Neutrons see atoms differently from X-rays
Neutrons scatter from nuclei, and how strongly an atom scatters them does not simply grow with atomic number. For X-rays, the small-angle atomic scattering amplitude is roughly proportional to electron number away from absorption edges, although the actual contrast depends on scattering angle and photon energy. Even isotopes of one element can scatter neutrons very differently. Shull’s lecture tells how weak early neutron sources gave way to reactor beams strong enough for useful diffraction. Wollan and his collaborators were essential to the apparatus and the measurements.
Neutrons also carry a magnetic moment, so magnetic scattering can reveal ordered moments in a sample and how they are arranged. A diffraction pattern can therefore mix contributions of different origin, and they must be told apart. Reading every peak as the position of a nucleus can misidentify magnetic order.
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Elastic peaks point to the arrangement of atoms
In elastic scattering, the neutron leaves with the energy it arrived with, to within the instrument’s resolution. The directions of momentum transfer and the peak intensities then constrain the periodic structure. Each atom is weighted by its nuclear scattering length, and magnetic scattering by a magnetic form factor, in place of the weights used for other probes.
Because the resolution is finite, the elastic window also catches fluctuations that are slow enough. An elastic peak therefore does not prove that every atom is still. Refining a structure from the peaks also needs the composition, the symmetry, the background and a physical model of the scattering.
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Brockhouse measured the energy left with the sample
A triple-axis spectrometer uses one crystal to pick the incident energy, scatters the neutrons from the sample, and uses a second crystal to pick the final energy. The rotation angles set the momentum transfer and the energy transfer. Brockhouse’s lecture describes the early instrument and the later method that holds momentum transfer constant.
Phonon and magnon branches come from following peaks across these momentum and energy coordinates; no single image of the crystal shows them. In the formula, wavevector transfer is incident minus final, both wavevectors have units of inverse length, and a positive energy transfer means energy given to the sample. The neutron is treated as nonrelativistic.
Sources: [1]
Resolution and count rate decide which excitations you can see
The mosaic spread of the monochromator and analyzer crystals, the collimation and the angle settings blur each measurement over a small volume in momentum and energy, called the resolution volume. A measured linewidth therefore includes instrumental broadening. A weak source or a narrow acceptance lengthens the counting time and can hide a mode that is really there.
Brockhouse and Shull shared the 1994 award for complementary techniques. Relabeling the particle in an electron-diffraction Lab as a neutron would not reproduce their work: interaction strength, magnetic coupling, energy selection and interpretation all differ.
Find the analyzer crystal in Brockhouse’s figure
In Brockhouse’s Fig.3, find both crystals and the sample, then compare the layout with Shull’s diffraction apparatus. The linked reciprocal-space model covers the geometry only. A real neutron model would also need scattering amplitudes that depend on the isotope, and a way to measure and record energy transfer.