Concurrent Pathways in the Phase Transitions of Alloys and Oxides: Towards an Unified Vision of Inorganic Solids - Inorganic 3D Structures - page 176

and was dissected by Vegas et al. [ 105 ]. Although FeB is considered as the
aristotype, we will take, for convenience, the isostructural TiSi alloy as the refer-
ence compound [ 106 ].
The resemblance of both structures (Ca 2 SnO 4 and FeB) disappears when the
structures are drawn in perspective, as it can be observed in Fig. 24c, d . As stated
above, in Ca 2 SnO 4 , the central prisms Ca 8 Sn (3.26

5.27 ˚ ) are close to

3.17

4.95 ˚ ) (Fig. 24c ), whereas in
TiSi (FeB) the prisms are trigonal and are filled with the Si(B) atoms (Fig. 24d ) .
To illustrate these differences, the two sorts of prisms are drawn in Fig. 25 . They
are projected along the fourfold and threefold axes in Ca 2 Sn (Fig. 24a ) and TiSi
(Fig. 24c ), respectively. This drawing reflects clearly the difference in stoichiome-
try which entails that, in Ca 2 Sn (2:1), the Sn atoms are surrounded by 8 Ca atoms,
in contrast to the Ti 6 trigonal prisms, filled by the Si atoms in the TiSi (FeB)
structure (1:1).
In spite of the discrepancies between both patterns (Fig. 25a, c ), the TiSi
structure (Fig. 25c ) could ideally be derived from that of Ca 2 Sn (Fig. 25a ), by
eliminating one half of the Ca atoms. This would lead to the drawing of Fig. 25b ,
which corresponds to the stoichiometry 1:1 (CaSn), as in TiSi. In this state, the Ca
and Sn atoms should rearrange to form the trigonal prisms of the TiSi structure
(Fig. 25c ). To achieve this, the Ca atoms of the upper and lower lines of Fig. 25b
should move in opposite directions along the c axis (the shortest axis) leading to the
pattern of TiSi (Fig. 25c ). The opposite conversion (TiSi

the unit cell of Indium ( I 4/mmm) ( a ¼ 3.25, c ¼

Ca 2 Sn) could also be
imagined if two Ti atoms are added to the TiSi trigonal prisms (Fig. 25c ). In this
case, atoms must move to convert two rhombs into two squares, as illustrated in
Fig. 24a .
We believe that this is the appropriate point to reaffirm the formulation of the
Ca 2 Sn subarray as Ca + CaSn, in the same manner that, as was advanced in the
previous Sect. 7 , Ca 2 SnO 4 can be contemplated as the intergrowth of blocks of
CaSnO 3 (In 2 O 3 type) and CaO (rocksalt).

!

a b c

Fig. 25 (a) The tetragonal prisms of Ca 2 Sn, viewed along the fourfold axis. If the Ca atoms
located at the upper right and the lower left corners were eliminated, as shown in (b), the
remaining atoms would rearrange to form the pattern of the trigonal prisms of TiSi, which are
represented in (c)