelike structures manifesting both skyrmionlike and Hopf fibration features--dubbed "torons"--composed of looped double twist cylinders and point defects embedded in a uniform director field. In these two-dimensional lattices, we then introduce various dislocations, defects in positional ordering of the torons. We show that the periodic defect lattices with and without dislocation are light- and voltage-tunable reconfigurable two-dimensional diffraction gratings and can be used to generate various controlled phase singularities in the diffracted laser beams. The results of computer simulations of optical images, diffraction patterns, and phase distributions with optical vortices are in a good agreement with the corresponding experimental findings.

Software Design for Simulation and Analysis of Electron Diffraction Patterns

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 – August 2, 2012.

Dynamical Simulation of Electron Backscatter Diffraction (EBSD) Patterns of Imperfect Crystals.

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 – August 2, 2012.

Radiation-induced bending of silicon-on-insulator nanowires probed by coherent x-ray diffractive imaging

Coherent x-ray diffractive imaging (CXDI) is a powerful technique to study the bending of silicon-on-insulator nanowires. Radiation-induced bending causes the nanowires to exhibit highly distorted diffraction patterns in reciprocal space, from which a strain distribution is inferred. To confirm this, we simulate diffraction patterns using finite-element-analysis (FEA) calculations, which show excellent agreement with the experimental measurements. Our findings provide details of how silicon-on-insulator MOSFET devices might become strained during radiation damage of the underlying oxide.

Atomic structure of a single large biomolecule from diffraction patterns of random orientations

The short and intense pulses of the new X-ray free electron lasers, now operational or under construction, may make possible diffraction experiments on single molecule-sized objects with high resolution, before radiation damage destroys the sample. In a single molecule imaging (SMI) experiment thousands of diffraction patterns of single molecules with random orientations are recorded. One of the most challenging problems of SMI is how to assemble these noisy patterns of unknown orientations into a consistent single set of diffraction data. Here we present a new method which can solve the orientation problem of SMI efficiently even for large biological molecules and in the presence of noise. We show on simulated diffraction patterns of a large protein molecule, how the orientations of the patterns can be found and the structure to atomic resolution can be solved. The concept of our algorithm could be also applied to experiments where images of an object are recorded in unknown orientations and/or positions like in cryoEM or tomography.

Evidence of a medium-range ordered phase and mechanical instabilities in strontium under high pressure

We provided the first theoretical evidence for a medium-range ordered phase in high pressure strontium from the first-principles calculations. At the absolute zero temperature, the enthalpy–pressure relation shows that the bcc and hcp are energetically more favorable than the other experimentally observed phases between 24 and 27GPa. In the present work, we concentrate on the bcc phase because we found a link to a medium-range ordered phase. Our results reveal that the bcc phonon dispersion at the N and H points starts softening at around 24.1GPa. The ab initio molecular dynamics at 300K and 27GPa showed that the bcc is quickly transformed into a lower energy structure with R3c symmetry and distorted basis. The simulated diffraction patterns showed that the R3c structure has only a single major peak at low angle. The R3c peak locates near the first peak of the bcc structure. This is the evidence of the so-called medium-range ordered phase. This structure is a strong candidate for the unsolved S-phase reported by experiments.

Effects of Cu and Al on the crystal structure and composition of η (MgZn2) phase in over-aged Al–Zn–Mg–Cu alloys

Heat treatable Al–Zn–Mg alloys can be strengthened by the precipitation of second phase particles. In this paper, Al–6.57%Zn–2.83%Mg and Al–6.57%Zn–2.83%Mg–3.92%Cu alloys (in wt%) in T7 state (140 °C for 96 h) have been prepared. The effects of Cu and Al on the concentration and structure of equilibrium η (MgZn2) phase have been investigated by high resolution transmission electron microscopy, aberration-corrected scanning transmission electron microscopy, selected election diffraction pattern simulations, and first-principles calculations. The effects of Cu and Al substitution on the diffraction characteristics of the η phase and the general rule of Cu and Al substitution in the η phase have been discussed.

