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Kramers-Kronig analysis for Cu

The Kramers-Kronig transform analysis of the Cu DAFS and XAFS measurements was done in two different ways. First, the Kramers-Kronig transform of the normalized Cu(111) DAFS tex2html_wrap_inline1594 was compared to the XAFS tex2html_wrap_inline1454 (see Fig. 6a); tex2html_wrap_inline1594 is dominated by tex2html_wrap_inline1584 since the tex2html_wrap_inline1586 and tex2html_wrap_inline1454 contributions accidentally cancel. The agreement is excellent. Second, the DAFS f' and f'' functions were extracted from the raw data using the Kramers-Kronig method. The resulting f' and f'' functions are compared in Fig. 6b with the Cromer-Liberman tex2html_wrap_inline1814 and tex2html_wrap_inline1816 values.

The Kramers-Kronig method f' and f'' functions were splined to determine the associated DAFS tex2html_wrap_inline1584 and tex2html_wrap_inline1586 functions. The resulting tex2html_wrap_inline1584 and tex2html_wrap_inline1586 functions are compared with the normalized Cu(111) DAFS tex2html_wrap_inline1594 in Fig. 6c and with the XAFS tex2html_wrap_inline1454 signals in Fig. 6d. The agreement between these signals is excellent. The Kramers-Kronig iterative fitting procedure is clearly a very useful method for analyzing DAFS data.

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