Chemical Bonding Analysis in Ti1-x-yAlxTayN Solid Solutions

A comprehensive study of the evolution of electronic structure and chemical bonding in disordered Ti1-xAlxN and Ti1-x-y AlxTayN systems was performed by means of ab initio density functional theory calculations using crystal orbital Hamilton population technique. Abstract A comprehensive study of the evolution of electronic structure and chemical bonding in disordered Ti 1 − x Al x N and Ti 1 − x − y Al x Ta y N systems was performed by means of ab initio density functional theory calculations using crystal orbital Hamilton population technique. Progressive changes in the character of interatomic chemical bonding were revealed when sequentially alloyed TiN with Al and Ta. Alloying TiN with Al leads to the change in the Ti-N bonding character from ionic to covalent, whereas Al-N bonds being strongly ionic. The following alloying of Ti 1 − x Al x N solid solutions with Ta results in a signiﬁcant reduction of the ionicity of the Al-N bonds, while retaining the covalency of the Ti-N bonds. In addition, alloying with Ta introduces metallic character of chemical bonding in Ti 1 − x − y Al x Ta y N, with the degree of metallicity increasing with growing Ta concentration. The gain in metallicity was found to be provided not only by Ta-Ta bonds, which make the main contribution, but also by Ta-N bonds, which have covalent-metallic character. A strong dependence of bonding energies in Ti 1 − x Al x N and Ti 1 − x − y Al x Ta y N on local atomic surrounding was found.

Introduction fast diffusion paths, dramatically decreasing the oxidation resistance of the coatings. 29 Moreover, Ti 1−x Al x N is fully oxidized at 1000 • C. 20 Therefore, over the past two decades intensive efforts have been directed towards finding ways to further improve the characteristics of the Ti-Al-N system.
Along with formation of hierarchical microstructures, which allow improvement of mechanical characteristics of Ti-Al-N, 30,31 the most effective way for solving this problem is the introduction of additional alloying elements into Ti 1−x Al x N, that is, obtaining of quaternary, quinary, etc.
solutions. 32,33 In particular, the addition of elements of the IV and V groups (Zr, Nb, Hf and Ta) to the Ti 1−x Al x N coatings is very promising. So, Zr increases the oxidation resistance of the coatings, contributing to the formation of a dense protective oxide layer on their surface. 29,34 In addition, the introduction of its small additives leads to an increase in the hardness of the coatings and the critical temperature of spinodal decomposition. Doping with Nb leads to an increase in thermal stability and ductility of Ti 1−x Al x N coatings, however, there is a slight decrease in their hardness. 35 Hf provides the growth of hardness and thermal stability of Ti 1−x Al x N coatings, whereas the effect on their oxidation resistance is ambiguous. 36 Finally, one of the most promising alloying element is Ta, which allows not only significant enhancing of the hardness, toughness and oxidation resistance of Ti 1−x Al x N coatings, but also increasing the temperature of formation of the AlN wurtzite phase up to 1200 • C, which ensures maintaining high hardness values up to this temperature. 32,[37][38][39] It is well-known that the properties of the multicomponent solid solutions strongly depend even on small variations of the relative content of the constituting chemical elements. 32 To a large extent this is due to the changes in the electronic structure and chemical bonding of the transition metal nitrides caused by variations of their elemental composition. Despite the numerous experimental and theoretical investigations of the mechanical properties, 32,35,40 solar selective characteristics, 41,42 oxidation behavior, 32,38,43 biocompatibility 44,45 and thermodynamic stability [46][47][48][49] of different ternary and quaternary TiN-based solutions, the quantitative analysis of the evolution of chemical bonding of these materials at an ab initio level was not thoroughly addressed. In the present paper, within density functional theory (DFT) calculations, we examine the evolution Figure 1: Supercell for disordered Ti 1−x−y Al x Ta y N constructed on the base of 2×2×2 cell of the cubic TiN with 25% of Al and 25% of Ta atoms randomly distributed on the Ti sublattice. The presented ball-and-stick atomic structure was created with VESTA. 50 of electronic structure and the interatomic chemical bonding in multicomponent TiN-based solid solutions from TiN through Ti 1−x Al x N to Ti 1−x−y Al x Ta y N with different atomic ratios of Ti, Al and Ta, using crystal orbital Hamilton population formalism. We also discuss the effect of the chemical bonding on elastic properties of the TiN-based systems.

Calculation methods
The density functional theory calculations were done with the Vienna ab initio simulation package (VASP) 51,52 using the projector augmented wave (PAW) method. 53,54 The electron exchange-correlation functional was described by the generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE). 55 The Ti 1−x−y Al x Ta y N solid solutions were modeled by 2×2×2 rocksalt cubic supercells containing 64 atoms in which the metal sublattice was occupied by randomly distributed Ti, Al, and Ta atoms. As an example of such supercells, the structure containing 50% of Ti, 25% of Al and 25% of Ta atoms on the the metal sublattice is shown in Fig. Figure 1. The structure relaxation considering both the atomic positions and lattice vectors was performed by the conjugate gradient scheme until the maximum force on each atom was less than 0.001 eV/Å, and the total energy was converged to 10 −6 eV with the tetrahedron method with Blöchl corrections. The Brillouin zone (BZ) integration was sampled by using a 9×9×9 Monkhorst-Pack k-points grid for the calculations of relaxation and electronic structure. The elastic constants C i j were calculated by an automatic procedure 56,57 implemented in VASP. The cubic elastic constants for disordered Ti 1−x−y Al x Ta y N solid solutions, C 11 , C 12 , and C 44 , were obtained by averaging as C 11 = 1/3(C 11 + C 22 + C 33 ), C 12 = 1/3(C 12 +C 13 +C 23 ), and C 44 = 1/3(C 44 +C 55 +C 66 ). Isotropic bulk B and shear G moduli were evaluated as described in Ref. 58.
To study the interatomic chemical bonding in multicomponent systems based on TiN, we used crystal orbital Hamilton population (COHP) analysis. 59 This technique adopted for plane-wave electronic structure calculations (projected COHP) 60

Results and discussion
TiN belongs to NaCl-type cubic structure with the Ti atom sitting at the 1a (0, 0, 0) site, and the   In Fig. Figure 6, left panel, it is presented the total valence charge density of TiN in the (001) plane, which shows almost spherical shape of the charge distribution that corresponds to strong ionic character of the Ti-N bonds. The charge transfer from the titanium atom to the nitrogen atom calculated using the Bader method 67 amounts 2.12 e. In Ti 0.75 Al 0.25 N (Fig. Figure 6, central panel), the Al-N bonds are also highly ionic, since the aluminum valence electrons are almost completely transferred to neighboring nitrogen atoms. At the same time, as can be seen from As can be seen from the average COHP for Ta-N bonds (Fig. Figure 7), for any y the Ta charge density (Fig. Figure 9)