X-ray powder diffraction investigation of the faulted crystal structure of MnH2P3O10· 2H2O

The crystal structure of manganese(III) dihydrogen triphosphate dihydrate, MnH2P3O10 · 2H2O, has been studied by means of X-ray powder diffraction data using the Rietveld method. The compound crystallizes in the monoclinic space group P2/c, with unit cell dimensions a = 7.8286(2), b = 4.9503(2), c = 12.25415(18) Å, β = 95.7922(11)°, V = 472.47(2) Å3, Z = 2. It has a layered structure, with manganese-triphosphate polymeric layers, parallel to the bc plane, and water molecules located in the interlayer space. Powder pattern of the compound exhibits anisotropic peak broadening, which cannot be explained by crystallite size effects. The reflections with k = 2n remain narrow, whereas those with k = 2n + 1 and h ≠ 0 are widened substantially. These features have been assigned to stacking faults with a b/2 translation. Simulated diffraction patterns, calculated with the program DIFFaX by recursion method for different values of stacking faults probability, reproduced the experimental X-ray powder pattern. A phenomenological treatment of anisotropic peak broadening was used to complete the Rietveld refinement.

Coralloite, Mn2+Mn23+(AsO4)2(OH)2{middle dot}4H2O, a new mixed valence Mn hydrate arsenate: Crystal structure and relationships with bermanite and whitmoreite mineral groups

Coralloite is a new mineral found at the Monte Nero Mine (Rocchetta Vara, La Spezia, Liguria, Italy) having the simplified formula Mn2+Mn23+(AsO4)2(OH)2·4H2O. It occurs as sub-millimetric lamellar cinnabar-red crystals elongated on [100] and flattened on (001), isolated or forming wisps up to 0.5–1 mm long. Associated phases are calcite, inesite, quartz, brandtite, sarkinite, and tilasite in a chert matrix. Crystals are pleochroic, yellow along [100] and orange-red in directions normal to it. Extinction is parallel to the cleavage traces and elongation is negative. The small crystal size does not allow accurate determination of refraction indices. Crossed polar observations of crystals placed in diiodomethane ( n = 1.74) suggest that the mean refractive index is close to that value. Coralloite is triclinic, space group P 1, a = 5.5828(7), b = 9.7660(13), c = 5.5455(7) A, α = 94.467(3), β = 111.348(2), γ = 93.850(2)°, V = 279.26(6) A3, Z = 1. The five strongest lines in the simulated powder diffraction pattern ( d obs, I , hkl ) are: 9.710 A, 100.0, (010), 5.166 A, 77.1, (100); 5.136 A, 79.7, (001); 3.342 A, 64.8, (121); 3.324 A, 33.6, (121). The structure of coralloite (final R all 0.044 for 3092 observed reflections) shows similarities with bermanite: Mn2+Mn23+(PO4)2(OH)2·4H2O and ercitite: Na2Mn23+(PO4)2(OH)2·4H2O. In particular, these three minerals exhibit the same structural slab formed by [[6]Mn23+([4]XO4)2(OH)2]; X = As or P. However, these structural slabs are connected by interposed layers of different polyhedra for each mineral species.

DIANNA (Diffraction Analysis of Nanopowders): Software for structural analysis of ultradisperse systems by X-Ray methods

An X-ray approach to analyzing ultradisperse systems is suggested. The approach is based on the simulation of diffraction patterns from an ensemble of nanoparticles with a given structure, size, and shape, including intensity calculations at each profile point. A program for calculations was developed. Its possibilities were demonstrated for the example of studies of samples prepared by solid-state oxidative thermolysis of iron oxalate dihydrate. The size of sample crystallites (coherent scattering regions) did not exceed 1–2 nm.

Synthesis of 3R1and 1H Polytypes of Sulfate-Intercalated Layered Double Hydroxides (LDHs) by Postintracrystalline Oxidation and Simultaneous Intercalation-Oxidation of Thiosulfate

Well ordered 3R1 polytypes of sulfate-intercalated Zn–Al and Zn–Cr LDHs could be synthesized at room temperature by intracrystalline oxidation of thiosulfate-intercalated LDHs by hydrogen peroxide. When the intercalation-oxidation sequence was slightly modified in such a way that the intercalation and oxidation of thiosulfate took place simultaneously, 1H polytypes were formed. The formation of these polytypes is confirmed by simulation of powder X-ray diffraction patterns and phase transformation on heating. Interestingly, the two polytypes show different anion exchange behavior.

