Introduction to crystallography

Crystallography:

The subject of crystallography is included in mineralogy, which discusses crystals and laws that govern their growth, external shape, and interior structure. Very few minerals are crystalline, but most of the minerals are found in crystalline form. When minerals crystallize under favorable conditions, they take the form of crystals. Thus the crystal form of a mineral reflects its orderly internal arrangement of atoms.

Crystals:

A solid which possesses a regular geometrical shape is called a ”crystal”. A crystal is bounded by faces, which lie parallel to the planes of atoms in the crystal structure. In addition to faces, crystals contain edges and solid angles arranged in regular order. “Edges” are formed where two adjacent faces meet and a ”solid angle” is formed where three or more edges meet.

Zones:

In many crystal groups, the faces are arranged in such a manner that their intersection edges are parallel to each other. Such faces constitute a ”zone”. A line, which passes through the center of the crystal and lie parallel to the line of the face intersections is called the ”zone axis”. In the below figure, the faces m’, a, m, and b are in one zone, and b, r, c, and r’ in another. The lines [001] and [010] are the zone axis.

Interfacial Angle:

In a crystal, the angle between adjacent faces is called ”interfacial angle”. Because crystal faces have a direct relationship to the internal structure, it follows that the faces have a definite relationship to each other. This relationship is expressed ”law of constancy of interfacial angles”, which states that ”the interfacial angles between corresponding faces are constant for all crystals of a given mineral”.

Interfacial angles are measured either with a contact goniometer or a reflecting goniometer. A contact goniometer is a simple device, which consists of a pivoted metal arm, called a pointer. This slides over a semicircular scale and measures the interfacial angle between two adjacent faces of a crystal as shown in the following figure.

Crystallographic Axes:

In order to describe the faces and symmetry of crystals, a set of three or four reference axes are established. These imaginary reference axes are established. These imaginary reference lines are called ”crystallographic axes” and are generally taken parallel to the intersection edges of major crystal faces. In fact, crystallographic axes are the reference lines which rin parallel to the edges of the unit cell and their lengths are proportional to the lengths of the unit cell edges. Thus when we say that the three edges of the cubic unit cell are equal and mutually perpendicular. The lengths of the unit cell edges measured in the direction of crystallographic axes, are called ”unit lenghts” and are generally expressed as a, b, and c.