In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical -Al2Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate.

An exact analytical solution of the Fick's second law was developed and applied to the mixed-mode growth of a multicomponent ellipsoidal precipitate growing with constant eccentricities in the quasi-stationary regime. The solution is exact if the nominal composition, equilibrium concentrations and material properties are assumed constant, and can be applied to compounds having no limitations in the number of components. The solution was compared to the solution calculated by a diffusion-controlled application software and it was found that the solute concentrations at the interface can be determined knowing only the nominal composition, the full equilibrium concentrations and the coefficients of diffusion. The thermodynamic calculations owing to find alternative tie-lines are proven to be useless in the mixed-mode model. From this, it appears that the search of alternative tie-lines is computationally counterproductive, even when the interface has a very high mobility. A more efficient computational scheme is possible by considering that a moving interface is not at equilibrium.

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Control of microstructure features that affect the Al-TiC master alloys grain refining efficiency is leading to improve the aluminum grain refinement. This study has been done to find the solute effect theory to produce new Al-TiC master alloys to get more possibility to control these features. The produced master alloys were examined by scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and X-ray diffraction (XRD); also, the influence of them on pure aluminum was studied. Produced Al-6Ti-1C master alloy contained Ti and TiC particles in the aluminum matrix and Al-4Ti-1C contained TiC particles in the aluminum matrix. As the result, the produced Al-6Ti-1C master alloy is a more efficient grain refiner for pure aluminum as compared to the Al-4Ti-1C. This confirms the influence of Ti particles for grain refinement. The results showed that Al-6Ti-1C master alloy had maximum grain refining performance with 2 minutes holding time , at 983 o K temperature , and 1% wt master alloy addition. Finally, a new Al-TiC master alloy with excellent refinement has been prepared successfully.