Debye-Waller Parameter Research Articles

Structure characteristics of nanocrystalline element selenium with different grain sizes

Porosity-free nanocrystalline (nc) element Se samples with mean grain sizes ranging from 13 to 70 nm were synthesized by crystallizing a melt-quenched amorphous Se solid. Microstructures of the nc-Se (with a hcp structure) samples were characterized by means of quantitative x-ray-diffraction measurements. The Bragg reflection-and the background intensities, as well as the reflection shape of the x-ray-diffraction patterns for the ne Se were analyzed according to data fitting of Me measurement results. The grain-size dependencies of the microstrain, lattice parameters, unit-cell volume, and the mean Debye-Waller parameter were determined. With a reduction of grain size, the microstrain increases significantly along [100] direction but decreases along [104] direction, and exhibits an increasing anisotropic microstrain behavior. The lattice parameter a was found to increase evidently while c decreased slightly with a decreasing gain size, resulting in a significant lattice distortion vith a dilated unit-cell volume. it agrees with the observation that the mean Debye-Waller parameter increases with a reduction of grain size, suggesting larger displacements of atoms from their ideal lattice sites in the nc-Se samples with smaller grains. The similarity of the grain-size dependencies of these structural parameters as that of the grain-boundary volume fraction implies that the intrinsic microstructure feature of ne materials is closely related to the crystallite dimension and the amount of grain boundaries.

The X-ray diffraction study on a nanocrystalline CU processed by equal-channel angular pressing

The precise X-ray diffraction structural study of a nanocrystalline Cu sample processed by severe plastic deformation was carried out. The obtained results were compared with the data from an initial reference Cu sample. By analysis of the centroid position, broadening, shape of Bragg reflections and background integrated intensities from these two samples, such structural features as a lattice parameter, crystallite size, r.m.s. microstrain, dislocation density, Debye-Waller parameter and atomic displacements were determined. A conclusion concerning the specific defect structure in the nanocrystallite Cu sample was drawn.

Structural characterization of nanocrystalline copper by means of x-ray diffraction

Quantitative x-ray-diffraction measurements were performed on a nanocrystalline Cu sample made by severe plastic deformation. The shape of Bragg reflections was found to be represented primarily by a Lorentzian function. A difference of as much as 6%±3% was revealed between the integrated intensities from the nanocrystalline and a reference coarse-grained Cu samples. The broadening of Bragg reflections from the nanocrystalline Cu sample was mainly induced by small crystallite sizes and microstrains inside the grains and/or the deformed layers near the grain boundaries. It was found that the grain sizes of nanocrystalline Cu in different crystallographic orientations are essentially the same, while the microstrains exhibit a significant anisotropy. The Debye–Waller parameter B of the nanocrystalline Cu sample was 0.97±0.06 Å2, which suggests that the atomic displacement from their ideal lattice positions equals on average 0.111±0.004 Å or 4.3% of the nearest-neighbor spacing.

Prominent peculiarities of X-ray diffraction of solid helium

Since3He and4He atoms are the lightest stable mono-atoms with atomic number 2, they cause a variety of macroscopic quantum effects, including large zero point vibrations in liquid and solid phases. Some quantities relevant to X-ray diffraction of solid helium, i.e., the atomic-scattering factor, mass-absorption coefficient, the reciprocal of which is the characteristic length defined by absorption and the extinction distance etc., show either larger or smaller values by approximately two orders of magnitude compared with 3d transition metals. An incidental disappearance of Laue spots due to the downward X-ray diffraction of solid helium (2θB = 90°) could be explained by two factors. One is that the fraction of recoil-free emission is weakened by the great ratio of the huge recoil energy to the phonon energy through the zero-point energy in the Debye-Waller parameter. The other is that the great difference in the linear scatterer density in downward diffraction from that in forward diffraction results from the irradiation of a line-focus X-ray beam to take section topographs weakens the downward X-ray diffraction. The dislocation line of solid helium could not be observed with sharp contrast. Considering the two-orders higher magnitude of the extinction distances and the high dislocation density of more than 2.6· 105cm−2, dynamical X-ray diffraction seems to lose validity.

Grain-boundary atomic structure in nanocrystalline palladium from x-ray atomic distribution functions.

