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

Area of Science:

• Crystallography
• Materials Science
• X-ray Diffraction

Background:

• Graphite monochromators in X-ray diffraction exhibit significant wavelength dispersion.
• This dispersion can introduce systematic errors in intensity measurements.

Purpose of the Study:

• To analyze the wavelength dispersion of a graphite (002) monochromated Mo K alpha beam.
• To quantify the impact of scan-angle-induced spectral truncation on X-ray diffraction data.
• To investigate the resulting systematic errors in crystallographic structure refinement.

Main Methods:

• Analysis of wavelength dispersion (delta lambda/lambda) in a graphite (002) monochromated Mo K alpha beam.
• Experimental data collection on spherical crystals of nickel sulfate hexahydrate and ammonium hydrogen tartrate.
• Comparison of monochromatic reference structures obtained via synchrotron and 'balanced' tube experiments.

Main Results:

• A significant wavelength window (0.68 < lambda < 0.79 A, delta lambda/lambda = 0.14) was identified.
• Systematic intensity errors due to spectral truncation increase with Bragg angle.
• Truncational component to the temperature factor (B(truncation)) was quantified, e.g., 0.05 A2 at 50 kV and 0.22 A2 at 25 kV for Mo tube.
• B(truncation) was found to be temperature independent.

Conclusions:

• Scan-angle limitations are necessary to avoid spectral truncation during omega/2 theta measurements.
• Systematic errors in X-ray diffraction intensity data can lead to inaccuracies in refined crystallographic structures.
• Accurate structure refinement requires accounting for the truncational component of the temperature factor, which is dependent on experimental conditions like tube voltage.