= Neutron diffraction
{wiki}
In <neutron diffraction>, <coherent elastic scattering> adds <scattering amplitudes> from regularly positioned scatterers. Since $E_f=E_i$, the <neutron scattering kinematics> gives $k_f=k_i=2\pi/\lambda$ and
$$
Q=\frac{4\pi}{\lambda}\sin\theta.
$$
For <lattice planes> of <interplanar spacing> $d_{\mathrm p}$, constructive addition requires $Q=2\pi n/d_{\mathrm p}$ along the plane normal. Equating these expressions proves <Bragg's law>:
$$
2d_{\mathrm p}\sin\theta=n\lambda.
$$
For example, stipulate $d_{\mathrm p}=2$ <ångströms> and $\lambda=2$ <ångströms>. The first <diffraction order> has $\theta=30^\circ$ and detector deflection $60^\circ$. A peak position constrains a period; its <intensity (physics)> also depends on the <crystal basis structure factor>.
<Clifford Glenwood Shull> describes powdered <sodium chloride>, a <crystal> <monochromator>, and a shielded counter recording angular counts. Inserting <cadmium> measured background; substantial diffuse scattering complicated peak interpretation.<Early Development of Neutron Scattering by Clifford Glenwood Shull>[1994 lecture, pp. 100–103, Figs. 3–4]{ref}
Powdering supplies many <crystal> orientations. Comparing the angular peaks with <Bragg's law> constrains <crystal structure>; a background estimate helps distinguish specimen peaks from unwanted counts. A two-axis diffraction instrument has no separate outgoing <energy> analysis, so an angular pattern alone does not separate every inelastic contribution. The richer magnetic example, including a warm/cold comparison and its limits, is the <manganese monoxide neutron diffraction experiment>. Its extra peaks reveal <magnetic order> beyond the chemical periodicity; the associated <magnetic neutron diffraction> model is developed there.
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