Hexagonal crystal family

The hexagonal crystal family is a major group in crystallography.

It is one of the six main crystal families. This family is unique because it includes two different crystal systems: the trigonal system and the hexagonal system. It also encompasses two distinct lattice systems, known as the hexagonal and rhombohedral lattices. Understanding this family is essential for studying how atoms arrange themselves in solids. These arrangements determine the physical properties of minerals and man-made materials.

To understand the mechanism of these crystals, we must look at the lattice systems. The hexagonal lattice is often described using a right rhombic prism unit cell. This unit cell has two equal axes, labeled 'a', and a height, labeled 'c'. The angle between the base axes is 120 degrees. The rhombohedral lattice is different. It can be described as a rhombohedron, where all sides are equal but the angles are not 90 degrees.

While the rhombohedral description shows certain symmetries, scientists often prefer the hexagonal description. This is because the hexagonal coordinate system uses 90-degree angles, which makes calculations easier.

There are specific rules that separate the two crystal systems within this family. The trigonal crystal system is defined by having a single three-fold axis of rotation. This means the structure repeats itself every 120 degrees of rotation.

The hexagonal crystal system is defined by a six-fold axis of rotation. This means the structure repeats every 60 degrees. Interestingly, the trigonal system is the only one that can belong to more than one lattice system. Some trigonal crystals, like alpha-quartz, possess trigonal symmetry but actually belong to a hexagonal lattice.

History and classification involve complex mathematical groups. The hexagonal crystal family includes 12 different point groups. These are combined into 52 distinct space groups.

These space groups are divided between the two lattices. The trigonal system contains 5 point groups. These groups result in 7 space groups assigned to the rhombohedral lattice and 18 assigned to the hexagonal lattice. The hexagonal system contains 7 point groups. All 27 of its space groups are assigned to the hexagonal lattice. This complex organization allows scientists to categorize almost any crystalline substance.

Specific minerals provide clear examples of these mathematical patterns. In the trigonal system, you can find dolomite, ilmenite, and hematite.

Calcite and corundum are also members of this group. The hexagonal system features very different minerals. Beryl, graphite, and even ice follow this hexagonal pattern.

These minerals show how the same underlying symmetry can produce very different looking substances. The way atoms pack together determines if a mineral is soft like graphite or hard like corundum.

Some materials use even more complex arrangements called multi-element structures. One example is the wurtzite structure, which has the Pearson symbol hP4.

In this structure, two different types of atoms interpenetrate. Each atom type forms its own hexagonal close-packed sublattice. This structure is common in semiconductors like gallium nitride (GaN) and zinc oxide (ZnO). Another example is the nickel arsenide structure. In this arrangement, nickel atoms are octahedrally coordinated to six arsenic atoms.

This shows how different elements can combine to form unique, stable patterns.

These tiny structures have massive impacts on modern technology. Because some wurtzite crystals lack inversion symmetry, they are non-centrosymmetric. This allows them to possess properties like piezoelectricity. Piezoelectricity is the ability to generate an electric charge when the material is mechanically stressed.

This property is vital for creating high electron mobility transistors (HEMT). These electronic devices are essential for modern communication tools. Thus, the hexagonal crystal family is not just a way to group rocks; it is a blueprint for the digital age.