Extended x-ray-absorption fine-structure (EXAFS) of copper has been measured from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion. The comparison between parallel mean square relative displacements (MSRD) of the first four coordination shells has allowed detecting a significant deviation from a pure Debye behavior. The firstshell EXAFS thermal expansion is larger than the crystallographic one: the difference has allowed evaluating the perpendicular MSRD, whose Debye temperature is slightly larger than the one of the parallel MSRD, due to anisotropy effects. High-order first-shell cumulants are in good agreement with quantum perturbative models. The anharmonic contribution to the first-shell parallel MSRD amounts to less than 1.5 percent. The third cumulant cannot be neglected in the analysis, if accurate values of the first cumulant are sought; it cannot however be used to directly estimate the thermal expansion. The shape of the effective pair potential is independent of temperature; a rigid shift, partially due to the relative motion perpendicular to the bond direction, is however observed.

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...

The EXAFS Debye-Waller factor depends on the correlation of atomic motion and can yield original information on the vibrational dynamics of crystalline solids. In this paper an introductory treatment of thermal disorder in EXAFS, based on thc cumulant approach, is given. Thc general relation between mean-square relative displacement (MSRD) measured by EXAFS and atomic thermal vibrations in harmonic approximation is explored. Strengths and limitations of the phenomenological Einstein- and Debye-correlated models are discussed. Some of the most significant results so far obtained are reviewed. A relatively simple method for estimating anharmonic corrections to the MSRD is proposed.

Light-emitting silicon nanocrystals embedded in SiO 2 have been investigated by x-ray absorption measurements in total electron and photoluminescence yields, by energy filtered transmission electron microscopy and by ab initio total energy calculations. Both experimental and theoretical results show that the interface between the silicon nanocrystals and the surrounding SiO 2 is not sharp: an intermediate region of amorphous nature and variable composition links the crystalline Si with the amorphous stoichiometric SiO 2. This region plays an active role in the light-emission process.