The commensurate composite sigma-structure of beta-tantalum

The single-crystal investigation of the self-hosting sigma-structure of beta-tantalum (beta-Ta) at 120 K (low-temperature, LT, structure) and at 293 K (RT-I before cooling and RT-II after cooling and rewarming; RT represents room temperature) shows that this structure is indeed a specific two-component composite where the components have the same ( or an integer multiple) lattice constants but different space groups. The space groups of both host ( H) and guest ( G) components cause systematic absences, which result from their intersection. The highest symmetry of a sigma-structure can be described as [H: P4(2)/mnm; G: P4/mbm (c(G) = 0.5c(H)); composite: P4(2)/mnm]. A complete analysis of possible symmetries is presented in the Appendix. In beta-Ta, two components modify their symmetry during the thermal process 293 K (RT- I)) double right arrow 120 K (LT)) double right arrow 293 K (RT-II): [H: P (4) over bar2(1)m; G: P (4) over bar2(1)m; composite: P (4) over bar2(1)m]) double right arrow [H: P (4) over bar, G: P4/mbm (c(G) = 0.5c(H)), composite: P (4) over bar]) [H: P (4) over bar2(1)m, G: P4/mbm (c(G) = 0.5c(H)), composite: P (4) over bar2(1)m]. Thus, the phase transition is reversible with respect to H and irreversible with respect to G.