Atomic mobility in Cahn’s diffusion model

Martin, G.

doi:10.1103/physrevb.41.2279

Cited by 213 publications

(155 citation statements)

References 5 publications

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“…This is also in accordance with the form of composition dependence of the jump probabilities in kinetic Monte Carlo (see Appendix Appendix A) and the jump frequencies in kinetic mean field models [17], where the activation energies of the jump frequencies depend linearly on the composition in a homogeneous alloy (see Appendix Appendix B).…”

Section: Theorysupporting

confidence: 81%

“…25,26,17 and the Appendixes for more information on the models) were used to study how m ′ influences the critical nucleus size. Although the KMF is deterministic and limited to one dimension, and its results cannot be exactly compared to that of KMC, in order to save time we used the KMF to map roughly the ade- The temperature and the regular solid solution parameter (proportional to the mixing energy; see Appendixes for detailed information) were chosen to be T = 800 K and V = 0.025 eV, respectively.…”

Section: Theorymentioning

confidence: 99%

“…Our model to calculate the time evolution of the composition on a one-dimensional lattice is based on Martin's equations [17]. However, we use our own composition dependent activation barriers (diffusion asymmetry) in the exchange frequencies, which unify the advantages of other barriers used in the literature as was shown in Ref.…”

Section: Appendix B One Dimensional Kinetic Mean Filed Model (Kmf)mentioning

confidence: 99%

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Kinetic critical radius in nucleation and growth processes – Trapping effect

2010

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The critical nucleus size-above which nuclei grow, below dissolve-during diffusion controlled nucleation in binary solid-solid phase transformation process is calculated using kinetic Monte Carlo. If atomic jumps are slower in an A-rich nucleus than in the embedding B-rich matrix, the nucleus traps the A atoms approaching its surface. It has not enough time to eject A atoms before new ones arrive, even if it would be favourable thermodynamically. In this case the critical nucleus size can be even by an order of magnitude smaller than expected from equilibrium thermodynamics or without trapping.

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Section: Theorysupporting

confidence: 81%

Section: Theorymentioning

confidence: 99%

Section: Appendix B One Dimensional Kinetic Mean Filed Model (Kmf)mentioning

confidence: 99%

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Kinetic critical radius in nucleation and growth processes – Trapping effect

2010

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“…020601-1 0031-9007͞01͞ 87(2)͞020601 (4) Their explicit form depends on the assumptions in their derivation, but the general trend is that the coefficient is large in the disordered phase and small in the ordered phase [14,15]. These coefficients have been introduced in the context of phase separation in binary mixtures, either to explore ad hoc their influence, or by necessity to take into account the effect of a gravitational field [16].…”

mentioning

confidence: 99%

Noise-Induced Scenario for Inverted Phase Diagrams

et al. 2001

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We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions. From a fundamental point of view, however, the most interesting example is that of noise-induced ordering phase transitions (NIOPTs) [7]. In this case, transitions between true extended phases (in a thermodynamic sense) are produced when the noise intensity is used as a control parameter. These nonequilibrium phase transitions can therefore be characterized using standard techniques of critical phenomena, such as dynamic renormalization group, mean-field approximations, as well as finite-size scaling analyses using, for instance, results obtained from numerical simulations of stochastic partial differential equations. Until now, all the arguments presented to account for the occurrence of NIOPTs have been dynamical ones. This is mainly because it has been impossible thus far to find a nonequilibrium model whose steady-state probability distribution and the associated effective potential are known. In particular, noise-induced phase transitions have been systematically explained in terms of a short-time instability of the local dynamics, which becomes "frozen" at larger times by the spatial coupling [7,8].In this Letter, we introduce a class of systems exhibiting NIOPTs for which the steady-state probability distribution can be obtained exactly, so that one can define the corresponding nonequilibrium free energy or potential. As a consequence, the NIOPT can be studied in the steady state, with no dynamical reference. It turns out that the noiseinduced phase transition that appears in these model systems is not a consequence of an instability of the disordered homogeneous state. Rather, the situation is similar to what happens for noise-induced transitions in zero-dimensional systems, where the disordered state is linearly stable, but the effective nonequilibrium potential in the steady state is bimodal [9,10]. A phase transition is obtained by coupling adequately many of those zero-dimensional systems. For a strong enough spatial coupling, the neighboring variables tend to a common value and a macroscopic ordered phase appears as a result of ergodicity breaking. This situation contrasts vividly with NIOPTs reported thus far, where the need of a short-time dynamical instability prevents systems that undergo noise-induced transitions in 0D from exhibiting NIOPTs in the presence of spatial coupling [7].The phase transition that we report in what follows shares som...

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“…The SCMF theory developed by Nastar, Dobretsov and Martin [25,26,27] starts from a more recent atomic diffusion model introduced by Martin [28] and extended by Nastar et al [29], Athenes and Bellon [30] and Le Bouar and Soisson [31] including a variation of the saddle point energy as well as equilibrium energy with the surrounding nearest neighbours (nn) of the exchanging atom-vacancy pair. This theory leads to a complete Onsager matrix in a multicomponent system : matter fluxes are evaluated under gradients of chemical potential, and correlations due to the vacancy mechanism are described by a time dependent effective Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

Barbe

Nastar

2006

Philosophical Magazine

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International audienceWe present an improvement of the self-consistent mean field (SCMF) approximation of the L._ij, which extends its applications to alloys presenting high jump frequency ratios. The theory uses a vacancy-atom exchange model which depends on temperature and local composition through thermodynamic and kinetic parameters. Kinetic correlations due to the vacancy mechanism are represented by a time dependent effective Hamiltonian. In the case of high jump frequency ratios it is shown that long return paths of the vacancy need to be considered, which is shown to be equivalent to introduce many-body long-range effective interactions. We compare this theory to existing formalisms and Monte Carlo simulations for systems both without and with atomic interactions

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Atomic mobility in Cahn’s diffusion model

Cited by 213 publications

References 5 publications

Kinetic critical radius in nucleation and growth processes – Trapping effect

Kinetic critical radius in nucleation and growth processes – Trapping effect

Noise-Induced Scenario for Inverted Phase Diagrams

A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

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