## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **Nominal Composition** & **\%at Co** & **\%at Co** & **\%at Co** & **Co\({}^{2+}\)/cm\({}^{3}\)** & **Co\({}^{2+}\)/cm\({}^{3}\)** \\  & & **Sample** & **MgO** & **MgAl\({}_{2}\)O\({}_{4}\)** & **MgO** & **MgAl\({}_{2}\)O\({}_{4}\)** \\ \hline Co0.04-750 & & 0.04 \(\pm\) 0.02 & 0.14 \(\pm\) 0.02 & 0.03 \(\pm\) 0.02 & 1.5 \(\times\) 10\({}^{20}\) & 2.7 \(\times\) 10\({}^{19}\) \\ Co0.04-50 & & 0.04 \(\pm\) 0.02 & 0.13 \(\pm\) 0.02 & 0.03 \(\pm\) 0.02 & 1.4 \(\times\) 10\({}^{20}\) & 2.7 \(\times\) 10\({}^{19}\) \\ Co0.12-50 & & 0.12 \(\pm\) 0.02 & 0.36 \(\pm\) 0.02 & 0.08 \(\pm\) 0.02 & 3.9 \(\times\) 10\({}^{20}\) & 8.6 \(\times\) 10\({}^{19}\) \\ Co0.15-750 & & 0.15 \(\pm\) 0.02 & 0.53 \(\pm\) 0.025 & 0.07 \(\pm\) 0.02 & 5.7 \(\times\) 10\({}^{20}\) & 7.6 \(\times\) 10\({}^{19}\) \\ \hline Co0.22-50 & & 0.22 \(\pm\) 0.02 & 0.69 \(\pm\) 0.03 & 0.12 \(\pm\) 0.02 & 7.4 \(\times\) 10\({}^{20}\) & 1.3 \(\times\) 10\({}^{20}\) \\ Co0.29-750 & 67.09 MgO-32.41 Al\({}_{2}\)O\({}_{3}\)-0.5 Co\({}_{3}\)O\({}_{4}\) & 0.29 \(\pm\) 0.02 & 1.02 \(\pm\) 0.03 & 0.16 \(\pm\) 0.02 & 1.1 \(\times\) 10\({}^{21}\) & 1.7 \(\times\) 10\({}^{20}\) \\ Co0.48-750 & & 0.48 \(\pm\) 0.02 & 1.69 \(\pm\) 0.03 & 0.26 \(\pm\) 0.02 & 1.8 \(\times\) 10\({}^{21}\) & 2.8 \(\times\) 10\({}^{20}\) \\ \hline Spinel0.06-50 & 49.89 MgO-49.89 Al\({}_{2}\)O\({}_{3}\)-0.22 Co\({}_{3}\)O\({}_{4}\) & 0.06 \(\pm\) 0.01 & - & 0.06 \(\pm\) 0.01 & - & 5.9 \(\times\) 10\({}^{19}\) \\ \hline Spinel0.17-50 & 49.62 MgO-49.62 Al\({}_{2}\)O\({}_{3}\)-0.76 Co\({}_{3}\)O\({}_{4}\) & 0.17 \(\pm\) 0.01 & - & 0.17 \(\pm\) 0.01 & - & 1.8 \(\times\) 10\({}^{20}\) \\ \hline Spinel0.29-50 & 48.75 MgO-48.75 Al\({}_{2}\)O\({}_{3}\)-2.5 Co\({}_{3}\)O\({}_{4}\) & 0.29 \(\pm\) 0.014 & - & 0.29 \(\pm\) 0.014 & - & 3.0 \(\times\) 10\({}^{20}\) \\ \hline MgO:Co & - & 0.14 \(\pm\) 0.01 & - & 1.5 \(\times\) 10\({}^{20}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nominal composition (%mol) and composite-, MgO- and MgAl\({}_{2}\)O\({}_{4}\)- cobalt contents (%at) for all the samples. Atomic Co percentages were determined by EDS; Co\({}^{2+}\) ions/cm\({}^{3}\) in each phase were calculated using cobalt atomic content obtained by EDS and volume of MgO and MgAl\({}_{2}\)O\({}_{4}\) single crystal lattices. The atomic Co percentages are given relative to the total number of ions in the sample or phase, including oxide ions calculated by stoichiometry. MgAl\({}_{2}\)O\({}_{4}\) cobalt-doped crystals around 0.7 mm thick and a 2.4 mm thick prism of MgO:Co were used for the in-line absorption measurements. Directional hemispherical transmittance and reflectance was measured on 7 mm long pieces of the as-grown rods. The internal-DRA accessory coupled to the Cary UV-VIS-NIR spectrometer was used. It consists of a 110 mm diameter integrating sphere coated with PTFE and with transmittance and reflectance sample ports. The sample bars were inserted into a 2 \(\times\) 7 mm\({}^{2}\) slit cut in an absorbing flexible diaphragm fitted into the respective port for the measurements. Transmittance measurements were made against the empty slit-cut diaphragm, and for 100% reflectance reference we used a flat Halon reflector on the slit-cut diaphragm. The incident light beam hit the samples perpendicularly to the rod axis.