= Bragg's law
{c}
{title2=$n\lambda=2d\sin\theta$}
{wiki}
<Bragg's law> selects directions of <constructive interference> in <coherent elastic scattering> from equally spaced <lattice planes>:
$$
n\lambda=2d\sin\theta,\qquad n=1,2,3,\ldots.
$$
Here $d>0$ is the perpendicular <interplanar spacing>, $\lambda>0$ the incident <wavelength>, $n$ the positive integer <diffraction order>, and $\theta$ the <Bragg angle>, measured between the incoming beam and the <lattice planes>. The scattering deflection, between incoming and outgoing propagation directions, is $2\theta$. Thus a plotted detector angle $2\theta$ must be halved before insertion into <Bragg's law>. The $\theta$ in the parent <elastic Bragg scattering condition> denotes the full deflection; the present $\theta$ denotes half of it. <Online Dictionary of Crystallography by International Union of Crystallography/Bragg's law>[Online Dictionary of Crystallography, Bragg's law, Definition: spacing, wavelength, glancing angle and reflection order]{ref}
The <lattice planes> organize <wave interference> throughout a <crystal structure>; they are not literal metal mirrors or separate reflecting surfaces. The picture assumes <elastic scattering>, hence an unchanged <wavelength>, and sufficiently stable relative <wave phases> across the contributing <lattice planes>. <X-ray> <wavelengths> comparable with atomic <interplanar spacings> make these directions experimentally accessible. The <sine> cannot exceed one: an order exists geometrically only if $n\lambda/(2d)\leq1$. For $\lambda>2d$, even the first <diffraction order> is inaccessible. A geometrically possible direction need not have nonzero <wave intensity>; the <crystal lattice structure factor> and <crystal basis structure factor> also matter. <Online Dictionary of Crystallography by International Union of Crystallography/Structure factor>[Online Dictionary of Crystallography by International Union of Crystallography; Definition and Derivation: coherent addition of the atoms within the unit cell]{ref}
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