Free energy and entropy of diffusion by<i>ab initio</i>molecular dynamics: Alkali ions in silicon

Milman, Victor; Payne, Mike C.; Heine, Volker; Needs, R. J.; Lin, Jingxiang; Lee, M. H.

doi:10.1103/physrevlett.70.2928

Cited by 87 publications

(57 citation statements)

References 23 publications

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“…This 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 14 lower barrier for Li diffusion is in agreement with both experimental 44 and computational 53 findings. The increased barrier height upon inclusion of thermal vibrations, may be ascribed to entropy loss at the TS 71 . We further note that the contribution of thermal vibrations to the rate are significantly greater using NMA than when using the PI-EV approach.…”

Section: Theoretical Methodsmentioning

confidence: 95%

Classical and Quantum Modeling of Li and Na Diffusion in FePO₄

et al. 2015

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Lithium diffusion in olivine phosphates has been widely studied both experimentally and theoretically. However, nuclear quantum effects (NQEs) of the Li ions have not been accounted for in theoretical studies thus far. In the current work, we compared Li and Na diffusion in Li 0.25 FePO 4 and Na 0.25 FePO 4 by computing density functional theory based classical diffusion barriers in conjunction with NQEs for the Li and Na ions. The NQEs are computed using a novel three-dimensional wave function method based on a path integral formulation. The calculations of both the potential and free energy diffusion barriers suggest that Li diffusion is faster than Na diffusion, in agreement with recent experiments. The NQEs for lithium ions in Li 0.25 FePO 4 are higher than those for sodium ions in Na 0.25 FePO 4 . Although the contribution of NQEs to the computed Li and Na ion diffusion rates is rather small, the quantum behavior of the Li ions is unusual. Indeed, we observe a reduction in the computed diffusion rate for Li ions due to quantization. We ascribe this effect to the ability of FePO 4 to tightly bind the Li ions in the transient tetrahedral transition state, which reduces the classical diffusion barrier but also enhances quantum confinement.

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Section: Theoretical Methodsmentioning

confidence: 95%

Classical and Quantum Modeling of Li and Na Diffusion in FePO₄

et al. 2015

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“…However, first-principles MD studies of selfdiffusion in silicon are only practical at temperatures close to the melting point, since at lower temperatures the diffusion events are too rare to be observed on the timescale of the MD simulation. An alternative method was employed by Milman et al [22] to study Li, Na, and K ions diffusing in silicon, which involves thermodynamic integration along the diffusion path. However, to use this method one has to know the diffusion path beforehand.…”

Section: Migration Energiesmentioning

confidence: 99%

First-principles calculations of self-interstitial defect structures and diffusion paths in silicon

Needs¹

1999

J. Phys.: Condens. Matter

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Abstract.A first-principles pseudopotential study of neutral self-interstitial defects in silicon is reported, together with calculations for Pandey's concerted exchange mechanism for selfdiffusion. The energies and structures of the fully relaxed hexagonal, tetrahedral, split-110 , 'caged' (Clark S J and Ackland G J 1997 Phys. Rev. B 56 47), split-100 , and bond-centred interstitials are calculated using supercells with up to 128 + 1 atoms. We present results obtained using the local density approximation (LDA) and the PW91 generalized gradient approximation (GGA) for the exchange-correlation energy. Both the LDA and PW91-GGA functionals give the hexagonal and split-110 defects as the lowest-energy self-interstitials. The hexagonal and split-110 defects are essentially degenerate in energy with formation energies of about 3.3 eV (LDA) and 3.80 eV (PW91-GGA). Energy barriers are studied by calculating saddle-point structures using a simple 'ridge-walking' method. The energy barrier for a diffusive jump between the hexagonal and split-110 interstitial sites is calculated to be 0.15 eV (LDA) and 0.20 eV (PW91-GGA) and the barrier between neighbouring hexagonal sites is 0.03 eV (LDA) and 0.18 eV (PW91-GGA), but we have not found a low-energy path between split-110 interstitial sites. The results suggest that self-interstitial diffusion in silicon occurs via diffusive jumps between the hexagonal sites and between hexagonal and split-110 defects.

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“…The prefactor A m can be calculated using the transition-state theory 54,55 or ab initio molecular dynamics. 56 According to the transition-state theory A m is of the general form 54,55 A m ϭC m •exp͑⌬S/k B ͒, ͑8͒…”

Section: Prefactorsmentioning

confidence: 99%

First-principles study of migration, restructuring, and dissociation energies of oxygen complexes in silicon

et al. 2002

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Migration, restructuring, and dissociation energies of oxygen complexes in silicon are studied theoretically through density-functional total-energy calculations. We find that the stablest oxygen complexes are straight chains that also have the lowest migration energies. The calculated migration energies decrease from 2.3 eV for an interstitial oxygen atom (O i ) to low values of 0.4 -1.6 eV for O 2 -O 9 chains and 1.9-2.2 eV for longer chains. The oxygen chains ͑which are thermal double donors͒ are expected to grow so that the migrating oxygen chains capture less-mobile but abundant O i 's: O n ϩO i →O nϩ1 . Restructuring energies of chains with a side O i into straight oxygen chains are 1.9-2.5 eV. Restructuring gives an essential contribution to the fast diffusion. We find that the shorter O 2 -O 9 chains dissociate primarily by ejecting one of the outermost oxygen atoms.

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Free energy and entropy of diffusion byab initiomolecular dynamics: Alkali ions in silicon

Cited by 87 publications

References 23 publications

Classical and Quantum Modeling of Li and Na Diffusion in FePO₄

Classical and Quantum Modeling of Li and Na Diffusion in FePO₄

First-principles calculations of self-interstitial defect structures and diffusion paths in silicon

First-principles study of migration, restructuring, and dissociation energies of oxygen complexes in silicon

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Free energy and entropy of diffusion byab initiomolecular dynamics: Alkali ions in silicon

Cited by 87 publications

References 23 publications

Classical and Quantum Modeling of Li and Na Diffusion in FePO4

Classical and Quantum Modeling of Li and Na Diffusion in FePO4

First-principles calculations of self-interstitial defect structures and diffusion paths in silicon

First-principles study of migration, restructuring, and dissociation energies of oxygen complexes in silicon

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Classical and Quantum Modeling of Li and Na Diffusion in FePO₄

Classical and Quantum Modeling of Li and Na Diffusion in FePO₄