Temperature dependence of intrinsic infrared absorption in natural and chemical-vapor deposited diamond

Empirical rules are derived that describe the temperature dependence of the infrared absorption spectra of pure diamond for photons of energy hν=500–4000 cm−1. We show that with increasing temperature in the range 14<T<850 K, all the features in the infrared spectrum shift to lower frequency at very similar fractional rates. The rate for all the features is, to ±13%, Δν/ν=cn(Ee) where c=−0.027 and n(Ee) is the Bose–Einstein population factor with Ee=860 cm−1. The intensities of the optical absorption involving the creation of two phonons of energies E1 and E2 are expected to increase with T in proportion to [1+n(E1)][1+n(E2)]. This expression, combined with the fractional shift rule for the energies of each mode, allows high temperature two-phonon spectra to be simulated accurately from a low temperature spectrum. The temperature dependence of the three-phonon band between 2665 and 3900 cm−1 is precisely fitted without adjustable parameters by using the shift rule in conjunction with a modified density of three-phonon states. Absorption at 10.6 μm is shown to involve the simultaneous destruction and creation of phonons. Its strong temperature dependence in the range 300<T<800 K is accurately described, without any adjustable parameters, in terms of three main components: the destruction of one phonon of 335 cm−1 and the creation of a second of 1275 cm−1; the shift to lower energy of the phonons; and a three-phonon process involving the destruction of one and the creation of two phonons. The analysis demonstrates why diamond has to be effectively cooled when used for the windows of a high-power CO2 laser.