The Intensity of Reflection of X-Rays by Powdered Crystals, I. Sodium Chloride and Sodium, Lithium and Calcium Fluorides

Abstract

Through measurements by the ionization method of the relative intensities of reflection of x-rays by the different planes of powdered crystals, the author has obtained data which are free from the errors inherent in the work with large single crystals. Darwin's formula for the intensity of reflection from an ideally imperfect crystal may be applied to these results without correction for primary or secondary extinction. In order to get reflected radiation of sufficient intensity to permit accurate measurement, a focussing method has been used, in which a primary beam of wide divergence strikes the surface of a briquet of the powder under investigation and the reflected beam is focussed sharply at the ionization chamber slit. Measurements were made out to angles slightly larger than $\ensuremath{\theta}=45\ifmmode^\circ\else\textdegree\fi{}$. The absolute values of the intensity of reflection were determined by comparison with reflections from powdered sodium chloride, the results of Bragg, James and Bosanquet on the latter crystal, after allowance for secondary extinction, being taken as correct.Structure factor and atomic scattering curves.---Application of the equation for the intensity of x-ray reflection to the experimental results gives the structure factors for the reflections from the different crystals. These factors, when plotted against $sin\ensuremath{\theta}$, fall upon smooth curves from which can be obtained the atomic scattering curves representing the variation of the atomic structure factors with the angle of reflection. For fluorine in all three fluorides, the $F$ curves are almost identical, but for sodium in NaF and NaCl there is a notable difference, indicating that the electron distribution for Na is not the same in the two compounds. The effect of the excess positive or negative charge which tightens or loosens the electron atmosphere of an ion is made evident by comparison of the $F$ curves for ions of different charge but with the same number of electrons. Use of experimental structure factor curves in crystal analysis is discussed.