We discuss the scattering theory of nanocrystalline solids, based on an evaluation of the intragrain and intergrain parts of the atomic distribution function. The results are applied to experimental x-ray scattering data obtained on a set of nanocrystalline Pd samples, prepared by inert-gas condensation, with different consolidation, aging, and annealing parameters. The experimental results show that the number of atomic neighbors in the crystal lattice coordination shells of nanocrystalline Pd is substantially lower than the one in the coarse-grained polycrystal lattice. The findings suggest that as a function of their age and thermal treatment, the samples have two different atomic structures. In samples aged for several months at room temperature, and in annealed samples, practically all atoms are located on crystal lattice sites, and the reduction in nearest-neighbor coordination number is an effect of the finite size of the crystallites. In fine-grained samples examined within 10 days of preparation, about 10% of the atoms are located on nonlattice sites with little or no atomic short-range order. This corresponds to about two atomic monolayers of atoms on nonlattice sites at the grain boundaries in as-prepared samples, as compared to about one-quarter of a monolayer in aged or annealed samples. The distribution of nearest-neighbor interatomic spacings for atoms on crystal lattice sites in nanocrystalline Pd is not measurably widened compared to the one of coarse-grained reference samples, indicating that disorder in the crystal lattice, as probed by the x-ray Debye-Waller parameter, involves displacements correlated over several lattice parameters, rather than short-range, uncorrelated atomic displacements.

On the two-state microstructure of nanocrystalline chromium

High-angle neutron powder diffraction was used to investigate the grain size dependence of the Debye–Waller parameter (DWP) of nanocrystalline and coarse-grained chromium samples. The DWP measured at 20 K depends linearly on inverse grain size and is consistent with a two-state model in which defects with short-ranged displacement fields are present in differing concentrations in two distinct microstructural regions within individual grains. One possible model microstructure consists of grain boundary and free surface regions with significantly larger concentrations of point defects than in grain interiors. Evidence is also seen for an enhancement of the temperature-dependent component of the DWP of chromium with decreasing grain size, indicating different behavior than seen previously for nanocrystalline palladium.

X-ray diffraction characterization of defect behavior in nanocrystalline nickel during annealing

Nanocrystalline nickel samples were annealed while collecting high angle X-ray diffraction data in order to correlate changes in strain arid defect content with changes in grain size.The microstrain broadening magnitude decreased rapidly prior to any grain growth, while the Debye-Waller parameter was not reduced significantly prior to the onset of grain growth.

Atomic structure of nanocrystalline metals studied by diffraction techniques and EXAFS

The relation between the nanometer-scale structure and scattering and EXAFS experimental data is discussed on the basis of the atomic density distribution function. The available experimental information is reviewed, with an emphasis on the model substance Pd. Decreasing the grain-size to the nm-scale induces lattice strains and a modified Debye Waller parameter. Immediately after preparation, the grain boundaries are in a non-equilibrium state, which relaxes to a state with higher atomic short-range order upon aging at room temperature. Strong grain-growth at room temperature indicates a high atomic mobility in the grain boundary regions. Small-angle scattering appears to be dominated by porosity for all but the densest available samples.

Effect of grinding on the rate of oxidation of pyrite by oxygen in acid solutions

Solubility of pyrite (FeS 2) ground for different periods was investigated in acid solutions in air. In the initial dissolution, up to 50 h, the dissolution rate, r, was high, due to oxidized species such as FeSO 4 formed by grinding. After 50 h, the surface of pyrite was exposed and the dissolution rate decreased. The formation and dissolution of oxidized species were confirmed by X-ray photoelectron spectroscopy, XPS. From the dissolution rates of Fe and S species, r Fe and r S , for 50–200 h, it was found that pyrite dissolves nonstoichiometrically ( r S r Fe < 2 ) and that grinding promotes the dissolution of sulfur species leading to the stoichiometric dissolution ( r S r Fe = 2 ). The increase in r S can be explained by the displacement of S atoms in the crystal due to the grinding. The effective Debye-Waller parameter, B eff , depends on the displacement of constituent atoms in the crystal from their equilibrium positions and is measured from the diffraction intensities of X-rays. The parameter for S atoms in pyrite, B eff ( S), increased by one or two orders of magnitude with increasing grinding time, t G , while that for the pyrite, B eff ( FeS 2), did not change markedly. It was established that r S is closely related to B eff ( S). The phenomenon may be regarded as a type of mechanical activation.

