Application of the ratio method of EXAFS analysis to disordered systems

Bunker, Grant

doi:10.1016/0167-5087(83)90655-5

Cited by 462 publications

(319 citation statements)

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“…19 A convenient way to allow for anharmonicity is to add the third and fourth cumulants as parameters in the EXAFS fit. 4,6,[8][9][10] proposed that for small supported Pt clusters the thermal factor for all samples should be similar at each temperature. 19 In another study, ∆σ 2 of lead increases linearly with temperature (10 -4 Å 2 /K) up to the melting temperature.…”

Section: Fitting Exafs Data Collected At Elevated Temperaturesmentioning

confidence: 99%

“…The phase shift is affected and thus the distance determination. 4,6,7 Equations (2) and (3) are invalid if the PDF is broad or non-Gaussian and have to be adjusted. A commonly used procedure is to describe the distances in a coordination shell by a probability distribution.…”

Section: Introductionmentioning

confidence: 99%

“…4,6,8,9 C 0 is zero if the distribution is normalized. The second cumulant is the Debye-Waller factor.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of in situ EXAFS data of supported metal catalysts using the third and fourth cumulant

Bus

Miller²,

Kropf

et al. 2006

Phys. Chem. Chem. Phys.

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[DO NOT ALTER/DELETE THIS TEXT]X-ray absorption spectra of supported Pt catalysts with various Pt cluster sizes were collected between 77 and 673 K, in inert and hydrogen atmospheres. When analyzing these spectra with the standard EXAFS equation a Pt-Pt bond contraction and a large increase in the inner potential correction were observed with increasing temperature.These errors are up to 0.08 Å and 10 eV for clusters of 1 nm in diameter. They were corrected by including the third and fourth cumulants as fit parameters. Fit guidelines were developed to analyze EXAFS data of supported metal catalysts collected at elevated temperatures, allowing for asymmetry and broadening or sharpening of the pair distribution function. These comprise fixing fit parameters, using different k-weightings, and identifying trends in series of experiments. By fitting the EXAFS spectra using these guidelines, it was determined that in small Pt clusters the Pt-Pt bond is 0.10 Å shorter than in bulk Pt. These contracted bonds relax to distances near that of bulk Pt upon hydrogen chemisorption.2

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Section: Fitting Exafs Data Collected At Elevated Temperaturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of in situ EXAFS data of supported metal catalysts using the third and fourth cumulant

Bus

Miller²,

Kropf

et al. 2006

Phys. Chem. Chem. Phys.

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show abstract

“…19,20 In the next Section we present experimental details on synthesis, scanning electron microscopy characterization and EXAFS measurements of NPG. Section III describes the data processing and analysis.…”

Section: Introductionmentioning

confidence: 99%

Thermal properties of nanoporous gold

et al. 2012

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We measured the thermal expansion coefficient and Debye temperature of nanoporous gold (NPG) using Extended X-ray Absorption Fine Structure technique. Reduction of the nearest neighbor distances in NPG by ca. 0.01 Å compared to the bulk gold was attributed to the surface tension caused, in turn, by the finite size effect of the NPG ligaments. We also obtained that the Debye temperature in NPG is 5% lower than in bulk gold. We interpreted these observations in the framework of a bimodal distribution of surface and bulk bonds with different values of Debye temperature. The surface bonds with low Debye temperature extend within ca. 4 layers of Au atoms located on the pore surface, in a good agreement with prior resistivity measurements and theoretical predictions. 63.22.Dc, 61.05.cj, 65.40.De, PACS number(s):

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“…As early recognized in ref. 32 while odd moments contribute to the EXAFS phase φ(k)=2c 1 k-(4/3)C 3 k 3 +... 36 . While the fitting of bulk systems makes use up to the squared term of the k-series expansion, the point is that the k 3 behavior (third cumulant) is important for "disordered" systems; as surface atoms have a less symmetric environment with respect to bulk ones and correspond to a significant part in nanostructured materials, the cumulant expansion need to be considered in analyzing EXAFS data.…”

Section: Xafsmentioning

confidence: 99%