Direct spline analysis for Cu

Figure 5b shows the diffraction and absorption fine structure signals extracted by the direct spline method from the data in Fig. 5a. The strong similarity between the Cu(111) and the Cu(222) DAFS signals is evident, as is an apparent difference between the two DAFS signals and the XAFS signal. Figure 5c shows the Fourier transform magnitudes of the three signals in Fig. 5b. The agreement between the two DAFS and the XAFS Fourier transforms is very good. Consequently, although the multishell DAFS and XAFS signals in Fig. 5b appear to be different, they actually have identical Fourier magnitudes and therefore can only differ in their phases. Figure 5d shows that, within the experimental errors, each shell has the same phase shift for a fixed Bragg reflection. The apparent differences between the signals in Fig. 5b are caused by this phase shift of each shell.

The experimental DAFS-to-XAFS phase shifts determined from multiple back-filtered data sets, by assuming that the bond lengths for the XAFS signal were identical to those for the DAFS signal, are: Cu(111) first shell and second shell ; and Cu(222) first shell and second shell . For the Cu(111) Bragg reflection, the DAFS contribution and the absorption correction contribution accidently cancel, leaving only the oscillating DAFS contribution which has the form . Consequently, the Cu(111) first and second shells are simply shifted by with respect to the Cu XAFS signal. For the Cu(222) Bragg reflection, the DAFS component is larger than the absorption contribution. The measured phase shifts agree quite well with the values calculated using tabulated values of , , and .

Without constraining the distances to be equal, and by using the XAFS ratio method [20] to calculate the relative bond length shift, , between each DAFS signal (treated as an ``unknown'') and the Cu XAFS signal (treated as a ``known'' standard), the following 's are obtained: Cu(111) first shell Å and second shell Å; Cu(222) first shell Å and second shell Å. This demonstrates that DAFS measurements can be used to provide neighbor distances with accuracies comparable to XAFS measurements, and that experimental or theoretical XAFS standards can be used to analyze DAFS measurements by simply shifting the phases appropriately.