Crystallography and
Evidence of Regular Structure

X-Ray Evidence of Regular Structure
In 1912, while attempting to prove a similarity in character between the vibrations of X-raysand light, Dr. Laue conceived the idea of using the ordered arrangement of the atoms in a crystal as a “diffraction grating” for their analysis. He argued that if the distances between the parallel atomic layers in the crystal net-work were of the same order as the wave lengths of the X-rays that diffraction of the X-ment was tried of placing a photographic plate behind a crystal section which in turn lay in the path of a beam of X-rays, with the result that not only did the developed plate show a dark spot in its center where the direct pencil of X-rays had hit it but it also showed a large number of smaller spots arranged around the center in a regular geometrical pattern. This pattern was formed by the interference of waves which had been diffracted in different directions by the atomic structure of the crystal. In addition to a new method of studying the characters of X-rays this experiment gave a most important means for the study of the internal structure of crystals. Figure 1 gives a diagrammatic representation of a Laue photograph obtained by directing a beam of X-rays normal to a cube face of a crystal of halite, sodium chloride. The dark spots indicate the relative position in the crystal net-work of various atomic planes parallel to possible crystal faces and their arrangement indicates the symmetry of the crystal.

Other important methods have since been devised of studying crystal structure by means of X-rays. Among these is one which involves the reflection of the X-rays from the different atomic planes of the crystal. In general the rays reflected from the successive planes would be in different phases of vibration and so would tend to interfere and neutralize each other. But with a certain angle of incidence and reflection it would happen that the different reflected rays would possess on emergence from the crystal the same phase of vibration and would therefore reinforce each other. This angle would vary with the wave length of the X-ray and with the spacing between the atomic layers of the crystal. By the use of a special X-ray spectrometer the angles at which these reflections take place can be accurately measured. By this method the distances between the atomic layers of the crystal can be determined. Still another method should be mentioned. This is the so-called “powder method,” in which a tube of powdered material is subjected to a beam of X-rays and the position of the diffracted rays shown by lines produced on a photographic film which has been placed around the tube in a circular arc. Since the powder will contain particles in all possible crystal orientations the diffracted rays indicate the position of all the different atomic planes in the crystal structure.

By these various methods it has been possible in many cases, particularly of the simpler compounds, to definitely determine the crystal structure. As an example the case of halite may be cited. We now know that the sodium and chlorine atoms are arranged in the crystal net-work as shown in Fig. 2. We also know with precision the distances between the atomic layers of its crystals.

The Outward Crystal Form May be Varied with the Same Internal Crystalline Structure. There may be several different limiting forms possible upon crystals of the same mineral. Galena, PbS, for example, usually crystallizes in the form of a cube, but it also at times shows octahedral crystals. The internal structure of galena is constant, but both the cube and octahedron are forms that conform to that structure. The models shown on Plate I illustrate this point. Both are built upo of similar particles and their arrangement is the same in each case. In one, however, (Fig. A), the planes of a cube, and in the other (Fig. B) the planes of an octahedron, limit the figure.

With the same internal structure there are, however, only a certain number of possible planes which can serve to limit a crystal. And it is to be noted, moreover, that of these possible planes there are only a comparatively of a crystal are determined by those directions in which on account of the internal structure a large number of the individual mineral units lie. And those planes which include the greater number of units are the ones most commonly found as faces upon the crystals. Consider Fig. 3, which might represent one layer of units in a certain crystal network. These units are equally spaced from each other and have a rectilinear arrangement. It will be observed that there are several possible lines through this network that include a greater or less number of units. These lines would represent the cutting direction through this network of certain possible crystal planes; and it would be found that of these possible planes those which include the larger number of units, like those cutting along the lines A-B and A-C, would be the more common in occurrence.