Infrared reflectance, transmittance, and emittance spectra of MgO from first principles

By using density functional theory calculations we determined the influence of anharmonic effects on the infrared reflectance, transmittance, and emittance of MgO. The goal is to determine the limit of validity of a perturbative (multiphonon) approach. MgO is chosen as a test material because of the availability of different kinds of radiative properties measured experimentally. Nonanalytic terms of the three-phonon scattering coefficients are explicitly calculated and do not provide measurable effects. The agreement is overall very good to such an extent that, already at room temperature, one can clearly identify regions in which four-phonon scattering processes are dominant with respect to the three-phonon ones. The influence of isotopic disorder at cryogenic temperatures is also settled.

Figure 1

(a) and (b) MgO infrared room-temperature reflectance and transmittance for a $d=0.3$ mm thick plate. Measurements (exp.) are from Ref. [14]. All the other lines are calculations done at the different levels of approximation described in the text. $\mathrm{\Pi }\left(\omega \right)$ represents our best result. The vertical arrow indicates the harmonic TO phonon frequency. (c) and (d) $\mathrm{\Gamma }\left(\omega \right)=-\mathrm{Im}\left[\mathrm{\Pi }\right(\omega \left)\right]$, where $\mathrm{\Pi }$ is the calculated self-energy of the TO mode, Eq. (4). Data taken from Ref. [14] (exp.) vs the present calculation (tot.) decomposed into three-phonon (3ph), four-phonon (4ph), and isotopic-disorder (isot.) contributions. (c) and (d) report the same data on different scales.

Figure 2

IR reflectivity at various temperatures: calculations (calc.) vs measurements (exp.) from Ref. [35].

Figure 3

IR emittance at various temperatures: calculations (calc.) vs measurements (exp.). (a) Measurements from Ref. [14] (the same as in Fig. 1) and (b) measurements digitized from Ref. [36]. Here, $d$ is the thickness of the plate. Dotted lines are $T=295$ K calculations including only three-phonon scattering (and not four-phonon ones).

Figure 4

Temperature evolution of the MgO transmittance for a 0.5-mm-thick plate. Dots are measurements digitalized from [37]. Dotted lines are calculations in which the isotopic-disorder contribution is set to zero. Solid lines are our best calculations (which include isotopic disorder).

Figure 5

Calculated imaginary part of the dielectric constants and extinction coefficient at various temperatures.

Figure 6

Room-temperature emissivity (defined as $1-\tau$) calculated for various thicknesses $d$. (a) Present calculations. (b) Data digitalized from Ref. [38] (see the text).

Figure 7

Self-energy of the q = 0 optical phonon of MgO at room temperature: variation of the imaginary part after the inclusion of the nonanalytic corrections to the three-phonon scattering. $\mathrm{\Delta }\mathrm{\Gamma }\left(\omega \right)$ is defined in the text.