First-principles calculation and molecular dynamics simulation of fracture behavior of VN layers under uniaxial tension
Introduction
Transition metal nitrides, vanadium nitride (VN) and titanium nitride (TiN), have attracted a great deal of attention due to their excellent physical and mechanical properties, including high melting points, high hardness, high electrical conductivity, high resistance against corrosion and oxidation [1]. These excellent properties are suitable for a wide range of applications, such as the coatings for surface protection of cutting tools and thin films for electronic devices [2], [3], [4]. It has been found that TiN/VN nano-multilayered coatings, which are composed of alternatively arranged TiN and VN layers of nanometer thickness, possess a hardness of over 56 GPa, much higher than that of each respective nitride constituent [5]. However, the origin underneath the improvement of hardness for the TiN/VN nano-multilayered coatings remain not understood yet. To date, several explanations to the superhardness of the nano-multilayered coatings have been proposed such as the dislocation pile-up at the interface [6], [7], the Hall–Petch effect [8], the strain mismatch effect at the interface [9], and the super-modulus effect [10]. Nevertheless, none of them has been confirmed.
To clarify the superhardness mechanism for nano-multilayered nitride coatings, it is requisite to understand the deformation and failure behavior of each respective transition metal nitride. This requires in-depth knowledge on microstructures of the nano-multilayered coatings, especially at the atomic scale. However, such microstructures are often difficult to obtain experimentally, yet can in principle be captured through theoretical calculations [11]. First-principles calculation represents a powerful tool to obtain accurate ground-state energies and fundamental physical and mechanical properties of materials at the atomic scale. It has already been used to investigate elastic properties (e.g. bulk modulus, elastic constants, and Young's modulus) [12], [13], [14], [15], [16], [17], surface energy [18], [19], phase stability [20], [21], [22], and electronic structures [23], [24], [25], [26] of the V–N systems, as well as the bonding configuration and bond length change of nano-multilayer nitride coatings during deformation [27], [28]. It has been realized that the strength and hardness testing can reveal inelastic deformation and failure behavior, thereby allowing us to gain insights into the structure–property interplay. For instance, the uniaxial tension tests along different crystallographic orientations have been simulated on the first-principles levels [23], [29], but such simulations are usually performed using such a small sample that it may not possible to identify defects and their evolution during the simulation process. On the other hand, the temperature effect has to be considered.
Molecular dynamics (MD) simulations can also be applied to investigate behavior of materials, taking into account the effect of temperature. However, to the best of our knowledge, there is still no available interatomic potential for the binary V–N system, thus limiting the use of MD simulation. Here, we develop a second nearest-neighbor modified embedded atom (2NN MEAM) potential for the V–N system by fitting the results from the first-principles calculations. We apply both the first-principles calculations and MD simulations to clarify the deformation and failure mechanism of the VN thin layers subjected to a uniaxial tension at 0 K, 1 K and 293 K. The failure mechanism of the VN layers under uniaxial tension is discussed.
Section snippets
Potential formalism
In the MEAM, the total potential energy of a system can be expressed as [30], [31], [32], [33],where is the contribution from the atom i embedded in a background electron density , Sij and ϕij(Rij) are respectively the screening function and the pair-interaction between the atoms i and j distant by Rij. The introduced Sij differs from that in the conventional embedded-atom method (EAM). In the original MEAM [32], only the first nearest-neighbor (1NN)
First-principles calculation
Calculations are performed using the Vienna ab initio simulation program (VASP) within the framework of the density-functional theory (DFT). The pseudopotential and GGA (PW91) [39] are used and the cutoff energy of 450 eV and 6×6×2 k points [40] are used for VN. The VN has a size of a×a×a (a=0.412 nm is the lattice constant of the NaCl-type VN). These parameters can ensure the convergence of total energy to less than 0.01 eV/atom. The tensile strain–stress relationship is calculated by applying
Conclusions
We have conducted both first-principles calculations and molecular dynamics simulations to investigate the stress–strain relationship and clarify the failure mechanisms of the VN layers under uniaxial tension. We have selected the second nearest-neighbor modified embedded atom method interatomic potential for the MD simulations, and identified the material parameters for the VN in terms of the MEAM potentials. The properties of the VN with several different structures and the stress–strain
Acknowledgements
The authors acknowledge the financial support from National Natural Science Foundation of China (NSFC 11332013 and 11272364). Z.C.W. thanks financial supports from Grant-in-Aid for Young Scientists (A) (Grant no. 24686069), the JSPS and CAS under Japan-China Scientific Cooperation Program, and the Murata Science Foundation.
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