Periodic table (crystal structure)

Many metals adopt close packed structures i.e. hexagonal close packed and face-centred cubic structures (cubic close packed). A simple model for both of these is to assume that the metal atoms are spherical and are packed together in the most efficient way (close packing or closest packing). In closest packing every atom has 12 equidistant nearest neighbours, and therefore a coordination number of 12. If the close packed structures are considered as being built of layers of spheres then the difference between hexagonal close packing and face-centred cubic is how each layer is positioned relative to others. Whilst there are many ways that can be envisaged for a regular buildup of layers:

• hexagonal close packing has alternate layers positioned directly above/below each other: A,B,A,B,... (also termed P6₃/mmc, Pearson symbol hP2, strukturbericht A3) .
• face-centered cubic has every third layer directly above/below each other: A,B,C,A,B,C,... (also termed cubic close packing, Fm3m, Pearson symbol cF4, strukturbericht A1) .
• double hexagonal close packing has layers directly above/below each other, A,B,A,C,A,B,A,C,.... of period length 4 like an alternative mixture of fcc and hcp packing (also termed P6₃/mmc, Pearson Symbol hP4, strukturbericht A3' ).[9]
• α-Sm packing has a period of 9 layers A,B,A,B,C,B,C,A,C,.... (R3m, Pearson Symbol hR3, strukturbericht C19).[10]

In the ideal hcp structure the unit cell axial ratio is ${\textstyle 2{\sqrt {\frac {2}{3}}}\approx 1.633}$. However, there are deviations from this in some metals where the unit cell is distorted in one direction but the structure still retains the hcp space group—remarkable all the elements have a ratio of lattice parameters c/a < 1.633 (best are Mg and Co and worst Be with c/a ~ 1.568). In others like Zn and Cd the deviations from the ideal change the symmetry of the structure and these have a lattice parameter ratio c/a > 1.85.

More content relating to number of planes within structure and implications for glide/slide e.g. ductility.

Similar to the ideal hcp structure, the perfect dhcp structure should have a lattice parameter ratio of ${\textstyle {\frac {c}{a}}=4{\sqrt {\frac {2}{3}}}\approx 3.267.}$ In the real dhcp structures of 5 lanthanides (including β-Ce) ${\textstyle c/2a}$ variates between 1.596 (Pm) and 1.6128 (Nd). For the four known actinides dhcp lattices the corresponding number vary between 1.620 (Bk) and 1.625 (Cf).[11]

This is not a close packed structure. In this each metal atom is at the centre of a cube with 8 nearest neighbors, however the 6 atoms at the centres of the adjacent cubes are only approximately 15% further away so the coordination number can therefore be considered to be 14 when these are ong one 4 fold axe structure becomes face-centred cubic (cubic close packed).