X-ray Intensities (x-ray + intensity)

Distribution by Scientific Domains

Terms modified by X-ray Intensities

  • x-ray intensity data

  • Selected Abstracts

    Application of the parametric bootstrap method to determine statistical errors in quantitative X-ray microanalysis of thin films

    Summary We applied the parametric bootstrap to the X-ray microanalysis of Si-Ge binary alloys, in order to assess the dependence of the Ge concentrations and the local film thickness, obtained by using previously described Monte Carlo methods, on the precision of the measured intensities. We show how it is possible by this method to determine the statistical errors associated with the quantitative analysis performed in sample regions of different composition and thickness, but by conducting only one measurement. We recommend the use of the bootstrap for a broad range of applications for quantitative microanalysis to estimate the precision of the final results and to compare the performances of different methods to each other. Finally, we exploited a test based on bootstrap confidence intervals to ascertain if, for given X-ray intensities, different values of the estimated composition in two points of the sample are indicative of an actual lack of homogeneity. [source]

    Interbranch transient beating of X-ray intensities in deformed crystals

    M. Shevchenko
    X-ray dynamical diffraction in a deformed crystal is studied using the interbranch resonance concept. It is shown that appreciable beating of the X-ray intensities may be induced by a lattice distortion that produces interbranch transformations of the local dispersion surface. In X-ray plane-wave topography, this effect may be observed as interference fringes arising around the kinematical image of a defect. It is predicted that such interbranch fringes can be induced by edge dislocations. [source]

    Two-wavelength inversion of multiply scattered soft X-ray intensities to charge density

    J. C. H. Spence
    A method is described for reconstructing the two-dimensional real-space charge density of an isolated object from measurement of the soft X-ray transmission diffraction pattern when it is affected by strong multiple scattering. The Bloch-wave scattering-matrix approach is used to show that the diffracted amplitude depends only on a simple product of X-ray wavelength and sample thickness (unlike the case of relativistic electron diffraction) under reasonable approximations. The multislice formulation then gives the effect of a small change in wavelength, which involves only single scattering. Dynamical diffraction patterns are recorded at two adjacent wavelengths, phased by iterative methods, transformed to real space and divided to give a single-scattering wavefunction. This can then be used to produce a charge-density map. The extension of the method to tomography is discussed. Consideration is first also given to the possibility that absorption due to the photoelectric effect may be so severe for soft X-rays that multiple elastic scattering becomes so much less probable than photoelectric absorption that it may be neglected entirely. A discussion of signs in soft X-ray, positron and electron multiple-scattering theory is given. [source]

    The pair-functional method for direct solution of molecular structures.


    The pair-functional principle shows how to construct a unique statistical ensemble of strongly interacting atoms that corresponds to any feasible measured set of X-ray intensities. The ensemble and all its distribution functions are strictly periodic in the crystal lattice, so that each unit cell has exactly the same arrangement of atoms at all times. The mean particle density in the cell is uniform because the ensemble has undefined phases and the origin is not fixed. The atoms in this maximum-entropy ensemble interact through pairwise additive periodic statistical forces within the unit cell. The ensemble average pair-correlation function is matched to the observed originless Patterson function of the crystal. The derived pairing force then becomes approximately proportional to the Ornstein,Zernicke direct correlation function of the ensemble. The atoms have a many-body Boltzmann distribution and the logarithm of the likelihood of any particular conformation is related to its total pairing potential. The pairing potential of a group of atoms acts like a local field in the cell. This property is used in the pair-functional method. Molecular structures can be solved by a direct search in real space for clusters of atoms with high pair potentials. During a successful search, the atoms move from their original random positions to form larger and larger clusters of correctly formed fragments. Finally, every atom belongs to a single cluster, which is the correct solution. [source]

    The pair-functional method.


    The theory of the pair-functional ensemble is developed to provide estimates of the pairing forces from experimental X-ray intensities. The statistical mechanics of the grand ensemble leads to a diagram expansion for the forces, in terms of the direct correlation function of the fluid ensemble combined with a series of small higher-order corrections. A simpler treatment, based on a biased Gaussian probability distribution, gives approximate formulae, valid for reflections of any type in all space groups. The role of symmetry is analysed. The entropy of an asymmetrical ensemble can always be increased by averaging it over equivalent positions of the atoms in the true space group, with the result that the atoms naturally tend to adopt the highest symmetry compatible with the data. In a cell with different types of atom, the atoms experience a single force function but they interact with a strength proportional to the products of their scattering factors. Numerical estimates are given for typical cases. [source]

    Cation movement and phase transitions in KTP isostructures; X-ray study of sodium-doped KTP at 10.5,K

    Stefan T. Norberg
    An accurate structure model of sodium-doped potassium titanyl phosphate, (Na0.114K0.886)K(TiO)2(PO4)2, has been determined at 10.5,K by single-crystal X-ray diffraction. In addition to the low-temperature data, X-ray intensities have been collected at room temperature. When the temperature was decreased from room temperature to 10.5,K, both potassium cations moved 0.033,(2),┼ along the c -axis, i.e. in the polar direction within the rigid Ti,O,P network. This alkaline metal ion displacement can be related to the Abrahams,Jamieson,Kurtz TC criteria for oxygen framework ferroelectrics. Potassium titanyl phosphate (KTP) is a well known material for second harmonic generation (SHG), and the influence of sodium dopant on the TiO6 octahedral geometry and SHG is discussed. The material studied crystallizes in the space group Pna21 with Z = 4, a = 12.7919,(5), b = 6.3798,(4), c = 10.5880,(7),┼, V = 864.08,(9),┼3, T = 10.5,(3),K and R = 0.023. [source]

    Scanning texture analysis of lamellar bone using microbeam synchrotron X-ray radiation

    Wolfgang Wagermaier
    Texture analysis with microbeam scanning diffraction enables the local mapping of three-dimensional crystallite orientation in heterogeneous natural and synthetic materials. Cortical (compact) bone is an example of a hierarchically structured biocomposite, which is built mainly of cylindrical osteons, having a lamellar texture at the micrometre level. In this work, a combination of microbeam synchrotron X-ray texture analysis with thin sections of osteonal bone is used to measure the three-dimensional distribution of the c -axis orientation of the mineral apatite in bone with positional resolution of 1,Ám. The data reduction procedure needed to go from the stereographic projection of X-ray intensity to the determination of the local orientation of mineralized collagen fibrils is described. The procedure can be applied to other mineralized tissues (such as trabecular bone and chitin) with micrometre scale and biologically controlled fibrillar texture. [source]

    Radiation damage in protein crystals examined under various conditions by different methods

    Elspeth F. Garman
    Investigation of radiation damage in protein crystals has progressed in several directions over the past couple of years. There have been improvements in the basic procedures such as calibration of the incident X-ray intensity and calculation of the dose likely to be deposited in a crystal of known size and composition with this intensity. There has been increased emphasis on using additional techniques such as optical, Raman or X-ray spectroscopy to complement X-ray diffraction. Apparent discrepancies between the results of different techniques can be explained by the fact that they are sensitive to different length scales or to changes in the electronic state rather than to movement of atoms. Investigations have been carried out at room temperature as well as cryo-temperatures and, in both cases, with the introduction of potential scavenger molecules. These and other studies are leading to an overall description of the changes which can occur when a protein crystal is irradiated with X-rays at both cryo- and room temperatures. Results from crystallographic and spectroscopic radiation-damage experiments can be reconciled with other studies in the field of radiation physics and chemistry. [source]