A thorough discussion of crystallography is beyond the scope of this paper. However, to have a good understanding of the structure and properties of graphite a basic understanding of the graphite crystal is helpful. With this in mind, a basic introduction to the crystal systems and in particular the hexagonal system is presented below.
In general, most solid substances are crystals. A crystal is an outward topographic expression of the atomic or molecular structure and forces that hold a solid together. Due to the relative strength and direction of atomic and molecular bonds, as well as the size of atoms and ions that make up solids, one crystal is more likely to form than another. Webster's dictionary defines a crystal as, "a solidified form of a substance in which the atoms or molecules are arranged in a definite repeating pattern so that the external shape of a particle or mass of the substance is made up of plane faces in a symmetrical arrangement." This definition is as good as any.
Mineralogists and crystallographers have developed a series of six crystal systems into which are placed all of the crystalline substances known. Each system is defined by a group of crystallographic axis. It is the angular relationship and length of these axes relative to one another that defines the particular system. The six systems are, in order of decreasing symmetry: isometric (cubic), tetragonal, hexagonal, orthorhombic, monoclinic, and triclinic. It is the arrangement of atoms or molecules in a given substance that defines the crystal faces of that substance. It is the relation of these faces to the crystallographic axes that defines to which crystal system a substance belongs.
Graphite crystallizes in the hexagonal system. Four crystallographic axes define the hexagonal system. The four axes are designated as: "a1", "a2", "a3", and "c." The three "a" axis are all given the "a" prefix because they are all the same relative length. The "a" axes are co-planar and radiate from the same origin. The angle between adjacent "a" axes is 120°. All of the "a" axes have "negative" ends that are equal in length to the positive ends. The angle of intersection between any positive end and the nearest negative end is 60°. The "c" axis emanates from the same origin as the "a" axes, and is perpendicular to the plane of the "a" axes. The "c" axis is usually taken as being longer than the "a" axes. The hexagonal crystal structure is an anisotropic structure. If one looks at the 4 axes it is easy to see that the appearance of these axes will not change if the whole structure is rotated 120° positive or negative about the "c" axis. However, if the "c" axis is rotated 90° forward or backward with respect to the plane of the page the orientation of the entire figure changes. The structure has inherent anisotropy.
In contrast, if one performed the same axial rotation exercise on the isometric axes the difference would be apparent. Any rotation in 90° increments about any of the isometric axes gives back the same view. The isometric system is isotropic. The building block of a crystal is known as a unit cell. The unit cell is the smallest unit into which a given crystal can be divided. The unit cell of the hexagonal system is simply the "hexagonal unit cell." Note that the hexagonal unit cell is not a hexagonal prism, but is a rhombic prism. The structure of the HUC, including its dimensional constants will be described in the section Structure and Bonding.