The Scattering of X-Rays and Electron Distribution in the Atoms of Crystals

Abstract

Critical examination of the method of obtaining the atomic structure-factor and of the Fourier analysis method of determining electron distributions in crystals.—Theories of the Compton effect suggest that modified scattering of x-rays may take place at the expense of regular reflection, and consequently that the atomic structure-factor, which is determined from experimental measurements of the intensity of regular reflection and upon which is based our most direct means of determining electron distribution in atoms, may not represent all of the electrons in the atom. It is therefore necessary to consider critically the determinations of electron distribution in the atoms of crystals which have previously been made. The classical theory, when applied in the form of Darwin's equation to the measured intensities of regular reflection, gives values of the atomic structure factor for Li, C, O, F, Na, Al, Cl, Ca, Fe, which are in accord with our ideas concerning atomic structure. It is shown (this was previously an assumption) that the coefficients of the Fourier's series which is used in determining the electron distribution are all positive in the experimental cases heretofore dealt with. The application of the Fourier analysis to a model argon atom indicates that the accuracy of the analysis depends predominantly upon the accuracy of measurement of the intensities of reflection within angular limits which are easily subject to experimental investigation. Electron distributions obtained from Fourier analysis of the experimentally determined atomic structure-factor curves for several different atoms or ions contain almost exactly the amounts of electricity which we believe from other considerations to exist in the crystals, within radii in good agreement with those calculated from interatomic distances determined by ordinary crystal analysis. Modification of the calculated $F$ values of model atoms to take into account the Compton effect results in $F$ curves which give, upon Fourier analysis, unreasonable distributions of diffracting power. The Fourier analysis can give reasonable distributions of electron density only if the $F$ curves are approximately correct. Since the experimental $F$ curves do give reasonable distributions, it is concluded that any modification which is caused by the Compton effect in the intensity of regular reflection of x-rays is negligible.