Tests of the Validity of X-Ray Crystal Methods of Determininge

Abstract

The procedure in determining the electronic charge, $e$, from measurements of x-ray diffraction angles and the density of crystals has been criticized on the ground that while the density measurements are averages of a large volume, say 10 cc of crystal, the x-rays are diffracted from a surface layer as determined by "extinction" only about 4×${10}^{-4\mathrm{}}$ cm thick, a very small fraction of the total volume in an entirely specialized location. Partial answers to this criticism by Y. C. Tu and by Allison and Armstrong have rendered its validity much less probable. The present work with extremely fine powdered calcite samples whose density was determined with a pycnometer closes the question completely, we believe, leaving no ground whatever for the criticism and placing the x-ray determinations of $e$ on a very solid experimental foundation. Our work yields a value for $e$ of 4.799±0.007 abs. e.s.u. based on the scale of ruled grating wave-lengths in which Cu $K{\alpha }_1$ has a wave-length (Bearden's value) of 1.5406×${10}^{-8\mathrm{}}$ cm. Efforts to remove the above objection by studies on macroscopic calcite samples which failed to withstand our own criticisms are described since they emphasize the pitfalls that a conclusive test must avoid. Several new unexplained crystal diffraction effects discovered in this search for a conclusive test are also described. Agreement to one part in six thousand between Bragg and Laue diffraction angles was established for two different sets of Miller indices in macroscopic calcite.