First-principles calculation and molecular dynamics simulation of fracture behavior of VN layers under uniaxial tension

https://doi.org/10.1016/j.physe.2015.01.046Get rights and content

Highlights

  • The 2NN MEAM potential of VN presented can reproduce fundamental physical properties of V–N system of other phases.

  • MD simulation of the deformation and fracture of VN layers under tension showed that fracture occurs when broken bonds regions grow and coalesce to larger defects.

  • Temperature may reduce the energy applied for deformation and failure of V–N systems.

  • No dislocation and slip were detected in the VN layers during deformation.

Abstract

We develop the second nearest-neighbor modified embedded atom method (2NN MEAM) potential for vanadium nitride (VN) in terms of the individual vanadium and nitrogen. The potential parameters are determined by fitting the cohesive energy, lattice parameter, and elastic constants of the VN with the NaCl-type structure, which are obtained by first-principles calculations. We find that the developed potentials can be used to describe the fundamental physical properties of the V–N system with other lattice structures. The calculated tensile stress–strain curves of the VN layers by first principles agree with those obtained by molecular dynamic simulations, validating the use of the developed potential. The bond breaking and its growth and coalescence are found to play an important role in the formation of fracture. We also find that temperature influences markedly the breaking of bonds, which can be attributed to the deviation of atoms from their equilibrium positions due to the thermal activated vibration, or to the superposition of the thermal energy to the deformation energy. Moreover, no dislocations and slips are found throughout the deformation process.

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],E=i[Fi(ρ¯i)+12j(i)Sijϕij(Rij)],where Fi(ρ¯i) is the contribution from the atom i embedded in a background electron density ρ¯i, 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.

References (50)

  • P.M. Anderson et al.

    Nanostruct. Mater.

    (1995)
  • M. Kato et al.

    Acta Metall.

    (1980)
  • R.C. Cammarata et al.

    Scr. Metall.

    (1986)
  • Y.M. Kim et al.

    Acta Mater.

    (2008)
  • D.J. Siegel

    Acta Mater.

    (2002)
  • M.G. Brik et al.

    Comput. Mater. Sci.

    (2012)
  • M.B. Kanoun et al.

    Surf. Coat. Technol.

    (2014)
  • W. Liu

    Surf. Sci.

    (2006)
  • C. Stampfl et al.

    Appl. Surf. Sci.

    (2012)
  • S.K. Gupta

    Mater. Chem. Phys.

    (2014)
  • D. Yin et al.

    Physica E

    (2012)
  • D. Yin et al.

    Ceram. Int.

    (2014)
  • M.I. Baskes

    Mater. Chem. Phys.

    (1997)
  • M.A. Tschopp et al.

    J. Nucl. Mater.

    (2012)
  • C. Ravi

    Calphad

    (2009)
  • H.J. Holleck

    J. Vac. Sci. Technol. A

    (1986)
  • R. Freer

    The Physics and Chemistry of Carbides, Nitrides, And Borides

    (1990)
  • A. Matthews

    Surf. Eng.

    (1985)
  • H.O. Pierson

    Handbook of Refractory Carbides and Nitrides: Properties, Characteristics, Processing, and Applications

    (1996)
  • U. Helmersson et al.

    J. Appl. Phys.

    (1987)
  • J.S. Koehler

    Phys. Rev. B

    (1970)
  • X. Chu et al.

    J. Appl. Phys.

    (1995)
  • C. Stampfl

    Phys. Rev. B

    (2001)
  • P. Lazar et al.

    Phys. Rev. B

    (2007)
  • D. Holec et al.

    Phys. Rev. B

    (2012)
  • Cited by (24)

    • Effects of twin boundaries in vanadium nitride films subjected to tensile/compressive deformations

      2017, Applied Surface Science
      Citation Excerpt :

      The parameters in the potentials for the single elements V and N and those in the binary interatomic potential between V and N have been given by Baskes et al. [31], Lee et al. [32] and Fu et al. [33], respectively. MEAM potentials was found to be able to reproduce the fundamental physical and mechanical properties of materials, such as lattice parameters, cohesive energy, elastic property and surface energy, and have been successfully applied to analyze the fracture behavior of VN films [33] and explore the deformation mechanisms of VN under indentation, incorporating stacking fault energy [24,34–36]. As mentioned in Introduction, TBs were predicted to exist in transition-metal nitrides [23] using either first principle calculations or MD simulation of nanoindentation on VN (111) at 300 K[24].

    View all citing articles on Scopus
    View full text