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=500-4000cm ^-1. We show that with increasing temperature in the range 14<T<850K, 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(E _e) where c=-0.027 and n(E _e) is the Bose-Einstein population factor with E _e= 860cm ^-1. The intensities of the optical absorption involving the creation of two phonons of energies E ₁ and E ₂ are expected to increase with T in proportion to [1+n(E ₁)][1+n(E ₂)]. 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<800K 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 CO ₂ laser.