Theoretical study on the stability, elasticity, hardness and electronic structures of W–C binary compounds

Abstract

The ground state properties of W–C binary compounds (h-WC, c-WC, α-W₂C, β-W₂C, γ-W₂C, ɛ-W₂C) are studied in this paper by using first-principles calculations. Formation enthalpy and cohesive energy for each phase are calculated. The calculated elastic constants satisfy the Born–Huang's stability criterion, indicating all studied compounds are mechanically stable. All W–C compounds studied in this paper exhibit larger bulk modulus values than many other binary types of carbide such as Fe₃C, Cr₇C₃, Cr₃C, and TiC. Using a theoretical method based on the works of Šimůnek, the hardness of the crystal is estimated. The electronic structures of these compounds are calculated and discussed. Stoner's polarization theory for itinerant magnetism is applied to explain the observed paramagnetic behavior of the compounds. Moreover, the heat capacity is also calculated for each compound based on the knowledge of the elasticity and Debye temperature.

Introduction

In recent decades the transition metal carbides are extensively investigated both by theoretical calculations and by experimental methods; because many of them exhibit outstanding mechanical properties and chemical stability, for instance they are very hard compounds and have high melting point, high thermal conductivity, etc. One of the most important compounds is the tungsten carbides: hexagonal and cubic mono-carbides WC, and four polymorphs (α, β, γ, ɛ) of semi-carbide W₂C. The properties of thermal stability and high elastic modulus determine the usage of W–C compounds in the production of wear resistant hard alloys, which form the basis of the metal cutting instruments, for example, the cemented carbide [1], [2], [3], [4] and high-speed steel [5], [6], [7].

In all bulk W–C binary compounds, the investigations of hexagonal WC (h-WC) have been performed extensively, including the properties of bulk structures [8], [9], [10], the surfaces ((0 0 0 1) [11], [12], $(10\overline{1}0)$ [13] and $(11\overline{2}0)$ [13], etc.) and the different interfaces (Al/WC [10], Fe/WC [14]). Liu et al. [8] investigated the structural and electronic properties of h-WC by performing a pseudopotential total-energy calculation. The obtained bulk modulus was 413 GPa which lies in the range of the measured values (329–577 GPa). They also found that the Fermi level locates in a deep minimum of the DOS, and the strong W–C bonds play an important role in the stability of WC. Zhukov and Gubanov [9] confirmed the extraordinary high values of bulk modulus (655 GPa) and Debye temperature (648 K) of h-WC which explain in part the superior properties of WC as a cutting material. In addition to the hcp phase, WC also exists in the NaCl-type structure (c-WC). This is a high temperature phase and can be stabilized at room temperature by a rapid quenching process applied to the liquid state [15]. The c-WC is found to be superconducting with a transition temperature of 10.0 K [16], and the h-WC is more stable than the c-WC. The electronic band structure and density of states show that the instability of NaCl-type structure is due to the occupation of anti-bonding states [17]. While less information is available for the electronic structure, stability and mechanical property of W₂C polymorphs. Until recently, Kurlov and Gusev [18] summarized the phase equilibrium in the W–C binary system and the crystal structures of all W–C carbides, who pointed out that the hardness of WC decreases slightly with increasing temperature from 300 to 1200–1300 K. Suetin et al. [19], [20] reported that all W–C phases depending on their thermodynamic stability have the following sequence: h-WC > ɛ-W₂C > β-W₂C > γ-W₂C > α-W₂C > c-WC. Meanwhile, the abrasive resistance of WC/W₂C–(Co, Ni) alloys, the properties of cermets coatings and the WC/Metal matrix composites were investigated by other articles [21], [22], [23]. In this paper, our main interests are to study the chemical stability, electronic structures, mechanical properties (especially elastic modulus and hardness), and heat capacity of all W–C binary compounds.