text: The boundary between one grain and its neighbour (grain boundary) is a defect in the crystal structure and so it is associated with a certain amount of energy. As a result, there is a thermodynamic driving force for the total area of boundary to be reduced. If the grain size increases, accompanied by a reduction in the actual number of grains per volume, then the total area of grain boundary will be reduced.
  In the classic theory, the local velocity of a grain boundary at any point is proportional to the local curvature of the grain boundary, i.e.:
  where  is the velocity of grain boundary,  is grain boundary mobility (generally depends on orientation of two grains),  is the grain boundary energy and  is the sum of the two principal surface curvatures. For example, shrinkage velocity of a spherical grain embedded inside another grain is
  where  is radius of the sphere. This driving pressure is very similar in nature to the Laplace pressure that occurs in foams.
  In comparison to phase transformations the energy available to drive grain growth is very low and so it tends to occur at much slower rates and is easily slowed by the presence of second phase particles or solute atoms in the structure.
  Recently, in contrast to the classic linear relation between grain boundary velocity and curvature, grain boundary velocity and curvature are observed to be not correlated in Ni polycrystals, which conflicting results has been revealed and be theoretically interpreted by a general model of grain boundary (GB) migration in the previous literature. According to the general GB migration model, the classical linear relation can only be used in a specical case.