Ab Initio Modeling Of Atomic Tungsten Clusters Nucleation With Laser Surface Alloying Of Ceramics
Titanium carbide (TiC), due to its unique properties, is widely used in electronic devices, nuclear reactors and aerospace applications [1, 2]. In the processes of laser surface doping with d-metals, the physical and mechanical properties of the surface of the material are improved . The alloyed zones of the surface are characterized by a large saturation of the solid solution, which considerably exceeds the solubility under equilibrium conditions . The latter should lead to segregation of the atoms of the alloying element on the surface. It has been experimentally shown  that metal atoms can replace titanium positions in the upper layers of free TiC (100) and (111) surfaces with disordered vacancies. Experimental and theoretical studies of the TiC (111) atomic structure have shown that the polar surface is bounded by titanium atoms . Reconstruction of the surface in the surface layer of monoclinic WO3 was studied from the first principles in . DFT-calculations of surface energy and energy of formation of neutral oxygen defects have been performed. An experimental study of the segregation of the W atoms on TiC(001) surface using ion scattering spectroscopy and Auger electron spectroscopy has shown  that the topmost layer of TiC(001) is enriched with the W atoms. The latter are associated with carbon vacancies and are located in the vicinity. Calculations from the first principles have shown that TiC(100)/W(100) and TiC(100)/W(110) interfaces have thermodynamic stability. Ab initio calculations of Fe adsorption energy on the surface of MX (001) systems (M = Ti, V, Nb, Zr, Hf or Ta and X = C or N) were performed to study the initiation of Fe nucleation . A strong bond is predicted for Fe on NbC (001), and this carbide will have a high nucleation potential in the early stages.
MODEL AND METHOD
The theoretical model of the W/TiC(111) system under investigation is constructed by the scheme of a three-period plate. On the basis of a comparison of our DFT-calculations with the experiment, a TiC(111) unit cell with a size of (2 Ч 2) was selected. A thin TiC(111) plate model with three double layers (Ti, C) and a unit cell size (2 Ч 2) in the (111) plane was used here. The vacuum gap was chosen to be 12 Е wide, which made it possible to exclude any interaction between plate translations in the  direction. Figure 1a shows a fragment of the TiC(111) plate, and the possible positions of the tungsten atom are shown in Fig. 1b. We considered five different configurations of the arrangement of the tungsten atom on the TiC(111) plate: A – the oxygen atom was placed above the titanium atom of the first layer; B – the W atom was placed above the titanium atom of the third layer (fcc hollow); C – the W atom was placed above the carbon atom of the second layer (hcp hollow); Avac – above the surface vacancy of the titanium atom of the first layer; Cvaс – over the vacancy of the carbon atom of the second layer.
In , we tested the functionals for the exchange-correlation energy, so here all calculations were performed based on the theory of electron density functional using the pseudopotential approximation (Quantum-Espresso code) . For exchange-correlation energy, the functionals in the PBE form were used in the approximation (GGA). We used a scheme for generating k points with a planar lattice of 6 Ч 6 Ч 2. The convergence in the total energy of the cell was achieved at least 10–6 Read/cell. The energy of adsorption of the tungsten atom in the W/TiC(111) system was determined in the same way as in : where is the total energy of the W/TiC(111) system, is the total energy of the relaxed surface without oxygen, and is the energy of the isolated tungsten atom. The energy of formation of a point defect in the TiC(111) cell was calculated in a manner similar to .
When laser radiation is applied to the TiC(111) surface, in our opinion, three possible surface reconstruction mechanisms that are responsible for the formation of new material properties can be realized. The first mechanism can be that the titanium atoms can "fly out" from the uppermost layer of the (111) surface and their positions can be partially replaced by the tungsten atoms. Such violation of the symmetry of the crystal lattice and the processes of adsorption of tungsten lead to a significant reconstruction of the local atomic structure of the surface. The second mechanism may be that laser vaporization of the carbon atom of the TiC (111) subsurface layer can lead to a reconstruction of the local atomic structures W/TixCy, where the W atom can occupy vacancy positions, e. g., as a result of diffusion. The formation energies of Ti and C vacancies differ by 28%, i. e. a large amount of energy is required for the evaporation of carbon. However, e. g., when the radiation of Nd-YAG laser with wavelength of 1.06 μm and pulse duration of 40 ns was used, the radiation energy density on the surface of titanium carbide at a generation frequency of 2000 Hz was 2.06 ч 6.36 J/cm2 . At the observed laser emission density, the observed discrepancy in the values of the formation energies of Ti and C is insignificant. The third mechanism may be that when the titanium and carbon atoms of the two upper TiC (111) layers evaporate, their positions can be replaced by the W atoms, or the W atom can occupy one of the binding positions on the (111) surface.
