Mineralogy

It has already been mentioned that crystals are built up of an orderly arrangement of the atoms or atomic groups of the mineral. Examination of crystals by X-rays has led to the determination of the relative positions of the different atoms in the structure. If the atoms are represented by points, their arrangement in the crystal can be shown by a geometrical pattern or framework which is called the space-lattice or point-system. In this, the atoms are arranged in innumerable parallel rows which intersect in a regular pattern. The rows lie in planes to form what may be called a net-plane. Crystal faces are parallel to these net-planes, and crystal edges to the rows of atoms occurring at the intersections of net-planes.

We have seen that the atomic structure for the crystals of anyone mineral is fixed, so that it follows that the positions of the faces of such crystals are fixed also. This leads to the enunciation of the important law of the Constancy of Interfacial Angles. The corresponding interfacial angles are constant for all crystals of a given mineral, provided, of course, that the crystals have identical chemical compositions and that the measurements are made at the same temperatures.

Zones

Inspection of many crystals shows that their faces are so arranged that the edges formed by the intersections of certain of the faces are parallel with one another. Such a set of faces constitutes a zone, and the line with which the edges are parallel is called the zone-axis. For instance, the common crystals of quartz or rock crystal such as are illustrated in Fig. 121, show six faces meeting in parallel edges, and terminated by a set of six usually triangular faces which do not meet in parallel edges; the first set of six faces forms a zone.

Symmetry

Examination of a crystal either with the eye or a gonimeter shows that there is a certain regularity of position of like faces, edges, etc. This regularity constitutes the symmetry of the crystal. The degree of symmetry varies in different minerals and is employed, as seen later, in the classification of crystals. It is defined with reference to three criteria of symmetry:

• Plane of Symmetry
• Axis of Symmetry
• Centre of Symmetry

Plane of Symmetry

A plane of symmetry divides a crystal into two similar and similarly placed halves. In other- words, such a plane divides the crystal so that one half is the mirror-image of the other. Planes of symmetry can be illustrated by considering a cube. A cube has nine planes which divide it into two halves so that one half is the reflection of the other. The traces of these nine planes are indicated on the faces of the cube in Fig. 9 and the dissected planes are shown in Fig. 10.

The geometrical symmetry of a matchbox or a brick is obviously lower than that of a cube for, as inspection shows, there are only three planes that divide the object into similar and similarly placed halves.

Axis of Symmetry

If a crystal, on being rotated, comes to occupy the same position in space more than once in a complete turn, the axis about which rotation has taken place is called an axis of symmetry. Depending upon the degree of symmetry, a crystal may come to occupy the same position two, three, four or six times in a complete rotation. The terms applied to these different classes of axes are as follow:-

Two times: two-fold, diad, half-turn or digonal axis.

Three times: three-fold, triad, one-third-turn or trigonal axis.

Four times: four-fold, tetrad, quarter-turn or tetragonal axis.

Six times: six-fold, hexad, one-sixth-turn or hexagonal axis.

We can again use the cube and our brick to illustrate axes of symmetry. In the cube, as shown in Fig. ii, there are axes of four-fold, three-fold and two-fold symmetry. Rotation of the cube about the axis of four-fold symmetry shown in the figure causes the cube to take up the same position in space four times during a complete rotation, about the three-fold axis three times, and about the two-fold axis twice. It ‘is clear, moreover, that there are three axes of four-fold symmetry, four of three-fold symmetry and ,six of two-fold symmetry in the cube. This is expressed in the following way:

Axes of Symmetry of the cube - 3^iv, 4ⁱⁱⁱ, 6ⁱⁱ.

In our brick there are only three axes of symmetry and these are of two-fold type; they connect the middle points of the pairs of opposite faces of the brick.

Centre of Symmetry

A crystal has a centre of symmetry when like faces, edges, etc., are arranged in pairs in corresponding positions and on opposite sides of a central point. The cube and our brick obviously have centers of symmetry.

The Symmetry of Gypsum as an Illustration

A crystal of gypsum may be taken to illustrate these definitions of symmetry. The usual form of such a crystal is shown in Fig. 12.

There is one plane which divides the crystal into two similar and similarly placed halves. This plane is the only plane of symmetry for this crystal. At right angles to this plane is an axis of symmetry. Rotation about this axis causes the crystal to take up the same position twice in a complete rotation, and this axis is therefore an axis of two-fold symmetry. Lastly, for every face, edge or corner that occurs in one half of the crystal there is a similar face, edge or corner in a corresponding position in the other half. Therefore the crystal has a centre of symmetry.

Thus the symmetry of this gypsum crystal may be expressed in the following way:

• Planes of symmetry
• Axes of symmetry
• Centre of symmetry