Structural and elastic properties of ZrC under high pressure

Abstract

We have investigated the structural and elastic properties of ZrC under high pressures using the norm-conserving pseudopotentials within the local density approximation in the frame of density-functional theory. The calculated pressure dependence of the normalized volume is in excellent agreement with the experimental results. The (a − a₀)/a₀, (V − V₀)/V₀, the ductile/brittle, the elastic constants C_ij (GPa), shear modulus C′, bulk modulus B, shear modulus G (GPa), Young's modulus E (Gpa), Poisson's ratio σ and anisotropy factor A as a function of applied pressure are presented. Through the quasi-harmonic Debye model, we also study the thermodynamic properties of ZrC. The thermal expansion versus temperature and pressure, the thermodynamic parameters X (X: Debye temperature or specific heat) with pressure P, and the heat capacity of ZrC at various pressures and temperatures are estimated.

Introduction

Belonging to the group of binary A^NB^8−N compounds with a total of eight valence electrons, binary ZrC ceramic is characterized by high melting point, high hardness, high stiffness, and chemical inertness [1]. This combination of properties has made the carbides important in a wide variety of technological applications, for example, structural, chemical, electronic, and nuclear applications, etc. [2]. However, the poor oxidation resistance and intrinsic brittleness restrict its extensive applications [3].

Because of the technological interest, the extraordinary mechanical and thermal properties of ZrC have yet to be analyzed at the level of atomistic modeling and simulation. Such studies could play a significant role from the standpoint of predicting the performance of the material under service conditions, typically earmarked by stress or thermal loading, or a radiation field [4]. In theory, the band structure of ZrC has been extensively investigated by Refs. [5], [6], [7]. Recently, Méçabih et al. [3], Zaoui et al. [8] and Chen et al. [9] have studied the structural and electronic properties of ZrC, using the full potential-linear augmented plane-wave (FP-LAPW) method [10] with the GGA approximation [11]. And Wu et al. [12], have studied transition-metal (TM)nitrides and carbides in B₁ structure using the ab initio density-functional perturbation theory, which bases on plane-wave basis sets and norm-conserving pseudopotentials. Furthermore, Li et al. [4], have investigated the classical potential and thermal properties of ZrC in the form of a modified second-moment approximation which emphasis on the strong directional dependence of the C–Zr interactions in ZrC. Barsoum gives a review on the ternaries of ZrC with M_N+1AX_N Phases [13], and Warner et al. [14] and Music et al. [15] have studied the ternaries of ZrC with MAX Phases. In our case, we focus on investigating the EOS (equations of state) and the elastic properties of the ZrC in the range of −20 to 60 GPa by the plane-wave pseudopotential density-functional theory method through the Cambridge Serial Total Energy Package (CASTEP) program [16] and the quasi-harmonic Debye model [17], which allows us to obtain all thermodynamics in the atomic level. As known, elastic properties are closely related to many fundamental solid-state properties, such as equation of state, specific heat, thermal expansion, Debye temperature, Grüneisen parameter, melting point, and so on, and are important in many fields ranging from geophysics to materials research and from chemistry to physics. The knowledge of elastic constants is essential for many practical applications related to the mechanical properties of solids, for example, load deflection, thermoelastic stress, internal strain, sound velocities and fracture toughness [18].