Structure determination

Détermination de la structure (Fr). Strukturbestimmung (Ge). Determinazione della struttura (It). Determinación estructural (Sp). Определение структуры (Ru).

Crystal structure determination is a two-part process: (a) the determination of the size and shape of the unit cell (i.e. the lattice parameters) from the geometry of the diffraction pattern and (b) the determination of the lattice type and distribution of the atoms in the structure from the (relative) intensities of the diffraction spots.[1] In very simple words, to get a 3D representation of a molecular compound. In fact, it is the process of elaborating the three-dimensional positional coordinates (plus the three-dimensional anisotropic displacement parameters) of the scattering centres in an ordered crystal lattice. Where a crystal is composed of a molecular compound, the term generally includes the three-dimensional description of the chemical structures of each molecular compound present.[2]

Most structure determination techniques involve the diffraction of electromagnetic or matter waves of wavelengths comparable to atomic dimensions.* Bragg’s law specifies the condition for plane waves to be diffracted from lattice planes. The diffracted radiation passing through a crystal emerges with intensity varying as a function of scattering angle. This variation arises from constructive and destructive interference of scattered beams from the planes associated with the different atoms present in the lattice. The result is seen by an imaging detector as a pattern of diffraction spots or rings.

Among diffraction-based techniques are:

· X-ray diffraction (single-crystal, fibre, powder)[3]

· Electron diffraction (Nano-crystals, selected area, convergent beam)[4]

· Neutron diffraction (single-crystal, powder)[5]

· Gamma-ray diffraction Other techniques for three-dimensional structure determination that are complementary to diffraction methods include

· transmission electron microscopy (CryoEM for example)

· nuclear magnetic resonance spectroscopy (used largely for biological macromolecules in solution)

*Atomic diameter range is 62 pm (He) to 520 pm (Cs) (1 picometer (pm) = 1×10−12 m.[6]

Structure determination using electron diffraction techniques has a great advantage over all other diffraction methods. That is, there is no need to grow “bigger” crystals that could produce diffraction conditions under the radiation source used. For 3D-ED experiments it suffice (or even it is necessary) that the nanoparticles are in the range of 20 – < 1000 nm. This range of particles is almost inaccessible with any other kind of diffraction technique.

References:

1 C. Hammond, “The Basics of Crystallography and Diffraction”, 3rd Ed., Oxford University Press Inc., New York 2009.

2 “Structure determination”, accessed on September 21, 2020, https://dictionary.iucr.org/Structure_determination

3 U. Shmueli, “International tables for crystallography”, Volume B, 2nd Ed., Springer, Dordrecht 2006, 534-551. 

4 Id., 552-556.

5 Id., 557-569.

6 “Atom”, accessed on September 21, 2020, https://en.wikipedia.org/wiki/Atom