KineCluE: A kinetic cluster expansion code to compute transport coefficients beyond the dilute limit

Abstract

This paper introduces the KineCluE code that implements the self-consistent mean-field theory for clusters of finite size. Transport coefficients are obtained as a sum over cluster contributions (in a cluster expansion formalism), each being individually computed with KineCluE. This method allows for the calculation of these coefficients beyond the infinitely dilute limit, and is an important step in bridging the gap between dilute and concentrated approaches. Inside a finite volume of space containing the components of a given cluster, all kinetic trajectories are accounted for in an exact manner. The code, written in Python, adapts to a wide variety of systems, with various crystallographic structures (possibly under strain), defects and solute amount and types, and various jump mechanisms, including collective ones. The code also features a set of useful tools, such as the sensitivity study routine that allows for the identification of the most important jump frequencies to get accurate transport coefficients with minimum computational cost. PROGRAM SUMMARYProgram Title: KineCluE (KINEtic CLUster Expansion) Licensing provisions: LGPL Programming language: Python 3.6 Nature of problem: Providing a general method for computing transport coefficients from atomic jump frequencies, taking into account kinetic correlations.Solution method: The program relies on the selfconsistent mean field (SCMF) theory. The system is described in terms of lattice sites, defects and jump mechanisms. The first part of the code translates the diffusion problem for such system into an analytical linear eigenvalue problem. The second part of the code assigns numerical values to each analytical variable and then solves the linear problem.

Efficient and transferable machine learning potentials for the simulation of crystal defects in bcc Fe and W

“…The formation free energy of mono-vacancies is an important quantity for parametrization of multi-scale models like kinetic Monte Carlo, cluster dynamics, dislocation dynamics, etc. Its magnitude controls the density of vacancies, which acts as a driving force of self-diffusion [119], vacancy flux coupling [155][156][157][158], Ostwald ripening [159], climb mechanisms [160][161][162], phase transformations [160], etc. Until now, in bcc metals there are no studies that investigate the anharmonic contribution to the formation free energy of vacancies in Fe and W. The vast majority of multiscale models, cited above, use the values of vibrational entropy suggested by experience or the values computed using ab initio techniques within the harmonic approximation.…”

Solute diffusion by self-interstitial defects and radiation-induced segregation in ferritic Fe–X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys

“…Lengths are given in units of a 0 /2. In the cluster development framework [49,48] of SCMF [25], each total transport coefficient L ij is obtained as a weighed sum of cluster contributions:…”

“…Since the defect diffusion coefficient is given by D δ = L δδ /C, and L δδ is proportional to C (Eq. (B.10)), the K factor can be written as: (D.5) Table B.6: Summary of formulas used to infer transport properties and RIS tendencies from the KineCluE output [4,49,47,48]. Subscripts '(V)' and '(I)' refer to monomers (isolated defects), '(VB)' and '(IB)' to solute-defect pairs.…”

Ab-initio calculations of hydrogen diffusion coefficient in monoclinic zirconia

“…We transferred the calculated jump frequencies and migration paths to the KineCluE code to obtain hydrogen diffusion coefficients. KineCluE [53,54] is an open-source code that implements the selfconsistent mean-field theory [55] in an automated and efficient way to compute transport coefficients from the atomic scale.…”

“…Because directions a and c are not orthogonal to each other, there are some correlations between the displacements in these directions, and these correlated displacements can be written as a diffusion coefficient: The expressions for the proton ion are much more complicated because there are many available sites that are not equivalent by symmetry, and therefore, the solution of the diffusion problem requires the inversion of a 4x4 matrix. Given the length of the expression, printing the analytical result here would not make much sense, and interested readers can directly use the KineCluE code [53] to reproduce the results.…”