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

Abstract

Integrated X-ray intensities for MnF2 have been gathered for all reflections up till sin ϑ/λ = 1.0 Å−1. AgKα radiation was used monochromated by a graphite monochromator. The distribution of χ2 = (n – 1) s2/σ2, σ2 = υσP2, taken over 234 twice (n = 2) repeatedly measured intensities agreed best with the theoretical χ2 distribution, if all Poisson variances σP2 were multiplied by υ = 1.013. The agreement between symmetry equivalent intensities was checked by means of a χ2-test and intensities having a χ2 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 Rw = 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.