Closely copacked compounds

Lattice is closely copacked, if its Madelung constant is greater than that of randomly packed spheres of opposite charges. The calculation of Madelung constant is rather cumbersome and the concept of closely copacked lattice has no such clear geometrical interpretation as close-packing. Nevertheless the analysis of the first coordination shells is very informative: if the minimal cation-anion separation is fixed, a closely copacked lattice has more counter-ions in the first coordination shell, larger distance to the nearest co-ion and less co-ions in this second coordination shell etc.

For equal size ions, closely copacked lattices are bipartitions of elementary lattices:

bcc8cbscB2 CsCl1.763
sc (compressed fcc)6ofccB1 rock salt1.748
compressed A3' (ABAC)6o/6psh+hcp B81 NiAs1.733
compressed hcp6pshBh WC1.723
hdia4thcpB4 wurtzite1.641
dia4tfccB3 zincblende1.638

* If the geometry is not fixed by the symmetry then either maximum M or M for the specified compound is given.

In the opposite case of largely unequal size ions, closely copacked lattices can be represented as close-packed lattice of larger ions with the smaller ones occupying some voids in that lattice:

 1/3o C2h  Cl3Y1.41
 3/4t  Th cI80O3In21.67
 1/4t OhlpC3Cu2O1.481
 1/8t Th  SnI4 
 1o+1tlpOhbcc BiLi3 
 1/8t+1/2o Oh H11O4MgAl2 
 2/3o D3d D51O3Al21.669
 1/2o D3d C6I2Cd1.46
 1/2o D4h C4O2Ti1.605
 1/3o C3i D05I3Bi 

See also Pauling's rules