Reciprocal Spots Are Indexed Addresses

Reciprocal Spot Sits on Integer Grid

A reciprocal map is an indexed grid, not a decorative constellation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Reciprocal spots are integer addresses

The map contains spots (1,0), (2,2), (3,1), and (1,3).

(1,0),(2,2),(3,1),(1,3)(1,0),(2,2),(3,1),(1,3)
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 flagship spot is the projected family

The Miller family (2,2,1) projects to reciprocal address (2,2) in this two-dimensional training map.

(h,k,l)=(2,2,1)↦(h,k)=(2,2)(h,k,l)=(2,2,1)\quad\mapsto\quad(h,k)=(2,2)
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