Bond-order potentials: Theory and implementation

Horsfield, A. P.; Bratkovsky, A. M.; Fearn, M.; Pettifor, D. G.; Aoki, Masato

doi:10.1103/physrevb.53.12694

Cited by 192 publications

(167 citation statements)

References 46 publications

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“…Full details have been published elsewhere [1,6,7], but we need to point out that complex intermetallics cannot be described by classical pair functionals such as embedded atom models, partly because neglected angular forces are responsible for Cauchy pressure anomalies that abound in intermetallics and partly because they cannot reliably predict planar fault energies and hence the stable core structures of dislocations. In contrast, bond order potentials are fitted to all the independent elastic constants and the potential we use for TiAl is known to reproduce planar fault energies that are fully consistent with those predicted by the local density functional theory [8].…”

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confidence: 99%

Microscopic Origin of Channeled Flow in Lamellar Titanium Aluminide

Katzarov

Paxton

2010

Phys. Rev. Lett.

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We employ a quantum mechanical bond order potential in an atomistic simulation of channeled flow. We show that the original hypothesis that this is achieved by a cooperative deployment of slip and twinning is correct, first because a twin is able to ''protect'' a 60 ordinary dislocation from becoming sessile, and second because the two processes are found to be activated by Peierls stresses of similar magnitude. In addition we show an explicit demonstration of the lateral growth of a twin, again at a similar level of stress. Thus these simultaneous processes are shown to be capable of channeling deformation into the observed state of plane strain in so-called ''A''-oriented mechanical testing of titanium aluminide superalloy.

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confidence: 99%

Microscopic Origin of Channeled Flow in Lamellar Titanium Aluminide

Katzarov

Paxton

2010

Phys. Rev. Lett.

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“…Unlike the MEAM potential for Pu, this MGPT potential has been demonstrated to capture reasonably well the phonon dispersion curves, although the anomalous softening of the transverse 111 phonon at the L point is not reproduced. Another possible candidate for the construction of a better interatomic potential is the tight-binding-based description within the bond order potential (BOP) [32] that has been shown to be imminently suitable for transition metals crystallizing in the bcc structure with approximately half-filled d bands (V, Nb, Mo, Ta, W) and α Fe. Although this BOP is not currently available, the first step was undertaken by Hachiya [33] who constructed a tight-binding description of fcc α phase of Th and δ Pu, both of which are characterized by approximately halffilled f orbitals.…”

Section: Discussionmentioning

confidence: 99%

Atomistic studies of transformation pathways and energetics in plutonium

Gröger

Lookman

Saxena

2009

Philosophical Magazine

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One of the most challenging problems in understanding the structural phase transformations in Pu is to determine the energetically favored, continuous atomic pathways from one crystal symmetry to another. This problem involves enumerating candidate pathways and studying their energetics to garner insight into instabilities and energy barriers. The purpose of this work is to investigate the energetics of two transformation pathways for the δ → α ′ transformation in Pu that were recently proposed [1] on the basis of symmetry. These pathways require the presence of either an intermediate hexagonal closed-packed (hcp) structure or a simple hexagonal (sh) structure. A subgroup of the parent fcc and the intermediate hexagonal structure, which has trigonal symmetry, facilitates the transformation to the intermediate hcp or sh structure. Phonons then break the translational symmetry from the intermediate hcp or sh structure to the final monoclinic symmetry of the α ′ structure. We perform simulations using the modified embedded atom method (MEAM) for Pu to investigate these candidate pathways. Our main conclusion is that the path via hcp is energetically favored and the volume change for both pathways essentially occurs in the second step of the transformation, i.e. from the intermediate sh or hcp to the monoclinic structure. Our work also highlights the deficiency of the current state-of-the-art MEAM potential in capturing the anisotropy associated with the lower symmetry monoclinic structure.

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“…The intersite elements of the Hamiltonian matrix are given as usually in terms of the radial bond integrals and Slater-Koster angular functions. The elements of the screening function S = (I + O) −1 can be obtained analytically using the same formalism as that employed in the original BOP theory [3]. Analytical expression for the elements of the screening function…”

Section: Theorymentioning

confidence: 99%

“…Atomistic calculations employing these methods are fast enough to treat systems of particles that are much larger than those attainable in ab-initio DFT based calculations. In recent years the tight-binding method with the orthogonal basis and two-center bond (hopping) integrals has been reformulated in terms of Bond-Order Potentials (BOP) [3]. This linear scaling TB scheme does not require use of periodic boundary conditions and all the calculations are performed in the real space.…”

Section: Introductionmentioning

confidence: 99%

Bond-Order Potentials with Analytic Environment-Dependent Tight-Binding Integrals: Application to BCC Molybdenum

et al. 2000

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We present a new Screened Bond-Order Potential (SBOP) for molybdenum in which the environmental dependence of two-center tight-binding bond integrals has been implemented via a recently developed analytic expression. These bond integrals reproduce very well the numerical ab-intio values of screened LMTO bond integrals. In particular, they display the large discontinuity in ddpi between the first and second nearest neighbor of the bcc lattice whereas they do not show any discontinuity in ddsigma. This dependence can be traced directly to the angular character of the analytic screening function and is shown to be critical for the behavior of the second nearest neighbor force constants. The new BOP eliminates the problem of the very soft T2 phonon mode at the N point that is found in most two-center tight-binding models. Preliminary study of the core structure of 1/2<111> screw dislocations performed using SBOP indicates that the core is narrower and less asymmetric than structures found in previous studies, in agreement with recent ab-initio calculations. Comments ABSTRACTWe present a new Screened Bond-Order Potential (SBOP) for molybdenum in which the environmental dependence of two-center tight-binding bond integrals has been implemented via a recently developed analytic expression. These bond integrals reproduce very well the numerical ab-intio values of screened LMTO bond integrals. In particular, they display the large discontinuity in ddπ between the first and second nearest neighbor of the bcc lattice whereas they do not show any discontinuity in ddσ. This dependence can be traced directly to the angular character of the analytic screening function and is shown to be critical for the behavior of the second nearest neighbor force constants. The new BOP eliminates the problem of the very soft T2 phonon mode at the N point that is found in most two-center tight-binding models. Preliminary study of the core structure of 1/2<111> screw dislocations performed using SBOP indicates that the core is narrower and less asymmetric than structures found in previous studies, in agreement with recent ab-initio calculations.

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Bond-order potentials: Theory and implementation

Cited by 192 publications

References 46 publications

Microscopic Origin of Channeled Flow in Lamellar Titanium Aluminide

Microscopic Origin of Channeled Flow in Lamellar Titanium Aluminide

Atomistic studies of transformation pathways and energetics in plutonium

Bond-Order Potentials with Analytic Environment-Dependent Tight-Binding Integrals: Application to BCC Molybdenum

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