On the Zener limit of grain growth through 2D Monte Carlo simulation

Extensive 2D Monte Carlo simulations were carried out on a square lattice to verify the Zener limit in the presence of inert second phase particles. Matrices of various sizes (from 100 to 10,000) were first run to stagnation to investigate the effect of matrix size on the limiting grain size, scaling constant and the fraction of second phase particles interacting with the grain boundaries (ϕ). The optimum matrix size selected was then run to stagnation for a wide range of particle fractions, at different Q-States, to arrive at limiting grain size and other parameters. Larger matrices (⩾1000) were found to be more suitable than smaller matrices to carry out simulation studies, while there was negligible effect on limiting grain size upon any variation in the Q-States. Based on our studies of particle-pinned regimes, a new relationship between the Zener limit and the fraction of second phase particles lying on the grain boundaries, i.e. R ( lim ) ∝ 1 / exp ( ϕ ) , is proposed, while the limiting grain size observed obeys a square root dependence on the particle fraction, agreeing largely with the earlier simulation results in 2D.