the neutron scattering length
When a neutron passes an atomic nucleus, some of its wave is scattered. The neutron scattering length, written b, is the single number that says how strongly — it is the neutron's answer to the X-ray's atomic scattering factor. It has the units of a length (measured in femtometres, fm, where 1 fm = 10^-15 metre) because it can be pictured as the effective radius of the nucleus as the neutron sees it. A big b means strong scattering; a small b, weak. Unlike the X-ray scattering factor, b hardly changes with scattering angle, because the nucleus is so much smaller than the neutron's wavelength that it acts like a point.
The startling thing about b is that it does NOT rise smoothly with atomic number. It jumps around from element to element in a way that looks almost random, and it even differs between isotopes of the same element, because it depends on the quantum details of how neutron and nucleus resonate. Some values are surprisingly large for light elements, some are small for heavy ones, and a few are even NEGATIVE — most famously ordinary hydrogen (protium, the H-1 isotope) has b about -3.7 fm, the minus sign meaning the scattered wave comes off with a half-wavelength phase flip. Deuterium (H-2), chemically identical, has b about +6.7 fm — opposite sign and larger size. This erratic, isotope-dependent table is precisely why neutrons can locate light atoms that X-rays miss and can be tuned by isotope substitution.
There is one more distinction that matters in practice. Each nucleus really has two scattering lengths rolled together: a coherent part (the same for every nucleus of that isotope, which produces the sharp Bragg peaks) and an incoherent part (which varies randomly from nucleus to nucleus and produces a featureless background). Ordinary hydrogen is notorious for an enormous incoherent cross-section — it drowns a diffraction pattern in background haze. This is the concrete reason experimenters so often replace hydrogen with deuterium, whose incoherent scattering is far smaller: not to change the chemistry, but to swap a noisy scatterer for a clean one.
In a metal hydride, X-rays see the heavy metal atoms strongly (large Z) but the hydrogen barely at all. With neutrons the roles nearly reverse: hydrogen's |b| of about 3.7 fm is comparable to that of many metals, so a neutron pattern pins down where each hydrogen sits — and swapping to deuterium (b about +6.7 fm) both boosts the signal and cuts the incoherent background.
b is a length in femtometres, erratic across the periodic table and different for each isotope — even negative for ordinary hydrogen.
Because b varies between isotopes and is not tied to atomic number, neutrons can distinguish neighbouring elements (say manganese and iron) that X-rays cannot. The catch: ordinary hydrogen's huge incoherent scattering swamps the signal, which is why samples are often deuterated.