On the Factors Affecting the Reflection Intensities by the Several Methods of X-Ray Analysis of Crystal Structures

Blake, F. C.

doi:10.1103/revmodphys.5.169

Cited by 38 publications

(5 citation statements)

References 77 publications

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“…In the original derivation [see, for example, Debye & Scherrer (1918) and Blake ( 1933)] the Lorentz factor was calculated for the case of a fine cylindrical X-ray beam and a point-like sample. Conventionally, the intensity was recorded on an X-ray film, mounted cylindrically around the sample with the cylinder axis perpendicular to the incoming beam.…”

Section: Introductionmentioning

confidence: 99%

The peak in neutron powder diffraction

Laar¹,

Yelon²

1984

J Appl Cryst

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For the application of Rietveld profile analysis to neutron powder diffraction data a precise knowledge of the peak profile, in both shape and position, is required. The method now in use employs a Gaussianshaped profile with a semi-empirical asymmetry correction for low-angle peaks. The integrated intensity is taken to be proportional to the classical Lorentz factor calculated for the X-ray case. In this paper an exact expression is given for the peak profile based upon the geometrical dimensions of the diffractometer. It is shown that the asymmetry of observed peaks is well reproduced by this expression. The angular displacement of the experimental profile with respect to the nominal Bragg angle value is larger than expected. Values for the correction to the classical Lorentz factor for the integrated intensity are given. The exact peak profile expression has been incorporated into a Rietveld profile analysis refinement program.

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Section: Introductionmentioning

confidence: 99%

The peak in neutron powder diffraction

Laar¹,

Yelon²

1984

J Appl Cryst

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“…where m is the mass of the atom, & the Boltzmann constant, 0 the Debye temperature and Qa quantization factor which has been tabulated and which does not deviate appreciably from unity unless ->1 (see Blake, 1933, for a good critical account of early work, and the accompanying article by Professor Max Born for an outline of the derivation of the formula). In considering the temperature variation of the Laue or Bragg intensities from a crystal containing more than one kind of atom, allowance must be made for the fact that each atom has its own temperature factor M a Zener and Rilinsky (1936) have also pointed out that 0 is not independent of T, and have obtained improved agreement at high temperatures by making a correction for this fact.…”

Section: E*lmentioning

confidence: 99%

Experimental study of x-ray scattering in relation to crystal dynamics

Lonsdale¹

1942

Rep. Prog. Phys.

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Kathleen Lonsdaleof short wave-length ; (iii) if the primary beam is monochromatized and consists mainly of long wave-length radiation, but contains short-wave harmonics, a differential method of elimination may be used, the absorbing aluminium being pIaced in the primary beam . The fluorescence coefficient is, . apart from the Kossel effect, independent of crystal orientation (Baltzer and Jauncey, 1939)) and also of the state of motion of the atoms in the crystal. Fluorescent radiation may be particularly troublesome if a heavy impurity is present in a light scatterer. 3 3. COMPTON SCATTERING Spectroscopic examination or analysis by absorption of the secondary * The kx unit, in terms of which the 200 spacing of NaCl is 2*81400 and the wave-length of CuKa is 1.537395, is about 0.2% greater than thehgstrom unit A. See Lipson and Riley (1943) and Wilson (1943), Imod. =IeR[36 -Z(.fik)K+ -zv&)Cl--ZxX (.f&)A1,

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“…Historically, this kinematic correction has followed the work of Blake (1933) where a correction based strictly on the dipole scattering from individual atoms is made. In the dipole scattering approximation, if the incoming electric field vector E i is perpendicular to the plane containing the incoming and outgoing rays ( polarization), the intensity of scattering is independent of the azimuthal angle around E (which is the diffraction angle 2), since E i is parallel to the outgoing E o .…”

Section: Introductionmentioning

confidence: 99%

Polarization effects of X-ray monochromators modeled using dynamical scattering theory

2021

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The difference in the diffracted intensity of the σ- and π-polarized components of an X-ray beam in powder diffraction has generally been treated according to equations based on dipole scattering, also known as kinematic X-ray scattering. Although this treatment is correct for powders and post-sample analyzers known to be of high mosaicity, it does not apply to systems configured with nearly perfect crystal incident-beam monochromators. Equations are presented for the polarization effect, based on dynamical diffraction theory applied to the monochromator crystal. The intensity of the π component relative to the σ component then becomes approximately proportional to |cos 2θm| rather than to cos22θm, where θm is the Bragg diffraction angle of the monochromator crystal. This changes the predicted intensities of X-ray powder diffraction patterns produced on instruments with incident-beam monochromators, especially in the regions far from 2θ = 90° in the powder pattern. Experimental data, based on well known standard reference materials, are presented, confirming that the dynamical polarization correction is required when a Ge 111 incident-beam monochromator is used. The dynamical correction is absent as an option in the Rietveld analysis codes with which the authors are familiar.

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On the Factors Affecting the Reflection Intensities by the Several Methods of X-Ray Analysis of Crystal Structures

Cited by 38 publications

References 77 publications

The peak in neutron powder diffraction

The peak in neutron powder diffraction

Experimental study of x-ray scattering in relation to crystal dynamics

Polarization effects of X-ray monochromators modeled using dynamical scattering theory

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