Past exam of the frontiers of experimental condensed matter physics course of the University of Cambridge / 2012 / Paper 1 / 1 / a / Solution

Both neutron diffraction and X-ray diffraction use interference from atomic arrangements. Elastic scattering gives reciprocal-space peaks when the momentum transfer matches a reciprocal lattice vector. For a basis with sites ${\mathbf{r}}_j$, the structural amplitude is $F(\mathbf{Q})={\sum }_j{b}_j(\mathbf{Q})e^{i\mathbf{Q}\cdot {\mathbf{r}}_j}$, and peak intensities constrain positions, occupancies and thermal displacement as well as lattice symmetry. Powder averaging loses some directional information that a suitable single-crystal measurement retains.

X-rays couple primarily to the electron distribution. Their atomic form factors generally favor heavier atoms and decrease with increasing scattering angle; the wavelength can also be tuned near an absorption edge for element-sensitive anomalous contrast. Neutrons scatter from nuclei with scattering lengths that vary irregularly with element and isotope. This can make light atoms visible beside heavy ones, and isotope substitution can change contrast without changing the nominal chemical element. In particular, replacing hydrogen with deuterium changes the balance of coherent and incoherent neutron scattering.

Neutron magnetic scattering also couples to electronic magnetic moments, allowing magnetic order to produce peaks distinct from the nuclear structure. X-ray magnetic scattering is possible too, especially under suitable resonant conditions; it is incorrect to say X-rays can never probe magnetism. Neutron experiments often require larger samples and dedicated sources, whereas X-ray scattering is available in laboratories as well as synchrotrons. Absorption, multiple scattering, texture and instrumental resolution affect both methods. Their complementarity comes from different contrast weights and magnetic sensitivity, rather than from two identical pictures of the same density.