Non-isothermal precipitate growth and the principle of additivity

Abstract A theory of diffusion-controlled growth and dissolution of precipitates in binary alloys, taking account of temperature variations, is proposed. Analytical solutions are derived for planar and spherical interfaces by a method which assumes chemical equilibrium to prevail at the moving interface. The diffusion equations are solved by using the stationary-interface approximation, which restricts the concentration field to have no memory of the past motion of the interface. Predictions of growth and dissolution rates for plate-shaped and spherical particles are formulated and compared using data from the Al-Si equilibrium phase diagram. Solutions by analytical methods are compared with results obtained more easily by using the additivity rule. Conditions for additivity are discussed on the basis of numerical examples. Since the exact moving-boundary solution is unknown, the validity of the stationary-interface approximation could not be discussed. However, isothermal results imply that this approximation is reasonable when precipitates with relatively high concentrations are growing or shrinking in dilute solutions.