Chemical bonding in crystals


Substances with metallic bonding prefer close-packed lattices implying high coordination number:

12fccA1Al, Ca, γ-Fe, Ni, γ-Mn, Cu
12hcpA3Mg, Sc, Ti, Co
8+6bccA2alkali metals, most metals before melting, V, Cr, α-Fe, δ-Fe, δ-Mn, W

Ionic crystals

Substances with ionic bonding prefer lattices with high Madelung constant, which are closely copacked lattices of anions and cations:

1.763bcc = sc + scB2cesium chlorideI+VIICsCl
1.748sc = fcc + fcc = fcc + octahedral voidsB1rock saltI+VII, II+VINaCl
1.680fcc + tetrahedral voidsC1(anti)fluoriteII+VII, I+VICaF2, Li2O
1.641*hdia = hcp + hcp = hcp + ½ tetrahedral voidsB4wurtziteII+VI, III+VZnS
1.638dia = fcc + fcc = fcc + ½ tetrahedral voidsB3sphaleriteII+VI, III+VZnS

* in ideal coordination

Covalent crystals

Due to local nature of bonds covalent crystals produce variety of structures even for fixed coordination:

tetrahedraldiamondA4IV (C, Si, Ge, α-Sn)the only pure covalent bonding
tetrahedral + tetrahedralzincblendeB3III (Al,Ga,In) + V(P,As,Sb), BPdonor-acceptor bonding
tetrahedral + tetrahedralwurtziteB4late III + N (GaN, InN)covalent-ionic bonding
tetrahedral + dihedral  IV+II (SiO2) 

The minimal coordination to build the 3D lattice is tetrahedral, therefore for lower coordination numbers we have heterodesmic or low-dimensional crystals. More covalent structures see here.

Molecular crystals

Molecular crystals have chemical bonding inside the molecules and physical bonding between the molecules thus forming close-packed molecular structures:

fcccrystals of inert gases, α-N2, β-O2, halogens (I2, Br2, Cl2)
hcpH2, β-N2, α-O2