Emissivity Control

Kirchhoff's law: at each wavelength and direction a surface emits as well as it absorbs, ε(λ) = A(λ). The substrate is taken as opaque (it absorbs everything the coating lets into it), so A = 1 − R and ε_nis the Planck-weighted 1 − R at normal incidence over the band. That holds for metals and for glass or oxides thick enough to absorb in the thermal IR; for a substrate that is transparent there (Si or Ge at 10 µm, say) light passes through instead, ε is lower and this page overstates it. A thin metal film is the low-e layer: its free electrons reflect the thermal IR. The overcoat is lossless with a constant index; real oxides absorb in parts of the thermal IR, which adds emittance. Ag uses the n, k Yang et al. (2015) measured on template-stripped silver (a matched Drude term beyond 24.9 µm), Al and Cr the Rakić et al. (1998) Lorentz–Drude model; real films, thin ones above all, emit more. Cr's fit was made to about 62 µm (0.02 eV); beyond that it is a Drude extrapolation. The default substrate is a lossless n = 1.52 stand-in, so its bare emittance is higher than real soda-lime glass (≈ 0.84 – 0.89, which has a reststrahlen band near 9–10 µm); enter n, κ for the thermal IR for real glass. Hemispherical emittance, which radiative heat loss uses, differs from ε_n: higher for metals, lower for dielectrics.