## 2. Optical properties of dustThe two sets of quantities that are used to describe optical
properties of solids are the real and imaginary parts of the complex
refractive index and the real and
imaginary parts of the complex dielectric function (or relative
permittivity) =
+ .
These two sets of quantities are not independent, the complex
dielectric function is related to the
complex refractive index, The problem of evaluating the expected spectral dependence of
extinction for a given grain model (i.e. assumed composition and size
distribution) is essentially that of evaluating the extinction
efficiency . It is the sum of
corresponding quantities for absorption and scattering;
. These efficiencies are functions of
two quantities; a dimension-less size parameter
(where
the grain radius and
the wavelength) and a composition
parameter, the complex refractive index A limit case within the Mie theory is the Rayleigh approximation for spherical particles. This approximation is valid when the grains are small compared to the wavelength, and in the limit of zero phase shift in the particle (). In the Rayleigh approximation the extinction by a sphere in vacuum is given as: ## 2.1. Measuring methods of optical propertiesA proper application of Mie theory to experimental data requires that the samples are prepared such that the particles are quite small (usually sub-micrometer), well isolated from one another, and that the total mass of particles is accurately known. In order to obtain single isolated homogeneous particles, the grains are often dispersed in a solid matrix. Small quantities of sample are mixed throughly with the powdered matrix material e.g. KBr or CsI. The matrix is pressed into a pellet which has a bulk transparency in the desired wavelength region. Some of the problems with this technique are that there is a tendency for the sample to clump along the outside rim of the large matrix grains and that the introduction of a matrix, which has a refractive index different from vacuum, might influence the band shape and profile. This matrix effect can be a problem for comparisons of laboratory measurements with astronomical spectra (Papoular et al. 1998; Mutschke et al. 1999). By measuring the sample on a substrate (e.g. quartz, KBr, Si or NaCl) using e.g. an infrared microscope, the matrix effect can nearly be avoided since the sample is almost fully surrounded by a gas (e.g. air, Ar or He). But the amount of material in the microscopic aperture remains unknown, which is an important disadvantage of this method. Therefore, these measurements are not quantitative but they reveal the shape of the spectrum nearly without a matrix effect (Mutschke et al. 1999). A major problem of both methods is clustering of the grain samples
either during the production of the particles or within the matrix or
on the substrate. Clustering can cause a dramatic difference in the
optical properties (Huffman 1988). A way to avoid this problem is to
perform the optical measurements on a polished bulk sample. For the
determination of both © European Southern Observatory (ESO) 1999 Online publication: August 25, 1999 |