The crystal structure of manganese difluoride (MnF₂): Reliability test of hypothetical intensity variances by means ofχ²distributions

Integrated X-ray intensities for MnF 2 have been gathered for all reflections up till sin ϑ / λ = 1.0 Å −1 . Ag Kα radiation was used monochromated by a graphite monochromator. The distribution of χ 2 = ( n – 1) s 2 / σ 2 , σ 2 = υσ P 2 , taken over 234 twice ( n = 2) repeatedly measured intensities agreed best with the theoretical χ 2 distribution, if all Poisson variances σ P 2 were multiplied by υ = 1.013. The agreement between symmetry equivalent intensities was checked by means of a χ 2 -test and intensities having a χ 2 larger than expected from statistics were rejected. Weighted least-squares refinement with anisotropic temperature factors yielded the goodness-of-fit parameter 1.7(1.06) and the agreement factors R w = 0.007(0.01) and R = 0.019(0.02), numbers in brackets were obtained if all reflections with sin ϑ / λ < 0.7 were omitted. The attempt to refine cumulant tensors of rank 3 and 4 has not shown any significant deviation from harmonic motion for both atoms Mn and F. With the lattice constants a = 4.8734 and c = 3.3099 Å the fluorine position parameter was determined to x = 0.3050.