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

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.