Annotation of the results obtained in 2020
1. In this work porous metal-inorganic frameworks WN10 (WN8 N2) and Os5N34 (Os5N28 3N2) with polymer nitrogen chains and guest molecules, obtained at a pressure of P ~ 100 GPa were studied. Research in collaboration with experimenters using synchrotron single-crystal X-ray diffraction and calculations within the density functional theory framework showed that WN8 N2 crystallizes in the rhombic space group Immm, consisting of one W and two nitrogen atoms in an independent asymmetric unit. The W atoms are coordinated with four planar polymer nitrogen chains. The WN8 3D framework has rectangular channels occupied by nitrogen molecules. Os5N28·3N2 crystallizes in the orthorhombic space group Pnnm, with two types of nitrogen units: N-N dumbbells and polyacetylene-like chains in the structure. The distance between nitrogen atoms in dumbbells varies in the range 1.22-1.33 Å, which is typical for a double bond. The framework contains rectangular and octagonal channels occupied by nitrogen molecules. Note that, the initial structural solution was precisely established experimentally only for the Os5N28 framework due to the presence of heavy Os atoms and the incompleteness of the X-ray diffraction data due to the experiment in a diamond anvil. The exact concentration of guest nitrogen molecules was established using theoretical calculations within the density functional theory framework showed that the final structure has the formula Os5N28·3N2. An important factor in the stability of the polymer nitrogen chain is resonance, which gives the character of a partial double bond for nitrogen-nitrogen bonds. These compounds have metallic properties due to electronic delocalization. The performed theoretical calculations of the density of states (DOS) for synthesis volumes (which corresponds to a pressure P ~ 95-110 GPa) and volumes corresponding to the calculated ambient pressure (P~0 GPa) showed that the main contribution to the density of states at the Fermi level is made by nitrogen chains that form delocalized π-bonds formed by nitrogen electrons and metal electrons obtained as a result of ionic interaction. In addition to the weak π-bond in the chains the nitrogen atoms in the polymer chains, dumbbells and molecules have a strong covalent bond, as shown by the calculated electron localization function (ELF). Analysis of the atomic bond between nitrogen and metal (Me = Os, W) reveals different types of ELF maxima, including those corresponding to the heteroatomic polar bond, where the pseudo sp2-lone pair is involved in the formation of the dative bond, which serves to enhance stability of connections in addition to the ionic component. Calculation of the optimized structure based study of the unit cell volumes pressures dependence of the studied structures was carried out showed that the calculated P-V values are in good agreement with the available experimental values. The phonon dispersion ratios calculated for the WN10 and Os5N34 show dynamic stability of this compounds at high pressures, as evidenced by the absence of imaginary phonon modes. The research results are published in [Angewandte Chemie - International Edition Volume 59, Issue 26, 22 June 2020, Pages 10321-10326]. 2. Studying the properties of bcc alloys of the Ti-V system was carried out. It was found that the mixing enthalpies calculated at high temperatures using ab initio molecular dynamics are positive for all V concentrations, in contrast to traditional static calculations with complete relaxation of atomic positions at T = 0 K, which predict negative values for alloys with low vanadium concentrations. Experimental measurements of the mixing enthalpy of bcc Ti-V alloys were carried out within the framework of the project since we were unable to find any experimental data in the literature. Four Ti-V alloys (10, 12, 15, 20 at. % V) were prepared for experimental studies. Calorimetric studies were carried out using the drop solution method for experimental determination of the bcc Ti-V alloys mixing enthalpies. The measurements were carried out on an isoperibol high-temperature Alexsys 1000 (Setaram, France) Tian-Calvet calorimeter. The instrument is equipped with a 3D sensor that provides high sensitivity and accuracy. The measurements were carried out in an atmosphere of high-purity protective argon (99.998%) in crucibles (Al2O3). It was shown that the mixing enthalpy calculations at high temperatures are in much better agreement with the experimental data. The inconsistency of the static approach adopted at zero temperature is associated with the dynamic instability of the bcc phase of Ti and its alloys at 0 K. This work shows the importance of lattice vibrations in thermodynamic properties theoretical predictions, especially for systems with dynamic instability, since in this case, atomic vibrations lead to a significant change in the local crystal structure near impurity atoms, which radically affects the properties of the material. The results of the study of alloys of the Ti-V system are published in [Acta Materialia Volume 188, 15 April 2020, Pages 145-154]. 