Large vibrational effects upon calculated phase boundaries in Al-Sc

The fee portion of the AI-Sc phase diagram is calculated from first principles including contributions to alloy foe energies associated with ionic vibrations. It is found that vibrational entropy accounts for a 27-fold increase in the calculated solubility limits for Sc in fee Al at high temperatures, bringing calculated and measured values into very good agreement. The present work gives a clear example demonstrating a large effect of vibrational entropy upon calculated phase boundaries in substitutional alloys.