Annotation of the results obtained in 2020
The new USPEX module was developed which allows working with the coordinates of the structural units centers rather than the atoms centers, which could be individual atoms, nanoclusters or individual fragments of two-dimensional layers. To work in the molecular mode, four variational operators were adapted and one new was created. The developed module has proven effective in the structure modeling of a methane molecules layer on a copper substrate. At a low value of the chemical potential, the stable configuration is one adsorbed molecule. With an increase in the concentration of methane in the environment, a gradual growth will occur, which will lead to further condensation. The study of the methane molecular structure in the presence of copper, the analysis of possible reactions leading to the nucleation of carbon atoms can tell a lot about the process of graphene formation. In addition, the analysis of the structures obtained during the calculation can demonstrate the intermediate hydrocarbon clusters structure which is necessary to determine the reaction characteristic barriers and provide a basis for predicting the growth kinetics. The research of the thermodynamic stability of BNO and BCN structures with different concentrations of oxygen and carbon was carried out. At the first step, the prediction of new two-dimensional structures depending on the concentration of oxygen and carbon was conducted. To compare the thermodynamic stability of the BNO structures, a triple phase diagram was calculated. The obtained results allow us to say that during the implementation of the project, not only a structure with a unique geometry was predicted for the first time, but this structure is also thermodynamically stable. In addition, it was found that an increase in oxygen concentration leads to the formation of structures that can be represented as boron oxide doped with nitrogen. Using a modified module of the USPEX software package, the prediction of new two-dimensional phases of alkali metal salts on substrates of various compositions was carried out. The results of the simulation on the SiC surface showed a significant difference from the analogous process taking place on diamond substrates, because in the case of SiC substrates, there is an interaction between the atoms of the thin film (Na and Cl) and the surface containing carbon and silicon atoms, which leads to the formation of alkali metal structures predominantly with a rectangular curved in the plane lattice. The lattice parameters were determined, which are dictated mainly by the parameters of the chosen substrate, and the bond lengths in the thin film structure were determined. The barriers of the transitions between the cubic phases of alkali metal salts and their hexagonal analogs were also evaluated. The research results indicate the importance of choosing the required substrate, even though the effect of strong bonding to the substrate. The above results indicate the need for a deeper understanding of the process of the substrates influence on the structure and properties of the final material. The search and construction of ternary diagrams in the coordinates of the formation energy – the composition for nonstoichiometric systems based on transition metals dichalcogenides was carried out. The research results show the existence of the possibility of experimental synthesis of new nonstoichiometric compositions based on TMDs, which have potential prospects for use in optics, as well as catalytically active surfaces. A new approach based on calculation of the formation energy of chalcogen vacancies in MoS2 and MoSe2 structures under the action of elements imitating the effect of substrates with different values of electronegativity was proposed in order to identify and evaluate the regularities affecting on the tendency of surface oxidation and further defect formation. The linear dependence of the monovacancy formation energy on the value of the charge redistribution was obtained, which indicates a direct relationship between the stability of the TMD and the doping value. The effect of charge flow from the substrate was demonstrated to be able to have a critical effect on the stability to the vacancies formation, which is confirmed by direct modeling of the process of elimination of the SO molecule from the MoS2 surface having an adsorbed oxygen atom and the same system with dopant atoms on the opposite side of the surface. The study results of the influence of covalent functionalization on the defect formation process showed a less pronounced dependence on the amount of charge redistribution between the surface and the molecule than in the