Neutrons bounce off the nucleus, not the cloud
This rung has been a tour of probes, and each one touches the crystal in a different place. X-rays, back in the last rung, scatter off the diffuse electron cloud, so an atom's scattering power climbs steadily with its atomic number Z — that is the atomic scattering factor f. Electrons, in guides 1 to 3, scatter off the electrostatic potential so ferociously that a TEM foil must be thinned to a whisper and the pattern is muddied by dynamical scattering. A neutron does neither: being electrically neutral it ignores the electrons entirely and dives to the tiny nucleus, colliding through the strong nuclear force. Yet the diffraction machinery is exactly the one you already own — the same neutron diffraction obeys the same Bragg's law, builds the same reciprocal lattice, and sums the same kind of structure factor. Only one ingredient changes: the per-atom scattering power f is replaced by the neutron scattering length b.
First, one number to anchor you: a neutron only diffracts if its wavelength is atom-sized, and it is. Neutrons let out of a reactor and moderated to room temperature — thermal neutrons — travel about 2200 metres per second, and their de Broglie wavelength lambda = h/(m v) works out near 1.8 angstrom (a handy rule is lambda in angstrom = 9.0 / sqrt(E in meV), so 25 meV gives 1.8). That is the same angstrom-scale ruler as Cu K-alpha, so neutrons diffract off the very same lattice planes. Now the twist that makes them special: unlike f, the neutron scattering length b does NOT climb with Z. It hops around erratically from element to element, fixed by the quantum details of each nucleus, and some values are even negative. That single fact is the seed of everything below — light atoms stop being whispers, and neighbours in the periodic table need not look alike.
Hydrogen, at last — and telling neighbours apart
Start with the gift that changed chemistry. To X-rays, hydrogen is one lonely electron: its f at zero angle is just 1, against iron's 26, so protons are nearly invisible and their positions are usually guessed rather than seen. For neutrons, b(H) = -3.74 fm sits at about 40 percent of iron's 9.45 fm — comparable, fully visible. So neutron diffraction is THE tool that locates hydrogen: the protons in a metal hydride, the H atoms in water and ice, and the exact geometry of a hydrogen bond — the weak but decisive link that shapes ice, clays, DNA and countless minerals. Where X-rays draw a structure with all its lightest atoms erased, neutrons fill them back in.
The second gift is telling neighbours apart. X-rays can barely separate elements that sit side by side in the table — iron (Z=26), cobalt (27) and nickel (28) scatter almost identically, so an ordered Fe-Ni or Fe-Co alloy looks nearly random to an X-ray beam. The neutron scattering lengths, by contrast, are wildly different: 9.45, 2.49 and 10.3 fm. So neutrons read out chemical ordering, site occupancies and which element sits on which site precisely where X-rays go blind. Position from the lattice, identity from the scattering length: the erratic b that looked like a nuisance is exactly what does the sorting.
X-RAY f vs NEUTRON b (relative per-atom scattering power) atom Z X-ray f(0) neutron b (fm) ---- -- ---------------- ---------------------------------- H 1 1 (a whisper) -3.74 visible! and phase-flipped D 1 1 (a whisper) +6.67 H's own isotope, opposite C 6 6 +6.65 O 8 8 +5.80 V 23 23 -0.38 nearly invisible -> sample cans Fe 26 26 +9.45 \ Co 27 27 +2.49 > wildly different Ni 28 28 +10.3 / X-ray f climbs steadily with Z -> H drowns, Fe/Co/Ni look alike neutron b hops around, some < 0 -> H shows up, Fe/Co/Ni differ
Now the honest catch with hydrogen. Besides its useful coherent scattering, ordinary H scatters INcoherently very strongly — the neutron's spin and the proton's spin flip each other at random, throwing neutrons every which way. That incoherent halo makes no Bragg peaks; it just dumps a huge flat background that can bury the very peaks you came for. The standard fix is deuteration: swap H for its heavier isotope deuterium, D, whose incoherent scattering is far smaller and whose b is a clean positive 6.67 fm. That the swap even works — that two forms of the same element scatter so differently — is a door onto the next gift.
Isotope contrast: same element, two different shadows
Here is something X-rays fundamentally cannot do. The X-ray f depends only on the electron count, so every isotope of an element looks identical to X-rays — same electrons, same scattering. But neutron b is set by the nucleus, and different isotopes of one element have different b. The star pair is hydrogen again: ordinary H at -3.74 fm and deuterium D at +6.67 fm — opposite in sign, different in size, yet chemically the same atom sitting in the same place. That difference is called isotope contrast, and it is a lever, not just a curiosity.
By mixing H and D in a chosen ratio you can tune the AVERAGE scattering length of, say, a solvent or a polymer to any value you like — even to exactly zero, matching it to the material around it so that part of the structure simply vanishes from the pattern. This contrast matching (or contrast variation) lets you make one component of a crowded assembly invisible while another glows: a single polymer chain inside a blend, a molecule bound in a protein's pocket, the water shell around a particle. You run the sample two or three times with different H-to-D ratios and read the structure by difference. Be honest about the small print: it works because H and D are chemically near-twins, though tiny isotope effects on bond lengths and dynamics do exist — usually negligible, occasionally not.
