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

Abstract The ( 3 + 1 )-dimensional crystal structure of a higher manganese silicide (MnSi γ ) 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 = c Mn / c Si . The in situ XRD results show that the MnSi γ 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 c Mn -axis lengths increase linearly and the thermal expansion coefficients are comparable with those of typical metallic electrode materials. In contrast, c Si -axis length changes its increment against temperature at T BD ∼773 K. As a result, the temperature dependence of γ starts to decrease gradually above T BD , from 1.7387(1) (at 773 K) to 1.7244(1) (at 1173 K). This finding implies that the MnSi γ phase consecutively changes its irrational composition above T BD , 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 A from 2.439(4) A at 773 K to 2.493(7) A 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).