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- Cesar Capillas, Eli Kroumova, Mois I. Aroyo, J. Manuel Perez-Mato, Harold T. Stokes, Dorian M. Hatch
- 2003

- Dorian M. Hatch
- 2011

All isotropy subgroups (and thus all quasicontinuous symmetry changes) corresponding to k points of symmetry have been obtained for the 80 diperiodic space groups. The detailed information for such phase transitions is given here for the diperiodic space group I' —— —. Only two distinct images (sets of representation matrices) occur for this example… (More)

- D. R. Trinkle, R. G. Hennig, +5 authors J. W. Wilkins
- 2003

We propose a new direct mechanism for the pressure driven ! ! martensitic transformation in pure titanium. A systematic algorithm enumerates all possible pathways whose energy barriers are evaluated. A new, homogeneous pathway emerges with a barrier at least 4 times lower than other pathways. The pathway is shown to be favorable in any nucleation model.… (More)

- Dorian M. Hatch
- 2011

Group-theoretical criteria which determine the possibility of group-subgroup phase transitions have been implemented on a computer. Lower-symmetry groups are determined by the subduction and chain criteria. %e list all possible such symmetry-restricted transitions in two dimensions corresponding to k points of symmetry. %'e indicate relative origins and… (More)

We have theoretically investigated the mechanism of the pressure-induced reconstructive zinc-blende to rocksalt phase transition in SiC. We obtained 925 possible transition pathways ͑TPs͒ using a group-theoretical analysis method. This extensive survey of possible TPs is a significant feature which distinguishes this study from previous studies. Of these… (More)

Martensitic phase transitions appear in a diverse range of natural and engineering material systems. Examination of the energetics and kinetics of the transformation requires an understanding of the atomic mechanism for the transformation. A systematic pathway generation and sorting algorithm is presented and applied to the problem of the titanium ␣ to … (More)

Three possible mechanisms for the reconstructive phase transition from the B1 to the B2 structure types are examined: ͑1͒ a modified Buerger ͑MB͒ pathway, ͑2͒ the Watanabe ͑W͒ pathway, and ͑3͒ a new pathway ͑T͒ proposed by Tolédano et al. ͓Phys. Rev. B 67, 144106 ͑2003͔͒. We use first-principles energy calculations to obtain barrier heights for these… (More)

A variety of structural transitions in nature do not involve a group-subgroup relationship. A two-dimensional example is the transition between a square lattice and a triangular lattice, which is known to occur in vortex lattices, Wigner crystals, skyrmion lattices, colloids, diblock copolymers, etc. A three-dimensional analog is the shock-induced BCC to… (More)

- Dorian M. Hatch
- 2011

A comparison is made of two different approaches to the description of phase transitions in the A2BX4 structure (space group D4&, I4/mmm) due to rigid octahedral tiltings. The lower-symmetry subgroups due to coupling of the K»f (X2) and E&2~ (P4) representations (6 tilts) to other tilting modes are listed. All observed transitions in the A2BX4 structure are… (More)

- Dorian M. Hatch
- 2011

The possible lower symmetries (subgroups) of the A2BX4 structure (space-group symmetry D4&) due to rigid octahedral tiltings at phase transitions are investigated. The method for obtaining subgroups determined by reducible representations (i.e., coupled order parameters) is described. This method depends upon subgroup information for irreducible… (More)