Effects of vibrational entropy on the Al-Si phase diagram

An Al-Si solid-state phase diagram is studied using first-principles electronic structure calculations of formation enthalpies and quasiharmonic vibrational free energies. The harmonic vibrational entropy of formation of a Si impurity in fcc Al is predicted to be Delta S-vib = +2.6 k(B) per Si atom, resulting in more than a ten-fold increase in the calculated solubility. Thermal expansion is found to further increase the maximum solubility at T = 850 K by approximately 55%. Surprisingly, when vibrational effects are included, the widely used local-density approximation (LDA) performs poorly in reproducing the experimental solvus boundary, which is overestimated by a factor of ten. This failure is attributed to the neglect of corrections to the calculated LDA impurity enthalpy Delta H stemming from the inhomogeneity of the electronic charge density. These corrections tend to favour the four-fold coordinated diamond structure over the twelve-fold coordinated fcc solid-solution phase. The generalized-gradient approximation (GGA) is found to remove most of the discrepancy between the experimental and calculated Delta H, giving a good agreement with the experimental Al-Si phase diagram.