Influence of microstructure on the optical properties of particulate materials: Gold black

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Abstract
A model is developed for the optical properties of particulate media within the realm of effective-medium theory, and is applied to gold black. This model assumes that the experimentally observed chains-of-spheres structure of the gold strands composing gold black can be approximated by spheroids (ellipsoid of revolution) for which the depolarization factor is well known from electrostatic theory. It is shown that the spheroid model is a generalization of the capacitor model of the optical properties of gold black. The spheroid model is applied to several gold blacks produced by inert-gas evaporation. It is found that excellent agreement between experimental and theoretical transmittance can be achieved in the solar spectrum by using a distribution of spheroids (gold-black strands) that is closely approximated by a log-normal function of the spheroid semimajor to semiminor axis ratio. An interpretation of the physical significance of this distribution is proposed. Experimental results for parameters such as packing factor and sample thickness are used without modification. Experimental data for the optical properties of bulk gold are used with a modification to account for an increase in the electron collision frequency due to scattering from the surfaces of the small gold crystallites.