Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron

Abstract

The diffusion properties of a wide range of impurities (transition metals and Al, Si, and P) in ferritic alloys are here investigated by means of a combined ab initio-atomic diffusion theory approach. The flux-coupling mechanisms and the solute-diffusion coefficients are inferred from electronic-structure calculations of solutedefect interactions and microscopic jump frequencies. All properties except the second-nearest-neighbor binding energy are found to have a characteristic bell shape as a function of the d-band filling for the 4d and 5d series, and an M shape for the 3d row because of the out-of-trend behavior of Mn. The solute jump frequencies are governed by compressibility, which makes diffusion of large solutes faster, although this effect is partially compensated for by lower attempt frequencies and larger correlations with the vacancy. Diffusion coefficients are predicted in a wide temperature range, far below the experimentally accessible temperatures. In accordance with experiments, Co is found to be a slow diffuser in iron, and the same behavior is predicted for Re, Os, and Ir impurities. Finally, flux-coupling phenomena depend on the iron jump frequencies next to a solute atom, which are mainly controlled by similar electronic interactions to those determining the binding energies. Vacancy drag and solute enrichment at sinks systematically arise below a solute-dependent temperature threshold, directly correlated with the electronic-level interactions at the equilibrium and the saddle-point states. Early transition metals with repulsive second-nearest-neighbor interactions also diffuse via vacancy drag, although they show a lower temperature threshold than the late metals. This confirms that drag is the most common solute-vacancy coupling mechanism in iron at low temperatures, and this is likely to be confirmed as well for impurity diffusion in other transition metals.

First-principles analysis of solute diffusion in dilute bcc Fe- X alloys

“…(9)] in bcc iron is computed to be about 4.14k B for PW91 in a 4 × 4 × 4 supercell. This value is in good agreement with the value obtained by Lucas and Schäublin [94], S vib, = 4.08k B , and a little less close agreement with the value by Messina et al [61], S vib, = 4.6k B . The vacancy formation vibrational entropy obtained in a 3 × 3 × 3 supercell is 3.79k B , quite close to our 4 × 4 × 4 result.…”

“…Density functional theory (DFT) calculations have proven successful in predicting experimental data such as lattice parameters [46,47], elastic properties [48,49], and energy barriers for diffusion, e.g., diffusivities in aluminum [50], magnesium [51,52], and nickel [53]. Many impurity diffusivities in bcc iron [54][55][56][57][58][59][60][61] have been calculated with DFT methods, but oftentimes only experimentally fitted data, such as activation energy for diffusion, have been compared with the computed results. The fact that the Arrhenius plot of the diffusivity in bcc iron is not linear makes it desirable to compare the computed and experimentally determined diffusivities directly.…”

Transport properties of C and O in UN fuels

“…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).…”

“…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.…”

“…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.…”