Abnormal grain growth in nonequilibrium systems: Effects of point defect patterning

We present a mean-field model for abnormal grain growth processes described by competition of both deterministic and stochastic mechanisms with the grain mobility depending on the grain size. The derived approach is applied to study delayed dynamics of grain growth in system of point defects subjected to irradiation according to the swelling rate theory for irradiated materials. We have shown that with the irradiation dose increase, the corresponding grain growth dynamics is slowed down and growth processes with power-law time asymptotics are realized. We discuss behavior of grain size distributions with competing regular and fluctuation mechanisms.

Figure 1

Phase diagram for noise-induced transitions.

Figure 2

Probability density functions $\varphi \left(u\right)$ at the large noise limit at different $\kappa$. Symbols correspond to numerical results; lines relate to the analytical approximation given in Eq. (21).

Figure 3

Phase diagram for the homogeneous system at $\varepsilon =10.5$, $\eta =1$, $\nu ={10}^{-2}$, $G=0.015$. Insertion is given at $\varepsilon =8$.

Figure 4

Snapshots of the deterministic system evolution at $K=0.05$ (a), $K=0.15$ (b) and $K=0.225$ (c). In order to illustrate the microstructure we present the system of $256\times 256$ sites.

Figure 5

Typical microstructure of grains shown in Fig. 4 as crops from snapshots in system with $1024\times 1024$ sites.

Figure 6

Typical patterns observed at different defect production rate $K$ and noise intensities ${\tilde{\sigma }}^2$.

Figure 7

Dynamics of both number of grains and averaged area of grains at $K=0.15$.

Figure 8

Scaling exponent $\alpha$ vs damage rate $K$.

Figure 9

Averaged grain area and number of grains vs $K$ at time fixed time $t=50$.

Figure 10

Universality of the probability density function of the grain size distribution at different times at $K=0.03$.

Figure 11

Probability density functions at different damage rates $K$.