The most stable crystal structure and the formation processes of an order-disorder (OD) intermetallic phase in the Mg–Al–Gd ternary system

The most stable crystal structure for an 18R-type order-disorder (OD) intermetallic phase in the Mg–Al–Gd ternary system and its formation processes by annealing at 525?°C have been investigated by means of transmission electron microscopy and scanning transmission electron microscopy. The most energetically favourable polytype at 525?°C is found to be the structurally simplest one, a maximum degree of order polytype (monoclinic, 1M, space group: C2/m), described with a single stacking vector in stacking six-layer structural blocks. The formation of this simplest polytype occurs in the sequence of (i) enrichment of Gd and Al in four consecutive close-packed planes while keeping the hexagonal close-packed stacking of the AB-type, (ii) formation of Al₆Gd₈ clusters in the four consecutive atomic planes, introducing a stacking fault in the middle of the four consecutive atomic planes, (iii) thickening by the formation of Gd and Al-enriched four consecutive planes at a distance of two or three close-packed Mg atomic planes from the pre-existing Gd and Al-enriched four consecutive atomic planes so as to form six-layer and, sometimes seven-layer structural blocks, (iv) in-plane ordering of Al₆Gd₈ clusters in the four consecutive atomic planes and the stacking of structural blocks in the preferential stacking positions to form the OD structure, and (v) elimination of different structural blocks (other than six-layer ones) and the long-range ordering in the stacking of structural blocks.     

Structural analysis of the c(4 × 2) reconstruction in Si(0 0 1) and Ge(0 0 1) surfaces by low-energy electron diffraction

The c(4 × 2) structures in (0 0 1) surfaces of Si and Ge have been studied by low-energy electron diffraction (LEED). Using a proper cleaning method for the Si surface, we were able to observe clear c(4 × 2) LEED patterns up to incident energy of ∼400 eV as well as the Ge surface. Extensive experimental intensity-voltage curves allowed us to optimize the asymmetric dimer model up to the eighth layer (including the dimer layer) in depth in the dynamical LEED calculation. Optimized structural parameters are almost the same for the Si and Ge except for the height of the buckled-up atom of the asymmetric dimer. For the Ge surface, the structural parameters are in excellent agreement with those obtained by a previous theoretical calculation. The tilt angle and bond length of the dimer are 18 ± 1 (19 ± 1)° and 2.4 ± 0.1 (2.5 ± 0.1) Å for the Si(0 0 1) (Ge(0 0 1)), respectively.