Theoretical X-Ray Scattering Factors Based on Energy-Band Structure

Arlinghaus, F. J.

doi:10.1103/physrev.153.743

Cited by 57 publications

(25 citation statements)

References 29 publications

(2 reference statements)

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“…The remaining nine experimental values werc quoted to be 'significantly smaller than the Hartree-Fock free-atom value and (to) oscillate around a theoretical value which is the average of the two different values obtained from band calculations by Arlinghaus (1967) and by Wakoh & Yamashita (1971)'. The data for these nine were therefore treated as subject only to random errors and the mean value deduced for f(220) was 16.46 + 0.02, where the quoted error is one standard deviation of the mean.…”

Section: The Original Data and Conclusionmentioning

confidence: 99%

The absolute measured value off(220) for Cu –the importance of extrapolation to zero extinction

Mackenzie¹,

Mathieson²

1979

Acta Cryst Sect A

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A method of deriving an extinction-free estimate of an X-ray structure-factor value is outlined. The method is based on the availability of experimental estimates of the level of extinction from the mosaic distribution of the crystal. A plot of the diffracted intensity or its corresponding structure factor (uncorrected or nominally corrected for extinction) against the percentage extinction effect yields an extinction-free value in the limit on extrapolation to zero level. Such a procedure can also reveal any inadequacy in the correction procedures by lack of internal consistency. An illustration of the potential of this procedure is given using the set of 11 experimental values off for the 220 reflexion of Cu derived by Schneider [Acta Cryst. (1977), A33, 235-243] from y-ray diffractometry. Use of the experimental estimates of the level of extinction together with the nominally corrected f data indicates the presence of systematic residual error. Linear extrapolation of these f values to zero extinction yields an estimate off(220) in the region of 16.77. A value in this region is more in accord with a Hartree-Fock value than with the band-structure value, which was favoured by Schneider's original estimate of 16.46.

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Section: The Original Data and Conclusionmentioning

confidence: 99%

The absolute measured value off(220) for Cu –the importance of extrapolation to zero extinction

Mackenzie¹,

Mathieson²

1979

Acta Cryst Sect A

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“…Attempts at resolving the differences with a band calculation were unsuccessful [5]. However, results obtained with imperfect single crystals [7] came closer to agreeing with RHF values [3] at large I k l (333,511).…”

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confidence: 58%

Experimental comparison of hartree-fock and slater exchange potentials in aluminum from the charge density point of view

Raccah

Henrich

2009

Int. J. Quantum Chem.

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Measurements on an absolute scale of the first nine structure factors of Al have been Excellent agreement with calculations using the Hartree-Fock exchange performed.potential was found for all but the first two, where solid state effects are important. (333, 511).In this paper we report experimental results which successfully distinguish between the two calculations, agreeing with the RHF values for scattering from the closed shell electrons. Our measurements were made on cold worked powder pellets using Ni-filtered CuK, radiation and monitoring the incident beam. T o put the results on a n absolute scale we used a monochromatic CuK, incident beam to measure the first three integrated intensities. The incident beam was then counted after attenuation by brass foils. The relative intensities were step-scanned while the * Operated with support from the US. Air Force. 797798 P. M. RACCAH AND V. E. HENRICH absolute intensities were obtained using the open slit technique. Full experimental details will be presented in another publication, but some salient points should be mentioned here. Extinction, porosity and surface roughness are wavelength dependent. All samples were examined by using Mo, Cu and CrK, radiation; none were used which showed measureable effects. Preferred orientation was studied by forming samples at different pressures. The samples finally used were formed at pressures from 1000 to 5000 psi. Mass spectrographic analysis showed the level of all impurities to be lower than 0.05 molar %.The polarization constant of the doubly bent LiF monochromator used in the absolute intensity measurements was determined experimentally by diffraction from a perfect crystal of germanium, as described by Jennings [8] ; it was found to be 0.753 f 0.015. The electronic dead time was measured, and all data were corrected for it. The mass absorption of the sample material was measured on a thin pressed pellet and found to be 50.4 f 0.3 cm2/g, in good agreement with a recent value of 50.6 cm2/g [9].

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“…Theoretical atom.c scattering factors have been calculated for free atoms by several investigators,e.g. Freeman & Watson (1961) (Hartree-Fock wave functions), Doyle & Turner (1968) Arlinghaus (1967) and Wakoh & Yamashita (I 971). No attempt at theoretical calculation has been made for solid Ti atoms, however.…”

Section: Calculation and Resultsmentioning

confidence: 99%

Accurate determination of atomic scattering factors of f.c.c. and h.c.p. metals by high-voltage electron diffraction

Arii¹,

Uyeda²,

Terasaki³

et al. 1973

Acta Cryst Sect A

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295around ~=0, 180 °. This eff:ct influences mostly the 'left-right' reflexion pairs and the R value improvement should be observed on all photographs, as indeed shown in Table 1.The absorption curve of Fig. 5(c) is again approximately symmetrical around ~ = 90 ° and 270 ° and the R value changes are as one would expect. Fig. 5(d) is an example of a large absorption effect. The R value improvement is particularly high.This R-value test of equivalent reflexions can, of course, give no indication as to whether the proposed method also provides a proper correction for the absorption variation between diffraction cones; nevertheless it may well do so.Eventual errors in this correction are, however, no serious problem, as the scaling procedure involves individual scaling factors and temperature factors for each film (Steigemann, unpublished). The 'temperature factor' can take absorption errors of this kind into account.We wish to thank G. Kopfmann for helpful discussions. The accelerating voltage Ec at which the second-order Kikuchi line vanishes has been measured for the 400 reflexions of A1, Ni and Cu and the 0004 reflexion of Ti. The X-ray atomic scattering factors fx for the first-order reflexion have been determined from the measured values of Ec and the results are compared with theoretical and X-ray experimental data.

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Theoretical X-Ray Scattering Factors Based on Energy-Band Structure

Cited by 57 publications

References 29 publications

The absolute measured value off(220) for Cu –the importance of extrapolation to zero extinction

The absolute measured value off(220) for Cu –the importance of extrapolation to zero extinction

Experimental comparison of hartree-fock and slater exchange potentials in aluminum from the charge density point of view

Accurate determination of atomic scattering factors of f.c.c. and h.c.p. metals by high-voltage electron diffraction

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