P. Fornasini

EXAFS Debye-Waller factor and thermal vibrations of crystals.

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.

On the cumulant analysis of EXAFS in crystalline solids

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.

Einstein and Debye models for EXAFS parallel and perpendicular mean-square relative displacements.

The correlated Einstein and Debye models for EXAFS parallel mean-square relative displacement (MSRD) are derived from the general expression in terms of eigenfrequencies and eigenvectors of the dynamical matrix, without ad hoc assumptions. The two models are generalized to parameterize also the EXAFS perpendicular MSRD. The physical meaning of Einstein frequencies, as well as the application of the Debye model to crystals with more than one atom per cell, are critically discussed.

Study of lattice dynamics via extended x-ray absorption fine structure

EXAFS (extended x-ray absorption fine structure), besides being a powerful structural probe, can also give original information on local dynamics in solids. EXAFS is peculiarly sensitive to the correlation of vibrational motion, both parallel and perpendicular to the bond direction, and to anharmonicity. This paper contains an introduction to the effects of thermal disorder on EXAFS of crystals and to the data analysis based on the cumulant expansion. Cumulants are easily connected to average local vibrational properties. Recently obtained experimental results concerning the mean square relative displacement and the thermal expansion in crystals confirm the potentialities of EXAFS as a dynamical probe.

EXAFS studies of silver ion coordination in silver borate glasses

EXAFS measurements at the K and L 3 edges of silver have been performed on the binary ion conducting glasses (Ag 2 O · n B 2 O 3 ), with n = 2, 3, 4, 6. The first coordination shell of silver is characterized by a mean Ag-O distance r = 2.27 A and a very low coordination number ( N 2). This result indicates the presence of a local structure in the environment of the silver cation, almost independent of the Ag 2 O content. This structure is different from those found in crystalline silver-borate compounds and in sodium-borate glasses. For the vitreous Ag 2 O · 2B 2 O 3 a further coordination Ag-O with r = 1.99 A is singled out, confirming the possible bond between silver ions and non-bridging oxygens at high Ag 2 O content.

Absolute total cross section measurements for intermediate energy electron scattering. II. N2, O2 and NO

For pt.I, see ibid., vol.12, p.3787 (1979). Total absolute cross section measurements are presented for electrons scattered by O2, N2 and NO molecules. The energy range covered spans from 100 to 1600 eV. Neglecting the systematic error introduced by the finite angular resolution of the apparatus, the experimental accuracy has been estimated to be +or-2.5%. This systematic effect could necessitate an upward correction of as much as 13% at 1000 eV in N2. No similar evaluation was possible for O2 and NO. A comparison is given for N2 with existing measurements. The agreement is reasonable. The results for O2 are compatible with the existing data in the low-energy range. No comparison was possible for NO.

The thermal behaviour of cuprite: An XRD–EXAFS combined approach

Abstract Cuprite (Cu2O) is a low thermal expansion material with a negative thermal expansion coefficient below room temperature. Its peculiar thermal behaviour encompasses the increase of the shear modulus with increasing temperature, and the presence of rather intense symmetry-forbidden eeo reflections below room temperature. The thermal expansion of cuprite was studied at low temperature (between 5 and 298 K) by means of high-resolution (10−5 A) X-ray powder diffraction at European Synchrotron Radiation Facility (Grenoble, BM16) and extended X-ray absorption fine structure (EXAFS) (BM29). Negative thermal expansion is confirmed up to 200 K, by EXAFS as well as by XRD measurements, and no sign of transition was found in XRD data. The comparison between EXAFS and XRD results provides a valuable insight into vibrational behaviour of cuprite at low temperature.

Short range order in AgI:Ag2O:B2O3 glasses: results from EXAFS and related techniques

Abstract The structure of the (AgI) x (Ag 2 O n B 2 O 3 ) 1−x superionic conducting glasses is being studied by X-ray absorption spectroscopy (EXAFS and related techniques). This paper reviews the results obtained up to date. The information obtained concerns the local environment of silver and iodine atoms and allows us to place constraints on the structural models consistent with the conductivity properties of the glasses.

On the sensitivity of the x-ray excited optical luminescence to the local structure of the luminescent Si sites of porous silicon

X-ray excited optical luminescence (XEOL) has been recorded in a wide x-ray energy range to obtain the extended x-ray absorption fine structure (EXAFS) at the Si K edge of porous silicon. A comparison between EXAFS measurements carried out simultaneously in photoluminescence yield (PLY) mode and in total electron yield (TEY) mode on red and orange porous silicon samples is presented. Experimental results suggest that TEY provides average structural information on all luminescent and nonluminescent Si sites. On the contrary, PLY is able to probe the local structure near the light emitting sites, and to monitor the modifications induced by current density changes during the sample preparation. PLY–EXAFS shows that the luminescent Si nanostructures are smaller and more disordered than the average structures of the porous layer probed by TEY, suggesting that the luminescent sites are located at the surface of the nanostructures.

Optical and X-ray absorption measurements on superionic (AgI)x(Ag2On B2O3)1−x glasses

Abstract The glasses (AgI) x (Ag 2 O n B 2 O 3 ) 1−x have been studied by optical and X-ray absorption spectroscopy at various x and n concentrations. The optical absorption of the n=4 glasses shifts linearly at the increasing of the AgI content x. Extrapolating to x=1, the corresponding value for α-AgI is crossed. The comparison of the EXAFS structures at the I L 3 edge of the n=3, x=0.3 glass and of β-AgI seems to indicate that the Ag-I coordination is substantially unmodified in the glass with respect to that in β-AgI. A further comparison of the EXAFS at the Ag L 3 edge allows to discuss the coordination Ag-O in the glass.