Structural strain in pyrites evaluated by X-ray powder diffraction

Two parameters for measuring the structural strain, the effective Debye-Waller parameter, B eff, and lattice strain, ɛ, were evaluated on a natural pyrite (FeS2) after grinding. The effective Debye-Waller parameter, B eff, which depends on the displacement of atoms in the crystal, was calculated for the overall crystal, B eff(FeS2), and for sulphur, B eff(S), from the intensities of the X-ray diffraction lines. The B eff(S) increased markedly with increasing grinding time, while B eff(FeS2) did not change significantly. The lattice strain, ɛ, was not recognized. These observations suggest that the displacement of sulphur atoms preferentially takes place by grinding. The relations between these B eff values and crystallite size, L, were observed to be common for two different methods of grinding. This tendency was considered to be an inherent property of pyrite. The value of B eff(S) is a useful index to estimate mechanically caused strain in pyrite.

Anomalous defect behaviour resulting from the hydriding of nanocrystalline palladium

Abstract X-ray diffraction measurements on a nanocrystalline Pd sample transformed in situ to PdH0·56 are described. Debye-Waller parameter measurements at several temperatures showed unexpected increases in both thermal and static atomic displacements caused by the hydriding. These increased displacements are associated either with the creation of new point defects on the Pd sublattice or with an increase in the magnitude of the strain fields of previously existing point defects. Substantial X-ray peak broadening due to the production of large numbers of dislocations is seen when coarse-grained Pd is hydrided. In contrast, measurable changes in the peak breadths were not observed for the nanocrystalline sample as a result of hydriding, indicating that dislocations with long-range displacement fields are not created when nanocrystalline Pd is hydrided. A preference to produce or modify short-range defects instead of dislocations during hydriding may occur as a result of the larger stresses required to gen...

The thermal properties of nanocrystalline Pd from 16 to 300 K

Abstract Quantitative X-ray diffraction measurements made over a temperature range 16–300K on a Pd sample of 8·3nm median grain size were compared with data acquired from a coarse-grained Pd reference sample. The larger Debye-Waller parameter of nanocrystalline Pd was found to be due to increased static displacements of atoms from their equilibrium sites compared with the static displacements in coarse-grained material. Consistent with this behaviour, the strain distribution determined from the width of intensity peaks was significantly broader in the nanocrystalline sample than in the coarse-grained sample. No grain-size-correlated differences in either thermal vibrational amplitude or lattice parameter were observed. In contradiction to previous reports of greatly increased thermal expansion coefficients in nanocrystalline metals, the change in lattice parameter of Pd from 16 to 300 K was observed to be independent of grain size. The results indicate that some regions of the nanocrystalline sample are in a state of compressive stress, while other regions are under a tensile stress. Comparisons with results for unconsolidated nanometre-sized powders indicate that the origin of the increased static displacements in nanocrystalline Pd may be due to the ultrafine powder production or subsequent consolidation processes, rather than being an inherent feature associated with a particular grain size.

Diffraction studies of the thermal properties of nanocrystalline Pd and Cr

Quantitative X-ray and neutron diffraction measurements were made on nanocrystalline and coarse-grained samples of Pd and Cr. For both materials, Debye-Waller parameter comparisons over a temperature range of approximately 20–300 K indicate that the nanocrystalline materials have increased static displacements of atoms from their equilibrium sites compared to coarse-grained material. No grain-size-correlated differences in thermal vibrational amplitude, lattice parameter, or thermal expansion coefficients were observed in either material. In contrast to earlier results on nanocrystalline Pd, significantly more non-peakintensity is observed from a nanocrystalline Cr sample than from a coarse-grained Cr sample. Impurities may account for the increased background intensity from nanocrystalline Cr. These results indicate that there is no significant grain boundary excess volume in nanocrystalline Pd, and therefore the reduced density typically observed in nanocrystalline Pd samples must be due to porosity.

Structural characterization of nanometer-sized crystalline Pd by x-ray-diffraction techniques.

Quantitative x-ray-diffraction measurements of ultrafine-grained (nanocrystalline) Pd samples and a coarse-grained polycrystalline reference foil were obtained using synchrotron radiation. The intensity profiles of the Bragg reflections from the nanocrystalline samples were considerably better represented by Lorentzian functions than by Gaussian functions, indicating that a large fraction of intensity from the Bragg peaks was found in the tails of the reflections. The remaining intensity differed only slightly for different grain-sized materials, therefore, atomic relaxations in the vicinity of grain boundaries in nanocrystalline Pd must be small in magnitude and/or extremely localized. The results of the present work do not support the previously proposed existence of either a ``gaslike'' grain boundary phase, or large quantities of vacancies or voids within the grains of nanocrystalline Pd, which produce broadly distributed diffuse scattering. The broadening of the Bragg reflections was related to the small particle size of nanocrystalline Pd, and strain located in the grains and/or interfacial regions. Evidence was seen for anisotropic grain shapes preferentially elongated along the [111] direction. The Debye-Waller parameter of nanocrystalline Pd was observed to be larger than the literature value for coarse-grained Pd, which suggests larger displacements of the atoms from their ideal lattice locations in the nanocrystalline material than in the coarse-grained material.

