Large vibrational effects upon calculated phase boundaries in Al-Sc

The fee portion of the AI-Sc phase diagram is calculated from first princip les including contributions to alloy foe energies associated with ionic vib rations. It is found that vibrational entropy accounts for a 27-fold increa se in the calculated solubility limits for Sc in fee Al at high temperature s, bringing calculated and measured values into very good agreement. The pr esent work gives a clear example demonstrating a large effect of vibrationa l entropy upon calculated phase boundaries in substitutional alloys.