Role of Sink Density in Nonequilibrium Chemical Redistribution in Alloys

Nonequilibrium chemical redistribution in open systems submitted to external forces, such as particle irradiation, leads to changes in the structural properties of the material, potentially driving the system to failure. Such redistribution is controlled by the complex interplay between the production of point defects, atomic transport rates, and the sink character of the microstructure. In this work, we analyze this interplay by means of a kinetic Monte Carlo (KMC) framework with an underlying atomistic model for the Fe-Cr model alloy to study the effect of ideal defect sinks on Cr concentration profiles, with a particular focus on the role of interface density. We observe that the amount of segregation decreases linearly with decreasing interface spacing. Within the framework of the thermodynamics of irreversible processes, a general analytical model is derived and assessed against the KMC simulations to elucidate the structure-property relationship of this system. Interestingly, in the kinetic regime where elimination of point defects at sinks is dominant over bulk recombination, the solute segregation does not directly depend on the dose rate but only on the density of sinks. This model provides new insight into the design of microstructures that mitigate chemical redistribution and improve radiation tolerance.

Figure 1

(a) Cr, (b) vacancy, and (c) self-interstitial concentration ($X$) profiles at steady state in a Fe-Cr alloy with $X_{\text{Cr}}^{\text{nominal}}=0.03$ and at 500 K with a dose rate of ${10}^{-6}\mathrm{dpa}/\mathrm{s}$ for three different interface densities (0.010, 0.048, and $0.165{\mathrm{nm}}^{-1}$). Results for interface densities of 0.048 and $0.165{\mathrm{nm}}^{-1}$ have been replicated from smaller simulation cells for clarity (in all simulations, there was only one interface in the simulation cell).

Figure 2

Total Cr segregation $S^{\text{Cr}}$ at steady-state as obtained by KMC simulations. $l_z$ is the interplanar distance in the direction perpendicular to the interface, $X_0$ represents the Cr concentration at $z=0$ (the farthest from the interface). The nominal Cr concentration ranges from 0.03 to 0.1 and the temperature from 500 to 900 K. Lines represent linear fits to the data. The black dot represents simulations where precipitation occurs.

Figure 3

KMC simulation results after an irradiation process at ${10}^{-6}\mathrm{dpa}/\mathrm{s}$, 500 K, and $X_{\text{Cr}}^{\text{nominal}}=0.1$ with (a)–(b) an interface density of ${\rho }^I=0.048$, and (c)–(d) ${\rho }^I=0.124{\mathrm{nm}}^{-1}$. The purple lines in (b) and (d) highlight the location of the interface.

Figure 4

(a)–(b) $X_V$ and (c)–(d) $[(\nabla X_V)/X_V]$ as obtained from KMC simulations for different temperatures where no second phase precipitation occurs, compared to analytical results for (a)–(c) $X_{\text{Cr}}=0.03$ and a density of interfaces ${\rho }_I=0.124{\mathrm{nm}}^{-1}$ and (b)–(d) $X_{\text{Cr}}=0.06$ and a density of interfaces ${\rho }_I=0.048{\mathrm{nm}}^{-1}$. Shaded regions represent the location of the interface. The solid black lines indicate the results of the analytical model as derived in Eqs. (4) and (5).

Figure 5

$X_{\text{Cr}}$ as obtained from KMC simulations for different temperatures at a nominal Cr composition of 0.06 and 0.1 where no precipitation occurs. Black solid lines represent analytical results from Eq. (6). Shaded regions represent the location of the interfaces.