case of doping. New two-dimensional crystal structures of PbS, PbSe, PbTe, CaF2 were predicted. The search results showed that the most favorable structures are those with the composition Pb, X (X = S / Se / Te), and PbX. For each of the predicted structures, their dynamic stability was estimated by calculating the spectra of phonon vibrations, and the band gap was estimated as a function of the number of layers. It was found that the transition from a bulk crystal to a bilayer leads to the opening of the band gap. It was found that PbX structures with a hexagonal unit cell are also semiconductors. The results achieved during the implementation of the third phase of the project were also published in the following information resources: https://rscf.ru/news/presidential-program/materialy-dlya-spinovoy-elektroniki/ https://indicator.ru/chemistry-and-materials/obnaruzheny-novye-materialy-spinovoi-elektroniki-14-12-2020.htm https://www.gazeta.ru/science/news/2020/12/08/n_15333853.shtml

 

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Annotation of the results obtained in 2018
To further describe the formation of two-dimensional materials and thin films on substrates of different compositions, the parameters of electrostatic interaction were determined by the method of empirical potentials, based on DFT results. The binding energy between the surfaces of the substrate and the two-dimensional material was described using the parametrization of the Lennard-Jones 6-12 potential. The main parameters of the interaction, such as the depth of the potential well and the distance at which the interaction energy becomes zero were determined. Using fitted parameters, the binding energies between the substrate surface and the desired materials were estimated. The correspondence between the results obtained by the two approaches was obtained. To simulate the formation of a two-dimensional material on a substrate, an adaptation of the USPEX algorithm module was carried out. The possibility of determining an additional vacuum region between the substrate and the added atoms of a different composition was added in order to avoid the unrealistic inserting of atoms to the substrate structure. In addition, an interface was written for interaction between the USPEX software package and the LAMMPS package. Relaxation algorithm for generated structures was modified. Molecular dynamics method and annealing process were added. The results of the calculations showed that this method allows us to quickly find the energy minimum of the studied structures. To check and test the correctness of the adapted USPEX algorithm, we simulated the formation of well-known 2D materials (including graphene, h-BN, and others) on metal substrates of various compositions (including Cu, Ni, etc. ) with different crystallographic orientation (including (001), (111), etc.). The simulation results showed a weak effect of metal substrates on the formation of stable two-dimensional materials, such as graphene and h-BN. The results obtained using DFT and empirical potentials method showed the same results. It is shown that, due to the smaller difference between the cell parameters, graphene forms on the Ni surface faster than on Cu. The next step was a simulation of more complex systems like thin alkali metal films such as NaCl and LiCl on metal substrates and diamond as well. The simulation results of NaCl and LiCl films on Cu and Ag substrates with crystallographic orientations (100) and (111) showed total agreement with the available experimental data, including the atomic structure of the film and the features of film orientation relative to the substrate surface. It is important that the simulation results of NaCl on the surfaces of Cu (311) and Ag (111) showed a result that differs from the predicted theoretical models described in the literature. It is important to perform simulations of the formation of NaCl film on the diamond surface. In contrast to metal substrates, the binding with a diamond surface is larger than that in case of metal substrates, which can affect the atomic structure of desired films. Indeed, performed calculations states about the formation of monoatomic hexagonal NaCl layers on the (110) diamond surface. In this case the final structure being dictated by the symmetry of the substrate due to strong binding. Similar results were obtained for the (111) diamond surface. The strong influence of the diamond substrate is confirmed by calculations of the interaction energy between diamond and NaCl thin films. It is obtained that it is an order of magnitude larger than in the case of metal substrates. The results of this study are preparing for publication. Obtained