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 understanding of the negative thermal expansion (NTE) mechanism remains challenging but critical for the development of NTE materials. This study sheds light on NTE of ScF3, one of the most outstanding materials with NTE. The local dynamics of ScF3 has been investigated by a combined analysis of synchrotron-based X-ray total scattering, extended X-ray absorption fine structure, and neutron powder diffraction. Very interestingly, we observe that (i) the Sc-F nearest-neighbor distance strongly expands with increasing temperature, while the Sc-Sc next-nearest-neighbor distance contracts, (ii) the thermal ellipsoids of relative vibrations between Sc-F nearest-neighbors are highly elongated in the direction perpendicular to the Sc-F bond, indicating that the Sc-F bond is much softer to bend than to stretch, and (iii) there is mainly dynamically transverse motion of fluorine atoms, rather than static shifts. These results are direct experimental evidence for the NTE mechanism, in which the rigid unit is not necessary for the occurrence of NTE, and the key role is played by the transverse thermal vibrations of fluorine atoms through the "guitar-string" effect.

The analysis of temperature-dependent EXAFS spectra based on the cumulant expansion is critically reviewed, seeking for accurate relations between EXAFS parameters and physical properties of crystals. The treatment is based on the distinction between the real and effective distribution of distances, and is divided into three logical steps. (a) The connection between lattice dynamics and cumulants C(n)* of the real distribution is studied and the extent of the usual approximations are numerically evaluated. Atomic vibrations perpendicular to the bond direction make the EXAFS thermal expansion larger than the crystallographic one; the difference is connected to a shift of the effective pair potential rather than to its asymmetry. Peculiar information on lattice dynamics of crystals can be obtained from accurate EXAFS measurements and their cumulant analysis. (b) The differences between cumulants of the real and effective distribution (C(n)* and C(n), respectively) are calculated for various physically realistic distributions. The largest discrepancy concerns the first cumulant: C(1)* measures the thermal expansion of the interatomic bond, while C(1) is a better estimate of the crystallographic thermal expansion. (c) The convergence properties of the cumulant series are discussed and some phenomenological procedures are suggested to monitor and possibly work out the connected failures of the cumulant method. Benefits and risks of the use of an effective pair potential are at last debated.

High-resolution x-ray powder diffraction and extended x-ray-absorption fine-structure ͑EXAFS͒ measurements have been performed on the iso-structural framework crystals Cu 2 O and Ag 2 O as a function of temperature. According to diffraction, both compounds exhibit a negative thermal expansion ͑NTE͒ of the lattice parameter over extended temperature intervals ͑from 9 to 240 K for Cu 2 O, up to 470 K for Ag 2 O͒ and anisotropic thermal displacements of M atoms ͑M = Cu,Ag͒. EXAFS measures a positive expansion of the nearest-neighbors M-O pair distance and a perpendicular to parallel anisotropy of relative motion, much stronger than the anisotropy of the absolute M motion. The M-O bond is much stiffer against stretching than against bending. According to EXAFS, out of the 12 MM next-nearest-neighbor pairs, the 6 connected via a bridging oxygen undergo negative expansion, while the 6 lacking the bridging oxygen undergo positive expansion. These results show a rather complex local behavior, which, while confirming the connection of NTE to strong perpendicular vibrations, is inconsistent with rigid unit modes models and suggests a more flexible model based on rigid M-O rods.

The control of thermal expansion of solid compounds is intriguing but remains challenging. The effect of guests on the thermal expansion of open-framework structures was investigated. Notably, the presence of guest ions (K ) and molecules (H O) can substantially switch thermal expansion of YFe(CN) from negative (α =-33.67×10 K ) to positive (α =+42.72×10 K )-a range that covers the thermal expansion of most inorganic compounds. The mechanism of such substantial thermal expansion switching is revealed by joint studies with synchrotron X-ray diffraction, X-ray absorption fine structure, neutron powder diffraction, and density functional theory calculations. The presence of guest ions or molecules plays a critical damping effect on transverse vibrations, thus inhibiting negative thermal expansion. An effective method is demonstrated to control the thermal expansion in open-framework materials by adjusting the presence of guests.