NIST Atomic Form Factors: Conclusion

X-Ray Form Factor, Attenuation, and Scattering Tables Main Page

10. Conclusion

Several generic difficulties of experimental and theoretical determinations of atomic form factors have been identified and resolved. We recommend intelligent application of a variety of the available experimental and theoretical sources, depending upon the user's purpose, and as summarized in Table 1 and Table 2, and section 8. Regions of solid state structure and XAFS limit the overall accuracy of such theoretical work unless explicitly modified to include such nearest neighbor effects, or comparison is made directly to monatomic gases. However, strong reasons favor use of theoretical sources at the present time for energies above 1 keV, for most applications. In this context, results based on Chantler [16] but with the current results presented here appear most reliable.

There are selected experimental data sets, which appear reliable, which suggest the accuracy of Chantler [16] compared to, e.g., Saloman, Hubbell, and Scofield [34]. Both theoretical approaches had large uncertainties in the soft x-ray near-edge region for a range of elements, for well-defined reasons. The convergence error of Chantler [16] was at all times within 1.5 σ. However, this still represented a large area of concern, particularly for present and future experimental investigations, even though it was often more accurate than ref. [34]. We have improved upon the theoretical uncertainty for f₂ in these regions (to an estimated σ = 20 % to 30 % in the difficult near-edge regions) and this appears to reduce the error of this approach to less than one standard deviation.

In regions above edges, the uncertainty in f₂ of this work and that of Chantler [16] reduces to an estimated 1 %. This is also the typical uncertainty quoted by other theoretical work, yet discrepancies between these often exist at the 6 % level. Uncertainties in f₁ are dominated by small errors or sharp discontinuities in f₂. Therefore, the precision of local structure in f₁ remains uncertain, as listed in Table 2. In all cases, uncertainties are quoted as percentages of f′ = f₁ - Z_eff, as this is the computed quantity. Near high-energy asymptotes, the accuracy of f₁ may therefore be very good, as explained in the previous section.

Future experimental and theoretical work holds the prospect of addressing many of the issues raised in this work. The tabulation presented here resolves many of the difficulties encountered with previous tabulations, while some aspects remain to be treated in greater depth in the future, perhaps including aspects of collective behavior and near-edge smoothing. There also appears to be a high priority for a comprehensive recalculation of scattering factors based on the approach of this work.

For general application, the tabulation presented here should be combined with Chantler [16] and may make use of scattering coefficients contained in Hubbell and Øverbø [13] (σ_coh), and Hubbell et al. [12] (σ_incoh), for example.