## 3 Results
### Room Temperature Absorption and Emittance
Absorption is also present at the short wavelength edge as one approaches the  
Figure 6: Optical absorption spectra of (**a**) MgO:Co and (**b**) MgAl\({}_{2}\)O\({}_{4}\):Co single crystals. Cobalt ion concentration, measured by EDS, is given in the legend. The dotted lines in the MgAl\({}_{2}\)O\({}_{4}\) spectra are magnified \(\times\)20 to better appreciate the long wavelength absorption band. transmittance cut-off of the material. For higher dopant content (not shown), all bands are deeper and the one at the long wavelength shows up. Outside the absorption bands, the transmittance and reflectance backgrounds show an approximate linear dependence with wavelength. As the wavelength increases the measured reflectance decreases and the transmittance increases. These trends are stronger for the samples solidified at 750 mm/h than for the samples solidified at 50 mm/h (with coarser microstructural features). This is the consequence of smaller scattering and increased transmittance as the microstructure size decreases, and which is expected from the microstructural data given above. This behavior is different to the one observed before in undoped samples, with a 1 mm diameter, from in-line transmission measurements [18]. In that work, the samples grown at 50 mm/h solidified in the coupled regime without  
Figure 8: Measured directional-hemispherical reflectance (continuous lines) and transmittance (dotted lines) of as-grown samples Co0.04-50 (red and light-red) and Co0.04-750 (green and light-green). The incident light beam is perpendicular to the samples rod-axes. Figure 7: Sum spectrum (blue curve) calculated as the volume fraction \(\times\)\(N_{Co}\) weighted sum of MgO:Co and MgAl\({}_{2}\)O\({}_{4}\):Co absorption cross-section spectra, as to represent absorption of sample Co0.48-750. The green line is the absorption coefficient of the single crystal Spinel0.17-50. The dotted lines show the spectra magnified \(\times\)3.5.  
forming colonies, so that their microstructural size was, in fact, smaller than in samples solidified at larger pulling rates. From [PERSON]'s laws [29], the spectral directional emissivity of the material along the direction perpendicular to the rod-axis equals the directional-hemispherical absorptance. Absorptance (\(A\)) is calculated, by energy conservation, as \(A=1-R-T\), with \(R\) being the directional-hemispherical reflectance and \(T\) the transmittance. The measured values, named \(R_{m}\) and \(T_{m}\) in the following, are not the real \(T\) and \(R\). This is evident from Figure 8, as outside the absorption bands, for example at long wavelengths or at 800 nm where there is no absorption in this very low-doped samples, \(R_{m}+T_{m}\) do not add to give 1. This is most probably a consequence of integrating sphere measurements for small samples with cylindrical shape. Some of the reflected or transmitted intensity emerges from the sample, backward or forward scattered, respectively, at angles which are not collected by the integrating sphere. We will assume that \(R\) and \(T\) are related to \(R_{m}\) and \(T_{m}\) by a factor, which is a good approximation in the case of uniform reflectance or transmittance. Note that as a reference white diffuse surface we have used a flat Halon reference. The values of the proportionality factors were estimated as follows. First, \(R_{m}\) and \(T_{m}\) for each sample were normalized to give 1 at a wavelength of 850 nm, where there is virtually no absorption. This corrects difference in sample position among measurements. Then, the absorptance is estimated as:  
\[A=1-f_{r}\ R_{norm}-f_{t}\ T_{norm}, \tag{1}\]  
where \(f_{r}\) and \(f_{t}\) are found by trial and error to obtain an \(A\) curve for sample Co0.04-50 with flat \(A\approx 1\) at long wavelengths. These are \(f_{r}=0.781\) and \(f_{t}=0.219\) and were used to evaluate \(A\) for all the samples. As cross-check, for sample Co0.04-750, a flat \(A\approx 1\) background results at long wavelength, as expected.