= Laue method
{c}
In the <Laue method>, a fixed single <crystal structure> receives a collimated beam containing many <wavelengths>. Each <reciprocal lattice> vector can select its own <wavelength>; waves with different <wavelengths> need not interfere with one another. For $\mathbf G\ne0$, the <elastic scattering> constraint gives the particularly useful test
$$
\lambda_{\mathbf G}=-\frac{4\pi\,\mathbf s_{\rm in}\cdot\mathbf G}{|\mathbf G|^2}.
$$
A candidate reflection requires $\lambda_{\mathbf G}>0$ within the source spectrum and an outgoing ray that reaches the detector. Varying <wavelength> changes the radius and center of the <Ewald sphere> while leaving the <reciprocal lattice> fixed. A <monochromatic wave> instead fixes the radius: rotating the <crystal structure> or varying the incident <wavelength> in a scan finds reflections sequentially. A white-beam photograph integrates many spectral selections in one exposure; it is not an angular scan at one known <wavelength>.
\Image[/laue-transmission-geometry.png]
{title=Transmission <Laue method>: apparatus roles and <reciprocal lattice> geometry}
{description=Original schematic, not a reconstruction of the 1912 apparatus. The lower panels calculate an <Ewald sphere> slice for a chosen <primitive cubic lattice> with $a=0.400\,\mathrm{nm}$. The vector $(2\pi/a)(2,0,-1)$ satisfies the <Laue equations> at $\lambda=0.160\,\mathrm{nm}$ but not at $0.100\,\mathrm{nm}$. The upper ray slopes are schematic; the lower coordinates are calculated.}
{source=laue-transmission-geometry.py}
The <Laue method> is useful for orienting a single <crystal structure>: tilting it changes which <reciprocal lattice> vectors meet the spectral and detector conditions. Absolute scale has an ambiguity if the <wavelengths> are unknown. Scaling all direct <lattice translations> by $c>0$ and all selected <wavelengths> by $c$ leaves every outgoing direction unchanged. Independently known spectral information or length calibration is needed to remove this ambiguity.
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