3. Using the temperature-dependent effective potential method (TDEP) with full consideration of the anharmonic effects of lattice vibrations, the temperature-dependent Kohn anomalies between the H – H and H – N directions were studied for phonon frequencies in bcc niobium. The vanishing of these anomalies with increasing temperature becomes clearly noticeable when compared with the quasi-harmonic results at finite temperatures. From a slight smearing and shift of the phonon spectral functions, it was concluded that phonon-phonon interactions are practically insignificant. Consequently, the main effect on phonons with increasing temperature between Г-H and Г-N gives a change in the electronic structure and its change is associated with the smearing of electronic states. This blurring affects the effective Fermi surface. It has also been demonstrated that the divergence in electron-phonon scattering is self-destructible, which means that there will be no sharp “kinks” in the phonon dispersion for nesting vectors. This is because the nesting of the Fermi surface will result in diffusion of the Fermi surface, and the nesting vector will no longer contain two parallel sharp segments, and therefore only smooth bends will be observed. Research findings are published in [Physical Review B Volume 101, Issue 11, 15 March 2020 Article Number 115119] 4. The influence of pressure on the thermodynamic stability of the new high-pressure phase Re7N3 was investigated. For this, within the density functional theory, the formation enthalpies of the Re-N system various phases with different nitrogen contents were calculated. It is shown that pressure and temperature stabilize the new Re7N3 phase. The paper has been prepared for publication. 5. When studying the effect of stresses on the behavior of disordered alloys based on bcc Fe, it was shown that the mixing enthalpies ΔH of binary Fe-Cr alloys at 0 GPa and under pressure are in good agreement with the previously calculated data. The pressure behavior of three-component alloys containing nickel and aluminum was also investigated. In addition, the behavior of four-component alloys under pressure, containing from 0 to 20 wt. % Cr and Ni, and additions of Nb, Mo, W, V was investigated. 6. Within the framework of the DFT + DMFT method, the electronic state, magnetic and lattice properties of the Fe3CO7 compound under pressure (at T = 390 K) were studied. The equation of state parameters obtained from the calculations are in good quantitative agreement with the experimental data. A systematic study of the electronic structure, spin and valence state of range of Fe(Si1-xFex)O3 compounds with x = 0, 0.15, and 0.25 at a high pressure of ~ 140 GPa was also performed. The calculations are in good quantitative agreement with the experimental data. 7. Within the framework of the DFT + DMFT method, the electronic structure and magnetic properties of Mn2GaC MAX phase were studied. The results indicate the extreme sensitivity of the local magnetic moments of Mn2GaC to the choice of the Hund exchange interaction J and allow us to conclude that Mn2GaC is a Hund metal, which is located in the phase diagram near the region of local magnetic moments formation. 8. During the study of the Re-C system properties, we analyzed the relaxed structures of rhenium carbide ReC2, which showed that the minimum distance between carbon atoms in monoclinic structures decreases. For the lattice with the minimum energy, the closest distance between carbon atoms is 1.587 Å, which is only 3% more than in diamond. This may indicate the appearance of a covalent bond between carbon atoms within the chain, the formation of which, based on the type of the energy profile, greatly reduces the total energy of the system. An analysis of the phonon dispersion revealed dynamic instability at the Г point in tetragonal and monoclinic structures. Along with the data on the energy profile, this may indicate the existence of a structure with even lower energy. Analysis of the lattice parameters dependence on the fraction of stacking faults shows that all three parameters simultaneously approach the experimental values at a defect concentration of about 20%. The energy dependence of structures with defects suggests that if the experimentally observed lattice parameters can be explained by the presence of stacking faults in atomic layers, then most likely this system is metastable, since a decrease in the fraction of ordered layers leads to an increase in the total energy. 