Axis Miller Spacing Denominator Scan - Biophysical Instrumentation VIII: X-Ray Crystallography and Reciprocal Evidence Step by Step

Axis-index families make the spacing denominator visible with exact rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One lattice constant can give three exact spacings

The lattice constant is fixed at 12 m. Only the Miller axis index changes across the scan.

d=a/\sqrt{h^2+k^2+l^2}

Three axis rows show the denominator directly

For axis families, the denominator is the nonzero axis index, so spacing shrinks exactly.

\begin{array}{c|c|c}h&\text{denominator}&d\\1&1&12\ \text{m}\\2&2&6\ \text{m}\\3&3&4\ \text{m}\\\end{array}

The middle row makes six metres

Index 2 makes denominator 2, so 12 m becomes spacing 6 m.

12/2=6\ \text{m}