Concurrent Pathways in the Phase Transitions of Alloys and Oxides: Towards an Unified Vision of Inorganic Solids - Inorganic 3D Structures - page 139

Fig. 3 (a) The Si 8 group extracted from the Si array in TiSi 2 . The Ti atoms ( green ) are centering
the hexagons of the graphite-like layers. (b) The MgCu 12 truncated tetrahedron existing in both
Laves phases (MgCu 2 ) and spinels (Mg 2 SiO 4 ). The Mg atoms ( green ) centre the Cu 12 polyhedra

a b

c

b

a

Fig. 4 (a) The diamond -like array of Ti atoms in TiSi 2 .(b) The same array formed by the Si atoms
in the spinel Mg 2 SiO 4

Before anything else, the TiSi 2 -type structure will be described briefly (Fig. 2b ) .
It consists of graphite-like layers of Si atoms (Na atoms in thenardite) whose Si 6
hexagons are centred by the Ti atoms (S atoms in thenardite). The Si and the Ti
atoms in TiSi 2 (Na and S atoms in thenardite) complete altogether hexagonal close-
packed layers ( hcp ). The Ti subnet (green spheres) is four-connected, forming a
distorted diamond-like network, represented separately in Fig. 4a . Surprisingly, this
network is the same as that formed by the X atoms (Si atoms) in spinels, for instance
in Mg 2 SiO 4 . Remember that the Si atoms occupy the centre of the Mg 12 truncated
tetrahedron, as shown in Fig. 3b . Stated in other words, in a hypothetical phase
transition TiSi 2 ! MgCu 2 , the adamantane structure of the Ti subnet in TiSi 2 would

remain unaltered in the MgCu 2 structure, as it is shown in Fig. 4 .
The hcp -layers formerly described are perpendicular to the c axis and are stacked
in a

sequence. When Si atoms of two adjacent layers are
connected, one can identify fragments (Fig. 3a ) of the complete truncated tetrahedra
MgCu 12 (Fig. 3b ). Those fragments contain 8 of the 12 Si atoms which form the
truncated tetrahedron existing in both the cubic Laves phases (MgCu 2 type) and
spinels [ 5 ] .

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