The　thermodynamic　properties　of　FCC　Al,　HCP　Sc,　B2　AlSc,　C15　Al2Sc,　B8(2)　AlSc2,　and　L1(2)　Al3Sc　were　studied　using　ab　initio　calculations　based　on　density　functional　theory.　The　0　K　(-273　A　degrees　C)　total　energies　were　calculated　using　the　ab　initio　plane-wave　pseudopotential　method　within　the　generalized　gradient　approximation.　The　ab　initio　calculations　of　the　phonon　dispersion　curves　and　the　density　of　state　of　FCC　Al,　HCP　Sc,　B2　AlSc,　C15　Al2Sc,　B8(2)　AlSc2,　and　L1(2)　Al3Sc　have　been　performed　using　the　density　functional　theory　and　the　direct　method.　Deduced　from　Helmholtz　free　energy,　the　thermal　expansion,　enthalpy,　heat　capacity,　and　entropy　as　a　function　of　temperature　were　calculated　and　compared　considerably　with　the　experimental　data　and　other　computational　results.　Our　calculations　show　that　the　enthalpies　of　formation　are　temperature-dependent,　and　the　slope　is　about　-3.4　J/mol/K　for　B2　AlSc,　-2.3　J/mol/K　for　C15　Al2Sc,　-0.8　J/mol/K　for　B8(2)　AlSc2,　and　-2.7　J/mol/K　for　L1(2)　Al3Sc,　respectively.