Interpretation of diffractometer line profiles

The accuracy of stress measurement using the X-ray diffraction method relies on both the accuracy of peak location and the goodness-of-fit of the assumed linear model that relates the peak shift to the specimen orientation. In the absence of systematic effects it is the uncertainty in peak location due to random counting statistics that provides the major source of error. This note derives an analytical expression to describe the effect of these counting statistics on the ultimate precision of diffraction peak location and hence derived stress value. The results are discussed with reference to the available instrumentation and used as a basis for optimizing the performance of a system that incorporates a linear position-sensitive proportional counter for stress measurement.

Section: Accuracy Of Peak Locationmentioning

confidence: 99%

The accuracy of stress measurement using the X-ray diffraction method

Lonsdale¹

1986

“…Or de nombreuses 6tudes utilisent les profils complets des raies lors de la (2), soit en utilisant la m&hode de la variance suivant Wilson (1962) soit les coefficients de Fourier A(,)d'un profil unique de raie Gangulee (19741 et Mignot & Rondot (1975). Comme ront montr6 notamment Ladell, Parrish & Taylor (1959), la composante K% n'est exactement, ni de mfime largeur ni de m6me forme que K~,. L'examen des profils reconstitu& 5. partir de l'expression (5), des raies pour lesquelles le doublet est exp6rimentalement en partie r6solu (Fig.…”

Section: Contr6le Des R~sultats Diverses Caract6ristiquesunclassified

Application du lissage des raies de diffraction des rayons X à la séparation du doubletKα₁Kα₂

Mignot¹,

Rondot²

1976

It may be very useful to know a mathematical expression which helps reconstruct the X-ray diffraction profile. It is in fact easier to work on one relation I(0)=f(0) rather than on a series of experimental points.The relation proposed in this paper,gives a good correspondence between experimental values and the values calculated in the case of a monochromatic source. Its use still remains very simple in the case of a doublet, K~I K~2, which can be expressed as follows:Ir, l(x) is given by the previous expression, A represents the angular separation of the doublet. Different forms of profiles are used in order to verify the validity of the relation proposed and the results are compared with those resulting from the Rachinger classical method.

“…Ladell, Parrish & Taylor (1959) have given an analytic representation of the doublet spectral distribution: where and I(z)= Ii(z)+ I2(z) (4) Ii(z) = 1/(1 +aZz2);…”

Section: Mathematical Basis Of the Methodsmentioning

confidence: 99%

CuKα₂elimination algorithm

Ladell¹,

Zagofsky²,

Pearlman³

1975

Self Cite

The existence of the Ka2 lines in powder diffractograms has always obscured the interpretation of the diffraction patterns. Studies involving integrated intensity measurements, peak intensities and line broadening have been hampered owing to these extraneous lines. Crystal monochromators are ineffective for eliminating the Ka2 profile. This paper presents an algorithm which practically removes the Cu K~2 profile. Previous procedures to remove the Ko~z line or resolve the K~ doublet assumed the shape of the ~2 component to be identical to that of the a, component. The algorithm presented here uses the actual shape relationship between observed ~1 and ~2 components as a basis for elimination of the ~z profile. This algorithm has been applied to an on-line computer-controlled diffractometer to produce 'real time' Cu K~2-free diffraction patterns. The method is quite general and can be extended to remove the Ka2