Miller Index Spacing Scan - Biophysical Instrumentation II: From Signals to Genomes Step by Step

A fixed schematic lattice becomes clearer when three Miller-index rows are compared. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A Miller index is a spacing scale, not just a name

The schematic lattice constant is 12 meters. Holding that lattice fixed lets the index change the spacing by exact division.

d=\frac{a}{h}

Three index rows show inverse scaling

The table keeps the lattice constant fixed and changes only the Miller index. The repeat spacing shrinks as the index grows.

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

The third row gives the tightest family

For the tight row, h is 3 and the spacing is 4 meters. The diagram shows the computed repeat arrow, not an empirical crystal.

d=\frac{12\ \text{m}}{3}=4\ \text{m}