Riesz transform

The thermodynamically stable structures of metallic elements adopted at standard temperature and pressure (STP) are color-coded and shown below. The only exception is mercury, Hg, which is a liquid and the structure refers to the low temperature form. The melting points of the metals (in K) are shown above the element symbol. Most of the metallic elements crystallize in variations of the cubic crystal system, with the exceptions noted. "Non-metallic" elements, like the noble gases, are not crystalline solids at STP, while others, like carbon, may have several meta stable allotropes at STP which of course can also occur for typical metals like e.g. tin.

Unusual structures

Element	crystal system	coordination number	notes
Mn	cubic	distorted bcc – unit cell contains Mn atoms in 4 different environments
Zn	hexagonal	distorted from ideal hcp. 6 nearest neighbors in same plane- 6 in adjacent planes 14% farther away
Ga	orthorhombic	each Ga atom has one nearest neighbour at 244 pm, 2 at 270 pm, 2 at 273 pm, 2 at 279 pm.	The structure is related to Iodine.
Cd	hexagonal	distorted from ideal hcp. 6 nearest neighbours in the same plane- 6 in adjacent planes 15% farther away
In	tetragonal	slightly distorted fcc structure
Sn	tetragonal	4 neighbours at 302 pm; 2 at 318 pm; 4 at 377 pm; 8 at 441 pm	white tin form (thermodynamical stable above 286.4 K)
Sb	rhombohedral	puckered sheet; each Sb atom has 3 neighbours in the same sheet at 290.8pm; 3 in adjacent sheet at 335.5 pm.	grey metallic form.
Hg	rhombohedral	6 nearest neighbours at 234 K and 1 atm (it is liquid at room temperature and thus has no crystal structure at ambient conditions!)	this structure can be considered to be a distorted hcp lattice with the nearest neighbours in the same plane being approx 16% farther away
Bi	rhombohedral	puckered sheet; each Bi atom has 3 neighbours in the same sheet at 307.2 pm; 3 in adjacent sheet at 352.9 pm.	Bi, Sb and grey As have the same space group in their crystal
Po	cubic	6 nearest neighbours	simple cubic lattice. The atoms in the unit cell are at the corner of a cube.
Sm	trigonal	12 nearest neighbours	complex hcp with 9 layer repeat, ABCBCACAB....
Pa	tetragonal	body centred tetragonal unit cell, which can be considered to be a distorted bcc
U	orthorhombic	strongly distorted hcp structure. Each atom has four near neighbours, 2 at 275.4 pm, 2 at 285.4 pm. The next four at distances 326.3 pm and four more at 334.2 pm.
Np	orthorhombic	highly distorted bcc structure. Lattice parameters: a=666.3 pm, b=472.3 pm, c=488.7 pm
Pu	monoclinic	slightly distorted hexagonal structure. 16 atoms per unit cell. Lattice parameters: a= 618.3 pm, b=482.2 pm, c=1096.3 pm, β= 101.79 °

Usual crystal structures

Close packed metal structures

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 each layer is positioned relative to others. Whilst there are many ways can be envisaged for a regular build up 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' ).
• α-Sm packing has a period of 9 layers A,B,A,B,C,B,C,A,C,.... (R3m, Pearson Symbol hR3, strukturbericht C19).

Hexagonal close packed

In the ideal hcp structure the unit cell axial ratio is $2\sqrt{\frac{2}{3}}$ ~ 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.

Face centered cubic (cubic close packed)

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

Double hexagonal close packed

Similar as the ideal hcp structure, the perfect dhcp structure should hava a lattice parameter ratio of $\frac{c}{a}=$ $4\sqrt{\frac{2}{3}}$ ~ 3.267. In real dhcp structures of the 5 lanthanides (including β-Ce) $\frac{c}{2a}$ variates between 1.596 (Pm) and 1.6128 (Nd). For the 4 known actinides dhcp lattices the corresponding number variate between 1.620 (Bk) and 1.625 (Cf).

Body centred cubic

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 included. Note that if the body centered cubic unit cell is compressed along one 4 fold axis the structure becomes face centred cubic (cubic close packed).

Trends in melting point

Melting points are chosen as a simple, albeit crude, measure of the stability or strength of the metallic lattice. Some simple trends can be noted. Firstly the transition metals have generally higher melting points than the others. In the alkali metals (group 1) and alkaline earth metals (group 2) the melting point decreases as atomic number increases, but in transition metal groups with incomplete d-orbital subshells, the heavier elements have higher melting points. For a given period, the melting points reach a maximum at around group 6 and then fall with increasing atomic number.

See also

• Crystal structure

In general the s-block elements have a lower melting point than d-block elements. The s-block elements have only metallic bonding. The bonding between d-block elements has degrees of both covalent and metallic character, so the strength of interactions is greater for these metals, hence the higher melting points.

References

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General

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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

External links

• Strukturbericht Type A – structure reports for the pure elements
• Crystal Structures for the solid chemical elements at 1 bar