The structure of crystalline α-AlMnSi is examined by electron diffraction. Six distinct zone axes are examined, including both normal crystallographic and non-crystallographic zone axes, allowing the space group symmetry of α-AlMnSi to be studied. A method for indexing the non-crystallographic zone axis diffraction patterns, which involve reflections from several nearby crystallographic zone axes, is described and applied to electron diffraction patterns of the quasi-5-fold, 3-fold and 2-fold axes of the icosahedral building units of cubic α-AlMnSi. These are compared with electron diffraction patterns from the corresponding 5-fold, 3-fold and 2-fold axes of the quasicrystalline phase i-AlMnSi, from which we may make some conclusions concerning the occupancies of the icosahedral units in i-AlMnSi. Electron diffraction patterns characteristic of [Formula: see text] were obtained for thicker specimens. However, for thin specimens, as used for HRTEM imaging, the electron diffraction patterns were characteristic of [Formula: see text] space group symmetry. This unusual behaviour arises because the structural basis for the [Formula: see text] to [Formula: see text] phase transition is a weak effect, involving changes in occupancy of the icosahedral structural elements located at the corners (double-MacKay icosahedra) and body-centers (MacKay icosahedra) of the cubic unit cell. The effects of changing the occupancies of the outer shells of the MI and DMI structural units on the diffraction intensities of the weak reflections were examined. Thus, calculation of the dynamical diffraction amplitudes shows that in fact the weak reflections characteristic of [Formula: see text] only develop sufficient intensity if two conditions are satisfied: namely (1) the crystal thickness exceeds approx. 50 nm and (2) if a significant proportion of [Formula: see text] occupancies are included in the structural model. By fitting the observed thickness variation of the diffraction intensities we propose a new set of occupancies for α-AlMnSi, which is consistent with the electron, X-ray and neutron diffraction data.
Unconventional superconducting gap structure protected by space group symmetry
