A crystallography row starts from a checked plane-family spacing. 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 family fixes a plane spacing

The training lattice constant is 15 m. The family is 2, 2, 1.

h2+k2+l2=9h^2+k^2+l^2=9
X-ray reflection ledgerThe Miller spacing, Bragg path, and projected reciprocal spot share one source.spacingspacingplane familyhkl=2,2,1spot=2,2d=5 mlambda=6 mpath=6 maccepted=1planeplanepath: 6 m

The exact spacing is five metres

The denominator is three, so 15 m gives spacing 5 m.

d=15 m/3=5 md=15\ \text{m}/3=5\ \text{m}
X-ray reflection ledgerThe Miller spacing, Bragg path, and projected reciprocal spot share one source.spacingspacingplane familyhkl=2,2,1spot=2,2d=5 mlambda=6 mpath=6 maccepted=1planeplanepath: 6 m