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Coarsening in the Ising model with vacancy dynamics

Author

Listed:
  • Fratzl, P
  • Penrose, O
  • Weinkamer, R
  • Žižak, I

Abstract

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.

Suggested Citation

  • Fratzl, P & Penrose, O & Weinkamer, R & Žižak, I, 2000. "Coarsening in the Ising model with vacancy dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 100-109.
    • Handle: RePEc:eee:phsmap:v:279:y:2000:i:1:p:100-109
    DOI: 10.1016/S0378-4371(99)00527-0
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