Agreement between experimentally determined and refined anomalous scattering factors.



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Agreement between experimentally determined and refined anomalous scattering factors.

The poor quality of solution 7 produced by the two X11 data sets is the result of poor contrast in between the data sets. This can be seen in Table gif which shows the relative isomorphous and anomalous occupancies for Iridium site 3 output by MLPHARE from solution 9 using all seven data sets.

  
Table: List of the refined isomorphous and anomalous occupancies for Iridium site 3 produced by MAD phasing solution 9. The corresponding and values are shown along with , the difference in with respect to the reference data set (4). ( indicate theoretical values obtained from the program CROSSEC.) The relative magnitudes of the isomorphous and anomalous occupancies agree well with those suggested by the respective anomalous scattering factors and .

Since no temperature factor refinement was performed for the heavy atoms the occupancy factors produced by MLPHARE include contributions from the actual occupancy of the atoms, the anomalous scattering factors and the atomic temperature factors. If however we restrict ourselves and inspect occupancies of only one heavy atom site, in this case site 3, we can assume that the actual heavy atom occupancy and the temperature factor contribution are the same for each of the seven cases shown. The isomorphous and anomalous occupancies ( and ) should therefore reflect only the magnitudes of the respective anomalous scattering factors at the seven X-ray energies scaled by a constant multiplicative factor accounting for the overall scale of the data, the actual atomic occupancy and the atomic temperature factor. To allow direct comparison of the experimentally measured anomalous scattering factors and the refined occupancy factors the latter were scaled as follows:-

and

where the average scale factors and are calculated using data sets 1, 2, 3, 5, and 6 only since there are no estimates of the anomalous scattering factors for data set 7.

Figs. gif

  
Figure: Values of and plotted together with the isomorphous and anomalous occupancies calculated by MLPHARE for all seven data sets. The occupancy factors have been scaled to allow direct comparison with the experimentally measured anomalous scattering factors.

and gif

  
Figure: Experimentally measured curves of and plotted with scaled occupancy factor calculated from MLPHARE for data sets 2, 3, 4, 5 and 7 in the neighbourhood of the iridium absorption edge. The r.m.s deviations of the refined and scaled occupancies about the experimentally determined values of the anomalous scattering factors are 1.36e for and 0.87e for . The poor agreement of for data set 7 with the experimental curve suggests an error in the estimation of the X-ray energy for this data set.

show the anomalous scattering factors plotted along with and as a function of the data set number and as a function of X-ray energy near the absorption edge. The r.m.s. deviations of and about the experimental curve are 1.36e and 0.87e respectively. The values of and for data set 7 correspond to anomalous scattering factors of and .

It is immediately apparent that very little contrast in has been achieved in the X11 experiment. The values of the refined isomorphous occupancies imply a difference in between data sets 6 and 7 of . This compares poorly with a difference of observed between data sets 1 and 4 collected on X31.

The effect of the broader bandpass of X11 on the anomalous scattering factors of Iridium is demonstrated in Fig. gif. The experimental data measured on X31 is shown after convolution with a Gaussian functions with FWHM's of the resolution of the X31 beam line using a Si(111) monochromator, the calculated energy resolution of the X11 beam line and an arbitrary intermediate resolution.

Given the magnitudes of the isomorphous and anomalous occupancies for data set 7 and the expected bandpass of the X11 beam line we can conclude that data set 7 was in fact collected at an X-ray energy which was below the iridium absorption edge. It is however also clear that given an energy resolution of the attainable contrast in the scattering factor is severely limited. The minimum value of becomes . In addition the white line feature in the curve is almost eliminated by the effect of the broad band pass.

  
Figure: Experimental anomalous scattering data for the Iridium edge convoluted with three Gaussian functions of varying widths chosen to approximate X-ray beam line instrument functions with different bandpasses. Results are shown after convolution with Gaussians of FWHM 4, 15 and 33.



next up previous contents index
Next: Discussion. Up: MAD experiments. Previous: MAD phasing of



Gwyndaf Evans
Fri Oct 7 15:42:16 MET 1994