Definitional boundaries

As with any technical field, learning about scattering involves absorbing a host of new definitions and jargon. As usual, definitions are not always as clear and consistent as we would like. This page tries to highlight some of the ambiguities.

In the scattering field, the core of the problem is that various techniques were developed to address different limiting cases. However, the fundamental interactions are the same in all cases. As more complex materials began being studied, the resultant data included a mixture of effects; it was no longer so easy to define which 'idealized' experiment one was performing. As instruments have become more versatile, a technique/dataset intended to measure a certain property can now be used to measure many different things. New kinds of samples (nano-materials, aperiodic crystals, etc.) have also upended historical assumptions.

Scattering Experiments

The terms diffuse scattering, scattering, diffraction, crystallography, etc. are used somewhat inconsistently. Traditionally, diffraction was used to refer to the study of highly crystalline materials, where distinct Bragg peaks would be observed. If the material was a single-crystal, it would be thought of as crystallography, whereas if it was poly-crystalline, it would be a powder diffraction experiment. In this context, scattering was thus implicitly diffuse scattering: the unwanted background coming from disorder. This is similar to how scattering is used for visible-light: where light scattering refers to the diffusion of light through disordered media. SAXS (small-angle x-ray scattering) was so-named because traditionally the small-angle regime was used to quantify the diffuse scattering from disordered systems (such as polymers in solution).

However, as nanoscience has evolved, a wide variety of well-defined nanoscale structures became available. These structures give rise to well-defined peaks in the small-angle regime; these are diffraction peaks arising from the nano superlattice, strictly analogous to the wide-angle diffraction peaks one obtains for atomic or molecular lattices/crystals. However, these experiments were historically still called SAXS (or SANS) experiments, and thus GISAXS similarly inhereted the term scattering even when though it was very frequently used to study diffraction features. (They should have perhaps been called 'small-angle diffraction' experiments.)

Modern materials may be complex and hierarchical; they are studied simultaneously across a wide q-range, and may exhibit both diffraction peaks and diffuse scattering in both the small- and wide-angle. It is thus not obvious what to call these experiments or datasets.

An evolving trend in the x-ray and neutron communities to use the term scattering as a super-class, which includes all possible experiments where there is an interaction between a sample and radiation. Then, more specific terms can be used to describe the specific kind of experiment/data (diffuse scattering, inelastic scattering, diffraction, crystallography, etc.). However this is not a universal definition, and so 'scattering' remains an ambiguous term (either being shorthand for 'diffuse scattering', or being used to define the broad class of matter-radiation experiments).

Angle ranges

There is no unambiguous delineation between WAXS, SAXS, and USAXS. On some instruments, they even define an additional regime: MAXS (Medium-Angle X-ray Scattering) (e.g. if they have a three-detector setup). The following should only be taken as rough guidelines:

Technique	Angle range	q range	Size range
Backscattering	180° to 90°
Diffraction/XRD	90° to 5°	6 Å−1 to 0.3 Å−1	Angstroms to ~2 nm
WAXS	45° to 1°	5 Å−1 to 0.1 Å−1	Angstroms to ~6 nm
MAXS	8° to 0.08°	1 Å−1 to 0.01 Å−1	~0.6 nm to ~60 nm
SAXS	1° to 0.01°	0.1 Å−1 to 0.001 Å−1	~6 nm to ~100 nm
USAXS	0.05° to 0.0001°	0.006 Å−1 to 0.00003 Å−1	~100 nm to ~20 µm

GIXD

Grazing-incidence experiments collecting data at large angles may be called GIWAXS (Grazing-Incidences Wide-Angle X-ray Scattering), or may be called GIXRD/GIXD (Grazing-Incidence X-ray Diffraction). These terms are sometimes used interchangeably. On the other hand, GIWAXS may be more appropriate when discussing disordered or partially-ordered materials, whereas GIXRD may be more appropriate when discussing data with sharp diffraction peaks.

Crystallography

Crystallography typically refers to measuring a single-crystal sample to generate a 2D image with a large number of diffraction peaks. Peak indexing can be used to determine the symmetry and size of the unit cell. The peak intensities can then be used to fit for the probable electron-density distribution within the unit cell; i.e. to solve the crystal structure. Conceptually, a crystal is thus assumed to be a material that has a well-defined unit cell, which is repeated translationally throughout space (normally in all three dimensions). However, the more recent discovery of quasicrystals has forced a rethink of this definition. Quasicrystals do not have translational symmetry, yet they have well-defined local packing that is repeated throughout space, and indeed their diffraction patterns have well-defined peaks. Modernly, a crystal might instead be defined by as an ordered solid that exhibits an essentially discrete diffraction pattern.

• Carlos Basílio Pinheiroa and Artem M. Abakumov Superspace crystallography: a key to the chemistry and properties IUCrJ 2015, 2(1), 137-154. doi: 10.1107/S2052252514023550