## Abstract

The dependence of the solubility of a precipitate particle in a matrix on its radius considerably modifies the solute currents to the particle and hence the kinetics of its rate of growth. The effect of particle size on the solubility is large if the interfacial energy is large and the radius $R$ of the particles is small. This effect has been included in the theory of precipitation from a supersaturation of solute. In the extensively used formula, $1-W$ = e$^{-(t/\tau)^{n}}$, (1) describing the time dependence of $W$, the fraction of solute precipitated, the effect increases the value of $\tau $ but leaves $n$ practically unaltered. It does not therefore solve the problem that although Ham's theory of precipitation on a periodic array of dislocations gives $n$ = 1, the experimentally observed values are $n=\frac{1}{2}$ to $\frac{2}{3}$. It is shown that the use of the $n$ = 1 equation for non-periodic arrays is invalid in most cases of practical interest and is responsible for the discrepancy. The effective interdislocation distance, $\lambda _{1}$, which determines $\tau $, is the average of interdislocation distances of only a few dislocations surrounding the dislocation line, more distant dislocations have no strong influence. In view of this and the fact that even small percentage changes in $\lambda _{1}$ cause appreciable changes in $\tau $, inhomogeneities in the distribution of $\lambda _{1}$ cause different groups of particles to grow with different relaxation times $\tau $, and 1 - $W$ is given by the sum of more than one exponential term. The effect of closely spaced particles or unequally sized particles is similar. Numerically these effects mean that 1 - $W$ can be represented by (1) but with $n$ reduced to a value less than 1. When inhomogeneities observed by electron microscope studies are taken into account, values of $\frac{1}{3}$-$\frac{2}{3}$ for $n$ are obtained and experiments on precipitation of iron carbide in alpha iron (or steel) and in other systems are satisfactorily explained.

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