The basics of crystallography and diffraction (3rd Edition)

130 Crystal symmetry
Fig. 4.24. Image (10 nm × 10 nm) of a surface of the alloy Al 70 Pd 21 Mn 9 showing the five-fold ‘dark
star’ quasiperiodic pattern. (Photograph by courtesy of Prof. Ronan McGrath, University of Liverpool.)
the ‘middle’ ring of six atoms is planar with a group of three close-packed atoms above
and three below. In icosahedral packing the corresponding ring of six atoms is puckered
(resulting in a ∼10% smaller central cavity) with again three close-packed atoms above
and three below. Hence, the transformation may proceed by such small displacive atom
movements.
Exercises
4.1 Draw the space group Pba2 with(
the pattern unit ○ at the following positions:
(a) on the b glide plane, i.e. at x ′ 4 1 z′) ;
(
(b) at the intersections of the a and b glide planes, i.e. at 14 1
4 z ′) ;
(c) on a diad axis through the origin, i.e. at (00z ′ );
(
(d) on a diad axis through the mid-points of the cell edges, i.e. at 12
0z ′) .
Hence, show that only (c) and (d) constitute special positions.
4.2 Make and examine the crystal models of NaCl, CsCl, diamond, ZnS (sphalerite), ZnS
(wurtzite), Li 2 OorCaF 2 (fluorite), CaTiO 3 (perovskite). Identify the Bravais lattice and
describe the motif of each structure.