Concurrent Pathways in the Phase Transitions of Alloys and Oxides: Towards an Unified Vision of Inorganic Solids - Inorganic 3D Structures - page 150

Table 2 Atomic coordinates of Na and S atoms, in the Ni 2 Al-type structure, obtained after the
displacements applied to the layers of the anti-fluorite structure, leading to the structure of
Fig. 11a . The transformation is made in the non-centrosymmetric 3 space group. The original

coordinates and cell dimensions are those quoted in Table 1 . As seen in Fig 11a , the c axis of the
final unit cell is reduced to ½ of the original unit cell with values of a

P

5.63 ˚ ¼ 4.61, c ¼

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

1 b

S 1/3 2/3 1/6

1 b

S 1/3 2/3 2/3

S 1 c 2/3 1/3 1/3

Na 1 a 0 0 1/4

Na 1 a 0 0 1/2

Na 1 a 0 0 3/4

Na 1 b 1/3 2/3 0.4167

Na 1 c 2/3 1/3 0.5833

Na 1 c 2/3 1/3 0.0833

Table 3 Atomic coordinates of Na 2 SO 3 (P3) as derived from the experimental determination
of the crystal structure. Compare with the values listed in Table 2 . In both structures, the Na 2 S
subarrays are Ni 2 Al type. The unit cell dimensions are a

6.473 ˚ . The insertion of
O atoms produces an expansion of the unit cell axes (compare with those of Table 2 )
Atom

¼ 5.509, c ¼

x/a y/b c/z

Wyckoff position

Na 1 a 0 0 0

1 a Na 0 0 0.5368

1 b Na 1/3 2/3 0.8351

1 c Na 2/3 1/3 0.1798

S 1 b 1/3 2/3 0.3395

S 1 c 2/3 1/3 0.6877

O 3 d 0.2200 0.4302 0.2344

O 3 d 0.8640 0.6667 0.7689

them are centred by the Na(2) atoms, forming fragments of bcc -Na (Fig. 8 ) . In the
Na 8 S cubes, the S-Na distances are 1 3.33 ˚

(mean value 3.28 ˚ ), hence longer than the equivalent bonds in the anti-fluorite
Na 2 S structure (8

3.05, 1 3.13, 3 3.30 and 3

2.83 ˚ ). However, in the bcc -Na blocks, the distorted cubes
have edges of 3.76 ˚

3.32 ˚ (mean
value 3.25 ˚ ), dimensions that are smaller than the unit cell of elemental bcc -Na at
ambient conditions ( a

and Na-Na distances of 2 3.09 and 6

3.72 ˚ )[ 42 ] . The result is that in Na 2 SO 3 ,
the anti-fluorite fragments are expanded at the expense of the Na blocks, which are
compressed.
From the equation of state of Na [ 42 ], it can be deduced that in Na 2 SO 3 the
dimensions of the Na-centred rhombohedra ( a

¼ 4.29, d ¼ 8

3.76 ˚ ) are in the range of
stability of bcc phase under pressure, in such a way that the unit cell parameter of
3.76 ˚ would correspond to a pressure of about 5.3 GPa. It should be remembered
that at this pressure, the anti-fluorite

¼

anti-cotunnite transition has not yet
occurred in Na 2 S. The diffraction peaks of the anti-cotunnite phase begin to appear
at 6.4 GPa [ 7 ], in agreement with the fact that the Ni 2 In-type structure is not reached
in Na 2 SO 3 .

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