Atom-based bond-order potentials for modelling mechanical properties of metals

Aoki, Masato; Nguyen-Manh, D.; Pettifor, D. G.; Vítek, V.

doi:10.1016/j.pmatsci.2006.10.004

Cited by 54 publications

(35 citation statements)

References 137 publications

(195 reference statements)

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“…Following Eqs. (6) and (15), Figs. S4 and S5 in the Supplemental Material [23] show similar cancellation between the attractive three-center and the repulsive overlap contributions to the OTB intersite bond integralsβ 1 for the square, pentagon, hexagon, octahedron, cube, and octagon.…”

Section: Figs S2 and S3 In The Supplemental Materialsmentioning

confidence: 97%

“…The tight-binding (TB) approximation provides not only a conceptual framework for understanding the properties of covalent materials [1][2][3], but also a theoretical framework from which to derive interatomic potentials for performing largescale atomistic simulations [4][5][6][7][8]. However, as the modeling of materials becomes ever more sophisticated, the TB approaches have been faced with the challenge of how best to obtain a robust set of parameters that is fully transferable from one structure type or environment to the next.…”

Section: Introductionmentioning

confidence: 99%

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Competition between crystal-field, overlap, and three-center contributions inHNeigenspectra

Margine

Pettifor

2014

Phys. Rev. B

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The environment dependence of the on-site energy levels and intersite bond integrals within an orthogonal tight-binding (OTB) model for s-valent systems is determined by the competition between the attractive crystalfield and three-center terms and the repulsive overlap contribution. This is demonstrated explicitly for the case of symmetric H N clusters, where the OTB parameters can be expressed analytically in terms of the nonorthogonal tight-binding (NOTB) on-site, intersite, and overlap matrix elements. The values of the OTB parameters are obtained directly from the density-functional theory eigenspectra of the H N clusters with the on-site energy levels being found to be very sensitive to the local atomic environment but the intersite bond integrals much less so. This different behavior is shown to result from the large cancellations between the crystal-field, overlap, and three-center contributions. The common first-order expression for the OTB on-site energy level as the sum of the NOTB crystal field and a two-body overlap repulsion is found to be a poor approximation due to the sizable values of the overlap in these H N clusters around equilibrium.

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Section: Figs S2 and S3 In The Supplemental Materialsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Competition between crystal-field, overlap, and three-center contributions inHNeigenspectra

Margine

Pettifor

2014

Phys. Rev. B

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“…For example, in the numerical BOP for W developed by Mrovec et al [106], the repulsive term was described by a screened Yukawa-type potential, the screening exponent of which was fitted to experimental data for bcc W to ensure the reproduction of the correct sign of the Cauchy pressure, thus allowing the BOP to be applied to the investigation of extended defects. Similarly, Aoki et al [107] applied the same principles in the parametrization of numerical BOPs in order to model mechanical properties in hcp Ti and bcc Mo. DFT predicts that for the three common crystal structures fcc, bcc, and hcp, that AFM2 bcc δ-Mn has the smallest unrelaxed vacancy formation energy, with the close-packed AFM fcc γ -Mn and AFM hcp -Mn having larger energies.…”

Section: E Vacancy Formation Energiesmentioning

confidence: 99%

Magnetic analytic bond-order potential for modeling the different phases of Mn at zero Kelvin

2014

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It is known that while group VII 4d Tc and 5d Re have hexagonally close-packed (hcp) ground states, 3d Mn adopts a complex χ -phase ground state, exhibiting complex noncollinear magnetic ordering. Density functional theory (DFT) calculations have shown that without magnetism, the χ phase is still the ground state of Mn implying that magnetism and the resultant atomic-size difference between large-and small-moment atoms are not the critical factors, as is commonly believed, in driving the anomalous stability of the χ phase over hcp. Using a canonical tight-binding (TB) model, it is found that for a more than half-filled d band, while harder potentials stabilize close-packed hcp, a softer potential stabilizes the more open χ phase. By analogy with the structural trend from open to close-packed phases down the group IV elements, the anomalous stability of the χ phase in Mn is shown to be due to 3d valent Mn lacking d states in the core which leads to an effectively softer atomic repulsion between the atoms than in 4d Tc and 5d Re. Subsequently, an analytic bond-order potential (BOP) is developed to investigate the structural and magnetic properties of elemental Mn at 0 K. It is derived within BOP theory directly from a new short-ranged orthogonal d-valent TB model of Mn, the parameters of which are fitted to reproduce the DFT binding energy curves of the four experimentally observed phases of Mn, namely, α, β, γ , δ, and -Mn. Not only does the BOP reproduce qualitatively the DFT binding energy curves of the five different structure types, it also predicts the complex collinear antiferromagnetic (AFM) ordering in α-Mn, the ferrimagnetic ordering in β-Mn, and the AFM ordering in γ -, δ-, and -Mn that are found by DFT. A BOP expansion including 14 moments is sufficiently converged to reproduce most of the properties of the TB model with the exception of the elastic shear constants, which require further moments. The current TB model, however, predicts values of the shear moduli and the vacancy formation energies that are approximately a factor of 2 too small, so that a future more realistic model for MD simulations will require these properties to be included from the outset in the fitting database.

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“…Moreover, the involved relation of the electronic structure to the local topology and coordination of the material leads to a physically transparent description of local bond formation. Detailed reviews of bond-order potentials for transition metals, semiconductors and hydrocarbons are given elsewhere (Aoki et al, 2007;Drautz et al, 2007;Finnis, 2007a;Mrovec et al, 2007). Some of us recently compiled a more tutorial-like approach to bond-order potentials ) and an overview of applications .…”

Section: Tight-binding and Bond-order Potentialsmentioning

confidence: 99%

“…(Finnis, 2007b;Horsfield et al, 1996;Pettifor, 1989). The resulting functional form of the bond energy is derived as a function of the atomic positions, where the different ways of integrating the DOS lead to the numerical bond-order potentials (Aoki et al, 2007) and the analytic bond-order potentials for semiconductors (Pettifor & Oleinik, 1999; and transition metals (Drautz & Pettifor, 2006). The latter use an expansion of the DOS in terms of CHEBYSHEV polynomials where the expansion coefficients σ n are related to the moments of the DOS by expressing the CHEBYSHEV polynomials explicitly in polynomials with coefficients p mk ,…”

Section: Tight-binding and Bond-order Potentialsmentioning

confidence: 99%

Closing the Gap Between Nano- and Macroscale: Atomic Interactions vs. Macroscopic Materials Behavior

Böhme¹,

Hammerschmidt²,

Drautz³

et al. 2011

Thermodynamics - Kinetics of Dynamic Systems

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Atom-based bond-order potentials for modelling mechanical properties of metals

Cited by 54 publications

References 137 publications

Competition between crystal-field, overlap, and three-center contributions inHNeigenspectra

Competition between crystal-field, overlap, and three-center contributions inHNeigenspectra

Magnetic analytic bond-order potential for modeling the different phases of Mn at zero Kelvin

Closing the Gap Between Nano- and Macroscale: Atomic Interactions vs. Macroscopic Materials Behavior

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