A new analytical approach to predict spacing selection in lamellar and rod eutectic systems

The Jackson and Hunt (JH) theory has been modified to relax the assumption of isothermal solid/liquid interface used in their treatment. Based on the predictions of this modified theory, the traditional definitions of regular and irregular eutectics are revised. For regular eutectics, the new model identifies a range of spacing within the limits defined by the minimum undercooling of the α and β phases. For the irregular Al-Si eutectic system, two different spacing selection mechanisms were identified: (1) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing λ _I ; (2) the average spacing (λ _av >λ _I ) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model, a semiempirical expression has been developed to account for the influence of the temperature gradient, which is dominant in the irregular Al-Si system. The behavior of the Fe-Fe₃C eutectic is also discussed. The theoretical calculations have been found to be in good agreement with the published experimental measurements.