Abstract
Available information concerning the elastic moduli of refractory carbides at temperatures (T) of relevance for practical applications is sparse and/or inconsistent. Ab initio molecular dynamics (AIMD) simulations at T = 300, 600, 900, and 1200 K are carried out to determine the temperature-dependences of the elastic constants of rocksalt-structure (B1) TiC, ZrC, HfC, VC, TaC compounds, as well as high-entropy (Ti,Zr,Hf,Ta,W)C and (V,Nb,Ta,Mo,W)C. The second-order elastic constants are calculated by least-square fitting of the analytical expressions of stress/strain relationships to simulation results obtained from three tensile and three shear deformation modes. Sound-velocity measurements are employed to validate AIMD values of bulk, shear, and elastic moduli of single-phase B1 (Ti,Zr,Hf,Ta,W)C and (V,Nb,Ta,Mo,W)C at ambient conditions. In comparison with the predictions of previous ab initio calculations – where the extrapolation of finite-temperature elastic properties accounted for thermal expansion while neglecting intrinsic vibrational effects – AIMD simulations produce a softening of shear elastic moduli with T in closer agreement with experiments. The results show that TaC is the system which exhibits the highest elastic resistances to tensile and shear deformation up to 1200 K, and indicate the (V,Nb,Ta,Mo,W)C system as candidate for applications that require superior toughness at room as well as elevated temperatures.
Highlights
Elastic moduli and elastic stiffness constants of crystals have primary importance in materials design and materials discovery
Previous 0-K ab initio calculations based on generalized gradient approximation (GGA) slightly overestimate the experimental lattice parameters of B1 transition-metal carbides (TMC)
Our ab initio molecular dynamics (AIMD) results closely match with the lattice constants and thermal expansion coefficients determined by experiments at different temperatures (Table 2)
Summary
Elastic moduli and elastic stiffness constants of crystals have primary importance in materials design and materials discovery. Realistic modeling and evaluation of mechanical properties as hardness and toughness, which would require simulation boxes with volumes of the order ≈103–105 nm3 [15], is currently unfeasible for first-principles methods. For this reason, ab initio calculated polycrystalline elastic moduli, such as shear modulus and Poisson ratio, are widely employed to design empirical indicators of hardness and toughness of compounds and alloys [9, 1620] which, combined with the progress in machine-learning approaches [20,21,22], can lead to an increasingly more rapid identification of solids with enhanced mechanical performance. 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
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