3 The Sink/Source Term $\gamma$

According to the discussion presented in [50], the sink/source term $\gamma$ models the interaction of vacancies between the grain boundary and the grain. The vacancies are annihilated or produced inside the grain boundaries with a rate $\gamma$ which depends on the vacancy concentration in the vicinity of the grain boundaries [50],

$$\gamma = -\frac{C_V-C_V^{eq}}{\tau},$$ (240)

where $\tau$ is the average lifetime of the vacancy in the grain boundaries. The effect of the non-zero sink/source term in (4.21) is the prolongation of the time needed for vacancy concentration build-up.