High-energy X-ray Diffraction Data Research Articles

Diffraction study of pressure-amorphized ZrW2O8usingin situand recovered samples

High-energy x-ray diffraction data from a series of amorphous ZrW${}_{2}$O${}_{8}$ samples, recovered from a number of different pressures, have been measured and compared with similar data collected from a sample contained within a diamond anvil cell and measured in situ at high pressure. Samples at lower pressures are a mix of crystalline and amorphous phases, whereas those above 7 GPa (both recovered and in situ) appear to be completely amorphous. Although there are only very small changes in the diffraction data from the pure phase samples recovered from different pressures, larger changes are observed in situ as a function of pressure. However, the same structural model can be used to describe all data, albeit using different densities. This strongly suggests that the amorphous phase is undergoing nonreconstructive compression in this pressure range, without fundamental modification of the underlying topology.

A method for measuring single-crystal elastic moduli using high-energy X-ray diffraction and a crystal-based finite element model

This paper presents a method – based on high-energy synchrotron X-ray diffraction data and a crystal-based finite element simulation formulation – for understanding grain scale deformation behavior within a polycrystalline aggregate. We illustrate this method by using it to determine the single-crystal elastic moduli of β21s, a body-centered cubic titanium alloy. We employed a polycrystalline sample. Using in situ loading and high-energy X-rays at the Advanced Photon Source beamline 1-ID-C, we measured components of the lattice strain tensor from four individual grains embedded within a polycrystalline specimen. We implemented an optimization routine that minimized the difference between the experiment and simulation lattice strains. Sensitivity coefficients needed in the optimization routine are generated numerically using the finite element model. The elastic moduli that we computed for the β21s are C11=110GPa, C12=74GPa and C44=89GPa. The resulting Zener anisotropic ratio is A=5.

High temperature stress-induced “double loop-like” phase transitions in Bi-based perovskites

Polycrystalline 0.94(Bi1/2Na1/2)TiO3–0.06BaTiO3 samples were tested under uniaxial mechanical compression at various temperatures in the vicinity of the polar tetragonal to nonpolar tetragonal phase boundary. They are shown to display double loop-like stress-strain behavior, marked by a closed ferroelastic hysteresis loop. Thus, it forms a mechanical analog to the polarization-electric field hysteresis behavior of barium titanate above the Curie temperature. As temperature is increased there is an apparent loss of macroscopically observable ferroelasticity, despite the persistence of tetragonality. Macroscopic experimental results are discussed in conjunction with temperature-dependent and stress-dependent high-energy x-ray diffraction data. This reveals a phase transition below the Curie temperature, marked by a discontinuous change in lattice parameters and octahedral tilting during compressive mechanical loading.

The structure of alkali silicate gel by total scattering methods

The structure of the alkali silicate gel (ASR) collected from the galleries of Furnas Dam in Brazil was determined by a pair distribution function (PDF) analysis of high energy X-ray diffraction data. Since this method is relatively new to concrete structure analysis a detailed introduction on the PDF method is given for glassy SiO 2. The bulk amorphous structure of the dam material is confirmed as no Bragg peaks are observed in the scattered intensity. The real space results show that the local structure of the amorphous material is similar to kanemite (KHSi 2O 5:3H 2O) however the long range layer structure of the crystal is broken up in the amorphous state, so that ordering only persists of the length scale of a few polyhedra. The silicate layer structure is a much more disordered than predicted by molecular dynamics models. The X-ray results are consistent with the molecular dynamics model of Kirkpatrick et al. (2005) [1] which predicts that most of the water resides in pores within the amorphous network rather than in layers. The total scattering data provide a rigorous basis against which other models may also be tested.

