Bragg Order Boundary Three-Row Scan - Solid-State Physics: Lattices, Phonons, and Band Filling Step by Step

Order moves the Bragg path ledger below, onto, and above equality. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Low order misses the path equality

Plane spacing and wavelength stay fixed while order changes. The accepted bit comes only from the checked path comparison.

\begin{array}{c}n\lambda=2\cdot 4=8\ \mathrm{m}\ \ne\ 2d\\2d=2\cdot 6=12\ \mathrm{m},\quad accepted=0\end{array}

Matching order closes the path equality

Plane spacing and wavelength stay fixed while order changes. The accepted bit comes only from the checked path comparison.

\begin{array}{c}n\lambda=3\cdot 4=12\ \mathrm{m}\ =\ 2d\\2d=2\cdot 6=12\ \mathrm{m},\quad accepted=1\end{array}

High order overshoots the path equality

Plane spacing and wavelength stay fixed while order changes. The accepted bit comes only from the checked path comparison.

\begin{array}{c}n\lambda=4\cdot 4=16\ \mathrm{m}\ \ne\ 2d\\2d=2\cdot 6=12\ \mathrm{m},\quad accepted=0\end{array}