We shall not deal further with this branch of spectroscopy which will form the subject of a special section (see below), but we must mention here the fundamental law discovered by Moseley in 1913 and which can be expressed as follows : The X-ray spectra of all the elements are built up on a common model; the frequencies of their homologous lines, expressed as a function of the atomic number N of the elements, follow the law : It is well known how Bohr's theory accounts for this relation, one of the most important in physics, since it expresses the unity of structure of the different atoms by pointing to the gradual and regular change in their emission lines as one runs over the entire list of the elements. It will be noticed that Moseley's law is an expression of regular increase, and is not a periodic relation such as applies to the less fundamental properties of the elements of the Mendeleyev series. This distinction arises because the majority of the other properties of the elements, e.g., chemical and physical, depend upon the outer electrons of the atom, while X-ray spectra, especially the highest frequency series of the heavy elements, are governed by the electrons nearest the nucleus.
It goes without saying that the Laue diagrams furnish a most valuable means of study in the investigation of crystal structures and in general, of the different regular arrangements in which atoms and molecules may exist in material media. In this way a new method of investigation has been made available for crystal lographic study.
Employing the formula nX= 2dsine Sir William Bragg has evaluated d by making a simple assumption regarding the arrange ment of the atoms at the intersections of the crystalline lattices in the very simple cubic crystals of KCI, NaC1, etc., and then using the molecular mass and the number of atoms in a gram molecule (Avogadro's number). The estimation of the frequencies by the method based on photoelectric effect and Einstein's equation and above all the production of X-ray spectra by means of ordinary optical gratings utilising grazing incidence, have definitely estab lished the validity of the reasoning originally used to obtain the absolute value of d. We shall simply mention that d is 2.814X cm. for sodium chloride, and may increase to about roo X cm. for the distance between the regular stratifications presented by the layers of long chain fatty acids.
To obtain diffraction effects with X-rays it is not essential to employ crystals of large dimensions. Finely powdered crystals (and even micro-crystalline structures, such as those offered by metal sheets) give rise no longer to diagrams of spots, but to more or less clearly defined circles. Even homogeneous liquids
furnish diffuse halos under certain conditions, the theory of which, still somewhat uncertain, introduces the mean distances between the molecules.
For the first approximation theories of the diffraction of X-rays by arrangements of atoms assume the latter to be stationary, though they are, of course, continually displaced by thermal agita tion. It is not impossible to allow for this complication, and one is led to the conclusion that the temperature does not modify the position of the spots, but diminishes their intensity in relation to that of the adjacent continuous background. Experiment has confirmed these predictions at least quantitatively.
The intensity of crystalline diffraction, its distribution among the spectra of the different orders, the variation of the effects with the degree of perfection of the crystals and the study of the dis tribution of the electrons in the atoms by means of these data have all given rise to interesting researches which it is impossible to outline here, but which constitute a new chapter in physical chemistry.
The classical theory of the scattering of X-rays has been given by Sir Joseph Thomson. It led to a prediction of the distribution of the intensities of the scattered rays in different azimuths with relation to the incident beam and to their state of polarisation. To a first approximation these predictions have been verified by experiment, as Barkla in particular has shown.
Scattering by an atom is supposed to be due to the forced vibrations of the electrons of this atom. When the distance between these electrons is great in comparison with the wave-lengths, the total intensity scattered is the sum of the intensities due to each electron, but matters become complicated if the wave-length is comparable with the dimensions of the atoms. Debye thus ex plained the intense scattering of soft X-rays and showed how we pass gradually to Thomson's results for high frequencies.
The fundamental phenomena of diffraction of X-rays by crystal line media has been explained on the basis of the classical theory of scattering, and the latter has great success to its credit, but it is nevertheless certain that it is insufficient.