Formation of Deformation Textures in Face-Centered-Cubic Materials Studied by In-Situ High-Energy X-Ray Diffraction and Self-Consistent Model

The evolution of deformation textures in copper and α brass that are representative of fcc metals with different stacking fault energies (SFEs) during cold rolling is predicted using a self-consistent (SC) model. The material parameters used for describing the micromechanical behavior of each metal are determined from the high-energy X-ray (HEXRD) diffraction data. At small reductions, a reliable prediction of the evolution of the grain orientation distribution that is represented as the continuous increase of the copper and brass components is achieved for both metals when compared with the experimental textures. With increasing deformation, the model could characterize the textures of copper, i.e., the strengthening of the copper component, when dislocation slip is still the dominant mechanism. For α brass at moderate and large reductions, a reliable prediction of its unique feature of texture evolution, i.e., the weakening of the copper component and the strengthening of the brass component, could only be achieved when proper boundary conditions together with some specified slip/twin systems are considered in the continuum micromechanics mainly containing twinning and shear banding. The present investigation suggests that for fcc metals with a low SFE, the mechanism of shear banding is the dominant contribution to the texture development at large deformations.

Experimentally constrained density-functional calculations of the amorphous structure of the prototypical phase-change materialGe2Sb2Te5

Phase change materials involve the rapid and reversible transition between nanoscale amorphous $(a\text{\ensuremath{-}})$ and crystalline $(c\text{\ensuremath{-}})$ spots in a polycrystalline film and play major roles in the multimedia world, including nonvolatile computer memory. The materials of choice are alloys of Ge, Sb, and Te, e.g., ${\text{Ge}}_{2}{\text{Sb}}_{2}{\text{Te}}_{5}$ (GST) in digital versatile disk--random access memory. There has been much speculation about the structure of $a\text{\ensuremath{-}}$ GST, but no model has yet received general acceptance. Here we optimize the structure by combining the results of density-functional calculations with high-energy x-ray diffraction data and x-ray photoelectron spectroscopy (XPS) measurements of the electronic densities of states to determine the structure. The structure agrees very well with available experimental data, including the differences in the XPS data between the amorphous and crystalline structures.

Evaluation of the structural model for ferrihydrite derived from real-space modelling of high-energy X-ray diffraction data

AbstractA new structural model for ferrihydrite that challenges the standard ferrihydrite model established by X-ray diffraction and confirmed by neutron diffraction and single-crystal electron nanodiffraction was recently proposed by Michel et al. (2007a) from the simulation of the pair distribution function obtained by Fourier transformation of diffraction data measured at λ = 0.137 Å. The new ferrihydrite model is isostructural to akdalaite (Al10O14(OH)2), a mineral having the Baker-Figgis δ-isomer of the Al13-Keggin structure as its structural motif. The new model is unrealistic because: (1) it is completely periodic (i.e. defect-free); (2), it has 20% tetravalent octahedral iron (VIFe4+), 20% divalent tetrahedral iron (IVFe2+), and some IVFe–O distances equal to or larger than the VIFe3+–O distances, thus violating Pauling's 2nd rule; (3) it does not describe X-ray diffraction and EXAFS spectroscopic data; and, (4) it is inconsistent with electron microscopy results and contradicts previous X-ray scattering studies.

Experimental Bond Critical Point and Local Energy Density Properties Determined for Mn−O, Fe−O, and Co−O Bonded Interactions for Tephroite, Mn2SiO4, Fayalite, Fe2SiO4, and Co2SiO4Olivine and Selected Organic Metal Complexes: Comparison with Properties Calculated for Non-Transition and Transition Metal M−O Bonded Interactions for Silicates and Oxides

