Identifying the multiplicity of crystallographically equivalent variants generated by iterative phase transformations in Ti

Grammatikopoulos, P.; Pond, R.C.

doi:10.1107/S2052520615021897

Acta Crystallographica Section B
Acta Crystallographica
Section B STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS

IUCr IT WDC

home archive editors for authors for readers submit subscribe open access

view article

Figure 2
Tree-diagram that shows the increase in the number of variants for the first two generations. Degeneracy is not taken into account. The operators that produced the variants are also indicated. Starting from the progenitor, one can trace each particular variant by following a path determined by the operators used to create it. Note that the numerical values of matrices corresponding to H_1–6 symmetry operations are known, since they operate on the Pr, whereas those corresponding to $[{\bi C}_{\bi 1 - 12}^*]$ are not known, since they operate on crystals of different orientations. To indicate this, the latter are denoted with an asterisk superscript. Therefore, symmetry operation $[{\bi C}_{\bi 12}^*]$ operating on, for example, A₃ is not represented by the same matrix as $[{\bi C}_{\bi 12}^*]$ operating on A₄. As shown below, finding the numerical values of these matrices is not necessary.

STRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS

ISSN: 2052-5206

Volume 72| Part 1| January 2016| Pages 67-74

doi:10.1107/S2052520615021897

Follow Acta Cryst. B

Search IUCr Journals		doi		Advanced search
Author		volume	page