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

Abstract

The diffusivities of substitutional impurity elements in iron have been computed with ab inito electronic density functional techniques, using exchange-correlation functional PW91. Excess entropies and the attempt frequency for a jump were determined by calculating phonon frequencies in the harmonic approximation. The influence of the degree of spontaneous magnetization on diffusivity is taken into account by means of the Girifalco model. The activation energy for diffusion has been determined by computing the vacancy formation energy, impurity-vacancy binding energies, migration barrier energies, and the effective energy associated with correlation of vacancy-mediated jump. For each type of impurity atom these contributions have been evaluated and analyzed up to and including the fifth nearest-neighbor shell of the impurity atom. It is found that impurities that have a low migration energy tend to have high effective energy associated with vacancy migration correlation, and vice versa, so that the total diffusion activation energies for all impurities are surprisingly close to each other. The strong effect of vacancy migration correlation is found to be associated with the high migration energy for iron self-diffusion, so that movement of vacancies through the iron bulk is in all cases, except cobalt, the limiting factor for impurity diffusion. The diffusivities calculated with the PW91 functional show good agreement with most of the experimental data for a wide range of elements.

Analysis of Diffusion in Solid-State Electrolytes through MD Simulations, Improvement of the Li-Ion Conductivity in β-Li3PS4 as an Example

“…Using the presented method of obtaining attempt frequencies results in values between 7.6 × 10 12 and 9.3 × 10 12 Hz, comparable to reported attempt frequencies, between 1 × 10 12 and 1 × 10 13 Hz, for other materials by experiments 23 , 55 and DFT calculations. 25 , 26 This consistency indicates that the presented method of determining the attempt frequency from MD simulations, by a straightforward Fourier transformation of the ionic velocity, can be used to determine the attempt frequency.…”

Self‐Healing Phenomena in Metals

“…To this aim we designed a number of (binary) Fe‐X alloys for a selected creep temperature of 550 °C in which the following criteria are met: i) the system can be brought into a supersaturated state, with an intended level of supersaturation of about 1 at%, ii) the solute atoms have a larger atomic radius than that of Fe, such that when the solutes precipitate in the creep induced cavities there is a net volumetric filling process, iii) the precipitation of the reaction phase will not occur in the grain interior under the prevailing conditions, iv) the solute atoms diffuse faster than the self‐diffusion of Fe and v) in their passage from the grain interior to the damage site, the solute atoms do not interact with each other atoms to form an immobile intermetallic. In support of our program the diffusion coefficients of 28 alloying elements in pure bcc iron have been calculated using ab initio DFT modeling . As can be seen in Figure , it is found that the activation energy for the diffusion Q is of similar magnitude for all (substitutionally dissolved) elements investigated and with only minor variations in the preexponential factor D 0 .…”

“…With the temperature window for healing in metal alloys being defined, it is illustrative to make an estimate of the size of the defects that can be healed via diffusional processes. To this aim we take 10 5 s (≈1 d) as an acceptable healing time and use the diffusion coefficient D = D 0 e − Q / RT of Cu in aluminum (with D 0 = 6.5 × 10 −5 m 2 s −1 and Q = 136 kJ mol −1 ) and the diffusion coefficient of Au in iron (with D 0 = 7.0 × 10 −5 m 2 s −1 and Q = 227 kJ mol −1 ) (see the next sections why these elements were selected). Such a first‐order estimate is informative as it shows that the only very small scale damage, smaller than the characteristic diffusion length , can be healed.…”

“…The dashed lines are a guide to the eye. Reproduced with permission . Copyright 2017, American Physical Society.…”

Self healing of creep damage in iron-based alloys by supersaturated tungsten

“…Tungsten satisfies the key requirements to be an efficient healing agent in Fe-based alloys due to the larger atomic radius (r W / r Fe z 1.10) and the larger solute diffusivity [25] compared to that of Fe in the ferritic iron-rich matrix. With an appropriate heat pretreatment even low concentrations of W can be turned into a supersaturated state at creep temperatures of 500e700 C. In the present study it is demonstrated that supersaturated W can indeed act as an effective healing agent in Fe-W alloys by monitoring the filling of creep cavities by Fe 2 W Laves phase precipitates as a function of the creep time.…”