On the Kinetics of Precipitate Dissolution

Abstract

A theory of precipitate dissolution has recently been proposed by Aaron (Metal Sci. J., 1968, 2, 192) in which it is implied that a previous treatment by Thomas and Whelan (Phil. Mag., 1961, 6, 1103), where dissolution was considered to be approximately the reverse of growth, is in error in this assumption. Moreover, the time-dependence of the radius of a dissolving precipitate according to Aaron (<mml:math><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:mi>K</mml:mi><mml:msqrt><mml:mrow><mml:mi>D</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msqrt></mml:mrow></mml:math>) disagrees with that of Thomas and Whelan (dR ²/dt = −kD). It is pointed out that the “disagreement” arises because the situations treated are themselves dissimilar. Aaron's result is essentially one-dimensional and is derived from the transient part of the diffusion field in one dimension. The result of Thomas and Whelan is for three-dimensional diffusion and is obtained essentially from the steady-state part of the diffusion field around a spherical precipitate. The dissolution of a spherical precipitate, taking account of transient effects,is solved using an approximation for the diffusion field. The validity of the approximation is discussed and it is concluded that the time-dependence dR ²/dt = −kD is reasonable for the case of θ-phase precipitates in Al + 4 wt.-% Cu alloy.