Sensitivity of Extended X-Ray-Absorption Fine Structure to Thermal Expansion

Abstract

The sensitivity of extended x-ray-absorption fine structure (EXAFS) to thermal expansion has been studied by temperature-dependent measurements on germanium. The first cumulant does not reproduce the thermal expansion owing to vibrations normal to the bond. The perpendicular relative displacement ͗Du 2 Ќ ͘ has been for the first time experimentally obtained; the ratio ͗Du 2 Ќ ͘ ͞ ͗Du 2 k ͘ is in agreement with vibrational model calculations. Low-temperature quantum effects on the 3rd cumulant have been for the first time observed. The possibility of measuring thermal expansion from the 3rd cumulant is demonstrated, provided that quantum effects are taken into account. [S0031-9007(99)09215-7] PACS numbers: 63.20.-e, 65.70.+ y, 78.70.DmExtended x-ray-absorption fine structure (EXAFS) is a powerful tool for studying the local coordination and dynamics of selected atomic species in condensed matter [1]. In particular, the temperature dependence of the distance between absorber and backscatterer atoms can be used as a measure of the thermal expansion. It was early recognized that a harmonic analysis leads to an underestimation of the thermal expansion [2-4], owing to the EXAFS sensitivity to the pair potential asymmetry, while a more refined cumulant analysis [5,6] can satisfactorily take into account anharmonicity, at least for moderately disordered systems [7-10]. The EXAFS phase, which carries information on interatomic distance, is parametrized in terms of odd cumulants.Two subtle effects have to be taken into account when a connection between first EXAFS cumulant and thermal expansion is sought: (a) Spherical nature and mean free path of the photoelectron wave; (b) thermal vibrations perpendicular to the bond direction [10][11][12]. The former effect leads to a difference between real and effective distributions of distances r͑r͒ and P͑r, l͒ r͑r͒ exp͑22r͞l͒͞r 2 and their cumulants C ‫ء‬ i and C i , respectively [6], and can quite easily be accounted for. The latter effect has been for a long time neglected, in spite of its quantitative relevance; actually it represents a drawback in the determination of thermal expansion directly from EXAFS, since it has to be independently evaluated from vibrational calculations. Conversely, the difference between first EXAFS cumulant and thermal expansion could be exploited to gain original information on the correlation of vibrations normal to the bond direction.An alternative possibility for measuring thermal expansion from EXAFS is based on the third cumulant. Classically the temperature dependence of the third cumulant is, to first order, proportional to T 2 [7,13], and thermal expansion is given by C 3 ͞2C 2 [9]. Recent quantum statistical calculations have shown that quantum effects are not negligible, giving rise to a nonzero value at 0 K [14-16]; an expression connecting thermal expansion to EXAFS cumulants has been explicitly derived by Frenkel and Rehr [14].In spite of the many theoretical papers published on these subjects in the last years [12,[14][15][16][17][18][1...

Solution X-ray Absorption Fine Structure Study of the Eu2+and Sr2+Ions: Unexpected Solvent and Metal Ion Dependencies of the Solvation Numbers

“…A coordination number of 6 and a metal-to-solvent distance of 2.525 Å were extrapolated for the Eu 2+ ion in DMSO solution, for which no experimental data are available. We obtained for the Sr 2+ ion in DMF, DMSO, and MeCN solutions coordination numbers of 6.9(3), 7.0(3), and 8.1 (8) and metal-to-solvent distances of 2.555(5), 2.540(7), and 2.665(6) Å, respectively.…”

“…22 The ionic radii of these ions being slightly different than those of the Eu 2+ and Sr 2+ , scaling factors were applied for the M-O or M-N distances to match the distances in the system studied (see Table 2 for detail). Using the respective crystallographic coordinates of the selected compounds, we calculated the following clusters to obtain theoretical φ(π,k) and f(π,k) functions: (1) MO 8 (H 2 O) 16 6 , and (6) M(NCC) 8 . The computed muffin-tin radii for the different clusters are detailed in Table 2.…”

“…The experimental L 3 -edge X-ray absorption fine structure (XAFS) spectra of Eu 2+ , as well as the Sr 2+ K-edge, have been measured, analyzed, and compared using the cumulant approach combined with efficient analysis techniques. [4][5][6] Both theoretical (calculated ab initio 7 ) and experimental (extracted from crystalline reference 8 ) phases and amplitudes have been used. received.…”

Local vibrational properties of GaAs studied by extended X-ray absorption fine structure

“…More recently, the difference between the thermal expansions measured by EXAFS and by Bragg diffraction in crystals was experimentally detected, leading to the evaluation of the perpendicular MSRD; the role of the third cumulant was clarified too. 9,10 a) Permanent address: Ain Shams University, Cairo, Egypt. b) Author to whom correspondence should be addressed.…”

Thermal properties of nanoporous gold

“…13 Such investigations are particularly challenging due to the need to probe both the structure and dynamics of the surface atoms as a function of temperature and pressure, and to do so by maintaining high spatial and temporal resolution in order to sense both static and dynamic bond length characteristics. In this work we applied the by Extended X-ray Absorption Fine-Structure (EXAFS) method that was successfully used to analyze structural and thermodynamic properties of many bulk [14][15][16] and nanoscale 17,18 systems.…”