9. In the framework of the project, the electronic structure and properties of single-layer BeN4 were investigated. The calculated band structure and DOS showed that, in contrast to bulk BeN4, which is a metal, single-layer BeN4 is a Dirac semimetal with linear dispersion in the vicinity of the Fermi energy and two Dirac points coinciding with the Fermi energy, which is similar to graphene. The paper has been prepared for publication. 10. A thermodynamic description of the Ca - O system was proposed, including the description of the third generation of crystalline, liquid and amorphous CaO, as well as crystalline CaO2. To describe the thermodynamic properties of the CaO and CaO2 phases, the Einstein model with additional terms, according to the proposals adopted at the Ringberg 1995 seminar, was used Additional terms allow us to take into account the transfer from the heat capacity at constant volume to the heat capacity at constant pressure, anharmonic effects, the presence of vacancies, etc. During the optimization process, it was found that a satisfactory agreement with the high-temperature heat content data selected for crystalline CaO cannot be obtained using the additional terms in the form of temperature polynomials used so far in 3rd generation models. To achieve a correct description of thermodynamic properties at high temperatures, in this work, the terms Texp (A + BT) or T / (A + BT) ^ 3 were used, which allowed to obtain a reliable description of the crystalline CaO properties up to the melting point. The liquidus curve of the Ca - CaO system obtained as a result of calculations with the new model describes the existing data much better in comparison with the two previous models of the Ca-O system.

 

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Annotation of the results obtained in 2018
The main goal of this project is to carry out first-principle modeling of the behavior of pure elements, their alloys and compounds under ultrahigh pressure and to obtain on the basis of the calculations and experimental data a qualitatively new knowledge about the properties of materials that become available due to a significant increase in the range of changes of external parameters. At the 1-st stage of the project, the following tasks were solved: 1. A systematic study of the electronic structure of the 6th period transition metals, namely Hf, Ta, W, Re, Os, Ir, Pt, Au, was carried in the range of external pressures from 0 to 200 GPa. In Hf, Re and hcp Os, it was found that electronic topological transition takes place when the pressure changes to 200 GPa. At the same time in the cubic metals Ta, W, Ir, Pt, Au there is no change in the topology of the Fermi surface with pressure. We have investigated the so-called core-level crossing transitions (CLC), a novel type of the electronic transitions which is associated with the overlapping of 4f and 5p energy levels of the core electrons. Additionally, for disordered alloys from the binary Ir-Os, Ir-Pt, Os-Re, Os-Rh systems we investigated the possibility of ETT. It was shown that ETTs, associated with changes in pressure, exist in hcp alloys of Os-Re, Os-Rh, Ir-Os, whereas in FCC alloys of these systems and the Ir-Pt system there are no changes in the Fermi surface with increasing of pressure. 2. The ground state structural properties of IV- and V-coesites were calculated in the range of pressures of 0–74 GPa. The obtained structural properties of the IV-and V-coesite phases of silicon oxide are in good agreement with the experimental data. It is shown that with increasing pressure the phase transition between these phases takes place without energy-barrier. These phases were found to be dynamically stable. Interestingly, the bulk moduli of these phases are significantly lower than the bulk moduli of the well-known phases of silicon oxide. 3. Using the first-principle simulations we investigated the structural and thermodynamic parameters of iron pernitride FeN2 and iron tetranitride FeN4 in the ranges of their stability. Additionally, the equations of states and bulk moduli were determined theoretically. We demonstrated limitations of the calculation scheme that does not take into account one-site Coulomb correlations for the studied pressure interval. A detailed analysis of the structural properties depending on the change of Hubbard parameter U from 0 to 8 eV at a fixed value of Hund exchange parameter J = 1eV was performed. Comparison with experimental values allowed us to choose unified parameters U =4 eV, J=1 eV for all the investigated iron nitrides. The nature of the chemical bonds of nitrogen in the studied polynitrides was analyzed. Our results are in agreement with the experimental assumption about the possible dynamic stability of FeN4 at zero pressure. Note that iron polynitride FeN4 is the first experimentally verified nitrogen compound containing the polymer nitrogen chains. 