A Precision Comparison of Calculated and Observed Grating Constants of Crystals

Abstract

A precision comparison of the calculated and observed grating constants of calcite, rocksalt, artificial KCl, and diamond crystals is made with calcite as standard. The calculated values are determined from density measurements, while the observed values are calculated from the angles of reflection for the Mo $K{\alpha }_1$ line obtained by means of a precision double-crystal spectrometer. The value of $\lambda$ obtained from the calculated grating constant of calcite is used to determine the observed grating constants of the other crystals. The density of rocksalt and KCl is measured by immersion in Russian mineral oil whose density and change of density with temperature was found to be 0.88011 at 24°C. and 0.000064 per 0.1° respectively. The density of diamond is determined by weighing a solution of thallous formate and thallous malonate, in which the diamond just floats, in a calibrated specific gravity bottle of approximately 50 cc capacity. Two methods are used in the x-ray measurements, namely, the calcite method, de scribed by A. H. Compton and S. K. Allison and J. H. Williams, and the rocksalt method. The latter consists of measuring the peak position of the beam reflected from crystal $B$ by swinging the ionization chamber past the beam, with two narrow slits between it and the crystal, ranging in width from 0.04 to 0.08 mm and separated by a distance of 18 cm. Calculated and observed values of the grating constants of these crystals are found to agree within experimental error, ranging from 0.004 to 0.011 percent, showing no evidence of Zwicky's "secondary structure," which he offered as a possible explanation of the discrepancy between x-ray wave-lengths obtained by the crystal method and those by the ruled grating method. Measurements on two quartz crystals showed a decided variation in the internal structure of the crystal, and indicate that quartz is unsuitable for precise wave-length measurements.