Plastic deformation of natural diamonds by twinning: evidence from X-ray diffraction studies

AbstractA pink-purple diamond crystal from the Internatsional'naya kimberlite pipe (Siberia) was studied by single-crystal X-ray diffraction techniques using an area detector. Direct indexing of the diffraction pattern suggested a primitive hexagonal unit cell [ahex = 2.513(4), chex = 6.172(11) Å], instead of the well known face-centred cubic unit cell (acub ∼3.567 Å). Theoretical considerations and diffraction pattern simulation showed that the hexagonal diffraction pattern is the result of the superposition of two diffraction patterns with cubic symmetry due to spinel-law twinning along (111). These data are in good agreement with previous analyses of deformation microtwins in natural pink-purple diamonds using electron paramagnetic resonance spectroscopy and optical microscopy. The results suggest that natural epigenetic plastic deformation of diamonds occurs not only by dislocation slipping but also as a result of mechanical twinning.

No miscibility gap in Pt–Rh binary alloys: A first-principles study

Recently, diffraction experiments and bond-order calculations gave given cause for distrust in the widely accepted phase diagram of binary Pt–Rh, suggesting it forms a solid solution below 1100K. This is in contrast to the phase diagram published by Raub in 1959. In order to clarify this situation, we use a first-principles approach to conduct an exhaustive ground-state search and set up a cluster-expansion Hamiltonian. This allows for grand-canonical Monte-Carlo simulations in order to investigate the phase behavior. We show that the miscibility gap does not in fact exist. We also present simulated diffraction patterns extracted from the cluster-expansion Hamiltonian, which are in good agreement with experimental data.

Structure and properties of the low-density phase ι-Al2O3from first principles

Of the various phases of transition alumina, iota-alumina (\ensuremath{\iota}-Al${}_{2}$O${}_{3}$) is the least well known. It is considered to be the end member of the mullite series in the limit of zero Si content. The structural details of \ensuremath{\iota}-Al${}_{2}$O${}_{3}$ are not available and its physical properties are totally unknown. Based on an appropriately modified structure of a high alumina content mullite phase close to the 9-1 mullite, we have successfully constructed a structural model for \ensuremath{\iota}-Al${}_{2}$O${}_{3}$. The simulated x-ray diffraction (XRD) pattern of this model agrees well with a measured XRD pattern obtained from samples that claim to belong to \ensuremath{\iota}-Al${}_{2}$O${}_{3}$. \ensuremath{\iota}-Al${}_{2}$O${}_{3}$ is a highly disordered ultralow-density phase of alumina with a theoretical density of 2854 kg/m${}^{3}$. The calculated total energy per Al${}_{2}$O${}_{3}$ is much higher than \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$ and the other well-known disordered phase, \ensuremath{\gamma}-Al${}_{2}$O${}_{3}$. Using this theoretically constructed model, we have calculated the elastic, thermodynamic, electronic, and spectroscopic properties of \ensuremath{\iota}-Al${}_{2}$O${}_{3}$ and compared them with those of \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$ and \ensuremath{\gamma}-Al${}_{2}$O${}_{3}$. It is shown that the mechanical strength of \ensuremath{\iota}-Al${}_{2}$O${}_{3}$ is much weaker with bulk and shear moduli that are only 57 and 42% of \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$. Phonon dispersion results and the subsequently calculated thermodynamic properties point to the fact that \ensuremath{\iota}-Al${}_{2}$O${}_{3}$ is an alumina phase preceding \ensuremath{\gamma}-Al${}_{2}$O${}_{3}$ in the processing of alumina before reaching \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$. Electronic structure calculations show it to be an insulator with a direct band gap of only 3.0 eV at the \ensuremath{\Gamma} point and a higher ionic bonding character than \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$ and \ensuremath{\gamma}-Al${}_{2}$O${}_{3}$. It has a calculated static dielectric constant of 2.73 and a corresponding refractive index of 1.65 that are in agreement with reported data. Also calculated are the Al-$K$, Al-${L}_{3}$, and O-$K$ edges of the x-ray absorption near edge structure in \ensuremath{\iota}-Al${}_{2}$O${}_{3}$, showing sensitive dependence on its local bonding environment. However, only the weighted average of these spectra can be directly compared with the measured ones which are currently unavailable.