4. In the framework of the density functional theory and the quasi-harmonic approximation, we investigated the electronic and structural properties of the newly synthesized rhenium oxide ReO3 with orthorhombic structure. Also, we performed the analysis of equations states P-V, the densities of electronic states, phonon dispersions, and charge density maps. It is shown that in the range of synthesis pressures the values of the bulk moduli of orthorhombic ReO3 exceed 400 GPa. Optimized lattice parameters and the equation of state parameters are in good agreement with experimental data. An analysis of the densities of states and charge density maps shows that the oxide is a covalent metal. The calculated phonon dispersion spectra show that the orthorhombic phase is dynamically stable at a pressure of P = 42 GPa. 5. As part of the study of the electronic, magnetic, and lattice properties of Fe2O3 oxide under pressure, we proposed and described, for the first time, a new type of ‘insulator-metal’-Mott transition (MI: Mott insulator). It is a non-homogenous (site-selective) Mott transition (SSMI: site-selective Mott transition), associated with the collapse of local moments and the metallization (delocalization) of 3d electrons from only part (half) of Fe3+ ions. It was shown that in Fe2O3 the consideration of electron correlations effect is important for description of the transition from the local to the collective behavior of 3d electrons near the Mott insulator-metal transition. The sequence of phase transformations in Fe2O3 under pressure is represented as: structure of corundum (Mott-dielectric) 50 GPa → DPv (SSMI) 75 GPa → PPv (SS, metal). This behavior implies a complex, nonperturbative interaction between the chemical bond and the electron correlations effect in Fe2O3. 6. To calculate the thermodynamic properties of pure elements at different pressures for thermodynamic databases, we investigated the applicability of complex functionals corrected for van der Waals (vdW) forces to simulate the properties of hexagonal graphite with AB-packing and cubic diamond. Additionally we used the SCAN functional for description of main structural and magnetic properties of transition metals Fe, Co and Ni. Analysis of lattice constants and bulk modulus of graphite and diamond, as well as calculated interlayer bond energy in graphite, show that PBE+TS+SCS is the best functional for all descriptors with a total error of only 2.2%. It was found that isotropic pressure stabilizes AB-packed graphite with respect to AA-packed graphite with a rate of -2.2 meV/GPa in the range of studied pressures. Calculations within SCAN functional show that the equilibrium volumes in fcc-nickel and hcp-cobalt are overestimated; and their bulk moduli are underestimated. Regarding the magnetic moment values, the SCAN functional significantly overstates them for all three studied metals. It is shown that, with the possible exception of bcc iron, the SCAN functional does not improve the results in the PBE approximation regarding the structural properties of the pure elements. We therefore conclude that from the viewpoint of itinerant electron ferromagnetism, further development of exchange-correlation functionals is needed. 7. As a result of the integration of ab-initio calculations with experimental data into thermodynamic models for description of systems, we obtained the missing thermodynamic data for alpha and beta modifications of pure tin. Calculations, performed within the framework of the electron density functional theory, show that the local density approximation (LDA) for description of exchange and correlation effects gives the best results for alpha and beta modifications of pure tin, compared to other approximations. This was confirmed by a comparative analysis of the calculated equilibrium parameters and phonon spectra of both tin phases with the available experimental data. The heat capacities, calculated within harmonic and quasi-harmonic approximations (at constant volume and pressure, respectively), are in good agreement with the experimental data. 8. From combination of experimental and theoretical data, we evaluated the thermodynamic properties of the solid (crystalline and amorphous) and liquid phases of silicon oxide SiO2 with using SGTE models. The contributions of both harmonic and anharmonic lattice vibrations were taken into account; in addition, the model accounts for the electronic component and the Cp-Cv corrections. The heat capacities of various phases of silicon oxide, as well as their Gibbs potentials, were obtained in a wide range of temperatures.

