Far infrared absorption in ultrafine metallic particles: Calculations based on classical and quantum mechanical theories

Detailed calculations of far infrared absorption in ultrafine metallic particles are reported. Effective medium treatments of the composite of particles and their surrounding are carried out within the Maxwell Garnett and Bruggeman theories. Generalizations of these to encompass dipole-dipole interaction and oxide pellicles are discussed. The dielectric permeability of the particles is specified either by the Drude (D) model with a size limited mean free path, or by the quantum mechanical derivation of Gor'kov and Éliashberg (GE). Excepting narrow diameter (x) and frequency ( ) intervals the absorption coefficients can be approximated by =fCx , wheref is the filling factor (taken to be small),C is a constant which depends on the free electron parameters, and and are integers. Results for largerfs are included also. The magnitudes ofC, and differ in general for the Drude and Gor'kov-Éliashberg theories; they are also different forxx ^C , wherex _D ^C 5 nm andx _GE ^C is typically 20 nm. The quantityx ^c signifies a transition from a range where is dominated by the dielectric polarisation to one where the magnetic polarisation is largest. An interesting multiple peak structure is found from detailed calculations of _GE vs. for sufficiently small identical particles. Effects of log-normal size distributions are derived explicitely; any fine structure in the _GE vs.x functions is found to be completely washed out for practically attainable distribution widths.Work at Cornell University was supported by the National Science Foundation through the Materials Science CenterWork at Chalmers University of Technology was supported by the Swedish Natural Science Research Council