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In the concept of superspatial symmetry the crystal structure of Cu7SiS5I and Ag7SiS5I superionic conductors has been analyzed. To calculate the phonon spectra, the model of FCC superlattice (8а, 8а, 0; 8а, 0, 8а; 0, 8а, 8а) in the metric of protocrystal (а, а, 0; а, 0, а; 0, а, а) has been developed. For the developed model, the general (3+3)-dimensional basis, the array of modulation vectors and mass modulation functions have been presented. The model calculations of phonon spectra dispersion for Cu7SiS5I and Ag7SiS5I crystals in schemes with various partial occupation of crystallographic orbits by Cu(Ag) atoms have been performed. The dispersion dependences of phonon spectra for Cu7SiS5I and Ag7SiS5I crystals in the high-symmetric directions of Brillouin zone have been presented. The genesis of phonon branches of vibrational spectra has been analyzed.

Within the score of the density functional theory, we investigate the impact of point defects on the electronic structure of Hg3Te2Cl2 crystals, by using the supercell model [2×2×1]. The ab initio calculations for defect-free and defective Hg3Te2Cl2 crystals in the LDA approximation are performed for the first time, by using the quantum-chemical software package SIESTA. The studied crystal possesses an indirect band gap. According to the analysis of the obtained data, the indirect gap is equal to 2.628 eV, while the direct gap is 2.714 eV. The influence of vacancy defects on the conductive and optical properties of Hg3Te2Cl2 crystals is discussed in detail. The tellurium and chlorine vacancy defect states indicate the presence of additional energy levels below the bottom of the conduction band edge. We have shown that only tellurium vacancies produce the additional energy levels in a vicinity of the valence band maximum. It is found that the presence of point defects in Hg3Te2Cl2 changes the direction of optical transitions. Therefore, the defective crystal is a direct gap semiconductor. The satisfactory agreement with the experimental data is obtained., Представлено результати розрахункiв в рамках теорiї функцiонала густини для дослiдження впливу точкових дефектiв на електронну структуру кристалiв Hg3Te2Cl2 з використанням моделi суперкомiрки [2×2×1]. Вперше проведено ab initio розрахунки для бездефектних та дефектних кристалiв Hg3Te2Cl2 в наближеннi локальної густини, використовуючи квантово-хiмiчний програмний пакет SIESTA. Дослiджуваний кристал є непрямозонним напiвпровiдником. Згiдно з аналiзом отриманих даних, величини непрямого та прямого переходiв становлять 2,628 еВ та 2,714 еВ вiдповiдно. Вплив дефектiв вакансiй на провiднi та оптичнi властивостi кристалiв Hg3Te2Cl2 обговорюється в деталях. Дефектнi стани вакансiй телуру та хлору створюють додатковi енергетичнi рiвнi нижче дна зони провiдностi. Результати дослiдження показують, що тiльки вакансiї телуру створюють додатковi енергетичнi рiвнi в околi вершини валентної зони. Встановлено, що присутнiсть точкових дефектiв в кристалах Hg3Te2Cl2 змiнює напрямок оптичних переходiв i тому дефектний кристал є прямозонним напiвпровiдником. Одержано задовiльне узгодження з експериментальними даними.

This paper presents a systematic first-principles study of phonons and Raman spectra of cubic Hg 3 Te 2 Cl 2 within a framework of DFT in the GGA/PBE approximation. The phonon dispersion, total and partial density of vibrational states for Hg 3 Te 2 Cl 2 crystals are analyzed. The identification of the vibrational modes at the Brillouin zone center is conducted and discussed in details. The first-principles calculated Raman-active phonon frequencies and simulated Raman spectra are compared with experimental data. The assignment of the phonon lines to define atomic vibrations was made on the basis of their symmetries in close comparison with results of lattice-dynamical calculations. Satisfactory agreement is obtained with experimental mode frequencies.

The interrelation between structural and optical properties of the Hg 3 S 2 Cl 2 polymorphs have been theoretically investigated. This paper presents the results of calculations of the refractive indices and reflection coefficients for (α), (β), (γ) – Hg 3 S 2 Cl 2 crystalline phases using the Harrison bonding-orbital method. The refractive indices in the spectral region far from the absorption edge were determined within the generalized single-oscillator model. The Hartree-Fock values for the valence levels were used for evaluation the energies of filled electronic states in Hg 3 S 2 Cl 2 crystals. By analyzing the polarizability and susceptibility χ it is possible to calculate the refractive index and reflection coefficient; moreover the performed calculations demonstrate a satisfactory agreement with experimental results.

The phonons of two end members of Li1+xTi2-xO4 spinel system, i.e., the metallic LiTi2O4 and the insulating Li[Li1/3Ti5/3]O4, are calculated in superspace symmetry approach using a short-range force constant model. The composition dependence of zone-centre optical phonons in Li1+xTi2-xO4 near phase transition and Li1-xMgxTi2O4 has been investigated using different models of substitution. One- and two-mode behavior is therefore predicted for F1u and F2u modes in case of tetrahedral and octahedral substitution, respectively.