 

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Annotation of the results obtained in 2019
1. We performed a detailed theoretical study of the electronic structure, spin state, and lattice properties of the correlated monoxides MnO, FeO, CoO, and NiO in the paramagnetic state using the DFT + DMFT method. The DFT+DMFT calculations were carried out near the Mott insulator-to-metal transition and spin-state crossover under pressure. Our results explain the anomalous dependence of the critical pressure of the Mott transition pc for the MnO-FeO-CoO-NiO series (first, a 145-72-40 GPa decrease of pc for MnO-FeO-CoO and then its increase up to 429 GPa in NiO). This anomalous behavior is associated with a crossover of the effective degeneracy of the low-energy excitations from the 5-orbital (in MnO, FeO, and CoO) to 2-orbital case in NiO. The Mott transition and magnetic collapse in monoxides are accompanied by a crossover from localized to itinerant (delocalized) behavior of the 3d electrons and in the case of MnO, FeO, and CoO, it is accompanied by a change in the valence state of transition metal ions (accompanied by a crossover from 2+ to a mixed valence state with dominant contribution of 1+). 2. We performed a systematic study of the electronic structure, spin state, and lattice properties of iron (di-)oxide FeO2 in the paramagnetic state employing the DFT + DMFT method. In particular, we performed a complete structural optimization of the lattice parameters in the pyrite-type FeO2 (HP-PdF2 type crystal lattice) under pressure — the lattice volume and z-position of oxygen were determined as a function of compression, and the equation of state was calculated. We calculated the electronic and magnetic properties of FeO2 under pressure, and charge density maps. Our DFT+DMFT results are in good quantitative agreement with experimental data. We found that HP-PdF2 FeO2 is a correlated metal with a noticeable renormalization of the Fe t2g states, m/m* ~ 1.6. Our detailed analysis of the valence configurations shows that the valence of iron ions is near 3+ (abundance of the Fe3+ 3d5 configuration is 50 % and of the Fe2+ 3d6 state is 30%, at 69 GPa). Our results for the spectral properties show a weak ~ 2-3 eV bonding–antibonding splitting of the O 2p orbitals, which indicates a weak interaction between oxygen atoms. Our results agree with the analysis of charge density maps, which suggests the lack of oxygen dimers in FeO2 at a pressure up to ~ 180 GPa. The latter implies the presence of 1.5- valence of oxygen. Our results along with the X-ray diffraction and Mössbauer spectroscopy measurements for the FeO2 single crystals synthesized under high-pressures are summarized in the manuscript “Variation of oxygen oxidation state at the base of Earth's lower mantle”, E. Koemets, M. Bykov, E. Bykova, S. Chariton, G. Aprilis, S. Clément, J. Rouquette, J. Haines, V. Cerantola, K. Glazyrin, A. Abakumov, L. Ismailova, C. McCammon, V. B. Prakapenka, M. Hanfland, H.-P. Liermann, I. Leonov, A. V. Ponomareva, I. A. Abrikosov, N. Dubrovinskaia, L. Dubrovinsky., arXiv: 1905.05497. 3. We studied the electronic, magnetic, and lattice properties of the post-perovskite (PPv) phase of mineral hematite (Fe2O3) under ultrahigh pressures using the DFT+DMFT method. It was shown that in the region of stability of the PPv Fe2O3, up to pressures of ~ 250 GPa, Fe2O3 is a metal with site-selective localization of magnetic moments of half of the Fe3+ ions on the iron sublattice with prismatic oxygen surrounding. The Fe 3d electrons of the remaining half of the iron ions located on the sublattice with octahedral oxygen environment are delocalized. The effects of electronic correlations are important to explain the transition from localized to itinerant moment behavior near the Mott insulator-metal transition in Fe2O3 (at about 50 GPa). The site-selective phase transition is accompanied by the formation of charge disproportionality of iron ions with Fe3 ± δ and δ ~ 0.05–0.09, which implies a complex interplay between electronic correlations and the lattice. The obtained results indicate that site-selective local moments in Fe2O3 persist until ultrahigh pressures of ~ 250 GPa, i.e. significantly higher than the core-mantle boundary. These estimations are important for understanding the density and sound velocity anomalies in the lower mantle of Earth. Our results were published in Ref. “Charge disproportionation and site-selective local magnetic moments in the post-perovskite-type Fe2O3 under ultra-high pressures”, I. Leonov, G. Kh. Rozenberg, and I. A. Abrikosov, npj Computational Materials 5, 90 (2019). 