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- 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 D Allred, M Cai, Q Wang, D M Hatch, A Reyes-Mena
- Journal of X-ray science and technology
- 1992

Raman spectra are reported from MoSi2 polycrystalline powder and soft x-ray Mo/Si multilayers. The sharp lines at 323 and 438 cm-1 are all due to crystalline MoSi2. These lines in the powder sample intensify with annealing. The Raman spectra of as-deposited multilayers shows a broad asymmetric peak, highest at about 480 cm-1. We attribute this to α-Si which… (More)

- Harold T Stokes, Erich H Kisi, Dorian M Hatch, Christopher J Howard
- Acta crystallographica. Section B, Structural…
- 2002

Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolomé [Phase Transit. (2001), 74, 255-335] and a… (More)

- D R Trinkle, R G Hennig, +5 authors J W Wilkins
- Physical review letters
- 2003

We propose a new direct mechanism for the pressure driven alpha-->omega 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… (More)

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)

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)

We have implemented group-theoretical methods on the computer for the description of possible structural phase transitions. All isotropy groups (correspanding to k points of symmetry) for each of the 230 three-dimensional space groups as well as the Landau and Lifshitz conditions for each representation have been obtained. Here we compare our results with… (More)

We have classified continuous phase transitions in physical systems where the order parameter transforms as a six-dimensional representation of a space group. The Landau potential is minimized with the use of Kim's geometrical method and a table of isotropy subgroups recently obtained by Stokes and Hatch. For most images of the active six-dimensional… (More)

- Dorian M Hatch, Harold T Stokes, K S Aleksandrov, S V Misyul
- 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)

- 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)