Bragg Order Boundary Three-Row Scan - Condensed Matter and Plasma Physics Step by Step

A Bragg-order-boundary scan varies the diffraction order across three rows, checking that n * lambda = 2 * d * sin(theta) stays within the physical |sin(theta)| <= 1 bound for each. The arithmetic is exact only for the stated wavelengths, lattice spacings, orders, and rows in the ideal perfect-crystal Bragg model. Real measurements add defects, strain, temperature, finite crystal size, instrument calibration, peak fitting choices, finite precision, and measurement uncertainty.

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}