4. The theoretical description of a new material, metallic rhenium nitride pernitride Re2(N2)(N)2 with very low compressibility (K0 = 428 (10) GPa) and high hardness (nanoindenter hardness, hardness 36.7 GPa) was performed. This material, unlike known transition metal pernitrides, contains both N24- (N1) pernitride and discrete N3- anions (N2), which explains its exceptional properties. To confirm the experimental features of ReN2 and to better understand the mechanical and electronic properties of this compound, we performed a detailed study in the framework of density functional theory. The dynamical stability and metallic nature of the synthesized material was confirmed by calculating the phonon spectrum and electron density of states (DOS). Analysis of DOS and charge distribution maps show the formation of covalent bonds with a very high degree of electron localization between dumbbell-like pairs of nitrogen atoms, which contributes to a very low compressibility of nitride. Moreover, the bond between Re atoms and individual nitrogen atoms is formed by significantly less localized but strongly hybridized electronic states with a pseudogap. Such features optimize the electronic contribution to the atomic bond, which may explain the high hardness of ReN2. The results were published in Ref. «High-pressure synthesis of ultraincompressible hard rhenium nitride pernitride Re2(N2)(N)2 stable at ambient conditions» M. Bykov, S. Chariton, H. Fei, T. Fedotenko, G. Aprilis, A. V. Ponomareva, F. Tasnádi, I. A. Abrikosov, B. Merle, P. Feldner, S. Vogel, W. Schnick, V. B. Prakapenka, E. Greenberg, M. Hanfland, A. Pakhomova, H.-P. Liermann, T. Katsura, N. Dubrovinskaia, L. Dubrovinsky, Nature Communications, v.10, p. 2994 (2019). 5. The behavior of the sulfur-nitrogen system under high-pressure conditions was studied within international collaboration. Experimentally, diamond anvil and laser heating were used to stabilize new compounds. At pressures above 64 GPa, the orthorhombic (Pnnm space group) compound SN2 was synthesized. According to single-crystal and powder x-ray diffraction this compound has a CaCl2 type structure consisting of SN6 octahedra. The new compound is metastable up to ~ 20 GPa, after which it spontaneously decomposes into S + N2. The density functional theory calculations were carried out to provide an understanding of the physicochemical properties of SN2. Equations of state, oxidation states of elements, electron density maps and electron localization functions were calculated. The SN2 is nonmetallic in the entire range of the existence of the compound with an increasing band gap from 1.57 eV at P = 0 GPa to 1.72 eV at P = 80 GPa. The type of bond is defined as polar covalent, and the degree of polarity increases with increasing pressure. The experimental and theoretical structural characteristics are in good agreement with each other. This study shows that, despite the many metastable S-N compounds that exist under ambient conditions, none of them is formed under pressure. Moreover, the chemical composition of solid SN2 deviates from the vast majority of S-N solids, since it is not stabilized via aromatic rings. These results were published in Ref. D. Laniel, M. Bykov, T. Fedotenko, A. V. Ponomareva, I. A. Abrikosov, K. Glazyrin, V. Svitlyk, L. Dubrovinsky, N. Dubrovinskaia, “High pressure investigation of the S-N2 system up to the megabar range: Synthesis and characterization of the SN2 solid”, Inorg. Chem. 58, 9195 (2019). 