Solid-State Relation Cross Scans

Lattice Reciprocal Three-Row Scan

Three spacings show length growing while reciprocal spacing shrinks. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One-meter spacing gives the largest reciprocal row

With 4 cells and spacing 1 m, the total length is 4 m and the toy reciprocal is 1 per m.

L=4⋅1=4 m,b=1 per m,sites=5L=4\cdot 1=4\ \mathrm{m},\quad b=1\ \mathrm{per\ m},\quad sites=5
Lattice row a=1Length and reciprocal spacing cite the same lattice source.a=1 mb=1 1/ma*b=1

Two-meter spacing halves the reciprocal row

With 4 cells and spacing 2 m, the total length is 8 m and the toy reciprocal is one-half per m.

L=4⋅2=8 m,b=1/2 per m,sites=5L=4\cdot 2=8\ \mathrm{m},\quad b=1/2\ \mathrm{per\ m},\quad sites=5
Lattice row a=2Length and reciprocal spacing cite the same lattice source.a=2 mb=1/2 1/ma*b=1

Four-meter spacing quarters the reciprocal row

With 4 cells and spacing 4 m, the total length is 16 m and the toy reciprocal is one-fourth per m.

L=4⋅4=16 m,b=1/4 per m,sites=5L=4\cdot 4=16\ \mathrm{m},\quad b=1/4\ \mathrm{per\ m},\quad sites=5
Lattice row a=4Length and reciprocal spacing cite the same lattice source.a=4 mb=1/4 1/ma*b=1