Diffuse scattering

Diffuse scattering is the scattering that arises from any departure of the material structure from that of a perfectly regular lattice. One can think of it as the signal that arises from disordered structures, and it appears in experimental data as scattering spread over a wide q-range (diffuse).

Bragg diffraction occurs when scattering amplitudes add constructively. If there is a defect in a crystal lattice (e.g. atom missing or in a slightly 'wrong' position), then the amplitude of the Bragg peak decreases. This 'lost' scattering intensity is redistributed into diffuse scattering. The diffuse scattering thus arises from the local (short range) configuration of the material (not the long-range structural order).

In the limit of disorder, one entirely lacks a realspace lattice and thus scattering does not generate any Bragg peaks. However, a disordered structure will still give rise to diffuse scattering. The Fourier transform of a disordered structure will not give any well-defined peaks, but will give a distribution of scattering intensity over a wide range of q-values. Thus samples with an inherently disordered structure (polymer blends, randomly packed nanoparticles, etc.) will only generate diffuse scattering.

Causes

• Thermal motion causes atoms to jitter about their ideal unit cell positions, which decorelates them. This suppresses the intensity of the Bragg peaks, especially the higher-order peaks (see Debye-Waller factor), and instead generates high-q diffuse scattering. (One can also think of this in terms of phonons: in ordered systems the diffuse scattering is probing phonon modes.)
• Static disorder in crystals (vacancy defects, substitutional defects, stacking faults, etc.) similarly creates diffuse scattering.
• Grain structure in otherwise ordered materials will also contribute. The grains themselves can count as 'scattering objects', but since their size is ill-defined, the grain boundaries give rise to diffuse scattering.
• Nanoscale disorder gives rise to low-q diffuse scattering. For instance, a disordered polymer blend (or a bulk heterojunction) or a random packing of nanoparticles, will generate substantial low-q diffuse scattering.
• Surface roughness in thin films give rise to low-q diffuse scattering in GISAXS. Roughness will tend to broaden (and increase the intensity of) the specular rod, and will also generate intense low-q scattering.
• Polymer chains in solution generate scattering without a well-defined size-scale. This is normally interpreted in terms of the form factor of the polymer chain. However one can also think of it as the polymer chains having disordered arrangements and thus giving rise to diffuse scattering. (C.f. definitional boundaries.)

See Also

• Diffuse Scattering from ORNL
• Diffuse scattering in crystals from ETH Zurich