Counter diffractometer - the effect of vertical divergence on the displacement and breadth of powder diffraction lines

Abstract

The divergence of the beam in a counter diffractometer causes a broadening, and a shift of centre of gravity, of diffraction lines. The effects do not disappear as 2 theta tends to 180°, and hence present extrapolation methods fail to remove the errors introduced. Experimental results are quoted that are not explained by previous treatments, and a theoretical investigation is made of the diffractometer with no Soller slits, one set of slits, and two sets of slits. Results show a marked asymmetry about 2 θ = 90°, both in shift of centre of gravity and in line broadening, the maximum effects occurring at low values of 2 θ. The use of Soller slits for various practical applications of the diffractometer is discussed. For accurate lattice-parameter measurement it is shown that the fractional error in spacing introduced by vertical divergence may be written in the form Δd/d = - a + b cos2 θ where a and b are positive constants depending on goniometer radius, specimen height, and Soller-slit aperture (if used). Extrapolation against cos2 theta and addition of the constant a will therefore give the true lattice spacing. The magnitude of the correction for a Norelco high-angle goniometer with two sets of Soller slits is approximately 4 parts in 105.