Temperature dependence of EXAFS cumulants of Ag nanoparticles in glass

Ag nanoparticles of 1.5 to 7 nm size were produced by ion exchange of soda-lime glass for various duration. Information on local order and thermal vibrations were available by means of X-ray absorption spectroscopy using experiments at the Ag K-edge (25.514 keV). Ratio method and EXAFS fitting procedure were successfully applied to reveal the temperature dependence using the cumulant-expansion method up to third order ones. The temperature dependence of the nearest neighbor Ag-Ag distance appears different from that of polycrystalline Ag foil below 400 K. This effect can be explained by a thermoelastic model describing the mismatch of thermal expansion coefficients of Ag particles and the glass matrix. In addition, the parameter of Ag-Ag bond length of 1.5 nm particles is governed by precursor formation for crystalline Ag nanoparticles. The data of the second cumulant, the Debye-Waller factor (DWF), represent a higher static disorder, especially for nanoparticles of 1.5 - 3.5 nm size, caused by the increasing portion of surface or interface atoms. From the temperature dependent part of DWF we estimated a slightly increased Einstein temperature.