Determination Of Peak Positions Research Articles

Three dimensional strain measurements with x-ray energy dispersive spectroscopy

A feasibility study was performed to show the ability of energy dispersive x-ray diffraction (EDXRD) to measure three dimensional strain distributions in thick industrial materials. Photon energies up to 130 keV were used to guarantee penetration through the sample and curve fitting techniques applied to peak position determination. This system was used to measure the strain gradient through the thickness of a 9.5 mm thick cantilevered steel bar.

Electronic structure of strontium titanate

We have employed the techniques of photoelectron spectroscopy (with tunable synchrotron radiation $30\ensuremath{\le}h\ensuremath{\nu}\ensuremath{\le}100$ eV) and inverse photoemission spectroscopy at $h\ensuremath{\nu}=9.7$ eV to study respectively the occupied and unoccupied electronic states of $n$-type ${\mathrm{SrTiO}}_{3}$ doped with 1 at.% Nb. Doped samples have the advantage that charging effects are avoided and hence a rather accurate determination of peak positions is possible. The total (occupied and empty) experimental density of states agrees with the calculated density of states of Pertosa and Michel-Calendini when their band-gap energy is readjusted. We have no evidence for intrinsic surface states either in the band gap or in the conduction band, as was calculated by Wolfram et al. The admixture of Ti $3d$ states in the O $2p$ valence states is small, as can be concluded from the Ti $3p\ensuremath{\rightarrow}3d$ resonance behavior.

The 2θ determination of diffraction peaks from `poor' powder samples. Application to biological apatite

A method is presented for improving the accuracy of the determination of peak positions from step-scanned X-ray powder diffraction data. This method is intended to be used in situations where the nature of the sample produces broad asymmetric peaks with a low peak-to-background ratio. A Fourier series is fitted to the experimental step-scan observations and the peak position is calculated from this functional representation. The method has been tried on the mineral apatite from biological sources, mainly bone, where ionic substitutions affect the cell parameters.

A theory of measurement with applications to spectrometry

An analytic function operating on experimental data is optimized for making the most accurate measurement of a parameter of the expected data, under the conditions of non-stationary shot noise. The value of the parameter is obtained by equating the operation on experimental data with the same operation on the expected data which contains the parameter as an unknown value. If the operation is represented by a weighting function, the form of the optimum weighting function depends on the initial transformation of the experimental data by the measuring instrument. The optimum weighting function always contains the derivative of the expected signal with respect to the unknown parameter, divided by the time-dependent variance of the received signal. Weighting functions for the logarithmic output of a spectrophotometer are described. The superiority over least-squares curve-matching is shown. A method for determination of peak position by optimum slope measurement is derived. In general, the optimum weighting function is not a matched filter. The optimum result is the same for center-of-gravity measurements. The optimum parameter measurement is equivalent to a least-squares error minimization weighted by the inverse variance or mean-square noise level. This variance weighting is significant in photometric measurements limited by shot noise or other measurements described by Poisson statistics, such that the mean-square noise level varies with time. The form of the optimum filter, for non-white, non-stationary noise is derived.

Automatic peak determination in X-ray powder patterns

A new technique is presented for the automatic determination of peak positions, intensities and widths from complex numerically recorded X-ray powder diagrams. The method uses standard powders for the determination of the actual repartition of incoming radiations and the determination of the apparatus function (aberrations, calibration etc.). The first trials give results the accuracy of which is much better than one could except from manual determinations.

Effects of the Operating Conditions of Parallel Beam X-Ray Diffraction Apparatus on the Line Profile and the Peak Position

The variation of the diffraction line profile and the peak position with the operating conditions of X-ray diffraction apparatus was experimentally investigated with a view to attaining reasonable X-ray stress measurement.Cr-Mo steel (0.44%C) specimens of 25mmφ×10mm were selected for the experiment. The specimens were heat-treated at various conditions in order to obtain eight kinds of diffraction lines with half-value breadth from 1.6° to 7.2°. The surface of each specimen was electrolytically polished. The effects of time constant, scanning speed and direction of the counter were first examined. Then, the influences of the tube current, the irradiation area and the divergence angle of the Soller slit were observed.The results obtained are as follows:(1) The variation of line profile parameters had good correlation with the product of time constant T (sec) and scanning speed w(deg/min).(2) The peak position shifted to the scanning direction of the counter in proportion to T×w at any incident angle of X-ray. Consequently, the stress determined by sin2ψ method was not influenced by the time constant and the scanning speed. The tube current, the irradiation area and the divergence angle of the Soller slit had no effect on the shift of peak position.(3) The breadth of diffraction lines increased with T×w. However, the incident angle of X-ray, the irradiation area and the divergence angle of the Soller slit gave no effect on the half-value breadth in the range studied in this experiment.(4) The net peak intensity decreased with increasing T×w. The degree of this decrease was large as the diffraction lines were sharp, but small in case of the broad lines. The net peak intensity increased in proportion to the increase of the tube current, the irradiation area and the divergence angle of the Soller slit.(5) It is favourable for the determination of peak positions to have the smooth intensity contour recorded.When the intensity contour is jagged or saw-toothed, it is recommended to adopt the product of T and w, the tube current, the irradiation area and the divergence angle of the Soller slit as large as possible in the permissible range.