Mineralogy

In was noticed by the ancient Greeks that a certain mineral, quartz, usually occurred in forms having a characteristic shape, being bounded by flat faces. From the transparency of this mineral and the occurrence in it of included material, it was thought that quartz resulted from the freezing of water under intense cold, and hence the name krustallos-meaning clear ice-was given to the substance. There were, however, numerous other minerals known to the ancients which occurred in forms bounded by flat faces, and so, by a natural extension of the term, krustallos came to signify any mineral showing such forms.

By the researches of Steno, De l’Isle and Hauy, the study of crystals gradually evolved from mere speculation. It is to Hauy that we are indebted for an illuminating theory of the structure of crystals. Hauy argued that crystals were built up of minute bricks of the mineral, different modes of arrangement of the bricks producing different crystal forms. By more recent investigations Hauy’s notion of the arrangement of material bricks has been replaced by that of the arrangement of atomic groups. It is therefore apparent that chemical constitution has an important influence on crystalline form, and, indeed, Von Federov issued a list of some ten thousand substances, the chemical composition of which he was able to tell with certainty from an examination of their crystals.

The study of crystals is called crystallography. Crystals are bodies bounded’ by surfaces, usually flat, arranged on a definite plan which is an expression of the internal arrangements of the atoms. They are formed by the solidification of minerals from the gaseous or liquid states or from solutions,-a process known as crystallization.

From the definition of a crystal just given we see that the internal atomic structure is their fundamental property. Though we could construct a model of a crystal in glass or some other amorphous material, such a model would not be a crystal since it would lack the essential atomic structure. In this book, however, we are chiefly concerned with the determination of minerals, so that for us the external form of crystals demands most attention. In this chapter our crystallography will be almost entirely morphological. The atomic structure of crystals is considered in the next chapter.

Characteristics of Crystals

Faces

Crystals are bounded by a number of surfaces which are usually perfectly flat, but may be curved as in some specimens of siderite and diamond. These surfaces are called faces. Faces are of two kinds, like and unlike. Some crystals are limited by faces that are all alike. For instance, fluor-spar commonly crystallizes in cubes, and any one face of the fluor-spar cube is like all the other faces in its properties. Such faces that have the same properties are called like faces, whilst faces having different properties are unlike faces.

Forms

A crystal made up entirely of like faces is termed a simple form. For example, the cube and the octahedron are each of them simple forms, since all the faces of each have the same properties. The front face shown in the drawing of a cube in Fig. 5 can be replaced by any other of the cube faces without altering the drawing. A crystal which consists of two or more simple forms is called a combination. In Fig. 5, the cube and the octahedron are shown as simple forms and also as a combination such as occurs in crystals of galena.

Some simple forms occur by themselves in crystals as they can enclose space, but others can only occur in combinations, since they have too few faces to enclose space by themselves. Such latter forms are called open.

Edge

An edge is formed by the intersection of any two adjacent faces. The position in space of an edge depends, of course, upon the positions of the faces whose intersection gives rise to it.

Solid Angle

A solid angle is formed by the intersection of three or more faces.

Interfacial Angle

The angle between any two faces of a crystal ‘is termed the interfacial angle. In crystallography, the interfacial angle is the angle between the normals, or perpendiculars, to the two faces. The interfacial angle between the two faces shown in section is A. Interfacial angles are of great importance in crystallography and are recorded in works of reference in the following way, if the angle between the normals to two faces which we will call m and mIII is 630° 48′ it is recorded as mIII = 630° 48′.

Measurement of Interfacial Angle

The interfacial angles of crystals are measured by the goniometer (or angle measurer). Two types of this instrument are used, one termed the contact-goniometer, the other the reflecting goniometer.

The contact-goniometer consists of two straight-edged arms movable on a pivot or screw, and connected by a 3 graduated are, as shown in Fig. 7. These two arms are brought accurately into contact with adjacent faces of the crystal, and the angle between them read off on the graduated arc. In the illustration, the angle actually measured is the internal angle between the two faces, and this must be subtracted from 1800 to give the interfacial angle of the crystallographer.

Reflecting goniometers are rather elaborate instruments used with crystals possessing perfectly smooth or flawless faces. In general, the smaller the crystal, the more suitable for use with the reflecting goniometer will it be.

A common form of .reflecting goniometer consists of a vertical circle, graduated and capable of rotation, and a horizontal arm fixed at right angles to the plane of the circle. A mirror is fixed on the horizontal arm. The crystal is placed at the centre of the graduated circle with an edge parallel to the horizontal arm. The image of a distant signal is observed by reflection from the mirror, and also by reflection from the crystal face. By rotating the graduated circle and with it the crystal, the two images are made to lie in the same straight line. The circle is then rotated until an image is obtained by reflection from the adjacent face. The amount of rotation gives the angle between the normals to the two crystal faces, that is, the interfacial angle, as shown in Fig. 8. Here light reflected from the face AB of the crystal in the ABCD position is seen by the eye. If the crystal is rotated about the edge between AB and AD so that the face AD takes up the new position dA where dA and AB are in the same straight line, then the signal is again seen. The crystal has been rotated through the angle dAD, which is the supplement of the internal angle between the faces B AB and AD, and is therefore the interfacial angle.