Crystal Structures of Inorganic Oxoacid Salts Perceived as Cation Arrays: A Periodic-Graph Approach - Inorganic 3D Structures - page 48

salts considered in the previous part; however, the periodic-graph approach reveals
non-strict resemblances in many cases [ 17 ] .

3.2.1 Sulfites, Selenites, and Tellurites

Sulfites, selenites, and tellurites present some examples of nontrivial topological
relationships. According to [ 17 ], the

b g

phases of HgSeO 3 are the first example
of formally isostructural compounds that have similar geometrical parameters
(space group and unit cell dimensions) but different topologies, and hence are
related to different topological types. Indeed, both phases belong to the same
space group ( P 2 1 / c ) with very close unit cell volumes (309.5 and 306.2 ˚ 3 ) and
equal coordination numbers of corresponding atoms. This allowed the author [ 52 ]
to put them into the same structure type. However, the coordination sequences for
b

and

- and g -HgSeO 3 differ even in the second coordination shell: in b -HgSeO 3 each

SeO 3 2- anion is bonded to 6 Hg atoms via oxygens, while for -HgSeO 3 the number

of Hg atoms in the second coordination shell is 5; the same concerns the numbers of
Se atoms in the second coordination shell of Hg atoms. As a result, the underlying
nets in these polymorphs have the topologies of 6-coordinated uninodal and 5,5-
coordinated binodal nets, derived in [ 23 , 37 ] from 7-coordinated sev and 6,6-
coordinated nia nets, respectively (Table 7 ) . At the same time, the quasi-binary
representation allows one to discover similarities between geometrically and topo-
logically nonequivalent crystal structures. According to [ 17 ], there are three such
cases: between Na 2 SO 3 ,K 2 SO 3 ,K 2 TeO 3 , and Cs 2 TeO 3 ; between two phases of
PbSO 3 , PbSeO 3 , and BaSeO 3 ; between CdSO 3 -II, CdSeO 3 , and

g

-MnSO 3 . In fact,
the similarity of topological types in the quasi-binary representation means a
topological equivalence of cation arrays or packings of cations and structureless
anions. In particular, when comparing the underlying nets, the different coordina-
tion types of anions are ignored in Na 2 SO 3 (T 901 ) and K 2 SO 3 (T 631 ); only the total

b

Table 7 Underlying nets in sulfites and selenites
Underlying net Sulfite/selenite Correspondence LO 3

coordination type

T 33 pcu-b (NaCl) PbSO 3 , MSeO 3 (M ¼ Sr, Ba, Pb) Normal

T 6 nia (NiAs) MSeO 3 (M ¼ Mg, Mn, Co,

Ni, Cu, Zn, Cd, Hg)

Normal

T 51 sev-6- C 2/ m b -HgSeO 3

T 51 HIYXUJ CaSeO 3

T 32 nia-5,5- P 2 1 / c CdSO 3 , g -HgSeO 3

T 5 bnn (BN) MSeO 3 (M ¼ Cu, Zn) Normal

T 901 Ni 2 Al Na 2 SO 3

T 31 ,T 22 NASTEH M 2 (SeO 3 ) 3 (M ¼ Bi, Er)

T 4 stp Sc 2 (SeO 3 ) 3

T 3 rtl (TiO 2 , rutile) M(SeO 3 ) 2 (M ¼ Ti, Mn, Sn, Pb) Normal

T 3 pyr (FeS 2 ) a -Sn(SeO 3 ) 2 Normal