12.1.2: Intensity of Diffraction- Halite

Last updated
Save as PDF

Page ID: 18383

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

12.26.png — Figure 12.26: Atomic arrangement in halite and some planes in a unit cell

The preceding discussion was about a hypothetical 2D mineral. For a 3D example, let’s reconsider halite. Drawings a and b in Figure 12.26 show two different depictions of the atomic arrangement in halite. The diagrams in the bottom of the figure highlight (in red) some of the (111), (200), and (220) planes.

Halite is cubic and has lots of symmetry. Consider the (200) planes shown in drawing 12.26d. Equivalent planes with equal spacing (not shown) can be parallel to the top and bottom faces, or parallel to the front and back faces. We omitted them for clarity. So, these drawings only show a few of many equivalent planes with equal d-values. In total, a cubic crystal like halite contains 12 different orientations for planes equivalent to (111), 9 different orientations for planes equivalent to (200), and 18 different orientations for planes equivalent to (220). If we X-ray halite, diffraction by (111) planes is relatively weak. The (200) and (220) planes produce the most intense reflections because there are many of those planes and they contain many atoms (as seen in the atomic drawings in this figure). You can verify this by looking at the diffraction pattern for halite in Figure 12.24.