Systematic intensity errors and model imperfection as the consequence of spectral truncation

Abstract

The wavelength dispersion delta lambda/lambda in a graphite (002) monochromated Mo K alpha beam was analyzed. A wavelength window was found with 0.68 < lambda < 0.79 A, i.e. delta lambda/lambda = 0.14. The very large dispersion leads to systematic errors in Iobserved(H) caused by scan-angle-induced spectral truncation. A limit on the scan angle during data collection is unavoidable, in order that an omega/2 theta measurement should not encompass neighboring reflections. The systematic intensity errors increase with the Bragg angle. Therefore they influence the refined X-ray structure by adding a truncational component to the temperature factor: B(X-ray) = B(true) + B(truncation). For an Mo tube at 50 kV, we find B(truncation) = 0.05 A2, whereas a value of 0.22 A2 applies to the same tube but operated at 25 kV. The values of B(truncation) are temperature independent. The model bias was verified via a series of experimental data collections on spherical crystals of nickel sulfate hexahydrate and ammonium hydrogen tartrate. Monochromatic reference structures were obtained via a synchrotron experiment and via a 'balanced' tube experiment.

Electron density distribution in paramagnetic and antiferromagnetic CoO: A γ-ray diffraction study

“…The magnitude of the difference between U͑␥ ray͒ and U͑x ray͒ is of the same size as the values reported in Ref. 15 for Mo K␣ radiation. The spectral width of the 316.5 keV photon beam is ⌬/ϭ10 Ϫ6 and no monochromator is needed.…”

“…It has been recognized only recently that a graphite monochromated x-ray beam contains a Bremsstrahlung component with a large wavelength spread. 15 This fully contributes to the measured intensity at low Bragg angles and is progressively truncated at higher angles. The truncation depends on the tube voltage and leads to vibrational parameters which are systematically too large by about 30% for usual conditions.…”

Electron density distribution in paramagnetic and antiferromagnetic MnO: A γ-ray diffraction study

“…The discrepancy is due to the reduced monochromaticity of a graphite monochromated x-ray beam. 20 It contains a bremsstrahlung component with a large wavelength spread that fully contributes to the measured intensity at low Bragg angles and is progressively truncated at higher angles. The contribution of the bremsstrahlung depends on the tube voltage and leads to vibrational parameters that are systematically too large.…”

Structure, growth and optical properties of Zn0.24Ni0.76(SO4)·7H2O single crystal

“…Theoretical analysis showed that the spectra of Ni(OH 2 ) 6 2+ are sensitive to the O-Ni distances in the octahedral unit [12]. The average O-Ni distance calculated (Table 2) is 2.061Å for ZNSH, 2.049 Å for NSH [13] and surely a large distance for units in solution. We can infer the energy splittings between the nonequivalent d orbitals of octahedral unit in crystals are comparatively notable and it yields the blue shifts for transmission at UV and VIS region.…”