results demonstrate that an increase in the binding between the substrate and the film leads to a change in the atomic structure of the latter. The behavior of deposited Na and Cl atoms on the surface of NaCl crystal was studied depending on the crystallographic orientation of the surface. In this case, the interaction between the substrate and the desired material is much greater than in the case of metal substrates and diamond. The deposition of atoms on a substrate of the same composition leads to the formation of a surface reconstructions, the formation of an energetically more favorable surface. Two crystallographic orientations of NaCl films, such as (100) and (111), were considered. Four stable reconstructions were found for the NaCl(100) surface using the USPEX algorithm. A detailed study of the features of their atomic structure has been carried out, and the stability areas of each reconstructions have been evaluated depending on the chemical potential of chlorine. Similar studies were carried out for the case of the polar surface of NaCl(111). In this case five stable reconstructions were found. It was found that the reconstruction of the surface, which has a greater disordering on the surface, is energetically more favorable. This fact may be due to the fact that the disordering of the atomic structure leads to a decrease in the dipole moment directed normally in the NaCl (111) surface. This effect was previously predicted for freestanding NaCl layers. According to the obtained results the manuscript was prepared for submission to the journal. One of the important parts of the project is the study of stability to the oxidation of MoS2 and MoSe2 monolayers. Using the quantum chemistry methods, it was obtained, and then experimentally confirmed that the oxidation of the MoS2 surface occurs faster than the surface of MoSe2, which indicates the atmospheric instability of molybdenum disulfide. It should be noted that the opposite situation is observed in the case of oxidation of the edges of molybdenum dichalcogenides. The research results were published in the journal Nature Chemistry in 2018. A further development of this topic is to study the possibility of increasing the stability to the oxidation of molybdenum chalcogenide monolayers by doping them with halogen atoms. For all the structures considered, the formation energy of vacancy near the dopant and at a certain distance from it was estimated. Such a study made it possible to determine the effect of impurity atoms on the probability of vacancies formation in the surface of molybdenum dichalcogenides. A strong dependence of the vacancy formation probability on the type of dopant was obtained. Obtained results may indicate the possibility of controlling the stability of a two-dimensional material. It was found that the formation of S-vacancy near the Cl and Br dopant atoms is energetically favorable in the MoS2 monolayer, whereas doping with F atoms reduces the possibility of the formation of a vacancy next to it. In addition, an increase in the formation energy of a vacancy with distance from the dopant atom is obtained, which indicates that the formation of vacancies of sulfur atoms directly near the F and I atoms is energetically more favorable. It is possible to control the properties of two-dimensional structures by creating various defects as well as by adsorbing molecular groups onto the surface of the material. As a limiting case of the adsorption of molecular groups, formation of multilayer structures with a combination of molybdenum dichalcogenide layers with graphene were considered. Obtained results indicate a weak Van der Waals interaction between graphene and layers of disulfide and molybdenum diselenide and doping with fluorine leads to a further decrease in the binding energy of between with MoS2 and MoSe2 layers to graphene. The study of the growth mechanisms of 2D materials requires the development of original approaches, the implementation of which is possible within the framework of the evolutionary algorithm USPEX. The results of the first-year research showed that modifying and using the module 200 and the existing module 201 of the USPEX algorithm led to the possibility of correctly describing the homo and hetero-epitaxial formation of thin films on substrates of various compositions. Obtained results provided a basis for determining the directions of improvement and upgrading of the module 201 for predicting the structure with the number of atoms in the system> 2 (not including the substrate). An algorithm has been developed that makes it possible to calculate the objective function for determining thermodynamically stable structures of thin films on substrates.

