what is the driving force for growth of the particles with the same size in the matrix
The boundary between one grain and its neighbor (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.
This is hard to say, there are a number of factors involved in the process that need to be identified and carefully tuned. You should read some textbooks and try to identify the basic parameters and control them according to the requirements for the final products. Good luck!
The boundary between one grain and its neighbor (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.
Dear Dr. Sayyedan; In ordinary sense there are two main driving forces for the growth of a given particle in a matrix: 1) The Bulk (Gibbs for isobaric systems or Helmholtz for isovolumic systems) free energy of transformation. Where the rate of change in free energy should be negative. 2) The rate of surface free energy increase should be compensated by the bulk free energy variation.
In multi-component systems (alloys) the particle has different composition then the matrix therefore rejected solute at the interface should be taken out by diffusion in solid state transformations.
There is a very sophisticated theory using the irreversible thermodynamics advocated by Ogurtani, which takes care of the applied elastostatic (deformation) as well as electrostatic forces. The problem treated in this theory is nonequilibrium and it doesn't assume any shape for the particle that would be adjusted by capillary forces.
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