A crystal is a mass of molecules, all of the same composition. A molecule in its turn is made up of atoms, and each atom is a unit mass of an element. Thus the calcite molecule is made up of one unit or atom of calcium, one of carbon, and three of oxygen (CaCO₃). These atoms are held together by an attraction, and make a molecule, and for the study of minerals the molecule is the unit. The mineral, calcite, is a mass of molecules all like the one above, and each molecule so small as to be invisible even with the aid of the most powerful microscope. When calcite is in crystal form, the molecules, like ranks of soldiers, are arranged each in its place, each at a definite distance from the other. While each molecule may vibrate or wiggle within certain limits it does not leave its place. (The comparison with soldiers is a good one for the molecules of one layer, but it must be remembered that in a crystal there are also like spacings and ranks up and down as well.) As long as the molecules remain in fixed ranks, up and down, forward and back, and sideways, the crystal is perfect. Calcite may be heated until it melts and becomes liquid. Then the molecules leave their definite arrangement and move about in all sorts of directions, like the soldiers after ranks have broken. So long as the molecules are thus free to move about but keep together, the substance is a liquid. There are cases when the molecules in this disorder take fixed positions without falling into ranks. Such minerals are non-crystalline and usually appear glassy. If still greater heat is applied to the mineral in liquid form, a point is reached (the vapor point), above which the molecules go flying away from each (like soldiers in a panic), each seeking to get as far from the other as possible, so only a container will prevent their dissipation. When in this condition a mineral is gaseous. When cooled, the reverse order obtains. The molecules of gas gather into a miscellaneous mob or liquid: and if this is further cooled (but not too suddenly), they fall into ranks and make a crystal. This may be illustrated with water. When above 212° F. it is steam (molecules wildly dissipated); when between 212° and 32° it is water (molecules close to each other, but milling like a herd of cattle); and when below 32° it is ice, the molecules ranged in perfect order, rank on rank.
Crystal Systems
With all the possible forms that crystals can and do take, there are six systems of arrangement. First there is the case where ranks, files, and vertical rows are all equal, and now to be scientific, instead of talking about ranks, files, etc., we use the term axes to express these ideas; the files or arrangements from front to back, being called the a axis, the ranks, or side to side arrangement the b axis, and the vertical arrangement the c axis. (See [Plate 1].) These axes are imaginary lines, but they represent real forces.
Isometric system
When the axes are all equal and at right angles to each other, a crystal is said to be in the isometric system. The cube is the basal form and each side is known as a face. The ends of the axes come to the middle of the cube faces. The essential feature of this system is that whatever happens to one axis must happen to all, which is another way of saying that all the axes are equal. If we think of the cube as having the corners cut off, we would have a new face on each of the eight corners, in addition to the six cube faces. Then if each of these new faces were enlarged until they met and obliterated the cube faces, an eight-sided figure, the octahedron, would result. In this the axes would ran to the corners. Another modification of the cube would be to bevel each of its twelve edges, making twelve new faces in addition to the six cube faces. If we think of these new faces being developed until they meet and obliterate the cube faces, there will result a twelve-sided figure, the dodecahedron. And the 24 edges of the dodecahedron could be beveled to make a 24-sided figure, and so on. Of course in Nature the corners are not cut, nor the edges beveled, but as a result of the interaction of the forces expressed by the axes and the distribution of the molecules, the molecules arrange themselves in a cube, octahedron, dodecahedron or combination of these basal forms.
Crystal formation
Crystals are formed in liquids as they cool or evaporate and can no longer hold the minerals in solution. Crystals start about a center or nucleus, and molecule by molecule, the orderly arrangement is increased and the crystal grows, there being no size which is characteristic. If free in the liquid the crystal grows perfectly on all sides, but if crystals are growing side by side, there comes a time when they interfere with each other. Then the free faces continue to grow and the orderly internal arrangement is maintained, though externally there is interference.
Tetragonal system
In the second or tetragonal system one axis (the c axis) is different from the other two, but all three are still at right angles with each other. This is saying scientifically that the lines of force are greater or less in one direction than in the other two, but they act at right angles to each other. The a and the b axes are equal and anything that happens to one of these two must happen to the other, but need not happen to the c axis. Thinking of the molecules that arrange themselves under this system of forces, it is clear that the simplest form will be a square prism, i.e., front to back, and from side to side the numbers of molecules will be equal, but up and down there will be a greater or lesser number. If the eight corners of this prism were cut, and these corner faces increased in size until they met, the resulting octahedron would be longer (or shorter) from top to bottom than from side to side or front to back, but the measurement from front to back would be equal to the one from side to side. In this system we may have the vertical edges of the prism beveled, and not have to bevel the horizontal ones, or we may bevel the horizontal edges and not the vertical ones. There is no dodecahedron in this system or in any other system than the isometric. The forms in this tetrahedral system are really a combination of the four sides of the square prism with such modifications as equally affect them all, with two ends which may be flat, or pyramidal, or modified pyramidal faces.