Substances with metallic bonding prefer close-packed lattices implying high coordination number:
12 | fcc | A1 | Al, Ca, γ-Fe, Ni, γ-Mn, Cu |
12 | hcp | A3 | Mg, Sc, Ti, Co |
8+6 | bcc | A2 | alkali metals, most metals before melting, V, Cr, α-Fe, δ-Fe, δ-Mn, W |
Substances with ionic bonding prefer lattices with high Madelung constant, which are closely copacked lattices of anions and cations:
1.763 | bcc = sc + sc | B2 | cesium chloride | I+VII | CsCl |
1.748 | sc = fcc + fcc = fcc + octahedral voids | B1 | rock salt | I+VII, II+VI | NaCl |
1.680 | fcc + tetrahedral voids | C1 | (anti)fluorite | II+VII, I+VI | CaF2, Li2O |
1.641* | hdia = hcp + hcp = hcp + ½ tetrahedral voids | B4 | wurtzite | II+VI, III+V | ZnS |
1.638 | dia = fcc + fcc = fcc + ½ tetrahedral voids | B3 | sphalerite | II+VI, III+V | ZnS |
* in ideal coordination
Due to local nature of bonds covalent crystals produce variety of structures even for fixed coordination:
tetrahedral | diamond | A4 | IV (C, Si, Ge, α-Sn) | the only pure covalent bonding |
tetrahedral + tetrahedral | zincblende | B3 | III (Al,Ga,In) + V(P,As,Sb), BP | donor-acceptor bonding |
tetrahedral + tetrahedral | wurtzite | B4 | late 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 have chemical bonding inside the molecules and physical bonding between the molecules thus forming close-packed molecular structures:
fcc | crystals of inert gases, α-N2, β-O2, halogens (I2, Br2, Cl2) |
hcp | H2, β-N2, α-O2 |