MONOCHROMATIC X-RAY INTENSITIES VIA A 'BALANCED' TUBE EXPERIMENT. S. Maes, A. T. H. Lenstra, Department of Chemistry, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium
Diffraction intensities are accurate (reproducable), but unprecise due to the lack of monochromaticity in the incident X-ray beam. For a sealed tube equipment we find [[Delta]][[lambda]]/[[lambda]] of ~14% and ~3% for a C(002) and a Si(111) monochromator. Routine data collections were made with a Mo-tube using ammonium bitartrate as reference structure. With C(002) as monochromator we arrive at Ru=3.23%, Rw=4.24% and S=1.48; with Si(111) at Ru=3.83%, Rw=4.41% and S=1.28 In both experiments the reflection intensities are the sum of characteristic Mo-K[[alpha]] radiation and an unavoidable 'white continuum' component. The white continuum has an intensity distribution given by Kramer's formula I([[lambda]]) = K Z [E(tube)-E([[lambda]])] / E([[lambda]]) So for a fixed tube voltage E(tube) I([[lambda]]) only depends on the atomic number Z. This enables us to measure the 'white continuum' contribution separately by replacing the Mo-tube by e.g. a Cu-tube. The rather small 0.71Å Cu-tube intensities were measured and resulted in Ru=4.63%, Rw=4.95% and S=1.33 for graphite and Ru=5.89%, Rw=5.98% and S=1.28 for silicon. With Si(111) we find a constant ratio for I(0.71Å;Mo)/I(0.71Å;Cu). For the graphite monochromator we find I(0.71Å;Mo)~I(0.71Å;Cu) exp[+2B' sin2[[theta]]/[[lambda]]2] with B'=0.5Å2. This illustrates that a large [[Delta]][[lambda]]/[[lambda]]-error interferes with the ADP's. Subtraction of I(0.71Å;Cu) from I(0.71Å;Mo) produces a 'monochromatic' Mo-K[[alpha]] dataset, which fits almost ideal to the structure factor equation exploited in least squares. The Si(111) defined datasets result in Ru=3.61%, Rw=4.04% and S=1.18, which is a significant improvement compared to I(0.71Å;Mo) alone. Subtraction of the graphite datasets eliminates the systematic intensity errors. Refinement yielded Ru=3.79%, Rw=5.09% and S=1.79 These indicators are all larger than the single I(0.71Å;Mo) measurement. However, the 'monochromatic' model shows ADP's ~0.97 B(0.71Å;Mo). So B has become practically equal to B(neutron), which means that [[Delta]][[lambda]]/[[lambda]] is the driving force behind the hitherto unexplained inequality B(neutron)<B(X-ray).