Investigations on structural, elastic, thermodynamic and electronic properties of TiN, Ti2N and Ti3N2 under high pressure by first-principles

https://doi.org/10.1016/j.jpcs.2016.05.012Get rights and content

Highlights

  • N–Ti compounds become from brittle to ductile with pressure rise.

  • With N content increase in N–Ti compounds, the micro-hardness increases.

  • TiN and Ti2N present metallic character. Ti3N2 present semiconducting character.

  • The bonding behavior of N–Ti compounds is a combination of covalent and ionic nature.

Abstract

The lattice parameters, cell volume, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio are calculated at zero pressure, and their values are in excellent agreement with the available data, for TiN, Ti2N and Ti3N2. By using the elastic stability criteria, it is shown that the three structures are all stable. The brittle/ductile behaviors are assessed in the pressures from 0 GPa to 50 GPa. Our calculations present that the performances for TiN, Ti2N and Ti3N2 become from brittle to ductile with pressure rise. The Debye temperature rises as pressure increase. With increasing N content, the enhancement of covalent interactions and decline of metallicity lead to the increase of the micro-hardness. Their constant volume heat capacities increase rapidly in the lower temperature, at a given pressure. At higher temperature, the heat capacities are close to the Dulong–Petit limit, and the heat capacities of TiN and Ti2N are larger than that of c-BN. The thermal expansion coefficients of titanium nitrides are slightly larger than that of c-BN. The band structure and the total Density of States (DOS) are calculated at 0 GPa and 50 GPa. The results show that TiN and Ti2N present metallic character. Ti3N2 present semiconducting character. The band structures have some discrepancies between 0 GPa and 50 GPa. The extent of energy dispersion increases slightly at 50 GPa, which means that the itinerant character of electrons becomes stronger at 50 GPa. The main bonding peaks of TiN, Ti2N and Ti3N2 locate in the range from −10 to 10 eV, which originate from the contribution of valance electron numbers of Ti s, Ti p, Ti d, N s and N p orbits. We can also find that the pressure makes that the total DOS decrease at the Fermi level for Ti2N. The bonding behavior of N–Ti compounds is a combination of covalent and ionic nature. As N content increases, valence band broadens, valence electron concentration increases, and covalent interactions become stronger. This is reflected in shortening of Ti–N bonds.

Introduction

As one of transition-metal nitrides, Titanium nitride (TiN) was first separated by Story-Maskelyne from a meteorite. It crystallizes into well-known rock-salt structure. Titanium nitride and its derivatives have many remarkable properties and good potential applications, such as chemical stability, thermal stability, oxidative resistance, good adhesion to the substrate, high fracture toughness and high hardness [1], [2], [3], [4], [5]. TiN is one of the most important metal cutting tools and coating materials for surface protection due to its extreme hardness, high melting temperature, and excellent corrosion resistance [6]. TiN ceramics have a good resistance to corrosion by liquid steel for some steel making processes [7]. It is also have been used for diffusion barriers, superconducting devices, and energy-saving coatings for windows due to their strong infrared reflection [8], [9].

The interesting properties of the transition metal compound, TiN, have been studied with many methods in recent years [10], [11], [12], [13], [14], [15]. Up to now, TiN is still controversial in high-pressure structural phase transitions [7]. Under high-pressure condition, the studies of new ultra-incompressible materials with novel mechanical and electronic properties, such as TiN and its derivatives, are significantly interesting and practical important. There are a number of experiments devoted to various aspects of TiN film growth and many theoretical calculations about material behaviors for TiN [16], [17], [18], [19], [20]. Under ambient conditions, TiN crystallizes in the NaCl (B1) structure. TiN might undergo an isostructural phase transition from B1 structure to CsCl (B2) structure or other phase [7]. Theoretically, as early as in 1996, Ahuja et al. [21] investigated the electronic structure, elastic constants and pressure-induced structural phase transformation of TiN based on the Full Potential Linear Muffin-tin Orbital (FPLMTO) method. They predicted the structural phase transformation pressure for TiN from B1 structure to B2 structure to be 370 GPa. Li et al. [8] studied the interfacial structures of TiN/MgO interfaces with different orientation relationships and bonding configurations using first-principles with the density function theory (DFT). Yadav et al. [22] studied the generalized stacking faults energies in different slip planes of both TiN and MgO. Zhu et al. [7] investigated the phase sequence with pressures and elastic properties at high pressures of TiN using DFT method based on pseudopotential plane-wave method. Liu et al. [6] made first-principles calculations on the thermodynamic properties and the phase transition of TiN from B1 to B2 structure. Yin et al. [23] conducted a systematic first-principles investigation of ideal tensile stress and fracture behaviors of the TiN/VN interface. Xuan et al. [24] studied the making of TiN substrate with a high relative density and a low surface roughness. However, most of their studies focus on the stoichiometric rock-salt TiN, and there are a few studies of non-stoichiometric titanium nitrides. Yu et al. [25] made first-principles evolutionary searches for stable Ti–N compound and found, in addition to the well-known rock-salt TiN, new ground states Ti3N2, Ti4N3, Ti6N5 at atmospheric pressure, and Ti2N and TiN2 at higher pressure. They also gave the mechanical properties of the Ti–N compounds at 0 GPa. Hence, in our work, under pressure condition, the material behaviors for the stable Ti–N compounds are analysed based on the calculations by first-principles.

In this paper, the structural, elastic, thermodynamic, and electronic properties of TiN, Ti2N and Ti3N2 are calculated in the pressures range from 0 GPa to 50 GPa. The properties of c-BN are also calculated for the sake of comparison. The study may do something which can help people know more about those novel crystal structures. We hope this study will provide guidance for experimental groups aiming to synthesize those novel crystal structures.

Section snippets

Methods

In the calculations, the structural optimization and properties predictions of TiN and its derivatives are performed by using the DFT with the local density approximation (LDA) and the generalized gradient approximation (GGA) parameterized by Perdew, Burke and Ernzerrof (PBE) as implemented in the Cambridge Serial Total Energy Package (CASTEP) code [26]. The ultrasoft pseudopotentials introduced by Vanderbilt [27] have been employed for all the ion-electron interactions in the calculations of

Structural properties

Structure of unit cell plays a very important role in understanding the nature of solid materials. Fig. 1 shows the structures of c-BN, TiN, Ti2N and Ti3N2 at 0 GPa. Both of c-BN and TiN have a higher symmetrical structure. c-BN is the cubic structure with F-43M space group, and TiN is the the cubic structure with Fm-3m space group. Ti2N is tetragonal structure with space group of P42/mnm. Ti3N2 is orthorhombic structure which belongs to space group of Immm. By geometry optimization, the

Conclusions

The structural, elastic, thermodynamic, and electronic properties of TiN, Ti2N and Ti3N2 are analysed under high pressure. TiN is more incompressible than Ti2N and Ti3N2, but more compressible than c-BN. The results by first-principles are in accordance with the results by Birch–Murnagahan equation of states. The behaviors for TiN, Ti2N and Ti3N2 become from brittle to ductile with pressure rise. The Poisson's ratios of titanium nitrides are larger than that of c-BN. It is shown that the TiN, Ti

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