ATOMIC STRUCTURE OF THE SURFACE
The atomic structure of a three-layer plate with tungsten for six different configurations of the W/TiC (111) and W/TixCy (111) systems after relaxation is shown in Fig. 2. The equilibrium parameters of the lattices, atomic positions of the tungsten atom and atoms of the upper layer of titanium carbide are established. The lengths of the bond between the tungsten atom and the nearest-neighbor atoms of the plate of stoichiometric and non-stoichiometric titanium carbide are given in Table. 1.
Analysis of Table 1 allows us to note the significant rearrangement of the local atomic structure due to the binding position of the W atom adsorbate on the surface of two-dimensional TiC(111) carbide titanium films. The maximum deformation of the length of the Ti-C bond of the surface layer is observed for the binding position A and is 1.8% with respect to the bond length for the pure 2D TiC(111) surface. In addition, position A is characterized by the smallest distance between the W adsorbate and the surface Ti atom (= 2.17 Е), which is commensurable with the covalent Ti-C bond in a thin 2D TiC(111) film. In position A, the Ti atom closest to the tungsten has shifted downward in the  direction relative to the averaged surface of the upper layer (see Fig. 1c). According to , the atomic radii of Ti and W are 1.76 Е and 1.93 Е, respectively, and one should expect the establishment of a strong bond between the W atom and the TiC surface (111). For positions B and C, the W adsorbate is removed from the surface by 15% relative to position A (see Fig. 2). With an increase in the degree of tungsten coating to = 1.0 MS in position B, removal of adsorbate from the surface is observed to be 32% relative to position A. In the latter case, the length of the Ti-C bond in the surface layer (111) is increased by more than 3% relative to pure 2D TiC(111) surface. In terms of studying the elements of tungsten nucleation on the non-stoichiometric surface of TixCy(111), it is of considerable interest to establish the local atomic structure of 2D W/TixCy(111) systems.
The results of relaxation of different adsorption models are shown in Fig. 2 d, e, f. Analysis of these figures shows that, in the presence of a vacancy in the uppermost layer of titanium, the tungsten atoms are able to replace their positions, forming W-C bonds of length = 2.03 Е (see Fig. 2d,e). If titanium and carbon are simultaneously present, then the W atom can occupy the position of the vacancy Ti (see Fig. 2f). The nature of the observed rearrangement of the atomic structure of ultrathin titanium carbide films, associated with the W adsorption on their polar surface of the W/TiC(111) and W/TixCy(111) systems, can be understood by a detailed study of chemisorption processes and electronic structure of each considered tungsten adsorption models.
TUNGSTEN ADSORPTION ENERGY
The results of the DFT-calculations of the adsorption energy are given in Table 2. This table also demonstrates the vertical distances between the adsorbate and the upper layers of the atoms. Analysis of Table 2 allows us to note that in position B (fcc site), the tungsten atom is the most stable, having three W-Ti bonds (at a bond length = 2.52 Е) of metallic type and is characterized by an adsorption energy of = –8.33 eV/atom. The estimation of the adsorption energy of the W atom is comparable with the energy of adsorption of atomic oxygen (= –8.75 , –10.68 ) in position B on the TiC polar surface. The value = –8.33 eV/atom gives us the basis for the assumption that position B (fcc site) can be the nucleation center of the W atoms in the W/TiC (111) system in the early stages. The less stable, in our opinion, is the binding position A (top Ti atom) with the adsorption energy = –7.28 eV/atom and one W-Ti bond. This value, in our opinion, may be sufficient to form a strong W-Ti bond, which will be shown below.