X-ray diffraction study of the palladium-carbon system

The Pd-C solid solution was studied by wide angle X-ray diffraction. The Debye-Waller parameter and lattice strains were estimated for both carbon free and carburized palladium. Nearly equal values of the mean displacement of about 0.093 Å was found for palladium atoms in these two cases, a value of 0.17 Å was estimated for the carbon atoms in the carburized sample. An increase of lattice strains was found after decarbonization. The location of carbon atoms in the octahedral voids was confirmed.

Effective Debye-Waller parameter and emission intensity of calcium tungstate phosphors

The relation between emission intensity under ultraviolet excitation and Debye-Waller parameter was studied on calcium tungstate phosphors. The samples were prepared by precipitation from aqueous solition of calcium chloride and ammonia-alkaline solution of ammonium paratungstate and by firing at 400°–1000°C in air. The precipitating temperature has a strong influence on the form of precipitated particles, being spherical at 0°C and spindle-shaped at 90°C, and also on the preferred orientation of crystallites in precipitates. The change of emission intensity under ultraviolet excitation with firing temperature shows a correspondence to the change of effective Debye-Waller parameter, B eff, determined from X-ray diffraction intensity measurements. On the ground samples, of which the original is fired at 900°C and has spherical particles, a linear relation was found between the emission intensity under ultraviolet excitation and the dynamic component B d in B eff, which is due to thermal vibration of constituent atoms.

Luminescence of alkali earth tungstate

Calcium tungstate and the solid solution between calcium and barium tungstates were prepared by the precipitation from their aqueous solutions. The precipitate has a spherical form and the resultant phosphor did not change its form. By the grinding the luminescent intensity of pure calcium tungstate phosphor decreased linearly with the increase of the effective value of Debye-Waller parameter. Calcium tungstate and its solid solution activated by Eu 2+ were prepared and their luminescent properties were studied. It is possible to prepare the more efficient phosphor for X-ray intensify screen by activating the solid solution of alkali earth tungstate by Eu 2+.

Neutron powder diffraction study of the Debye–Waller factor in nickel using the reverse Fourier time-of-flight method

A high-resolution neutron diffraction investigation of a nickel powder sample at room temperature was performed at three different experimental geometries using the ASTACUS diffractometer at Otaniemi. In spite of the correlation between adjacent channels, the diffraction patterns were analysed by the ordinary profile-refinement procedure adapted especially to the present conditions. The correctness of the results was supported by an analysis of the integrated intensities. The weighted mean value for the Debye-Waller parameter, BNi, of 0.425 (±0.065) Å2 was in reasonable agreement with literature values.

The Debye–Waller parameter (\overline{\it B}) of TlCl by powder elastic neutron diffraction

The mean Debye-Waller parameter {\bar {\it B}}of TlCl has been determined by double- as well as triple-axis neutron diffraction for a powder sample. Thermal diffuse scattering (TDS) corrections have also been made to the intensity of the diffraction peaks obtained by these techniques. TDS was found negligible in the triple-axis diffraction pattern as expected. The {\bar {\it B}} values thus found are 3.08 ± 0.43 and 3.07 ± 0.22 A2, respectively, for double- and triple-axis methods. These values are in good agreement with those found by recent X- ray diffraction measurements.

Electron-density studies. II. Further comments on the electron density in diamond

X-ray powder diffraction data for diamond have been re-analysed, in terms of an 'at rest' deformation-density model of monopole, octupole, hexadecapole and hexacontatettarapole terms of exponential form. The values of the parameters describing the third and fourth-order terms, and the refinement indices, are no different from those of an 'at rest' valence-density model. Unlike earlier analyses, however, the model is consistent with experimental measurements of the absolute scale, and with independently determined values of the Debye-Waller parameter. The predicted values of physical properties such as the gradient of the electric-field gradient at the carbon nucleus are shown to be strongly model-dependent. It is noted that the fit to the data, and in particular to the observed structure factor of the overlapping 333-511 reflection, is poor for all published charge-density analyses. Recent theoretical (crystal 'Hartree-Fock') calculations indicate, within the convolution and harmonic approximations, an experimental B value of 0.172 ± 0.006 A2 and a scale factor of 1.004 ± 0.002. These theoretical results are, however, in poor agreement with the experimental structure factors.