Concurrent Pathways in the Phase Transitions of Alloys and Oxides: Towards an Unified Vision of Inorganic Solids - Inorganic 3D Structures - page 177

a b c

Fig. 26 (a) The structure of CaSn (CrB type), projected on the bc plane. The trigonal prisms of Ca
atoms ( green spheres ) are filled by the Sn atoms ( grey spheres ). (b) The same structure formed by
TiSi. The trigonal prisms (Ti atoms) are filled by the Si atoms. (c) The C 49 structure of TiSi 2
( mcm), projected on the bc plane. The blocks of trigonal prisms are identical to those of the B 33

structure in (b). The additional Si atoms have been intercalated between these blocks, forming
slightly distorted 4 4 planar nets

C

[ 14 , 33 ], because the
Ca 2 Sn structure can be derived from that of TiSi. Thus, at ambient conditions, the
M

This relationship makes sense when we apply the EZKC

mcm). This structure,
represented in Fig. 26a , is formed by walls of trigonal prisms of Ca(Ti) filled by Sn
and Si atoms, respectively. It is remarkable that the CrB structure appears in the
Pearson's Crystal Database (2008) as a FeB-stacking variant. Further evidence
supporting such similarities as well as our hypothesis is the FeB-CrB polymor-
phism existing in some related alloys such as ZrSi and ZrGe [ 107 ] . In the case of
ZrSi, the CrB

Sn ( M ¼ Ca, Sr, Ba) binary alloys are B 33 (CrB-type, C

FeB transition occurs above 1,853 K [ 108 ].
At this point, we could then describe the Ca 2 Sn structure as the insertion of a
Ca atom into a CaSn structure of the TiSi type. In other words, the “new” Ca atom
causes the previous CaSn array to adopt the TiSi-type structure. This reasoning is a
mere application of the

!

and can be explained as follows.
If Ca 2 Sn is formulated as Ca(CaSn), and we admit that the first Ca atom transfers
two electrons to the (CaSn) pair, the compound becomes Ca 2+ [

EZKC

C -TiSn)], where the

C -TiSn moiety adopts the TiSi-type structure. It is worthy of mention that the

analogue ZrGe [ 107 ] is also TiSi type! We must recall how the EZKC gave a
satisfactory explanation of the Ni 2 In structure, inducing the pseudo-formula Ni 2
+ [Ni

-NiSb (NiAs-type) structure [ 14 ].
In order to provide examples that could enhance our arguments, we have
searched for related structures in which comparable processes could occur. We
have found a meaningful example in the pair TiSi/TiSi 2 , whose structures are
depicted in Fig. 26b, c , respectively.
The relevant key issue here is that TiSi 2 ( C 49) (

C -Sb], and hence the formation of a C

mcm) can be formulated as Si
(TiSi), and hence it can be thought of as formed by simply inserting one additional
Si atom between the CrB-type blocks of the TiSi ( B 33) structure. These new Si

C