The adsorption energy in the bonding position C occupies a transition state (see Table 2). For a better understanding of the chemisorption processes, it is necessary to study the distribution of effective charges on the W atom and atoms of the nearest environment for different adsorption models. The results of DFT-calculations of effective charges on W, Ti, and C atoms of the nearest environment (local) and on Ti and C atoms (cell averages) for the configurations considered are given in Table 3.
In the second stage, the adsorption energy of tungsten on a defect surface in the W/TixCy (111) system was studied. As shown in Fig. 2 d, e, f, the W atoms occupy the positions of titanium vacancies. Surface configuration data are characterized by high values of adsorption energy (see Table 2). The highest value is = –12.21 eV/atom corresponding to the binding position A, where the adsorbate replaces the titanium vacancy position. It should be noted that during relaxation, the atom W from the position C can be displaced to the position of the vacancy Ti (position A) or remain in position C in the presence of a carbon vacancy. Analysis of the data in Table 2 shows that a decrease in the lattice symmetry associated with the Ti- and C-vacancies leads to an increase in the adsorption energy in the A position for W/TixCy systems by more than 1.2 times. The value = –12.21 eV/atom gives us the basis for the assumption that position A can be the nucleation center of W atoms in the W/TixC (111) system. Here, the atom W has occupied the vacancy position of the Ti atom in the uppermost layer, which confirms the high probability of realizing the first mechanism for structuring the surface at an early stage. Values of adsorption energy W in position A (on metal) in stoichiometric and non-stoichiometric systems in comparison with similar estimates are given in Table. 2.
Analysis of the results in Table 2 shows that the adsorption energy of d-metals on the polar surface is 1.9 times larger than on the (001) TiC surface. A similar relation holds for the adsorption energy of atomic oxygen on surfaces (111) and (001) of 2D (Ti) Ti. The increase in the degree of tungsten coating to = 1 MS in position B (fcc) on TiC (111) correlates with an increase in the adsorption energy by 1.2 times (see Table 2). It should be noted that in the early stages of tungsten nucleation on the polar surface of TiC (111), TixC (111) and TiCy (111) systems, the three possible surface reconstruction mechanisms responsible for the formation of new material properties can be realized.
In the W/TixCy(111) and W/TiC(111) systems considered above, the electron spectrum of carbon, titanium and tungsten atoms depends on the intensity of the charge transfer processes (see Table 3) between the W atom and the nearest-neighbor atoms. The layered electron energy spectrum calculated by us allows us to state that the titanium atoms of the uppermost layer are in a chemical bond with tungsten. The presence of a 2 eV shift in the energy band of the 2p-states band of the upper bilayer (Ti, C) carbon allows us to speak about the existence of the C2p-W5d interaction, which weakens in the underlying layers of carbon. The Ti and C atoms most distant from tungsten form the density of states at the Fermi level, formed mainly by the Ti3d- and C2p-states. Unsaturated states near the Fermi level arise as a result of overlapping and hybridization of the surface states of the W, Ti, and C atoms.
It was established for the first time that adsorption of tungsten on low-imperfect surfaces of TixCy(111) in different binding positions leads to a significant rearrangement of the local atomic structure and the band energy spectrum. It is shown that, in the presence of a vacancy in the uppermost layer of titanium, tungsten atoms are able to replace their positions, forming W-C bonds of length = 2.03 Е; if titanium and carbon are simultaneously present, then the atom W can occupy the position of the vacancy Ti. As a result of the study, it was suggested that in the early stages of tungsten nucleation on the polar surface of the TixCy (111) systems, three proposed surface reconstruction mechanisms that are responsible for the formation of new material properties can be realized.
The effective charges on the titanium and carbon atoms surrounding the tungsten adsorbed atom in different reconstructions are determined. Based on the DFT calculations, charge transfer from the titanium atom to tungsten and carbon atoms is established. Such a transfer of charge, in our opinion, is due to the reconstruction of local atomic and electronic structures. The decrease in the lattice symmetry associated with the Ti- and C-vacancies leads to an increase in the adsorption energy in the A position for W/TixCy systems by more than 1.2 times. The value of the adsorption energy = –12.21 eV/atom gives us the basis for the assumption that position A can be the center of nucleation of W atoms in the W/TixC (111) system.
 Ab initio is the Latin saying "from the beginning". Ab initio modeling in solid state physics makes it possible to calculate systems with a large number of atoms.