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

Abstract

The authors have continued their efforts to absolve the x-ray method of determining the electronic charge of the criticism that Bragg reflection determines the lattice dimensions in only a very shallow surface region whereas the density determinations have been made on a much larger volume of crystal. In earlier work by a powder method we were able to show that the above-mentioned superficiality criticism could not explain the discrepancy between $e=4.803\mathrm{}$ (the "x-ray value") and $e=4.770\mathrm{}$ (computed by the oil-drop method with Harrington's value of air viscosity). The powder method, necessarily somewhat less precise than the macroscopic calcite method, yielded a mean of $e=4.799\mathrm{}$, agreeing with the macroscopic calcite value well within the precision of the powder method. The present work gives a still more precise absolution of the macroscopic calcite results from the above-mentioned criticism. In the earlier work we abandoned efforts to measure lattice dimensions in the interior of a thin-cleaved slab of calcite by means of Laue reflection in a precision transmission spectrometer because photographs with the crystal adjacent to the slit, but on the same side as the photographic plate showed most of the Laue reflection coming from regions close to the front and back surfaces of the slab. Also strange unexplained fluctuations of intensity along the lengths of the spectral "lines" were observed with the crystal in this position. In a continuation of this work two thin crystal slabs have been studied. Each has been etched with HCl rather heavily all over one of its faces and over half the height of its opposite face. The upper half of the spectral lines selectively reflected to the photographic plate had thus traversed a crystal slab etched on both sides, while the lower half had traversed a slab etched on only one side. With this arrangement, and with the crystal on the side of the slit nearest the photographic plate, we are able to show that the enhanced Laue reflection from regions near the surface is completely suppressed by sufficient etching and that fainter reflection can then be definitely observed from the interior regions of the crystal. With the crystal on the opposite side of the slit from the plate we are able to compare very accurately on one and the same photographic plate the reflection angles for the enhanced surface reflection with the reflection angles for the interior planes. These angles turn out to be very precisely equal, thus furnishing clinching justification for the validity of the well-known precise determinations of $e$ by Bragg reflection from the surface of macroscopic pieces of calcite. The density fluctuations along the length of the lines are absent for the interior reflection and we conclude that they are probably the result of local variations of surface disturbance set up in the process of cleavage.