Crystal Structures of Inorganic Oxoacid Salts Perceived as Cation Arrays: A Periodic-Graph Approach - Inorganic 3D Structures - page 58

Table 12 Underlying nets in perchlorates, perbromates, and periodates
Underlying net Perchlorates/perbromates/periodates Correspondence XO 4 coordination

type

K 42 ,K 06 pcu-b (NaCl) MClO 4 (M ¼ Na, K, Rb, Cs, Tl, Ag) Normal

K 6 nia (NiAs) LiClO 4 Normal

K 8 ,K 62 ,K 44

CsBrO 4 ; MIO 4 (M ¼ Na, K,
Rb, Cs, Tl, Ag)

lsz Normal

K 43

MClO 4 (M ¼ Na, K, Rb, Cs);
MBrO 4 (M ¼ K, Tl)

FeB Normal

K 5 nia-5,5- P 2 1 / c LiIO 4

T 3 gfy (UCl 3 ) M(ClO 4 ) 3 (M La, Ce, Pr, Nd, Sm,

Eu, Ho, Er, Tm, Yb)

¼ Normal

T 11 ReO 3 M(ClO 4 ) 3 (M ¼ Tm, Yb, Lu) Normal

cation arrays (in particular, 8,8-coordinated scheelite-like lsz; Fig. 16c )thanthe
corresponding perchlorates. The data of Table 12 agree with the results of Vegas
and Jansen [ 7 ] as well as with other known relations between perhalogenates and
other classes of oxoacid salts with tetrahedral anions (scheelite-like structures [ 78 ] as
well as NiAs-like orthophosphates and sulfates [ 79 ], cf. Tables 9 , 10 ,and 11 ) .
g ¼

1:3. This group is represented only by lanthanide perchlorates that exist in
two crystalline forms: at ambient conditions the cation array is of the UCl 3 (gfy)
type [ 80 ] (Fig. 9 ) for all lanthanides except Lu, and the topologically less dense
ReO 3 -like Tm(ClO 4 ) 3 and Yb(ClO 4 ) 3 were obtained at a high temperature [ 80 , 81 ] .
In both cases, the perchlorate anion is tridentate but connects to a different number
of metal atoms (3 and 2 for T 3 and T 11 coordination types, respectively) that results
in the difference in topological density.

3.4 Uniformity of Cation Arrays in Inorganic Oxoacid Salts

The term “eutaxy” as applied to cation arrays means rather ordered, regular
arrangement of the cations in the crystal space. In [ 2 , 4 ], the eutactic placement
was treated similarly to a close sphere packing with 12 cations in the vicinity of the
given one. However, in the model of cation array the cations should be considered
as point charges rather than the rigid bodies touching each other. In this case, the
close-packing arrangement could not be a criterion of the “best” placement. In fact,
in the most eutactic arrangement the cations should be allocated farthest from each
other, i.e., the cation sublattice covers the crystal space most uniformly. The
uniformity can be estimated with the formula [ 82 ]:

Ð

Z P

Z

1

R 2 d V VP ðiÞ

1
3

i¼ 1

VP ðiÞ

Ghi¼ ;

5
3

Z P

Z

1

V VP ðiÞ

i¼ 1