Absolute Infrared Intensity Measurements in Thin Films. II. Solids Deposited on Halide Plates

Abstract

When a thin film of an absorbing substance is deposited on a halide plate, because of various reflection effects, the absorption coefficient measured experimentally in transmission will not correspond to the true absorption coefficient. This paper examines the relationship between this apparent absorption coefficient (α′) and the true absorption coefficient (α). Starting with a rigorous expression for the observed transmission, a relationship is established between α′ and α expressed as an infinite series in powers of d/λ (film thickness divided by wavelength). The result is valid for small d/λ. In the limit as d→0, a very simple relationship connects α and α′. For finite (but not too large) d, higher-order correction terms are derived. The theory is applied to the data of Wieder and Dows on SF6(s) deposited on AgCl and to the data of Yamada and Person on CS2(s) deposited on AgCl. For comparison and to calculate the higher-order correction terms, the data are also fit and analyzed using the damped oscillator model (DOM). The DOM results agree well with the theory. A marked change in band shape due to reflection effects is predicted for the two SF6 fundamentals. Some general suggestions are made concerning experimental procedures. It seems likely that the methods developed in this work will permit reliable corrections for reflection effects in thin film absorption measurements. In the final section, a rigorous method of treating the entire problem is outlined which is applicable, in principle, in all cases. This method depends on the fact that the transmission and phase shift can be related by a Kramers—Kronig-type dispersion relation. It is thus possible, in principle, to calculate α (and the refractive index) under any circumstances without any reference to a physical model. A preliminary application of this method to the SF6 data is presented.