Concurrent Pathways in the Phase Transitions of Alloys and Oxides: Towards an Unified Vision of Inorganic Solids - Inorganic 3D Structures - page 148

Fig. 10 Stereopair of the
structure of Na 2 S (CaF 2 type)
referred to a hexagonal R cell.
The figure shows the layers of
both filled and empty Na 8
cubes (characteristic of the
anti-fluorite structure), which
in this view are alternating
along the c axis

Table 1 At o mic coordinates of the cubic anti-fluorite structure of Na 2 S referred to the trigonal
unit cell ( 11.27 ˚ represented in Fig. 10 . These positions are P 3) of dimensions a ¼ 4.61, c ¼

splitted in the non-centrosymmetric S.G. P 3

Atom Wyckoff position x/a y/b c/z

S 1 a 0 0 0

S 2 d 1/3 2/3 2/3

Na 2 c 0 0 1/4

Na 2 d 1/3 2/3 0.4167

Na 2 d 1/3 2/3 0.9167

the common subgroup of lo w est symmetry, that is, P3. The atomic coordinates of
Na 2 S (anti-fluorite), in the P3 hexagonal cell, are collected in Table 1 .
An inspection of Fig. 10 allows us to propose a plausible mechanism for the
CaF 2 !

Ni 2 Al transition. As can be readily observed in Fig. 10 , the Na cubes are
oriented in such a way that their body diagonals run parallel to the c axis of the
hexagonal cell but where, both, Na and S atoms are placed in separated layers
perpendicular to c . The transition can be, then, thought of as a cascade displacement
of these atomic layers. The first step is the migration of the Na(1) atoms located at
(0, 0, 1/4) (the lower corner of an empty cube) towards the centre of the cube
situated at (0, 0, 1/2). This displacement corresponds to c/ 4 (2.83 ˚ ) and produces
the filling of the empty cubes of the fluorite by other Na atoms.
The empty corners are now occupied by the adjacent layer of Na atoms,
migrating from (2/3, 1/3, 1/12) to (0, 0, 1/4), thus completing the filled cubes.
Next, the S atoms at (0, 0, 0) are displaced to (1/3, 2/3, 1/6) and, finally, the next
layer of Na atoms at (1/3, 2/3, 1/12) migrates to (2/3, 1/3, 1/12). Thus, the

displacement of the first layer provokes that of the adjacent layers, producing a
“ domino-like ” effect. All the translations are defined by the vector

t ¼ (1/3 a

) corresponding to displacements of 3.24 ˚ . The resulting structure is
drawn in Fig. 11 .
It should be remarked that the regular Na 8 cubes, in fluorite, are rhombohedrally
distorted in Na 2 SO 3 with an average edge of 3.81 ˚ and average S-Na distances of
8

1/3 b þ 1/6 c

3.29 ˚ .InNa 2 S, the equivalent distances are 3.27 and 8 2.83 ˚ .