 

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Annotation of the results obtained in 2019
In the second stage of the project, the USPEX module was upgraded to be able to predict the formation of 2D materials on substrates of different composition. For this purpose, two variation operators were added and modified to the algorithm: a transmutation operator and an atom removal/addition operator. Also, at the program level, a criterion for considering the lattice mismatch the desired 2D material and the substrate has been added. Thus, for each structure, the basis is selected as a random linear combination of initial basis vectors of the substrate. The finite basis vector module is limited so that the maximum ratio between the area of a cell and the area of a substrate cell does not exceed some threshold value. To estimate the stability of structures, an adaptability function has been added, described by the energy of thin films formation per unit area. The estimation of chemical potential value has also been modified, which was determined from the phase diagram in coordinates "formation energy - composition per unit area", where a systematically improving set of the best in the generation of structures forms a convex hull. This approach can be effectively extended to systems with an arbitrary number of components, where the values of chemical potentials are derived as partial derivatives of the corresponding hyperplanes of a multidimensional convex shell. In addition, the approach of sideway accounting of interaction of 2D structures with the substrate was developed by introducing restrictions on the parameters of the cell in the plane of the 2D structure. For this purpose, the block responsible for changing the parameters of the cell during optimization in VASP was changed. Also USPEX algorithm was modified in the block responsible for checking the generated structures. This modification also made it possible to generate structures with variable element stoichiometry (A_xB_(1-x)). In summary, obtained approach allowed to search and optimize the structures that are under stress in two axes, which can be considered the influence of the substrate in approaching a strong two-dimensional binding of the material. To check the correctness of proposed algorithm, we have calculated the Na_xCl_(1-x) system with fixed cell parameters corresponding to the parameters of the diamond facet surface [110]. While searching, 3 energetically profitable compositions (Na, Cl and NaCl) were obtained. The energetically advantageous structure corresponds to NaCl with hexagonal symmetry. The obtained structure h-NaCl corresponds to the early results of NaCl studies on diamond substrates, where the hexagonal structure NaCl was obtained on the diamond substrate (110). To describe the stability of the hexagonal phase, the energy transition barrier between the cubic phase of NaCl and the hexagonal phase has been calculated, which is 0.1 eV/4f.u, indicating that the hexagonal phase will transfer into the stable cubic phase in the absence of stabilizing factors. The barrier to their transition to the cubic hexagonal phase was estimated to be 0.35 eV/4f.u. As a result, the approach of sideway accounting of the substrate interaction (imposing restrictions on the lattice parameters) for simulation the formation of two-dimensional materials and thin films was developed. A prerequisite for the applicability of this approach is a strong binding between the 2D structure and the substrate. Using this approach if there is a weak interaction, as in the case of metal substrates for example, may lead to incorrect results. By means of evolutionary algorithm, the formation of BxNyOz and BxCyNz composition structures was investigated without taking into account the atomic structure of the substrate. Its effect was considering by applying restrictions on the lattice vectors. During the evolutionary search new thermodynamically stable structures of BCN and BNO compositions with different concentrations of carbon and oxygen, respectively, were found. Unique structures of the triple composition, previously unexplored, were found. In addition, the structures above the decomposition line were analyzed. The results of the search for new BNO structures showed that in the case of a deficit of boron or nitrogen atoms, the incorporation of oxygen occurs only in the positions of substitution of nitrogen atoms, which is consistent with earlier data and indicates the correctness of such a method for predicting new two-dimensional materials. The features of the atomic structures of the predicted materials were analyzed in detail. During the study of the formation process of BNO and BCN on substrates (by sideway accounting) it was shown that the mismatch of the cell parameters leads only to the formation of corrugations in the studied layers. The unique atomic structure of the obtained nano-objects in combination with the stability of the two-dimensional crystal lattice to deformation indicates the need for a more in-depth study of their physical and chemical properties to understand the effects associated with the effects of the substrate on two-dimensional material. Based on the research results, manuscript was prepared for submission to Physical Chemistry Chemical Physics journal. In addition, it was obtained that the introduction of atoms Cl, Br, I into the structure of MoS2 leads to the appearance of semi-metallic properties and induce 100% spin