lecture notes2

This is because of causality electric polarization p

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Unformatted text preview: rbitals of the carbons can mix with each other, z such that the energy eigenstates are complicated linear combinations of these orbitals. The hydrocarbon is considered aromatic when the electrons occupying these levels can arrange themselves to give a lower energy (and hence greater stability) than one would expect by counting double bonds. Such structures often, but not always, involve hexagons. 5 atoms carry a single negative charge, and must be balanced by the incorporation of positive ions (e.g. Mg2+, Fe2+), leading to olivines (stoichiometry MgxFe2−xSiO4) or pyroxenes (stoichiometry MgxFe1−xSiO3). The silicate minerals may either be crystalline or amorphous; while crystalline silicates are observed in circumstellar material, the silicate content of ISM dust appears to be amorphous (narrow crystalline mid ­IR features not observed). In special environments, one may consider other grain materials: diamond, Si, SiC, Fe, iron oxides, etc., and in some cases there is evidence for these. In cold, dense environments, IR absorption spectroscopy also shows that ice mantles (including H2O) have condensed onto grain surfaces. B. DIELECTRIC CONSTANTS: GENERAL PROPERTIES The dielectric constant of a material is a function of frequency. It consists of a real part (conservative) and an imaginary part (dissipative). Both are needed to compute optical properties. However, it is a remarkable fact that the functions Re χ(ω) and Im χ(ω) encode precisely the same information, thereby allowing us to infer all optical properties of a material from its absorption Im χ(ω). This is because of causality: electric polarization P is caused by the electric field E, and the cause must precede the effect. In particular, if Ex is a δ ­function at...
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