Experimental measurements of the X-ray scale factor for charge density studies

Knowledge of the absolute values of X-ray intensities is highly desirable for a quantitative interpretation of experimental electron densities. In the present work X-ray scale factors are determined by three experimental methods. In the first method, a small aperture is used to measure the direct X-ray beam and the crystal volume is determined by weighing. In the second method, a single-crystal plate large enough to intercept the entire direct beam is used, while the third technique is based on powder diffraction intensity measurements. Scale factors are measured for orthorhombic sulfur, oxalic acid, glycylglycine, hexamethylenetetramine, sodium azide, and ammonium tetroxalate, all of which have been the object of previous electron density distribution studies. Results from the three methods agree within experimental errors and it is concluded that scale factors can be measured with an accuracy of about 1%. Comparison of the experimental scale with the results of various least-squares refinements indicates that scale factors from conventional least-squares refinements contain a considerable bias. Scale factors from refinements with improved models are generally in better agreement with experimental values. The effect of a variation in scale factor on the experimental electron densities is discussed.