Dispersion, Lorentz and polarization in the centroid method of precision lattice parameter determination

Ladell, J.; Mack, M.; Parrish, W.; Taylor, J.

doi:10.1107/s0365110x59001670

Cited by 14 publications

(7 citation statements)

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“…At very high 2θ values (ie., 2θ ≥ 150°) the cosθ terms arising from d2θ /dλ can change quite significantly over a profile and elevate the intensity in the high angle tail. In addition to dispersion, the distortional effects of the Lorentz factor on high profiles should also be incorporated when analysing profile shapes at very high angles [39,40,41].…”

Section: The Wavelength Distribution In Laboratory Diffractometersmentioning

confidence: 99%

Fundamental parameters line profile fitting in laboratory diffractometers

Cheary¹,

Coelho²,

Cline³

2004

J. Res. Natl. Inst. Stand. Technol.

598

430

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The fundamental parameters approach to line profile fitting uses physically based models to generate the line profile shapes. The instrument profile shape K(2θ) is first synthesised by convoluting together the geometrical instrument function J(2θ) with the wavelength profile W(2θ) at the Bragg angle 2θ B of the peak, K(2θ) = ∫W(2θ -2ϕ)J(2ϕ)d2ϕ = W(2θ) ⊗ J(2θ) (1) where the function J(2θ) itself is a convolution of the various instrument aberration functions associated with the diffractometer, ie., J(2θ) = J 1 (2θ) ⊗ J 2 (2θ) ⊗…⊗ J i (2θ)…..⊗ J N (2θ).Diffraction broadening is incorporated into the profile function I(2θ) by convoluting the broadening function B(2θ) into the instrument profile function as shown I(2θ) = K(2θ) ⊗ B(2θ).This technique of profile synthesis was first introduced 50 years ago by Alexander [1], but has only been implemented as a standard fitting procedure during the last ten years [2,3,4]. More recently, freeware and commer- FPPF has been used to synthesise and fit data from both parallel beam and divergent beam diffractometers. The refined parameters are determined by the diffractometer configuration. In a divergent beam diffractometer these include the angular aperture of the divergence slit, the width and axial length of the receiving slit, the angular apertures of the axial Soller slits, the length and projected width of the x-ray source, the absorption coefficient and axial length of the sample. In a parallel beam system the principal parameters are the angular aperture of the equatorial analyser/Soller slits and the angular apertures of the axial Soller slits. The presence of a monochromator in the beam path is normally accommodated by modifying the wavelength spectrum and/or by changing one or more of the axial divergence parameters. Flat analyser crystals have been incorporated into FPPF as a Lorentzian shaped angular acceptance function.One of the intrinsic benefits of the fundamental parameters approach is its adaptability to any laboratory diffractometer. Good fits can normally be obtained over the whole 2θ range without refinement using the known properties of the diffractometer, such as the slit sizes and diffractometer radius, and the emission profile. Fine tuning is sometimes necessary to accommodate a monochromator or to compensate for the fact that certain aberrations are not completely independent [8]. Under these conditions some of the instrument parameters need to be refined, but the refined values normally are within ±10 % of the actual values. Correlation between refined instrument parameters can occur when fitting to data over a restricted 2θ range. Such correlation occurs between the axial divergence parameters and absorption as both of these aberrations can produce similar forms of asymmetric profiles between 2θ = 50° and 100° in diverging beam diffractometers. Correlation is minimised by using data with a large 2θ range so that the unique angular dependence of individual aberrations becomes evident. When a set of instrument profiles cannot be fitted by FPPF, this...

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Section: The Wavelength Distribution In Laboratory Diffractometersmentioning

confidence: 99%

Fundamental parameters line profile fitting in laboratory diffractometers

Cheary¹,

Coelho²,

Cline³

2004

J. Res. Natl. Inst. Stand. Technol.

598

430

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“…The results are given in Tables 1 and 2. These results indicate that the approximations which lead to the characterization of the correction in terms of the variance and mean wavelength are reasonable and that there is no significant difference between the numerical approach of Ladell, Mack, Parrish & Taylor (1959) and that of Pike.…”

Section: /J(o)--(1mentioning

confidence: 59%

“…More recently with M. Mack (Ladell, Mack, Parrish & Taylor, 1959) the same authors have published values of this correction calculated for various radiations. A similar correction was earlier reported by Pike (1959) in a theoretical study of the role of the Lorentz factor.…”

mentioning

confidence: 89%

“…The correction term given by (4) can be compared with that reported by Ladell, Mack, Parrish & Taylor (1959) by calculating the spectral variance, I 7, and mean wavelength, ;~, on their spectral model and substituting these quantities in (4). The correction term given by (4) was calculated for…”

Section: /J(o)--(1mentioning

confidence: 99%

“…In and Ladell, Mack, Parrish & Taylor (1959) the suggested correction factor ALp accounts not only for the Lorentz, polarization, and trigonometric factor associated with the powder method but also accounts for the effect of physical absorption, a wavelength-dependent factor (see Wilson, 1958). The theoretical basis for the suggested correction factor, Z]Lp, has been established in a later work (Ladell, 1961), but the role of absorption was not recognized in the earlier papers.…”

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confidence: 99%

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The Lorentz factor in powder diffraction

Pike¹,

Ladell²

1961

Acta Crystallogr

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JOSHUA LADELL 53 (LPTa)) has been calculated for several radiations (LMPT, Fig. 2) and is used as prescribed in these earlier papers.The similarity between the angle factor previously derived for the integrated intensity formula in the classical case (J (2.31, 2.50)) (strictly monochromatic X-rays) and the angle factor for the case discussed here (where there is a spectral distribution in the incident beam) is manifest because the ~3 factor appearing in the integrated intensity formula is offset by the absorption factor (J 2.50), which to the first order is proportional to/t 8. Thus the integrated intensity (J 2.50) is virtually independent of wavelength.

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An Experimental Examination of Error Functions for Bragg-Brentano Powder Diffractometry

King¹,

Payzant²

1993

Advances in X-Ray Analysis

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Dispersion, Lorentz and polarization in the centroid method of precision lattice parameter determination

Cited by 14 publications

References 4 publications

Fundamental parameters line profile fitting in laboratory diffractometers

Fundamental parameters line profile fitting in laboratory diffractometers

The Lorentz factor in powder diffraction

An Experimental Examination of Error Functions for Bragg-Brentano Powder Diffractometry

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