A mean field theory for diffusion in a dilute multi-component alloy: a new model for the effect of solutes on self-diffusion

Nastar, Maylise

doi:10.1080/14786430500228390

Cited by 69 publications

(114 citation statements)

References 20 publications

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“…The self-consistent mean field method (SCMF) has seen growing interest and development in the last fifteen years [22][23][24][25][26][27][28] . For solute and point-defect diffusion, it provides a general link between the atomic scale (individual jump rates) and the macroscopic scale (transport coefficients).…”

Section: B Transport Coefficients Frameworkmentioning

confidence: 99%

“…The self-consistent mean-field (SCMF) method allows to compute transport coefficients (which control the kinetic properties of the system) from atomic jump rates computed with DFT [22][23][24][25][26][27][28] . It uses a thermal average of a microscopic master equation to compute the deviation of the probability of each configuration (with respect to equilibrium) under a chemical potential gradient.…”

Section: Introductionmentioning

confidence: 99%

“…The SCMF method provides a formal link between individual jump processes at the atomic scale and long range diffusion which is responsible for microstructure evolution. This method of growing interest has been applied to various crystal structures, various diffusion mechanisms, strained systems, and non-homogeneous driving forces [22][23][24][25][26][27][28] . In this work, the DFT+U+OMC and the SCMF method are applied to understand the mobility and long range diffusion of carbon and oxygen in the UN lattice.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, it is likely that a complete calculation of attempt frequencies would only shift solute diffusion coefficients by at most one order of magnitude. For these reasons, we used the simple Debye frequency value (23,8 THz) for all attempt frequencies, as in previous work 40 .…”

Section: A Density-functional Theory Calculationsmentioning

confidence: 99%

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Transport properties of C and O in UN fuels

et al. 2017

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Uranium nitride fuel is considered for fast reactors (GEN-IV generation and space reactors) and for light water reactors as a high-density fuel option. Despite this large interest, there is a lack of information about its behavior for in-pile and out-of-pile conditions. From the present literature, it is known that C and O impurities have significant influence on the fuel performance. Here, we perform a systematic study of these impurities in the UN matrix using electronic-structure calculations of solute-defect interactions and microscopic jump frequencies. These quantities were calculated in the DFT+U approximation combined with the occupation matrix control scheme, to avoid convergence to metastable states for the 5f levels. The transport coefficients of the system were evaluated with the self-consistent mean-field theory. It is demonstrated that carbon and oxygen impurities have different diffusion properties in the UN matrix, with O atoms having a higher mobility, and C atoms showing a strong flux coupling anisotropy. The kinetic interplay between solutes and vacancies is expected to be the main cause for surface segregation, as incorporation energies show no strong thermodynamic segregation preference for (001)-surfaces compared with the bulk.

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Section: B Transport Coefficients Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: A Density-functional Theory Calculationsmentioning

confidence: 99%

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Transport properties of C and O in UN fuels

et al. 2017

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“…In [9], a full set of activation energies was obtained for dilute Fe-X alloys with density functional theory (DFT), and the self-consistent mean field method [16] was applied to analyze the drag tendency of a solute atom by a vacancy. However, no information about the migration and the lifetime of the vacancy-solute pair was calculated.…”

Section: Akmc Parametrizationmentioning

confidence: 99%

Stability and mobility of small vacancy–solute complexes in Fe–MnNi and dilute Fe–X alloys: A kinetic Monte Carlo study

Messina

Malerba

Olsson

2015

Nuclear Instruments and Methods in Physics Research Section B:

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a b s t r a c tManganese and nickel solute atoms in irradiated ferritic steels play a major role in the nanostructural evolution of reactor pressure vessels (RPV), as they are responsible for the formation of embrittling nanofeatures even in the absence of copper. The stability and mobility of small vacancy-solute clusters is here studied with an atomistic kinetic Monte Carlo approach based on ab initio calculations, in order to investigate the influence of Mn and Ni on the early life of small radiation-induced vacancy clusters, and to provide the necessary parameters for advanced object kinetic Monte Carlo simulations of the RPV longterm nanostructural evolution. Migration barriers are obtained by direct ab initio calculations or through a binding energy model based on ab initio data. Our results show a clear immobilizing and stabilizing effect on vacancy clusters as the solute content is increased, whereas the only evident difference between the two solute species is a somewhat longer elongation of the cluster mean free path in the presence of a few Mn atoms.

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From the Atomic Jump Frequencies to the Phenomenological Transport Coefficients

Nastar¹,

Barbe²

2006

Adv Eng Mater

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Theories of phase transformations controlled by diffusion like the classical kinetic theories require an estimation of the transport phenomenological coefficients L ij . An example is the classical nucleation theory which starts from an estimation of the flux of solutes towards precipitates. Although there is an experimental procedure to determine the L ij , experiments are usually performed at high temperature, for a few compositions, and only some of the total set of the transport coefficients characterizing the diffusion properties of an alloy are measured. The link between these partial data and the L ij is not obvious. The previous attempts relating the diffusion coefficients of isotopes with the L ij turn out to be less and less valid as the Monte Carlo simulations become a more and more reliable test. [1] Moreover relations like the famous Manning's ones [2] never predict a negative sign of an off diagonal L ij although it has been observed between some solutes and the solvent atoms in aluminium alloys. [3] It is a case where a rough estimation of the L ij may affect not only the rate of reaction but also the path of reaction. A solution is to start from an atomic diffusion model for which the parameters are fitted on ab initio calculations or on the available partial diffusion data completed by thermodynamic data. The time evolution of the system is then described by a master equation. Either the L ij are extracted from the equilibrium fluctuations [4] or like within the Self-Consistent Mean-Field (SCMF) theory [5][6][7] they are estimated on a system subject to an external force using a time-dependent effective Hamiltonian to describe the non-equilibrium state. Thanks to the SCMF theory, it is possible to predict the L ij in both dilute and concentrated alloys. They are presented as the product of an uncorrelated coefficient times a correlation function f ij or f i that is the problematic term.After a short introduction of the diffusion atomic model and the principles of the SCMF theory, we present some applications to systems where the diffusion mechanism induces strong correlations between the site occupancies. The first case concerns a binary alloy AB with high jump frequency ratios between A and B. The second case shows how a strong variation of the vacancy-atom exchange probability of A with the surrounding nearest neighbours can reverse the sign of the off diagonal coefficient L AB . Diffusion Theory Atomic Diffusion ModelWe start from an atomic diffusion model introduced by Martin [8] that guarantees a coherency between the expression of the driving force and the transport coefficients. The exchange frequency W a between a vacancy and atom a has the classical thermally activated form:where j is the Boltzmann's constant and T the temperature. m a is the attempt frequency which is assumed to depend only on the jumping atom, and the term in the exponential is the 'migration enthalpy', that is the difference between the total energy of the system in the initial configuration and when the jumping atom ...

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A mean field theory for diffusion in a dilute multi-component alloy: a new model for the effect of solutes on self-diffusion

Cited by 69 publications

References 20 publications

Transport properties of C and O in UN fuels

Transport properties of C and O in UN fuels

Stability and mobility of small vacancy–solute complexes in Fe–MnNi and dilute Fe–X alloys: A kinetic Monte Carlo study

From the Atomic Jump Frequencies to the Phenomenological Transport Coefficients

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