Mechanism of nucleation and incipient growth of Re clusters in irradiated W-Re alloys from kinetic Monte Carlo simulations

High-temperature, high-dose, neutron irradiation of W results in the formation of Re-rich clusters at concentrations one order of magnitude lower than the thermodynamic solubility limit. These clusters may eventually transform into brittle W-Re intermetallic phases, which can lead to high levels of hardening and thermal conductivity losses. Standard theories of radiation-enhanced diffusion and precipitation cannot explain the formation of these precipitates and so understanding the mechanism by which nonequilibrium clusters form under irradiation is crucial to predict material degradation and devise mitigation strategies. Here we carry out a thermodynamic study of W-Re alloys and conduct kinetic Monte Carlo simulations of Re cluster formation in irradiated W-2Re alloys. We use a generalized Hamiltonian for crystals containing point defects parametrized entirely with electronic structure calculations. Our model incorporates recently gained mechanistic information of mixed-interstitial solute transport, which is seen to control cluster nucleation and growth by forming quasispherical nuclei after an average incubation time of 13.5($\pm 8.5$) s at 1800 K. These nuclei are seen to grow by attracting more mixed interstitials bringing solute atoms, which in turn attracts vacancies leading to recombination and solute agglomeration. Owing to the arrival of both Re and W atoms from the mixed dumbbells, the clusters are not fully dense in Re, which amounts to no more than 50% of the atomic concentration of the cluster near the center. Our simulations are in qualitative agreement with recent atom probe examinations of ion-irradiated W-2Re systems at 773 K.

Figure 1

Re-W phase diagram. The shaded region corresponds to the temperature range explored in the kMC simulations, while the crosses mark the 2% Re concentration point (adapted from Ref. [16]).

Figure 2

Enthalpy of mixing as a function of solute concentration from Ref. [30] and third-degree polynomial fit.

Figure 3

Configurations of V-Re clusters used to extract bond energy coefficients ${\varepsilon }_{\text{A-V}}$ and ${\varepsilon }_{\text{B-V}}$. Blue spheres represent vacancies, red spheres represents Re atoms. All other lattice sites are occupied by A atoms, which are omitted for clarity. Green spheres indicate the various equivalent sites for atoms to exchange positions with the vacancy.

Figure 4

Solute composition $X$ as a function of chemical potential $\mathrm{\Delta }\mu$ at different temperatures.

Figure 5

Short-range-order parameter $\eta$ as a function of global solute composition $X$ at different temperatures. The dashed line indicates the SRO interval caused by normal concentration fluctuations during the generation of atomistic samples.

Figure 6

Structural phase diagram showing regions of changing SRO. The dashed lines are the limits of applicability of the rigid bcc lattice model. The system displays slightly negative SRO throughout the entire temperature-concentration space, indicating a preference to be in a solid solution state. The gray band at low temperatures signifies the region of coexistence of the bcc and B2 phases (see Appendix pp1).

Figure 7

Structural phase diagrams for four different vacancy concentrations. (a) $C_v=0.01$ at.%. (b) $C_v=0.1$ at.%. (c) $C_v=0.2$ at.%. (d) $C_v=0.5$ at.%. The diagrams clearly show the emergence of regions of solute segregation, characterized by positive SRO and a shifting of the transition phase boundary, $\eta =0$, towards the right (higher concentrations).

Figure 8

Equilibrated configurations for W-Re alloys containing different defect concentrations at 600 K. (a) W–1.8 at.% Re alloy, 0.5 at.% vacancy concentration. (b) W–1.4 at.% Re alloy, 0.1 at.% mixed interstitials. Red spheres represent Re atoms; colored blue or green ones represent the defect in each case.

Figure 9

Structural phase diagram for 0.1 at.% mixed-dumbbell concentration. The diagram shows the emergence of regions of solute segregation, characterized by $\eta >0$, up to $X=0.1\%$.

Figure 10

Diffusivities of vacancies and solute atoms as a function of temperature and alloy concentration. (a) Vacancy diffusion. (b) Solute diffusion. The solid lines correspond to the Arrhenius fits shown in Table 5, while the dashed line corresponds to Eq. (29).

Figure 11

Phenomenological transport coefficients for solute-solute, vacancy-solute, and solvent-solute interactions. (a) Solute-solute transport coefficient. (b) Solute-vacancy transport coefficient. (c) Relation of transport coefficients for solute-vacancy and solvent-vacancy interactions.

Figure 12

Precipitate growth with time at 1800 K and ${10}^{-3}\mathrm{dpa}{\mathrm{s}}^{-1}$ in a W–2.0 at.% Re alloy. The dashed line represents perfect spherical growth (cf. Appendix pp2). A surface reconstruction rendition of one precipitate at various times is provided in the inset.

Figure 13

Radial concentration profile as a function of time for the precipitates formed in the kMC simulations. The experimental results are taken from the work by Xu et al. [14].

Figure 14

Evolution of the differential SRO during the nucleation and growth in the kMC simulations.

Figure 15

Spatial distribution of recombination events for several stages of precipitate evolution. (a) During cluster nucleation. (b) During precipitate growth. (c) After size saturation.

Figure 16

Atomistic snapshots of the equilibrium configurations of the W-50Re system and associated pair correlation function at 200 and 300 K. (a) $X\approx 0.50$. (b) Pair correlation function.

Figure 17

Atomistic snapshots of the equilibrium configurations of the W-25Re system and associated pair correlation function at 200 and 300 K. (a) $X\approx 0.25$. (b) Pair correlation function.