Index of Refraction of Calcite for X-rays

Abstract

Index of refraction of calcite for $\mathrm{Mo}\mathrm{K}{\ensuremath{\alpha}}_{1}$ rays.---Previous work has indicated that in the case of first order reflection from calcite the bending due to refraction is only 3\ensuremath{''}. As suggested by Bergen Davis, however, the effect can be greatly increased by using a wedge shaped crystal with a surface ground and polished so as to make an angle $\ensuremath{\phi}$ with the cleavage planes slightly less than the angle of reflection. The first crystal was ground with $\ensuremath{\phi}$ equal to 5\ifmmode^\circ\else\textdegree\fi{}48.3\ensuremath{'} so that rays which entered at an angle of 12.5\ifmmode^\circ\else\textdegree\fi{} with the surface, after first order reflection left making an angle of 54\ensuremath{'} with the surface. The refraction bending was 29\ensuremath{''}. A second crystal was ground with $\ensuremath{\phi}={6}^{\ensuremath{\circ}}{21.5}^{\ensuremath{'}}$ so that the glancing angle was only 21\ensuremath{'} and the refraction bending was 64\ensuremath{''}. The lack of symmetry due to the refraction bending at one surface was determined either by rotating the crystal about a horizontal axis perpendicular to the crystal planes or by using two halves of a split crystal, one ground and the other with natural cleavage, placed one over the other so as to get reflection from each in turn. The mean result is $\ensuremath{\mu}=1\ensuremath{-}(2.03\ifmmode\pm\else\textpm\fi{}.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. This agrees well with the value given by the Lorentz dispersion formula, 1---1.91\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$.Wave-length of $\mathrm{Mo}\mathrm{K}{\ensuremath{\alpha}}_{1}$ corrected for refraction.---The correction is.017 per cent for first order reflection by calcite. Special measurements gave the corrected wave-length as.70772A (assuming $d=3.028\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$), in good agreement with Duane's value.