Crystal Peaks Become Indexed Data

Miller Spacing Family

index sets repeat distance

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=ah=12 m1=12 md=\frac{a}{h}=\frac{12\ \text{m}}{1}=12\ \text{m}
Miller spacingA perfect-square Miller family gives an exact plane spacing.spacingplane family

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=12 m2=6 md=\frac{12\ \text{m}}{2}=6\ \text{m}
Miller spacingA perfect-square Miller family gives an exact plane spacing.spacingplane family