6. A systematic study of the electronic structure and physical properties of the TiPO4 phases at high pressure was carried out. Using first-principle calculations, the electronic structure of III, IV, and V phases was investigated, and structural transitions between them were also studied. It was shown that, at high pressure, phase V is a more energetically favorable structure compared to III and IV phases. The less dense IV phase is most likely kinetically stabilized. The transition into a metallic state, accompanied by the disappearance of the magnetic moment, destabilizes the phase III, leading to the appearance of phases IV and V with the band gaps. The calculations indicate that the structural transition is related to the Mott transition. Upon a structural transition to phase V, a stable magnetic moment 0.8 μB again appears in the system. The electronic structure calculations of phase V made it possible to classify this phase as a Mott antiferromagnetic insulator. Thus, the reverse Mott transition occurs in the TiPO4 system. The study of the density of electronic states in phase III shows the decrease of band gap with increasing pressure, whereas in phase V this parameter remains almost unchanged. An analysis of the band structure shows that phases III, IV, and V have indirect band gaps. Calculations demonstrate that the properties of the TiPO4 system have interesting features not only at low temperatures, but also at high pressures. These results were published in Ref. H. J. M. Jönsson, M. Ekholm, M. Bykov, L. Dubrovinsky, S. van Smaalen, and I. A. Abrikosov, “Inverse pressure-induced Mott transition in TiPO4”, Phys. Rev. B 99, 245132 (2019). 7. A review and assessment of thermodynamic properties of pure germanium dioxide was performed. Based on critically evaluated data, equations for the Gibbs energies of the solid and amorphous/liquid phases were obtained. The values of the standard entropies of phases at 298.15 K are refined based on modeling by the Planck-Einstein method. Solid phases were modeled using an extended Einstein model. The amorphous/liquid phase was modeled using a two-state fluid model. The obtained models make it possible to accurately describe the heat capacity and enthalpy increment from 0 K to temperatures above melting, as well as the temperatures and enthalpies of phase transitions. Although the a two-state fluid model allows one to obtain the required values of the enthalpy and phase transformation temperature, it is still not possible to describe the peak in the heat capacity associated with the transition in the glassy state. 8. Using the ab-initio molecular dynamics method and functional with correction for the van der Waals interaction in the Becke-Johnson form, we studied the effect of lattice vibrations on the behavior of carbon under cold compression. To understand the initial stage of the phase transition under pressure, the uniform compression was gradually increased from 0 to 30 GPa. Obtained results allows us to claim that the packing fault defects are relatively easy to form. This conclusion is confirmed by the analysis of literature data and static calculations of energies between ABAW and ABCABC packings of carbon planes. The simulations allow us to conclude about the possible important role of stacking faults at the initial stage of the phase transition during cold compression of graphite. 9. A first-principle calculation of the core-level shifts of Fe and Ni was carried out for the entire concentration range of fcc Fe-Ni alloys, including the so-called invar alloys with ~ 36 at. % Ni, as well as alloy compositions with a higher nickel concentration where we discovered the invar effect under pressure. For nickel, the calculated core-level shift is positive for the entire concentration range and increases from 0 to 0.7 eV with a decrease of the Ni concentration from 100 to 10 at%. Close to invar alloys, core-level shift in Ni demonstrate a feature associated with the transition of the alloy from a high-spin to a low-spin magnetic state. On the contrary, the core-level shifts in iron are negative in almost the entire concentration range and decrease from 0.1 to -0.3 eV with a decreasing Ni concentration from 100 to 30 at %. The change in the behavior of the core-level shifts in Fe is more significant: they reach a minimum for concentration where high-spin to low-spin transition takes place and begin to increase sharply with a further decrease of Ni concentration. Experimentally, the Fe1-xNix alloys (x = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.9) obtained by the arc melting method were studied by high-resolution X-ray photoelectron spectroscopy (XPS). A comparison of the calculated and experimental values of core-level shifts in Ni demonstrate a very good agreement between the two data sets. 10. The solution enthalpy of carbon impurity in Fe-Mn paramagnetic alloys was calculated