Theory of classical diffusion jumps in solids

Toller, M.; Jacucci, Gianni; DeLorenzi, G; Flynn, C. P.

doi:10.1103/physrevb.32.2082

Cited by 74 publications

(54 citation statements)

References 16 publications

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“…corresponding to the Hamiltonian vector field associated with H͑x͒. 150,154,186,187 The reactant phase space volume occupied by points initiated on the dividing surface DS in with energies between E and E + dE is therefore 32,55,56,156,157,184,185 dE ͵…”

Section: ͑24͒mentioning

confidence: 99%

Microcanonical rates, gap times, and phase space dividing surfaces

Ezra

Waalkens

Wiggins

2009

The Journal of Chemical Physics

112

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The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the average gap time, and the volume of phase space associated with reactive trajectories, are both rigorously defined and readily computed within the phase space approach. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN CNH, previously studied using the methods of phase space transition state theory. Both algebraic ͑power law͒ and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Correcting the RRKM estimate to account for the measure of the reactant phase space region occupied by trapped trajectories results in a drastic overestimate of the isomerization rate. Compensating but as yet not fully understood trapping mechanisms in the reactant region serve to slow the escape rate sufficiently that the uncorrected RRKM estimate turns out to be reasonably accurate, at least at the particular energy studied. Examination of the decay properties of subensembles of trajectories that exit the HCN well through either of two available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short time scale t Շ 0.5 ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential ͑nonstatistical͒ decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.

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Section: ͑24͒mentioning

confidence: 99%

Microcanonical rates, gap times, and phase space dividing surfaces

Ezra

Waalkens

Wiggins

2009

The Journal of Chemical Physics

112

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“…Not the least of these is that Wigner's formulation quickly leads to the recognition that the transition state (TS) is actually a general property of all dynamical systems, provided that they evolve from "reactants" to "products." The TS, therefore, is not confined to chemical reaction dynamics [4], but it also controls rates in a multitude of interesting systems, including, e.g., the rearrangements of clusters [5], the ionization of atoms [6], conductance due to ballistic electron transport through microjunctions [7], and diffusion jumps in solids [8]. Since transition state theory is fundamental for transformations in n degree-of-freedom systems, the work summarized here represents a general formulation of the nonlinear dynamics and geometry of classical reaction dynamics.…”

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confidence: 99%

Impenetrable Barriers in Phase-Space

et al. 2001

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Dynamical systems theory is used to construct a general phase-space version of transition state theory. Special multidimensional separatrices are found which act as impenetrable barriers in phase-space between reacting and nonreacting trajectories. The elusive momentum-dependent transition state between reactants and products is thereby characterized. A practical algorithm is presented and applied to a strongly coupled Hamiltonian.

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“…Our results, based on the analysis of a large number of events, show that multiple jumps are present and very effective in bending the Arrhenius plot near the melting point. An interpretation of their microscopic nature has also been needed, in order to integrate them into the framework of those recent developments in the theory of diffusion that explicitly take into account dynamical effects [8].…”

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confidence: 99%

Multiple Jumps and Vacancy Diffusion in a Face-Centered-Cubic Metal

Lorenzi¹,

Ercolessi²

1992

Europhys. Lett.

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The diffusion of monovacancies in gold has been studied by computer simulation. Multiple jumps have been found to play a central role in the atomic dynamics at high temperature, and have been shown to be responsible for an upward curvature in the Arrhenius plot of the diffusion coefficient. Appropriate saddle-points on the potential energy surface have been found, supporting the interpretation of vacancy multiple jumps as distinct migration mechanisms.

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Theory of classical diffusion jumps in solids

Cited by 74 publications

References 16 publications

Microcanonical rates, gap times, and phase space dividing surfaces

Microcanonical rates, gap times, and phase space dividing surfaces

Impenetrable Barriers in Phase-Space

Multiple Jumps and Vacancy Diffusion in a Face-Centered-Cubic Metal

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