Muffin-tin potentials in EXAFS analysis

Transcription

1 J. Synchrotron Rad. (5)., doi:.7/s Supporting information Volume (5) Supporting information for article: Muffin-tin potentials in EXAFS analysis B. Ravel

2 Supplemental materials: Muffin tin potentials in EXAFS analysis. XANES data for La and.6.4 La. normalized µ(e) Energy (ev) Figure : XANES data for (blue) and La (red).

3 La phase purity X-ray powder diffraction data were acquired in θ-θ mode with a Bruker D Phaser, operating with Cu Kα radiation and a Lynxeye position sensitive detector (a Ni filter was used to remove Cu Kβ radiation). The angular range was < θ < 8, with a step size of. and a count time of seconds per step. 4 () () (4) () (4) (4) () (6) (), (4) (8) () (8) (4) (8) 5 La calculated counts angle (deg) Figure : Diffractogram of the La sample compared with peak positions and intensities computed from the known crystal structure. Any mention of commercial products is for information only; it does not imply recommendation or endorsement by NIST.

4 sample preparation Polycrystalline was prepared by the same method as described in the main text for La. To achieve similar particle size, we started with. mmol of Ni(CH CO ) 4HO dissolved in ml of deionised water with the addition of. mmol of citric acid monohydrate. X-ray powder diffraction demonstrated formation of single phase (olive green) after heating the amorphous precursors at 9 C for 6 hours under flowing oxygen. The mean particle size of the powder was estimated as. µm by scanning electron microscopy. A sample of was prepared for X-ray Absorption Spectroscopy (XAS) measurements by dispersing enough fine powder in polyethylene glycol to make an edge step around.5. A pellet was then formed in an hydraulic press..4 Analysis of the EXAFS data is halite structured and analyzed to a radial distance which includes the first four coordination shells. The variables in this fit included parameters for S, E, an isotropic lattice expansion coefficient α, and σ parameters for each of the four single scattering paths. Various multiple scattering paths were included in the fit and parameterized without introducing new variables to the fit. S.7(5) E.79(55) α.(5) σ O, st shell.476(6) σ Ni, nd shell.59(56) σ O, rd shell.7(58) σ Ni, 4 th shell.7(95) Table : Results of fit to using the cubic halite model. The unit of E is ev and of σ is Å.

5 k χ(k) (Å ) Wavenumber (Å ) 4 χ(r) (Å ) fit st shell O 6 nd shell Ni rd shell O 4 th shell Ni + MS Radial distance (Å) Figure : Fit to using the cubic halite structure. The brown line includes the contribution from the fourth shell Ni scatterer plus several collinear MS paths at the same distance. The vertical lines show the ranges of the Fourier transform in k and the fit in R. 4

6 La fit using the constructed Ni SS path Upon addition of the Ni SS path (brown line in Fig. 4), the fit improved statistically. The R-factor reduced from. to.. The inclusion of the Ni SS path added floating parameters, taking the fit from 6 to 8 parameters and reducing the freedom ν of the fit from about 5 to about. The reduced chi-square χ ν went from 576 to 5 upon addition of the Ni SS path. See Table in the main text. k χ(k) (Å ) Wavenumber (Å ) χ(r) (Å ) Radial distance fit O La Ni+MS Ni SS path (Å) Figure 4: Fit to La using the constructed Ni SS path. The yellow line includes contributions from the third shell Ni scatterer plus several multiple scattering paths at the same path length. The brown line is the Ni SS path added to represent the contribution from the non-diffracting Ni oxide. The vertical lines show the ranges of the Fourier transform in k and the fit in R. 5

7 La fit using the Ni path from The figure below shows the same fit as in Sec..5 of this supplemental document excpet that the Ni scatterer at about Åis repesented in the fit by the nd shell Ni scatterer from. The R-factor here is. and the reduced chi-square χ ν is 5, both equivalent to the fit with the Ni SS path shown in Sec..5. The number of Ni atoms in the poorly-diffracting phase determined from this fit is 6.8(4.)% and their R is.(5) Å, both consistent with the results given in the main text. On visual inspection, this fitting result is indistinguishable from the result shown in Sec..5 using the Ni SS path. k χ(k) (Å ) Wavenumber (Å ) χ(r) (Å ) Radial distance fit O La Ni+MS Ni from (Å) Figure 5: Fit to La using the nd shell Ni path from. The yellow line includes contributions from the third shell Ni scatterer plus several multiple scattering paths at the same path length. The brown line is the nd shell Ni path from used to account for the non-diffracting Ni oxide. The vertical lines show the ranges of the Fourier transform in k and the fit in R. 6