Vacancies, interstitials and their complexes in titanium carbide

Abstract

Titanium carbide is a prototype transition-metal compound and is used in various applications due to its exceptional hardness and stability. Here we use first-principles calculations to elucidate the properties and interactions of TiC point defects and their role on the thermal stability of TiC films. We find that the stability of defects and defect complexes depends strongly on structural details. We also show via calculations of diffusion barriers that, while carbon interstitials are relatively mobile species, the migration of carbon vacancies is suppressed unless the sample is heated to extremely high temperatures. We close with a discussion on defect-related effects and a comparison with similar physical traits in transition-metal nitrides.

Introduction

Transition-metal carbides exhibit outstanding hardness, extremely high melting points, wear and corrosion resistance, biocompatibility, and low friction coefficients [1]. Because of these properties they are used in a wide range of applications. For example, they are commonly used in cutting tools and for mechanical reinforcement in cermet composites with titanium or nickel–cobalt matrices. Titanium carbide is regarded as a prototype transition-metal carbide. In addition to the above advantageous physical traits, TiC is relatively light, it has interesting catalytic behavior [2], and it forms solid alloys of tailored properties [3], [4], [5] with another prototype refractory material, titanium nitride [6]. TiC-based nanocomposites are candidates for superhard materials, [7] and they have been shown to provide enhanced toughness [8], [10], [9] and self-regulation between hard and ductile mechanical behavior [11]. Titanium carbide nanocrystals have also been detected in graphitic grains of meteorites and their origin has been linked to rapid mass loss from dying stars [12].

Although other stable crystal structures exist [13], the most common lattice phase of titanium carbide is the rock-salt (NaCl) face-centered cubic configuration. The structure is retained for significant deviations from the 1:1 stoichiometry ratio, and rock-salt TiC_x films with x as low as 0.5 have been reported [1], [14]. Several different experimental and theoretical techniques have been used to probe the details of the point defects that are responsible for substoichiometric and overstoichiometric concentrations. The properties of vacancies in substoichiometric TiC_x have been studied with X-ray photoemission [14], high-resolution X-ray diffraction [15], first-principles total-energy calculations [16], [17], [18], [19], [20] and modeling of electron energy loss spectra [21], [22]. In particular, early studies [16] identified so-called vacancy-states as the origin of pronounced peaks in the electronic density of states (DOS) in ordered substoichiometric TiC_0.75 samples. Tan et al. [17] used a tight-binding scheme to describe the outward relaxation around vacancy sites in TiC and reported a slight increase in lattice dimensions for small deviations from the 1:1 composition ratio. Hugosson et al. [18] and Korzhavyi et al. [19] employed a combination of a pseudopotential plane wave approach and the full-potential linear muffin-tin method in a detailed study of the energetics and structural properties for various configurations of substoichiometric TiC_x and for different crystalline phases. They confirmed the presence of vacancy-related peaks in the DOS and they provided new insights for the anomalous volume behavior of TiC at small vacancy concentrations. Dridi et al. [20] reported results for the vacancy-induced states and in addition they studied the variation of the bulk modulus and equilibrium volume with respect to C substoichiotmetry. Scott et al. [21] and Mirguet et al. [22] employed first-principles studies to model the effect of C vacancies on the electron energy loss spectra of substoichiometric TiC and demonstrated the sensitivity of spectral features to lattice dimensions and chemical composition.

The presence of vacancies has also been identified as a controlling factor for the thermal conductivity [23] of bulk TiC and for the wettability of TiC surfaces [24]. Most of the experimental studies find substoichiometric TiC_x films, and it is generally believed that carbon vacancies control the deviation from the nominal 1:1 ratio in these films. For this reason previous calculations have focused mainly on the properties of carbon vacancies. There are studies, however, that have provided evidence for positron annihilation at Ti vacancies [25], and for interstitial carbon atoms in TiC films [26], [27]. Experiments have also probed the diffusion of carbon in TiC and a wide range of activation energies has been reported [28], [29], [30]. Even though certain details of the structure and interaction of vacancies have been addressed by previous studies, several questions on the stability and interaction of native point defects of TiC remain open, including questions about the atomic-scale mechanisms of defect migration and transformation and their role on thermal stability.

In this paper we use first-principles calculations to study the four possible types of native point defects of titanium carbide: carbon (V_C) and titanium (V_Ti) vacancies, and carbon (I_C) and titanium (I_Ti) interstitials. We investigate the structural properties and the stability of isolated carbon vacancies and of C vacancy pairs. We find that the interaction of vicinal C vacancies depends strongly on the orientation of the V_C pair, and we confirm the outward relaxation around V_C sites in agreement with experiments and previous theoretical studies. We study various possible configurations of C interstitials (I_C) to show that the tetrahedral configuration is the most stable I_C structure, and we obtain an appreciable binding energy for a pair of proximal tetrahedral C interstitials. We also show that C and Ti vacancies manifest with the appearance of DOS peaks in the energy range around the Fermi level of TiC. We find that the activation of V_C migration can occur only at very high temperatures because of large diffusion barriers of 3.46 eV. I_C migration barriers are lower (2.5 eV), indicating that I_C are the most mobile native defects in TiC. We thus address pertinent experimental measurements on chemical diffusion in TiC. Finally, we discuss the role of C point defects on the thermal stability of TiC, and we point out similarities and differences with the physical properties of crystal imperfections in transition-metal nitrides [31], [32].