(Color online) Crystal structure of Bi12MO20 (M = Ti, Ge, Si). Each Bi3+ ion is considered to be surrounded by 7 O’s ions forming a (BiO7)11– distorted polyhedral, while each M4+ ion is coordinated by 4 O’s ions arranged in a (MO4)4– perfect tetrahedron.
(Color online) The local structure around the Bi ions in the BTO. Left: the structure determined on the basis of reported experimental data (Ref. 30), taken as a starting point in our calculations. Right: the resulting theoretical structure after computational optimization. A very similar situation is found for the BGO and BSO and therefore not shown here.
Calculated energy band structures in the vicinity of fundamental bandgap of the BTO (left), BGO (middle), and BSO (right) crystals along the high-symmetry directions in the first Brillouin zone. Dot line indicates the Fermi level.
Calculated total density of states (TDOS) of the BTO (top), BGO (middle), and BSO (bottom). Numbers 1-8 denote blocks of electronic states whose orbital character is described in the text. Dot line indicates the Fermi level.
Calculated partial density of states (PDOS) of the BMO’s in the energy interval which comprises blocks of states 5-7 defined in Fig. 4.
Imaginary part of dielectric function of the BTO (top), BGO (middle), and BSO (bottom) crystals directly proportional to their optical absorption spectra as a function of incident radiation energy. The ɛ 2 is interpreted in terms of electronic transitions between the groups of bands defined in Fig. 4.
The calculated reflectivity spectra of three sillenites. The experimental data (a) and (c) were taken from Ref. 14 and (b) from Ref. 16.
Calculated optical rotatory power θ F of three sillenites in a visible range. The magnitude of θ F is a measure of optical activity: greater θ F means larger activity and vice versa. The experimental data were taken from Ref. 7.
Calculated optical rotatory powers and Faraday ellipticities of three sillenites in ultraviolet range.
Real and imaginary part of diagonal component of the BTO’s dielectric tensor (top), real part of the off-diagonal component of the BTO’s dielectric tensor (middle), and optical rotatory power spectrum of the BTO (bottom), all in the range of 2–10 eV.
Calculated equilibrium lattice constants and interatomic distances (in Å) in the BTO, BGO, and BSO compared to experimental data.
Calculated equilibrium interatomic angles (°) within the Bi polyhedron in the BTO, BGO, and BSO crystals compared to experimental data.
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