Bond critical point (bcp) and local energy density properties for the electron density (ED) distributions, calculated with first-principle quantum mechanical methods for divalent transition metal Mn-, Co-, and Fe-containing silicates and oxides are compared with experimental model ED properties for tephroite, Mn 2SiO 4, fayalite, Fe 2SiO 4, and Co 2SiO 4 olivine, each determined with high-energy synchrotron single-crystal X-ray diffraction data. Trends between the experimental bond lengths, R(M-O), (M = Mn, Fe, Co), and the calculated bcp properties are comparable with those observed for non-transition M-O bonded interactions. The bcp properties, local total energy density, H( r c), and bond length trends determined for the Mn-O, Co-O, and Fe-O interactions are also comparable. A comparison is also made with model experimental bcp properties determined for several Mn-O, Fe-O, and Co-O bonded interactions for selected organometallic complexes and several oxides. Despite the complexities of the structures of the organometallic complexes, the agreement between the calculated and model experimental bcp properties is fair to good in several cases. The G( r c)/rho( r c) versus R(M-O) trends established for non-transition metal M-O bonded interactions hold for the transition metal M-O bonded interactions with G( r c)/rho( r c) increasing in value as H( r c) becomes progressively more negative in value, indicating an increasing shared character of the interaction as G( r c)/rho( r c) increases in value. As observed for the non-transition metal M-O bonded interactions, the Laplacian, nabla (2)rho( r c), increases in value as rho( r c) increases and as H( r c) decreases and becomes progressive more negative in value. The Mn-O, Fe-O, and Co-O bonded interactions are indicated to be of intermediate character with a substantial component of closed-shell character compared with Fe-S and Ni-S bonded interactions, which show greater shared character based on the | V( r c)|/ G( r c) bond character indicator. The atomic charges conferred on the transition metal atoms for the three olivines decrease with increasing atomic number from Mn to Fe to Co as the average M-O bond lengths decrease from 2.219 to 2.168 to 2.128 A, respectively.

Molecular dynamics study of structure and graphitization process of nanodiamonds

Nanodiamond (nD) particles with the shapes of a truncated octahedron and a sphere of an average size of about 23 Å constituted starting configurations for molecular dynamics (MD) simulations using the reactive empirical bond order potential for carbon–carbon interaction. Calculations performed at 300 K showed rebuilding of the surface structure, where trivalent atoms were localised, and in both cases about 72% of atoms localised in the nD interior had tetravalent coordination. The inter-atomic carbon–carbon distances were slightly larger than those for the ideal diamond structure. The results obtained from simulations match quite well the high-energy X-ray diffraction data for explosive diamond nanoparticles recorded at the European Synchrotron Radiation Facility. To study graphitization process of the nDs we performed MD simulations at elevated temperatures up to 1800 K. Transformation of the truncated octahedron nD into onion-like carbon was observed at 1200 K. In this case, bonds between {1 1 1} planes were broken firstly, and then the planes bent forming the onion structure. Graphitization of the spherical nD appeared at 1500 K. The process started at the surface, where fragments of quasi-spherical shells were formed, and evolved into the nD centre. For both nDs the process became faster and more effective with increasing temperature.

Structural studies of disordered materials using high-energy x-ray diffraction from ambientto extreme conditions

High-energy x-rays from a synchrotron radiation source allow us to obtain high-qualitydiffraction data for disordered materials from ambient to extreme conditions, which isnecessary for revealing the detailed structures of glass, liquid and amorphous materials. Weintroduced high-energy x-ray diffraction beamlines and a dedicated diffractometer for glass,liquid and amorphous materials at SPring-8 and report the recent developments ofancillary equipment. Furthermore, the structures of liquid and amorphous materialsdetermined from the high-energy x-ray diffraction data obtained at SPring-8 are discussed.

Analysis of high-energy x-ray diffraction data at high pressure: the case of vitreousAs2O3 at 32 GPa

The x-ray structure factor of vitreousAs2O3 has been measured at 32 GPa in a laser-perforated diamond anvil cell using amonochromatic, micro-focused high-energy x-ray beam. The experimental correctionprocedures are discussed in detail, and they yield reliable data over the rangeQ = 0.3–13.5 Å−1. The use of modified form factors to analyse the scattering data is presented to account for chargetransfer. Analysis of the radial distribution function yields an increase in the coordination numberfrom 3.1 ± 0.3 oxygen atoms surrounding an arsenic atom at normal pressure to4.8 ± 0.5 at 32 GPa with only a slight change in the As–O bond length. Substantial structuralchanges are observed at higher distances, extending up to 18 Å in real space.