in the framework of the density functional theory. The calculations were carried out by generalization of the model describing point defects in paramagnetic matrix for the case of alloys. The model allows one to take into account thermal magnetic fluctuations in a paramagnetic chemically disordered host alloy with point defects. Since the theoretical values of the lattice parameters corresponding to the minimum energy at zero temperature differ significantly from the experimental values at finite temperatures, a calculation scheme with pressure averaging in the matrix and alloy with impurity was used to calculate the solution enthalpy. According to theoretical results, in alloys with a Mn concentration of ~ 20 at.% the solution enthalpy of the carbon impurity becomes lower compared to pure paramagnetic gamma-iron. This behavior of the solution energy is in qualitative agreement with experiment. 11. We suggest a theoretical model to describe the nonlinear effects for hexagonal crystals beyond the standard linear theory of elasticity. This model makes it possible to define the high-order elastic constants for loaded crystals, analytical expressions and a method for calculation of second and third order elastic constants for hcp crystals hydrostatically compressed, and the relationships between elastic constants of a loaded and unloaded crystal for elastic constants of the 2nd and 3rd orders of the hcp crystal. We derived an expression for the free energy of hcp crystal as a function of deformation taking into account third-order elastic constants. By using various combinations of second and third order elastic constants we determine an analytical expression for the Grüneisen constants of the longitudinal and transverse acoustic modes is obtained in the long-wave limit. Following the suggested model with using first-principle modeling, all second and third order elastic constants for epsilon-iron were calculated; these data were used to calculate the Gruneisen parameters. The Grüneisen parameters were also calculated using the volume dependence of the phonon frequencies. The Grüneisen parameters obtained in this work by various methods are in excellent agreement with experimental data, i.e. the constructed model has successfully passed verification. These results were published in Ref. O. M. Krasilnikov, A. V. Lugovskoy, V. Dikan, M. P. Belov, Yu. Kh. Vekilov, I.A. Abrikosov, “Nonlinear elasticity of epsilon-Fe: the pressure effect”, Phys. Rev. B 99, 184101 (2019). 12. The electronic properties and the lattice dynamics of Nb were studied taking into account the of anharmonic effects. Precise calculation of anharmonic effects at finite temperatures leads to a smearing of the electronic bands. This affects the lattice dynamics and the disappearance of the Cohn anomaly in the acoustic mode near the Γ-point, which agrees well with experimental data. 13. The first-principle molecular dynamics (AIMD) calculations at 300 K are used to determine the inherent tensile strength, toughness, and resistance to fracture of defect-free B1 Ti1–xAlxN solid solutions (0 ≤ x ≤ 0.75). The results show that TiN and Ti0.75Al0.25N are strong materials, but cleave at their yield point via sudden bond snapping. In contrast, Ti0.5Al0.5N and Ti0.25Al0.75N exhibit similar strength, but significantly higher toughness than TiN and Ti0.75Al0.25N, due to the activation of local lattice transformations in the plastic-response regime which dissipates stress, thus preventing brittle failure. 14. An experimental and theoretical study of the defective structure in single crystals NiO was carried out. Single crystals of nickel oxide obtained by the floating zone melting method. Experimentally, it was found that in in addition to the block structure often observed in single crystals of metal oxide compounds with a characteristic block size of the order of a millimeter in each direction, there is also a nanoscale granular structure. Theoretical studies show that the presence of a nickel vacancy in a supercell NiO indices local lattice distortions and leads to the appearance of impurity states. The range of these distortions is approximately 1.3 nm. It was suggested that the presence of a nanoscale granular structure can be explained by local distortion effects.

 

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