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)=> 120 K (LT)=> 293 K (RT-II): [H: P(-)42(1)m; G: P(-)42(1)m; composite: P(-)42(1)m]=> [H: P(-)4, G: P4/mbm (c(G) = 0.5c(H)), composite: P(-)4]=> [H: P(-)42(1)m, G: P4/mbm (c(G) = 0.5c(H)), composite: P(-)42(1)m]. Thus, the phase transition is reversible with respect to H and irreversible with respect to G.