polarization near the Fermi level for the Mo and halogen atoms. The next step was to investigate the electronic properties of heterostructures based on graphene and molybdenum dichalcogenides doped with halogen atoms. Graphene was considered as the limiting case for coating of TMD layers. The electronic and magnetic properties of molybdenum dichalcogenides doped with halogen atoms (F, Cl, Br, I) were studied. It was obtained that the addition of a chalcogen atom as a dopant leads to a magnetic moment in its vicinity. The obtained magnetic moment is equal to ~1 µ per supercell containing one halogen atom. A detailed analysis of the spin order depending on the type of halogen has been performed. In addition, it was obtained that the incorporation of atoms Cl, Br, I into the structure of MoS2 leads to the appearance of semi-metallic properties and induce 100% spin polarization near the Fermi level for the Mo and halogen atoms. Further step was to investigate the electronic properties of heterostructures based on graphene and molybdenum dichalcogenides doped by halogen atoms. Graphene was considered as the limiting case for coating of TMD layers. It was obtained that doping of molybdenum dichalcogenides leads to induced spin polarization of charge carriers in graphene. The dependence of spin polarization on the electrical negativity of the halogen atom is obtained. In addition, we have studied the electronic properties of molybdenum diselenide coated with a PTCDA monomolecular layer and studied the features of charge redistribution between layers of the heterostructure. The binding energies both between the layers and within the monomolecular layer were evaluated. Density of states analysis of MoSe2/PTCDA heterostructure showed the presence of unoccupied electronic states in the 0.8 eV energy region. The charge transfer between the layers of the heterostructure was obtained based on DOS analysis, where a contribution from the MoSe2 monolayer was obtained. Based on the calculations performed, it can be concluded that the presence of the PTCDA layer leads to the appearance of electronic states in the band gap of MoSe2 monolayer and p-doping, which may affect the change in its optical properties. Based on Bader charge analysis and differential density of charges it was shown that in the heterostructure there is an accumulation of electrons on the PTCDA layer and outflow of electrons from the MoSe2 layer. The analysis of charges confirms this fact, also indicating the flow of electrons from the MoSe2 layer to the PTCDA layer (0.06 e to the molecule). Based on the research results, two articles were prepared and sent for publication in Nanoscale and JETP Letters. Prediction of new phases of compositions M1_nM2_(1-n)X_m, M_nX1_nX2_(2-n), M=Mo, W, etc., X=O, S, Se using the evolutionary algorithm showed the presence of thermodynamically stable intermediate phases, which are alloys with uniformly substituted atoms of metals and chalcogenes of corresponding compositions within one monolayer of TMD in the H-phase. For each of the presented compositions diagrams in coordinates of composition - enthalpy of formation have been calculated. Based on obtained data a convex hull on the boundaries of energy-beneficial compounds was constructed. The obtained structures were analyzed in detail. In addition to thermodynamically stable structures, metastable structures above the decomposition line by no more than 1 eV/atom were also considered. In addition, an evolutionary search for MoS(2-x)Sex compounds on a gold substrate was conducted. It was obtained that the presence of the substrate led to changes in the set of stable structures. Thus, three stable phases were found. Two of which are TMD layers on the gold surface with uniform mixing of chalcogen S and Se atoms with different concentrations. An interesting result is the prediction of an unusual structure with an equal number of MoS2 and MoSe2 fractions. This structure has no analogues among known 2D materials. Nor has it been found during the evolutionary search of MoS_2-xSe_x composition structures without substrate. One of the important parts of the project is the study of stability to oxidation of TMD monolayers in the presence of the substrate. At present, in the field of quantum-chemical simulation there is no universal approach that allows to effectively predict and evaluate the stability to oxidation of two-dimensional materials. The energy of vacancy formation as a function of the number of electrons flowing over the monolayer has been investigated. Lithium atoms were considered as a doping electron element. The results obtained suggest that with the increase in electron density flowing on the MoX2 monolayer the energy of vacancy formation decreases. It was obtained that the increase in the electron doping rate leads to a lighter formation of vacancies in the monolayer. It was shown that when dosing the MoS2 with the value of 0.097e/f.e. the energy of SO detachment and vacancy creation in the MoS2 layer differs by 0.8 eV, which indicates a decrease in oxidation stability in the case of monolayer doping. Based on obtained results the regularities affecting the oxidation of the MoS2 and MoSe2 monolayers were identified, which was a prerequisite for further creation of a universal approach to describe the oxidation of two-dimensional materials using the data obtained from quantum chemical simulation.

 

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