Kinetic theory of precipitation processes in solid solutions: I

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Abstract
The formation of precipitate particles in solid solutions is studied by regarding the process as comprising chain reactions, where the collision of two single solute atoms initiates the clustering. Calculations are greatly simplified if back-reactions, i.e. the decomposition of once-formed particles, are completely neglected. The reaction constant for particle growth are considered to be dependent on the size of particles, and the dependence is different for different growth mechanisms. The kinetics are examined for the two cases, size-independent and size-dependent (proportional to the number of solute atoms in the respective particle) reaction constants; the behaviour of actual systems may be inferred from the results of these two imaginary cases. The resultant distribution of particle size is very different for the two cases, especially when the rate for the initiation of the chain reactions is slow in comparison to those for subsequent reactions; for the latter case (size-dependent) the distribution is always a monotonically decreasing function of particle size while for the former it may have a maximum.

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