High temperature X-ray diffraction study on incommensurate composite crystal MnSiγ - (3+1)-dimensional superspace approach

The (3+1)-dimensional crystal structure of a higher manganese silicide (MnSiγ) phase is revealed using in situ high temperature powder X-ray diffraction (XRD) above room temperature. The compound consists of two tetragonal subsystems of [Mn] and [Si] with an irrational c-axis ratio γ=cMn/cSi. The in situ XRD results show that the MnSiγ phase is stable, in a vacuum of ∼1 Pa, up to 1093 K and partially decomposes into the monosilicide (MnSi) phase with further increase in temperature. Refined a- and cMn-axis lengths increase linearly and the thermal expansion coefficients are comparable with those of typical metallic electrode materials. In contrast, cSi-axis length changes its increment against temperature at TBD ∼773 K. As a result, the temperature dependence of γ starts to decrease gradually above TBD, from 1.7387(1) (at 773 K) to 1.7244(1) (at 1173 K). This finding implies that the MnSiγ phase consecutively changes its irrational composition above TBD, a typical temperature where the silicides exhibit a maximum figure-of-merit. An increase in hole carrier concentration is expected according to the valence electron counting concept. Although the nearest Mn-Mn and Mn-Si distances increase monotonically with temperature, the nearest Si-Si distance much increases by ∼0.05 Å from 2.439(4) Å at 773 K to 2.493(7) Å at 1173 K. The latter increase is considered to be caused by the introduction of excited electron carriers into the anti-bonding orbital, due to the bipolar diffusion (BD).