Temperature-dependent mechanical properties of ZrC and HfC from first principles

Abstract

In order to gain insight into the effect of elevated temperature on the mechanical performance of zirconium carbide (ZrC) and hafnium carbide (HfC), their temperature-dependent elastic constants have been systematically studied. This has been done using two different approximations, qusi-harmonic (QHA) and qusi-static (QSA) ones. The former is more accurate, but also more computational expensive. Isoentropic C11 gradually decreases, and C12 slightly increases for ZrC and HfC under temperature, while C44 of both is insensitive. For both ZrC and HfC, the decline of temperature-dependent C11 calculated from QHA is more pronounced than from QSA. Temperature effects on modulus of elasticity, Poisson's ratio, elastic anisotropy, hardness, and fracture toughness are further explored, and discussed. The results indicate that the decrease of bulk modulus B, shear modulus G, and Youngs modulus E approximated from QHA is more significant than from QSA at high temperatures. From room temperature to 2500 K, the theoretical decreasing slope (from QHA) of B,

Temperature-dependent elastic properties of binary and multicomponent high-entropy refractory carbides

“…Overall, our AIMD results closely match with experimental [64] and ab initio values retrievable from the literature (Tables 3-9). For example, the temperature dependence of the Young's moduli E of B1 zirconium carbides, previously determined by experiments [65][66][67] and other ab initio calculations based on the QHA [27], agrees with the results of AIMD simulations (Table 4). The variation of E vs. T shows that the elastic modulus of ZrC decreases at a quasi-linear decay rate…”

“…In contrast, information concerning finite-temperature elastic properties is rather sparse for these classes of materials. Finite-temperature estimations of SOEC can be efficiently obtained using static ab initio calculations that employ the quasiharmonic approximation (QHA) [23,27,62] or volume-scaling methods [28,31]. These methods account for lattice thermal expansion while neglect anharmonic vibrational effects.…”

“…Before conclusions, we offer a comparison of different computational techniques for the evaluation of finite-temperature elastic properties. As anticipated at the beginning of this section, finite-temperature elastic properties of some refractory nitrides and carbides have been calculated via the QHA [23,27,62] or volume-scaling methods [28,31] in the framework of static first-principles techniques. These, however, generally produce a slower decay in elastic stiffnesses vs. T than methods which account for intrinsic anharmonic effects, as demonstrated for B1 Ti1-xAlxN [28] and CrN [31] refractory compounds.…”

“…QHA results are from Ref. [27]; experimental results for ZrCx (x ≤ 1): pink square [36], black triangle [36], blue circles [92], orange solid line [67] {B = E/[3(1-2v)] and G = 3BE/(9B-E)}, red solid line [66]. (c) C44 vs. T in TiN.…”

“…In the case of refractory carbide, nitride, and boride ceramics, properties as hardness and toughness are of paramount importance, especially for high-temperature applications. Despite this, the elastic constants of these refractory ceramics have been primarily evaluated at 0 K. Ab initio estimations of elastic constants at finite temperatures are often done using static calculations at cell volumes determined in the quasiharmonic approximation for the thermal expansion (see, e.g., [23][24][25][26][27]). However, explicit inclusion of lattice vibrations in theoretical modeling is shown to result in significant differences in second-order elastic moduli and a change of elastic anisotropy of materials at moderate or high temperatures [28,29].…”