A high energy X-ray diffraction study of sol–gel derived (Ta2O5) x (SiO2)1−x glasses (x = 0.05, 0.11 and 0.25)—elucidating the role of tantalum in silica

High energy X-ray diffraction (HEXRD) has been used to study the atomic structure of (Ta2O5) x (SiO2)1−x (x = 0.05, 0.11 and 0.25) xerogels; the direct interpretation of the resultant data has been augmented using reverse Monte Carlo (RMC) modelling. For the first time in this type of material, two Ta–O correlations have been identified (at ∼1.8 Å and 2.0 Å). The RMC modelling approach explicitly used MAS-NMR data to define its constraints; when combined with HEXRD data, it helps to confirm the more directly determined total coordination of five for the two Ta–O correlation distances and suggests Ta···Si and Ta···Ta coordination distances of ∼3.3 Å and ∼3.8 Å, respectively. The O···O and Si···Si distances and coordination numbers associated with the host silica network suggest that the Ta (V) is acting as a network modifier. The way in which the Ta–O correlations are affected by composition and calcination temperature suggest some phase separation in the (Ta2O5)0.25(SiO2)0.75 sample. However, in general, the results indicate good mixing of the component oxides.

Structural study of supercooled liquid transition metals

Local structural models for supercooled liquid transition metals (Ti, Ni, and Zr) are proposed based on a reverse Monte Carlo analysis of high-energy x-ray diffraction data taken from the electrostatically levitated liquids. The resulting structures are characterized by their bond angle distributions, Honeycutt and Andersen indices [J. Phys. Chem. 91, 4950 (1987)], and bond orientational order parameters. All analyses suggest that an icosahedral short-range order is present in these supercooled liquids, but it is distorted in liquid Ti. These results are in agreement with the observed evolution of the high-q shoulder on the second peak in the structure factor S(q) and with an earlier analysis based on a local cluster model.

Changes of intermediate-range structure in the course of crystallization of zeolite beta

Silicate-ring structure in a dry silicate gel that can be transformed into zeolite beta by the steam-assisted crystallization (SAC) was investigated using high-energy X-ray diffraction (HEXRD). In total correlation function, T( r), determined from HEXRD data, a dry gel that was crystallized to zeolite beta exhibited a remarkable peak at 3.8 Å corresponding to second-neighbor Si–O separations in a 4-membered ring (4MR). The 29Si NMR results supported the existence of a large number of 4MRs in the dry gel with TEA +/Si = 0.37. The 4MRs in the dry gel, which are derived from double 3-memebered ring (D3R) structures stabilized by TEA + in TEA +–silicate solution, are essential in the formation of zeolite beta by the SAC method.

Structural study of amorphous Te 2X (X = Br, I): X-ray diffraction, neutron diffraction and reverse Monte Carlo simulations

Reverse Monte Carlo simulations of the Te 2Br 0.75I 0.25 chalcohalide glass structure using high-energy X-ray and thermal neutron diffraction data show that the glass structure consists of finite –Te–Te–Te– and –Te–Br–Te– chain fragments interconnected by 3-coordinated I atoms. The average Te–Te nearest-neighbor coordination is equal to 2.2 ± 1.4, the Te–Te next nearest-neighbor coordination is equal 7.3 ± 2.6 and the Br–Br coordination is equal to 5.6 ± 0.6. Detailed analysis of the coordination numbers, bond-angle distributions, ring statistics and Warren–Cowley parameters of the different models demonstrates that the short-range order of the glass differs from that of crystalline Te 2X (X = Br, I). The presence of long Te–Te bonds (>3.0 Å) typical for liquid Te and crystalline tellurium-rich polytellurides is also established.

In situHigh-Energy X-Ray Diffraction Study of the Local Structure of Supercooled Liquid Si

Employing the technique of electrostatic levitation, coupled with high-energy x-ray diffraction and rapid data acquisition methods, we have obtained high quality structural data more deeply into the supercooled regime of liquid silicon than has been possible before. No change in coordination number is observed in this temperature region, calling into question previous experimental claims of structural evidence for the existence of a liquid-liquid phase transition.

