13 | Elemental Structure Types#
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While there is an enormous number of different crystal structures that have been observed, a surprisingly large number unique chemical compositions adopt one of a few common structure types or can be described in relation to other common structural motifs. A structure type describes a unique atomic arrangement of atoms in relation to one another without regard for the specific elements that occupy a particular position. For example, \(\alpha\)-iron, and \(\alpha\)-manganese both have the exact same structure type (body-centered cubic). They differ in chemical composition, unit cell parameters, but both have atoms in the unit cell arranged such that there is an atom at the origin and at the center of the cell. If the symmetry and relative positions within the unit cell are exactly then the two structures are also said to be isostructural or iso-structures of one another.
Fig. 22 Crystal structure of \(\alpha\)-Fe (Fe) which adopts a body centered cubic (bcc) structure type.#
Elemental structure types are arrangments of atoms that include one and only one unique element. The most common elemental structure types are: cubic close packed (ccp), hexagonal close packed (hcp), and body centered cubic (bcc).
Close packing (hcp and ccp)#
The most common elemental structure types are the close packed structures. A close packed structure has an arrangement of atoms that is equivalent to the densest possible packing of hard spheres in 3D space. Curiously there are two possible ways to close pack spheres: hexagonal close packed (hcp) and cubic close packed (ccp). In both cases the 3D arrangements are derived by the stacking of 2D layers of close packed spheres.
In 2D, the densest possible packing of circles of equal radius is to arrange six circles around a central circle, resulting and a 2D hexagonal lattice. The coordination number of every atom in the 2D plan is six.
Fig. 23 Densest packing of circles in 2D is hexagonal close packed, CN = 6.#
To generate a 3D close packed structure, simply stack layers of the 2D close packed arrangement such that the atoms in the second layer nestle into the gaps of the first layer. If you do so then each atom will not have 3 additional nearest neighbors with the exact same interatomic distance as is present within a 2D plane. In a crystal formed of an infinite number of layers every atom will there for have 12 nearest neighbors: 6 in the 2D plane, 3 from the layer above, and 3 from the layer below. The coordination number of every atom in a 3D close packed structure is therefore 12. This arrangement of hard spheres will occupy 74% of the available volume in the crystal structure. This is the highest possible packing efficiency in 3D space.
However, upon attempting this exercise of stacking layer you’ll find that the second layer can only nestle atoms into 1/2 of the gaps present in the first layer. When only stacking 2 layers the choice is arbitrary but when adding the third layer, we could either nestle atoms such that that are eclipsed with the first layer (ABA… stacking) or we could pick choose the other set of gaps this does not overlap with the atoms in the first layer (ABCA… stacking). While the density of these two arrangements is identical, and teh coordination number is 12 or all atoms in both, clearly the symmetry and structures are different. The alternating ABA… stacking motif results in a crystal with a hexagonal lattice and the hexagonal close packed (hcp) structure type. The cyclic ABCA…stacking motif results in a crystal with a cubic lattice and the cubic close packed (ccp) structure type.
Zinc is a canonical element that adopts the hcp structure type. Other elements include Be, Mg, Ti, Zr, Hf, Ru, Os and Cd. The lanthanides with the exception of Sm and Eu adopt the hcp structure type or a slight distorted double hcp structure that is extremely similar but the c-axis of the unit cell is twice as long and the number of atoms in the unit cell is likewise doubled.
Aluminum and Nickel are canonical examples of elements that adopt the cpp structure type, Fig. 25. Other elements include Cu, Rh, Pd, Ag, Ir, Pt, Au, and the nobel gases (excluding He).
Fig. 24 Densest packing of circles in 3D. (left) The hexagonal close packed (hcp) ABA… stacking and (right) cubic close packed (ccp) ABCA… stacking structures are both derived from stacking 2D close packed layers. Unit cells are superimposed. For a cubic cell to describe 2D hexagonal layers we much orient the unit cell such that it is viewed along the diagonal or [1 1 1] direction.#
Fig. 25 The crystal structures of Zinc which adopts a hexagonal close packed (hcp) structure type (left) and Nickel which adopts a cubic close packed (ccp) structure type (right).#
Body centered cubic (bcc)#
Body centered cubic (bcc), Fig. 22, is the second most common elemental structure type. At the name implies, bcc structures adopt a cubic lattice with one atomic at the origin (corner) of the unit cell and another in the center of the cell. This arrangement of atoms is not densest possible packing of spheres owing to peculiarities in their chemical bonding. Harder spheres packed in this arrangement would have occupy only 68% of the available volume within the cubic unit cell. Elements that adopt the bcc structure type include the alkali metals (Li, Na, K, Rb, Cs, Fr), the alkalines Ba and Ra, the transition metals V, Nb, Ta, Cr, Mo, W, Mn, and Fe, as well as the lanthanide Eu.
Primitive cubic (pc)#
Primitive cubic (pc) is perhaps the simplest of the elemental structure types described by a cubit lattice with only one atom in the unit cell, at the origin (Fig. 26). The structure can also be imagined by a stacking of 2D layers of atoms in a square arrangement directly on top of eachother. This structure type occupied by hard spheres only has a packing efficiency of about 52%. The coordination number of 6 for each atom in the structure is also lower than for bcc (CN=8) or close packed structures (CN=12). The only element known to adopt this structure type is \(\alpha\)-polonium. However while the structure type is quite rare the primitive cubic structural motif is quite useful in the description of other more complex structure types and therefore worth committing to memory.
Fig. 26 The crystal structures of Zinc which adopts a hexagonal close packed (hcp) structure type (left) and Nickel which adopts a cubic close packed (ccp) structure type (right).#
Other elemental structures#
There are indeed quite a few other elemental structure types and many elements are know to adopt multiple different structures called allotropes. If a given chemical composition can adopt multiple structure types then those structures are referred to as polymorphs of one another. If the structures’ chemical composition also contains one and only one element then they are also referred to as allotropes. Carbon for example has has several crystalline allotropes including graphite, diamond, fullerene, and lonsdalite. Notably much of the p-block elements adopt structures that are not the simple packings described above. The covalence of chemical bonds formed by these elements results often prevents a reductive description of their structures as a result of a hard sphere packing model. Indeed even the primitive cubic structure of Po is a result is attributable to covalent bonding of the mutually orthogonal \(p_x\), \(p_y\), and \(p_z\) orbitals. We will return to the structures of covalent solids.