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

A Miller index family sets the lattice-plane repeat distance by dividing the lattice constant by the index, so a higher index gives a tighter spacing. In the schematic lattice with a = 12 m, index h = 1 gives spacing 12 m and h = 2 gives 6 m exactly for the stated toy lattice ledger; real crystal measurements depend on wavelength calibration, lattice disorder, finite resolution, and detector response.

A schematic crystal family can make plane spacing an exact arithmetic claim. 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 simple family has exact spacing

For this schematic lattice, the lattice constant is 12 meters. The family with h equal to 1 has spacing 12 meters.

d=\frac{a}{h}=\frac{12\ \text{m}}{1}=12\ \text{m}

Doubling the index halves the spacing

With h equal to 2, the same schematic lattice gives spacing 6 meters. Metre-scale lattices are training values, not atomic spacings.

d=\frac{12\ \text{m}}{2}=6\ \text{m}