Hexagonal crystal system

An example of the hexagonal crystals, beryl

Hexagonal

In crystallography, the hexagonal system is one of the 7 crystal systems. It contains 7 point groups. It has the same symmetry as a right prism with a hexagonal base. There is only one hexagonal Bravais lattice, which has six atoms per unit cell.

In some cases, it is useful or instructive to redraw a hexagonal structure with orthohexagonal axes, wherein the hexagonal a and c axes are retained and the b axis redrawn at 90 degrees to them.

Graphite is an example of a crystal that crystallizes in the hexagonal crystal system.

The point groups (crystal classes) that fall under this crystal system are listed below, followed by their representations in Hermann-Mauguin or international notation and Schoenflies notation, and mineral examples, if they exist.

name	international	Schoenflies	example
dihexagonal bipyramidal		D6h	beryl
dihexagonal pyramidal		C6v	greenockite
hexagonal bipyramidal		C6h	apatite
hexagonal pyramidal		C6	nepheline
hexagonal trapezohedral		D6	kalsilite and high quartz
ditrigonal bipyramidal		D3h	benitoite
trigonal bipyramidal		C3h	none

Hexagonal Phases In the Realm of Lipid Polymorphism

In lipid polymorphism, if the packing ratio of lipids is greater or less than one, lipid membranes can form two separate hexagonal phases, or nonlamellar phases, in which long, tubular aggregates form according to the environment the lipid is introduced.

Hexagonal I Phase (H_I)

This phase is favored in detergent-in-water solutions and has a packing ratio of less than one. The micellar population in a detergent/water mixture cannot increase without limit as the detergent to water ratio increases. Therefore, in the presence of low amounts of water, lipids that would normally form micelles actually form a larger aggregate in the form of micellar tubules in order to satisfy requirements of the hydrophobic effect. These aggregates can be thought of micelles that are fused together. These tubes have polar head groups facing out, and the hydrophobic, hydrocarbon chains facing the interior. This phase is only seen under unique, specialized conditions, and most likely is not relevant for biological membranes.

Hexagonal II Phase (H_II)

Lipid molecules in the HII phase pack inversely to the packing observed in the hexagonal I phase described above. This phase has the polar head groups on the inside and the hydrophobic, hydrocarbon tails on the outside in solution. The packing ratio for this phase is less than one, which is synonymous with an inverse cone packing.

Extended arrays of long tubes, as in the hexagonal I phase, and due to the nature of the polar head groups packing, aqueous channels are formed. These arrays can stack together like pipes. This way of packing may leave a finite hydrophobic surface in contact with water on the outside of the array. However, the otherwise energetically favorable packing apparently stabilizes this phase as a whole. It is also possible that an outer monolayer of lipid coats the surface of the collection of tubes to protect the hydrophobic surface from interaction with the aqueous phase.

It is suggested that this phase is formed by lipids in solution in order to compensate for the hydrophobic effect. This structures tight packing of the lipid head groups reduces their contact with the aqueous phase. This, in turn, reduces the amount of ordered, but unbound water molecules. The most common lipids that form this phase include phospatidylethanolamine (PE), which has unsaturated hydrocarbon chains. Diphosphatidylglycerol (DPG) in the presence of calcium is also capable of forming this phase.

Techniques Used To Detect Phases

There are several techniques used to map out which phase is present during perturbations done on the lipid. These perturbations include pH changes, temperature changes, pressure changes, volume changes, etc.

The most common technique used to study phospholipid phase presence is phosphorous nuclear magnetic resonance (31P NMR). In this technique, different and unique powder diffraction patterns are observed for lamellar, hexagonal, and isotropic phases. Other techniques that are used and do offer definitive evidence of existence of lamellar and hexagonal phases include freeze-fracture electron microscopy, X-Ray diffraction, differential scanning calorimetry (DSC), and deuterium nuclear magnetic resonance (2H NMR).

See also

• Crystal structure
• Close-packing (hcp)
• Wurtzite (crystal structure)

References

• Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 78 - 89, ISBN 0-471-80580-7
• Yeagle, P. (2005). The structure of biological membranes (2nd ed.). United States: CRC Press.
• Yeagle, P. (1993). The membranes of cells (2nd ed.). Michigan: Academic Press.
• Gennis, R. B. (1989). Biomembranes: Molecular structure and function. Michigan: Springer-Verlag.