Coarsening in the Ising model with vacancy dynamics

We simulate coarsening in an alloy at 50% concentration using the Ising model, under either Kawasaki (K-) or vacancy (V-) dynamics, on three different lattices (sc, fcc, bcc) at five different temperatures. At times t greater than 2000 MCS the first zero R of the spherically averaged pair correlation function obeys R≈R0+(λt)1/3 where R0,λ are constants. As the temperature falls, λK (the value of λ for K-dynamics) falls but λV rises, so that at low temperatures λV λK. The ratio λK/λV is approximately proportional to the equilibrium concentration of minority atoms in either phase. For the various lattices, the values of λ are roughly proportional to the diffusivities and, therefore, to the squared nearest-neigbour distances, i.e., λsc:λbcc:λfcc≈4 : 3 : 2. At T=0.9Tc, R0 is between 2 and 3 for both types of dynamics and all three lattices; as the temperature falls, R0 remains near 2 for K-dynamics but falls, very roughly in proportion to the temperature, for V-dynamics