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The structural stability of various elemental metals ͑Ti, Sc, Al, Mo, and Nb͒, ordered compounds ͑PtTi and PtV͒, and disordered Ni-Cr alloys along distortion paths linking high-symmetry structures are investigated. A number of high-symmetry nonequilibrium structures are found to be mechanically unstable for these deformation paths, even for structures that occur at high temperature. For Ti, the electronic entropy is found to stabilize of the bcc phase at high temperatures, but without vibrational effects the hcp↔bcc transition would occur at much higher temperatures than observed. To treat disordered alloys along the Bain distortion path, the cluster expansion method is applied to the body-centered-tetragonal lattice, with particular choices of clusters in order to guarantee that the effective cluster interactions comply with the symmetry conditions of the cubic lattices. For disordered Ni-Cr alloys, the range of composition where the bcc and fcc phases are mechanically stable is determined.

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