Cluster Dynamics Modelling of Precipitation Kinetics in Al(Zr,Sc) Alloys

Guyot, P.; Laé, Ludovic

doi:10.1002/adem.200600187

Cited by 2 publications

(1 citation statement)

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“…[9,18] Moreover an irradiation induced segregation leads to strong changes of composition close to the grain boundary even in a dilute alloy which requires a diffusion model valid on a large composition range.…”

Section: Long Range Correlationsmentioning

confidence: 99%

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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Section: Long Range Correlationsmentioning

confidence: 99%