Solute-point defect interactions, coupled diffusion, and radiation-induced segregation in fcc nickel

Radiation-induced segregation (RIS) of solutes in materials exposed to irradiation is a well-known problem. It affects the lifetime of nuclear reactor core components by favoring radiation-induced degradation phenomena such as hardening and embrittlement. In this work, RIS tendencies in face centered cubic (fcc) Ni-$X$ ($X=\mathrm{Cr}$, Fe, Ti, Mn, Si, P) dilute binary alloys are examined. The goal is to investigate the driving forces and kinetic mechanisms behind the experimentally observed segregation. By means of ab initio calculations, point-defect stabilities and interactions with solutes are determined, together with migration energies and attempt frequencies. Transport and diffusion coefficients are then calculated in a mean-field framework, to get a full picture of solute-defect kinetic coupling in the alloys. Results show that all solutes considered, with the exception of Cr, prefer vacancy-mediated over interstitial-mediated diffusion during both thermal and radiation-induced migration. Cr, on the other hand, preferentially migrates in a mixed-dumbbell configuration. P and Si are here shown to be enriched, and Fe and Mn to be depleted at sinks during irradiation of the material. Ti and Cr, on the other hand, display a crossover between enrichment at lower temperatures, and depletion in the higher temperature range. Results in this work are compared with previous studies in body centered cubic (bcc) Fe, and discussed in the context of RIS in austenitic alloys.

Figure 1

Three $\langle 100\rangle$ dumbbell configurations in an fcc lattice. (a) A pure nickel dumbbell with the solute in a compressed lattice site ($a$ type). (b) A pure nickel dumbbell with the solute in a tensed lattice site ($b$ type). (c) A mixed dumbbell. The red circles indicate the position of the solute atom.

Figure 2

Illustration of the solute-vacancy related migration barriers, denoted by their respective jump frequencies ω, explicitly calculated using DFT. The red circle indicates the position of the solute atom, the blue square that of the vacancy. The neighbor ordering is with respect to the solute atom.

Figure 3

Illustration of the solute dumbbell related migration barriers explicitly calculated using DFT. The red circle indicates the position of the solute atom.

Figure 4

Vacancy-solute binding energies (eV) in pure Ni as a function of nearest neighbor (nn) distance. Positive values represent binding configurations.

Figure 5

Ni self-diffusion coefficient ($D$*) due to thermal vacancies as a function of temperature, compared with experimental data from [63, 64, 65, 66, 67, 68]. The parameters used for each curve correspond to those presented in Table 5. The lower inset shows the vacancy concentration necessary to fit the calculated self-diffusion coefficient to the experimental values in the figure, when using the 0-K vacancy migration rate ${\omega }_0$ computed in this work.

Figure 6

Vacancy mediated tracer solute diffusion coefficient as a function of temperature for (a) Cr and (b) Fe. Results are compared to experimental data from [71], and with Arrhenius plot obtained with values from Hargather et al. [70]; “fitted $c_V$” has been inferred from the fitting of self-diffusion coefficients shown in Fig. 5.

Figure 7

Ratios of solute tracer diffusion coefficients due to vacancy and interstitial mechanism. As that interstitial diffusion is considered negligible for Ti and Mn, the species are not included in the figure. The lower inset displays the ratio of vacancy and interstitial concentrations used to calculate the diffusion coefficient ratios.

Figure 8

Diffusion coefficients by the preferred diffusion mechanism for the various species. Calculations were performed while assuming a constant vacancy to solvent fraction of ${10}^{-6}$.

Figure 9

(a) Vacancy drag ratio, $G_V=L_{VB}^{\left(VB\right)}/L_{BB}^{\left(VB\right)}$, (b) vacancy partial diffusion coefficient ratios, and (c) dumbbell partial diffusion coefficient ratios as functions of temperature. As interstitial diffusion is considered negligible for Ti and Mn, and the octahedral kickout mechanism dominates over the dumbbell mechanism for P, the three are omitted in (c).

Figure 10

RIS tendencies of Cr, Fe, P, Si, Ti, and Mn in bulk nickel. Positive values indicate enrichment at sinks.