Data analysis method to achieve sub-10 pm spatial resolution using extended X-ray absorption fine-structure spectroscopy

Du, Y.; Wang, J.; Jiang, L.; Borgna, L.S.; Wang, Y.; Zheng, Y.; Hu, T.

doi:10.1107/S1600577514010406

Figure 1
Validation of our method using numerical simulations. (a) g(r) is the theoretical curve built using three Gaussian peaks with n₁ = n₂ = n₃ = 2, r₁ = 1.923, r₂ = 2.012, r₃ = 2.086, $[\sigma^2]$ = 0.005. $[\Delta r_1]$ is the bond length difference between r₁ and r₂. $[\Delta r_2]$ is the bond length difference between r₂ and r₃. To resolve these three peaks, a spatial resolution better than the smallest one, $[\Delta r_2]$ , is needed. These three peaks merged into a single peak which is indistinguishable using existing EXAFS data analysis methods. (b) Simulated data are the EXAFS data $[\chi(k)]$ calculated using equation (1)

with added noise. Data are k³-weighted. The fitting curve is the curve fitted by our algorithm. A Hanning window for the FT is shown as a dashed line and the window parameter is 20. (c) The dashed line shows the phase- and amplitude-corrected FT spectrum (van Zon et al., 1984

) of the simulated data. The three peaks are indistinguishable using this method. The solid line shows the atom distribution function (ADF) calculated from our method. The peaks are clearly resolved. The peak position and the area are the bond length and coordination number, respectively. Calculated parameters are n₁ = 2.0, n₂ = 2.1, n₃ = 2.0, r₁ = 1.915 Å, r₂ = 2.007 Å, r₃ = 2.082 Å, $[\sigma^2]$ = 0.0049 Å², which are very close to the true values.

JOURNAL OF
SYNCHROTRON
RADIATION

ISSN: 1600-5775

Volume 21| Part 4| June 2014| Pages 756-761

doi:10.1107/S1600577514010406

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