Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 17, Issue 13, Pages 2197-2210Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0953-8984/17/13/017
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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.
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