The iterative Fresnel integrals method for Fresnel diffraction from tilted rectangular apertures: Theory and simulations

We applied the iterative Fresnel integrals method for the numerical computation of Fresnel diffraction patterns from rectangular apertures tilted at an arbitrary angle to the optical axis. Detailed theoretical formalism is developed and discussed, and then is applied for the numerical computation and simulation of the actual diffraction patterns for an arbitrary optical configuration. The generated intensity distributions (images) show distortion and stretching in the direction of the tilt, but not in the other orthogonal direction. Significant decrease of the intensity is also predicted and observed, the decrease being proportionate with the tilt angle. The simulated images qualitatively resemble those published in the literature. In addition to single-axis tilts, simultaneous rotations (tilts) of the aperture in two orthogonal coordinate axes were also briefly considered and simulated.

Novel Superhard Carbon: C-Centered OrthorhombicC8

A novel carbon allotrope of C-centered orthorhombic C(8) (Cco-C(8)) is predicted by using a recently developed particle-swarm optimization method on structural search. Cco-C(8) adopts a sp(3) three-dimensional bonding network that can be viewed as interconnected (2,2) carbon nanotubes through 4- and 6-member rings and is energetically more favorable than earlier proposed carbon polymorphs (e.g., M carbon, bct-C(4), W carbon, and chiral C(6)) over a wide range of pressures studied (0-100 GPa). The simulated x-ray diffraction pattern, density, and bulk modulus of Cco-C(8) are in good accordance with the experimental data on structurally undetermined superhard carbon recovered from cold compression of carbon nanotube bundles. The simulated hardness of Cco-C(8) can reach a remarkably high value of 95.1 GPa, such that it is capable of cracking diamond.

Isothermal Decomposition of Ferrite in a High-Nitrogen, Nickel-Free Duplex Stainless Steel

The formation and crystallography of second phases during isothermal decomposition of ferrite (α) in a high-nitrogen, nickel-free duplex stainless steel was examined by means of transmission electron microscopy (TEM). At an early stage of aging, the decomposition of α started along the α/γ phase boundaries where sigma (σ) phase and secondary austenite (γ2) precipitated in the form of an alternating lamellar structure. The combined analyses based on the simulation of diffraction patterns and stereographic projection have shown that most of the σ phase was related to the γ2 by the following relation: \( (111)_{\gamma } \parallel (001)_{\sigma } \) and \( [10\bar{1}]_{\gamma } \parallel [110]_{\sigma } . \)The intergranular and intragranular precipitation of Cr2N with trigonal structure were identified, and the orientation relationships (ORs) with α and γ matrix could be expressed as \( \left( {110} \right)_{\alpha } \parallel \left( {0001} \right)_{{{\text{Cr}}_{2} {\text{N}}}} \),\( \left[ {\bar{1}11} \right]_{\alpha } \parallel [\bar{1}100]_{{{\text{Cr}}_{2} {\text{N}}}} \,;\,(111)_{\gamma } \parallel (0001)_{{{\text{Cr}}_{2} {\text{N}}}} \), and \( \left[ {\bar{1}10} \right]_{\gamma } \parallel \left[ {\bar{1}100} \right]_{{{\text{Cr}}_{2} {\text{N}}}} , \) respectively. The precipitation of intermetallic χ phase was also observed inside the α matrix, and they obeyed the cube-on-cube OR with the α matrix. Prolonged aging changed both the structure of matrix and the distribution of second phases. The γ2, formed by decomposition of α, became unstable because of the depletion of mainly N accompanied by the formation of Cr2N, and it transformed into martensite after subsequent cooling. As a result, the microstructure of the decomposed α region was composed of three kinds of precipitates (intermetallic σ,χ, and Cr2N) embedded in lath martensite.