Orientational twins in an improper ferroelastic phase transition driven by theM5−zone-boundary phonon inRAg1−xInx

Dorian M. Hatch, Wenwu Cao, Avadh Saxena
2002 Physical Review B (Condensed Matter)  
Orientational twins involve two domain states that exhibit rotational symmetry relationships between them. For an improper ferroelastic cubic to tetragonal first-order phase transition driven by the M 5 Ϫ zone-boundary phonon in the CsCl structure, there are three possible directions for the tetragonal axis of the low-temperature phases. The existence of four antiphase-related-domain states for each given tetragonal orientation introduces additional possible pairing schemes for the twins. We
more » ... or the twins. We obtain only three distinct domain pair classes: two antiphase boundary classes and one orientational boundary class. For this O h 1 -D 4h 17 ( Pm3 m-I4/mmm) transition we derive the general governing equations for the orientational twins based on a Ginzburg-Landau theory, which constitute a system of four coupled nonlinear differential equations. General features of the orientational twin solutions are demonstrated through a special choice of the parameters for which the four coupled equations can be reduced to two. The orientational twin boundaries have relatively large elastic energy and, therefore, they are strongly restricted to preferred lattice planes. 65 094110-1 tetragonal low-temperature structure. DORIAN M. HATCH, WENWU CAO, AND AVADH SAXENA PHYSICAL REVIEW B 65 094110 2y ͉001͖, ͕ y ͉000͖, ͕C 4zϪ ͉000͖, ͕S 4zϩ ͉001͖, ͕C 4zϩ ͉001͖, ͕S 4zϪ ͉000͖, ͕C 2b ͉100͖, ͕ db ͉010͖, ͕C 2a ͉010͖, ͕ da ͉100͖ T 8,1 ͕C 34Ϫ ͉000͖, ͕S 64ϩ ͉010͖, ͕C 31Ϫ ͉100͖, ͕S 61ϩ ͉001͖, ͕C 33Ϫ ͉001͖, ͕S 63ϩ ͉100͖, ͕C 32Ϫ ͉010͖, ͕S 62ϩ ͉000͖, ͕C 2d ͉000͖, ͕ dd ͉010͖, ͕C 4xϪ ͉010͖, ͕S 4xϩ ͉000͖, ͕C 2 f ͉001͖, ͕ d f ͉100͖, ͕C 4xϩ ͉100͖, ͕S 4x ͉001͖ T 9,1 ͕C 32ϩ ͉000͖, ͕S 62Ϫ ͉100͖, ͕C 31ϩ ͉001͖, ͕S 61Ϫ ͉010͖, ͕C 34ϩ ͉010͖, ͕S 64Ϫ ͉001͖, ͕C 33ϩ ͉100͖, ͕S 63Ϫ ͉010͖, ͕C 4y ͉000͖, ͕S 4yϪ ͉100͖, ͕C 2c ͉100͖, ͕ dc ͉000͖, ͕C 2e ͉010͖, ͕ de ͉001͖, ͕C 4yϪ ͉001͖, ͕S 4yϩ ͉001͖ T 10,1 ͕C 2z ͉000͖, ͕ z ͉001͖, ͕C 2y ͉010͖, ͕ y ͉100͖, ͕C 2x ͉100͖, ͕ x ͉010͖, ͕E͉001͖, ͕I͉000͖, ͕C 2b ͉000͖, ͕ db ͉001͖, ͕C 2a ͉001͖, ͕ da ͉000͖, ͕C 4zϪ ͉100͖, ͕S 4zϩ ͉010͖, ͕C 4zϩ ͉010͖, ͕S 4zϪ ͉100͖ T 11,1 ͕C 33Ϫ ͉000͖, ͕S 63ϩ ͉010͖, ͕C 32Ϫ ͉100͖, ͕S 62ϩ ͉001͖, ͕C 34Ϫ ͉001͖, ͕S 64ϩ ͉100͖, ͕C 31Ϫ ͉010͖, ͕S 61ϩ ͉000͖, ͕C 2 f ͉000͖, ͕ d f ͉010͖, ͕C 4xϩ ͉010͖, ͕S 4xϪ ͉000͖, ͕C 2d ͉001͖, ͕ dd ͉100͖, ͕C 4zϪ ͉100͖, ͕S 4x ͉001͖ T 12,1 ͕C 34ϩ ͉000͖, ͕S 64Ϫ ͉100͖, ͕C 33ϩ ͉001͖, ͕S 63Ϫ ͉010͖, ͕C 32ϩ ͉010͖, ͕S 62Ϫ ͉001͖, ͕C 31ϩ ͉100͖, ͕S 61Ϫ ͉000͖, ͕C 2e ͉000͖, ͕ deϩ ͉100͖, ͕C 4yϪ ͉100͖, ͕S 4y ͉000͖, ͕C 4yϩ ͉010͖, ͕S 4yϩ ͉001͖, ͕C 2c ͉001͖, ͕ dc ͉010͖ ORIENTATIONAL TWINS IN AN IMPROPER . . . PHYSICAL REVIEW B 65 094110 094110-5
doi:10.1103/physrevb.65.094110 fatcat:l2ychgedanczhf32l4sdggydfi