高エネルギー放射光およびコンピュータシミュレーションを用いた“乱れた構造”の三次元可視化

The use of high-energy (E ≥ 50 keV) X-rays from SPring-8 allows us to perform X-ray diffraction experiments on disordered materials with the following advantages: high resolution in real space due to the wide range of scattering vector, small correction terms (particularly the absorption correction), and fast diffraction measurement with small amount of samples. Recently, high-energy X-ray diffraction data have been combined with neutron diffraction data from a pulsed neutron source to provide more detailed and reliable structural information than has hitherto been available. Furthermore, the use of reverse Monte Carlo modelling and PDF (pair distribution function) simulation based on high-energy X-ray diffraction data have succeeded in illustrating 3-dimensional structure of disordered materials and disorder in crystalline materials.

The Local Structure of Triphenyl Phosphite Studied Using Spallation Neutron and High-Energy X-ray Diffraction

Spallation neutron and high-energy X-ray diffraction experiments have been performed to investigate the local structural changes in triphenyl phosphite (TPP) in the crystalline, glacial, glassy, and supercooled liquid phases. The hydrogen/deuterium first-order difference method shows a large increase in intensity due to additional hydrogen correlations in the crystalline spectra compared to the glass and supercooled liquid at ∼3.0 and 3.4 Å. These features are shown to be largely due to inter-phenyl ring H−C/H interactions, which are probably associated in part with the formation of weak intermolecular hydrogen bonds. The high-energy X-ray diffraction data show a decrease in correlations at 3.12 Å which is attributed to changes in C−O/P intramolecular interactions between the glacial and crystalline forms. The structural evolution of the glacial state was also measured over time using total neutron diffraction. The largest structural differences between the early glacial and crystalline states are observed at 3.0 and 4.5 Å. Moreover, as the transformation progresses, the glacial spectra cannot be adequately described as a simple mixture of supercooled liquid and crystalline components. These results suggest that changes in molecular conformation and nearest-neighbor interactions are responsible for the existence of the glacial state.

Molecular dynamics study of structural, mechanical, and vibrational properties of crystalline and amorphous Ga1−xInxAs alloys

Using an interaction potential scheme, molecular dynamics (MD) simulations are performed to investigate structural, mechanical, and vibrational properties of Ga1−xInxAs alloys in the crystalline and amorphous phases. For the crystalline phase we find that: (i) Ga–As and In–As bond lengths vary only slightly for different compositions; (ii) the nearest-neighbor cation–cation distribution has a broad peak; and (iii) there are two nearest-neighbor As–As distances in the As (anion) sublattice. These MD results are in excellent agreement with extended x-ray absorption fine structure and high-energy x-ray diffraction data and also with ab initio MD simulation results. The calculated lattice constant deviates less than 0.18% from Vegard’s law. The calculated phonon density of states exhibits a two-mode behavior for high-frequency optical phonons with peaks close to those in binary alloys (GaAs and InAs), which agrees well with a recent Raman study. Calculated elastic constants show a significant nonlinear dependence on the composition. For the amorphous phase, MD results show that: (i) the nearest-neighbor cation–anion distribution splits into well-defined As–Ga and As–In peaks as in the crystal phase; (ii) the cation–cation distribution is similar to that in the crystal phase; and (iii) the As–As distribution is quite different from that in the crystal, having only one nearest-neighbor distance.

High-energy X-ray diffraction studies of disordered materials

With the arrival of the latest generation of synchrotron sources and the introduction of advanced insertion devices (wigglers and undulators), the high-energy ( E⩾50 keV) X-ray diffraction technique has become feasible, leading to new approaches in the quantitative study of the structure of disordered materials. High-energy X-ray diffraction has several advantages: higher resolution in real space due to a wide range of scattering vector Q, smaller correction terms (especially the absorption correction), reduction of truncation errors, the feasibility of running under extreme environments, including high-temperatures and high-pressures, and the ability to make direct comparisons between X-ray and neutron diffraction data. Recently, high-energy X-ray diffraction data have been combined with neutron diffraction data from a pulsed source to provide more detailed and reliable structural information than that hitherto available.