Phase Coarsening

    Coarsening is another commonly met phenomena.  The following pictures explain the coarsening of particles in a continuous matrix.  In the beginning, the particles are small and the total area of the phase boundaries is large.  The atoms at the phase boundaries have excess free energy.  To reduce the free energy, the total area of the phase boundaries must reduce.  Consequently, atoms leave small particles, diffuse in the matrix, and join large particles.  Over time the small particles disappear, and the large ones become larger.  The process is known as phase coarsening.  Time permitting, the phases will coarsen until only one big particle left in the matrix.

     Can coarsening from a stable pattern?  The answer is No.  Coarsening prefers large scale.  It can be observed from the above example that large particles grow and “eat” small particles.

Hence

 •  Phase boundary causes coarsening

 •  Coarsening can not stabilize periodic patterns

 The observed stable periodic structures suggest the existence of some refining mechanism.  So that the small ones can compete with the large ones and finally reach some balance.