The mean-square vibrational amplitude and isomer shift of gold atoms in small particles of gold metal embedded in gelatin were investigated by the Mössbauer effect. Nine samples with average particle diameters of 30-170 Å were examined, three of which (31, 52, and 168 Å) as function of temperature. All samples showed different, but positive, isomer shifts with respect to bulk gold without an apparent correlation with the particle size. At 4.2°K the Mössbauer fraction shows no significant difference with bulk gold, whereas at higher temperatures the Mössbauer fraction decreases more rapidly when the particle size becomes smaller. This temperature dependence is analyzed within the framework of the Debye continuum theory of lattice vibrations, which is a good approximation in case of bulk gold. It is shown that neither the application of a low-frequency cutoff on the phonon spectrum, nor the contribution of surface and edge modes or an independent treatment of bulk and surface atoms gives a satisfactory explanation of the observations, but, that the vibration of the particle as a whole has to be taken into account, which overshadows possible size effects.

• Received 24 May 1976

DOI:https://doi.org/10.1103/PhysRevB.15.72