The Reflecting and Resolving Power of Calcite for X-rays

With a precision double spectrometer, the rocking curves from three pairs of calcites in the (1, -1) positive have been observed for seven wave-lengths from 0.21A, (W $K{\alpha }_1$) to 2.3A, (Cr $K{\alpha }_1$). Three quantities were observed at each wave-length, (1) the percent reflection ($P_0$), defined as the ratio of the maximum ionization current obtainable from crystal $B$ to the ionization current produced by the x-rays incident on $B$ from $A$, (2) the coefficient of reflection ($R$), defined as the ratio of the area of the rocking curve from $B$ to the intensity incident on $B$ from $A$, (3) the half width at half maximum of the rocking curve from $B$. One of the pairs (crystals III) was obviously more perfect than the others, and its values of $P_0$, $R$, and $w$ are compared with theory. It is shown that none of the three quantities defined above is simply related to the analogous observations on a single crystal with monochromatic, parallel, incident x-rays, but that numerical predictions of the values of the above quantities may be obtained from somewhat laborious calculations based on Darwin's theory of diffraction by a perfect crystal as modified by Prins to take account of absorption. It is found that the predicted and observed coefficients of reflection are in good agreement in the wave-length range between 0.5 and 2.3A. On the basis of this agreement it is possible to state that calcite surfaces may be obtained for which there is no evidence of mosaic structure from measurements of the coefficient of reflection by double spectrometer methods in the wave-length region between 0.5 and 2.3A.