X-Ray Diffraction from Calcite for Wave-Lengths 1.5 to 5 Angstroms

Theoretical expressions for the coefficient of reflection, percent reflection, and width of the line to be expected from the second crystal of a double spectrometer in the (1, -1) position, based on Darwin's theory of reflection from a perfect crystal, as modified by Prins, are evaluated for calcite for six lines in the region 1.54 to 5A. This region includes, at 3.06A, the critical absorption limit of calcium. With a specially designed double-crystal spectrometer, these properties of the rocking curve from the second crystal for ten wave-lengths, copper $K\alpha$ radiation and nine spectrum lines selected from the uranium $M$ series, are experimentally measured and these results compared with the calculated values. The agreement between the observed and calculated rocking curve widths is excellent throughout the entire region and gives no evidence of mosaic structure in the crystals. The calculated values of percent reflection are consistently above those observed by some 16 percent. Good agreement is obtained for the values of the coefficient of reflection for wave-lengths shorter than 4A including those close to and on either side of the calcium absorption limit. No correction for temperature motion of the atoms has been attempted, but it seems possible that such a correction would give very satisfactory agreement between theory and experiment, showing that calcite surfaces may be obtained for which there is no evidence of mosaic structure from the diffraction of x-rays.