Systematic errors in precision lattice-parameter determination of single crystals caused by asymmetric line profiles

The convolution of the various contributions to X-ray intensity distribution curves measured in lattice-parameter determination leads to peak shifts and, hence, to systematic errors in the case that at least one of the contributing curves is asymmetric. For perfect crystals, depending on the collimator divergence, this effect may reach the order of magnitude of the refraction correction. It is caused by the asymmetry of the spectral distribution curve, which includes intrinsic asymmetry, dispersion and angle dependence of intensity (ADI). For imperfect crystals characterized by orientation and interplanar-spacing distributions, the distribution curves should be measured in order to correct accurately the peak shift. Examples of simulation calculations are given for Si, Cu Kα₁, Bond method for various reflections of perfect crystals and for crystals having orientation distributions, 444 reflection.