Bond-order potential for molybdenum: Application to dislocation behavior

Abstract

The bond-order potential (BOP) for transition metals is a real-space semiempirical description of interactions between the atoms, which is based on the tight-binding approximation and the d-band model. This scheme provides a direct bridge between the electronic level modeling and the atomistic modeling, where the electronic degrees of freedom have been coarse grained into many-body interatomic potentials. In this paper we construct BOP in which both the attractive and the repulsive contributions to the binding energy are environmentally dependent due to both the nonorthogonality of the orbitals and the breathing of the screening charges. The construction of the BOP is described and tested in detail. First, the energies of alternative crystal structures (A15, fcc, hcp, simple cubic) are calculated and compared with those evaluated ab initio. The transferability of the BOP to atomic configurations that deviate significantly from the bcc lattice is studied by computing the energies along tetragonal, trigonal, and hexagonal transformation paths. Next, the phonon spectra are evaluated for several symmetrical crystallographic directions and compared with available experiments. All these calculations highlight the importance of directional bonding and the investigation of phonons demonstrates that the environmental dependence of the bond integrals is crucial for the phonons of the N branch not to be unphysically soft. Finally, the constructed BOP was applied in the modeling of the core structure and glide of the 1/2⟨ ⟨111⟩ ⟩ screw dislocation. The calculated structure of the core agrees excellently with that found in the recent ab initio calculations and the observed glide behavior not only agrees with available ab initio data but is in agreement with many experimental observations and explains the primary reason for the breakdown of the Schmid law in bcc metals. The bond-order potential ͑BOP͒ for transition metals is a real-space semiempirical description of interactions between the atoms, which is based on the tight-binding approximation and the d-band model. This scheme provides a direct bridge between the electronic level modeling and the atomistic modeling, where the electronic degrees of freedom have been coarse grained into many-body interatomic potentials. In this paper we construct BOP in which both the attractive and the repulsive contributions to the binding energy are environmentally dependent due to both the nonorthogonality of the orbitals and the breathing of the screening charges. The construction of the BOP is described and tested in detail. First, the energies of alternative crystal structures ͑A15, fcc, hcp, simple cubic͒ are calculated and compared with those evaluated ab initio. The transferability of the BOP to atomic configurations that deviate significantly from the bcc lattice is studied by computing the energies along tetragonal, trigonal, and hexagonal transformation paths. Next, the phonon spectra are evaluated for several symmetrical crystallographic directions and compared with av...

Ab initiobased empirical potential used to study the mechanical properties of molybdenum

“…For the (101) plane the predictions of the Peierls stress vary between 1.8 GPa and 3.8 GPa depending on the method and simulation setup. 10,12,13,16,17,19 However, all these simulated Peierls stresses are 2-4 times higher than the experimental value of 0.87 GPa. This discrepancy between experimentally measured yield stresses and the values from the atomistic simulations has been noted for most bcc metals.…”

“…[1][2][3][4][5][6][7][8] In recent years progress has been made on the description of the properties of screw dislocations using density-functional theory (DFT), tight-binding calculations, and empirical potentials. [9][10][11][12][13][14][15][16][17][18][19] However, DFT and tight-binding techniques are limited to small system sizes which is problematic due to the long-range strain field of dislocations, and current empirical potentials lack the required accuracy for the description of the dislocation structure. Simulations of dislocation motion and interactions require efficient interatomic potentials which accurately describe the dislocation energies, core structures, and their motion.…”

Bridging the Gap Between Quantum Mechanics and Large-Scale Atomistic Simulation

“…In this regard, empirical fourth-moment schemes for transition metals have also been developed that do implicitly include angular-as well as radial-force contributions. The most complete and fundamental TB approach to QBIPs, however, is the bond-orderpotential (BOP) model of Pettifor (1995), which is based on an explicit expansion of the total energy within TB theory and has been considerably developed and applied over the last ten years (Mrovec et al, 2004). In all the TB schemes, an empirical repulsive pairpotential contribution is included in the total energy, as in Eq.…”

Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution

“…The latter can be performed using semi-empirical interatomic potentials (see e.g. Schroll, Vitek, Gumbsch [61], Mrovec, Nguyen-Manh, Pettifor, Vitek [47]), or more accurately using 'ab initio' electronic structure calculations (see e.g. Woodward, Rao [67], Blase, Lin, Canning, Louie, Chrzan, [10]).…”