The far extreme from hydrogen's loud halo is a metal that says almost nothing: vanadium, with a coherent b of about -0.38 fm — so close to zero that it makes practically no Bragg peaks at all. That near-invisibility is a feature: vanadium is the standard material for sample cans and holders (the container disappears, leaving only your sample's pattern), and its smooth, well-known incoherent scattering makes it the go-to standard for calibrating a neutron instrument. One element drowns the pattern in background; another is a ghost you build the apparatus from. Both extremes come straight from that erratic scattering-length column.
Magnetism you can diffract
The neutron's second superpower comes from its own spin. Though electrically neutral, the neutron carries a magnetic moment, so it feels the magnetic field of unpaired electron spins on atoms such as manganese, iron, or a rare earth. That opens a SECOND scattering channel running alongside the nuclear one: nuclear scattering off the nucleus (always present) plus magnetic scattering off ordered spins (present only when the material is magnetically ordered). X-rays and electrons see where the atoms are but are nearly blind to this spin arrangement; neutrons diffract off it directly. This is what makes neutron diffraction the primary tool for magnetic structure determination — reading not just where atoms sit, but which way their tiny compass needles point.
Picture the classic case. Above its ordering temperature (the Neel temperature) the spins point every which way, thermally scrambled, and only the nuclear peaks show. Now cool an antiferromagnet like MnO — an ordinary rock-salt structure — below about 118 K, and neighbouring (111) sheets of manganese spins lock antiparallel, up-down-up-down. Because a spin-up Mn and a spin-down Mn are no longer identical to the neutron, the true magnetic repeat is now DOUBLE the chemical one along that stack. A doubled real-space period is a halved reciprocal spacing, so brand-new magnetic Bragg peaks appear at positions like (1/2 1/2 1/2) — reflections that flat-out do not exist in the chemical cell or in any X-ray pattern. Clifford Shull's measurements of exactly this, around 1949 to 1951, earned a share of the 1994 Nobel Prize. A peak that materialises out of nowhere on cooling is the unmistakable fingerprint of antiferromagnetic order.
- Record diffraction patterns both above and below the ordering temperature; the peaks present in BOTH are nuclear (they come from the atoms, not the spins).
- Subtract them: any peaks that appear ONLY in the cold pattern are purely magnetic.
- Read their POSITIONS to get the magnetic propagation vector k — where the spin pattern repeats (cell-doubling puts k at a zone boundary, e.g. (1/2 1/2 1/2)).
- Read their INTENSITIES to get the size of the ordered moment, in Bohr magnetons per atom.
- Use a key rule — magnetic scattering only sees the moment component PERPENDICULAR to the scattering vector — so comparing intensities across reflections fixes the DIRECTION the spins point. Fold in the nuclear structure and you have the full magnetic structure.
One honest asymmetry rounds this out, and it is the mirror image of the note back in Section 1. Nuclear scattering stayed strong at all angles because the nucleus is a point. Magnetic scattering does the opposite: it FALLS OFF with angle, because the unpaired electron spins are spread over an angstrom-scale cloud rather than a point, so magnetic scattering carries its own form factor. That means magnetic peaks are strongest at low angle and fade at high angle — the reverse of the nuclear signal — and the way they fade is itself a clue that maps out the shape of the spin density. Point nucleus, flat with angle; extended spin cloud, falling with angle. Same neutron, two channels, two behaviours.
Choosing the neutron probe — gifts, costs, and the phase still hiding
One more physical gift, and then the bill. Because neutrons are neutral they barely interact with matter, so they punch centimetres deep instead of stopping at the surface the way electrons and even X-rays do. That makes neutron diffraction a genuinely BULK probe: you can measure the residual stress buried deep inside a thick weld or a turbine blade, watch a battery or a catalyst working inside its real cell (an operando experiment), or study a whole engineering part rather than a shaving off its skin. Where an electron beam sees only the top few nanometres, neutrons see clear through.
But the same weak interaction that lets neutrons penetrate also makes them scarce and faint. There is no benchtop neutron tube. Neutrons come from a nuclear reactor or a spallation source — building-sized machines, only a few dozen on Earth, and heavily oversubscribed — and even then the usable flux is minute compared with an X-ray tube, let alone a synchrotron. So you bring gram-sized samples, not the micrograms a TEM sips, and you count for hours or days, not the seconds a lab X-ray diffractometer takes. The upshot: neutrons are not a replacement for X-rays; they are the complement you reach for when the question is about light atoms, isotopes, next-door elements, magnetism, or the deep bulk. The richest structures come from refining X-ray and neutron datasets TOGETHER — X-rays fixing the heavy-atom skeleton, neutrons filling in the hydrogen and the spins.