Spectroscopic ellipsometry study on the dielectric function of bulk $Ti2AlN$⁠, $Ti2AlC$⁠, $Nb2AlC$⁠, $(Ti0.5,Nb0.5)2AlC$⁠, and $Ti3GeC2$ MAX-phases

The averaged complex dielectric function $ε=(2ε⊥+ε∥)/3$ of polycrystalline $Ti2AlN$⁠, $Ti2AlC$⁠, $Nb2AlC$⁠, $(Ti0.5,Nb0.5)2AlC$⁠, and $Ti3GeC2$ was determined by spectroscopic ellipsometry covering the mid infrared to the ultraviolet spectral range. The dielectric functions $ε⊥$ and $ε∥$ correspond to the perpendicular and parallel dielectric tensor components relative to the crystallographic $c$-axis of these hexagonal compounds. The optical response is represented by a dispersion model with Drude–Lorentz and critical point contributions. In the low energy range the electrical resistivity is obtained from the Drude term and ranges from $0.48μΩm$ for $Ti3GeC2$ to $1.59μΩm$ for $(Ti0.5,Nb0.5)2AlC$⁠. Furthermore, several compositional dependent interband electronic transitions can be identified. For the most important ones, $Im(ε)$ shows maxima at: 0.78, 1.23, 2.04, 2.48, and 3.78 eV for $Ti2AlN$⁠; 0.38, 1.8, 2.6, and 3.64 eV for $Ti2AlC$⁠; 0.3, 0.92, and 2.8 eV in $Nb2AlC$⁠; 0.45, 0.98, and 2.58 eV in $(Ti0.5,Nb0.5)2AlC$⁠; and 0.8, 1.85, 2.25, and 3.02 eV in $Ti3GeC2$⁠.