X-ray crystal structure resolution

Before describing the various phases in the resolution of a structure, it is worth recalling that the theoretical model used to establish resolution methods involves assumptions that must be formulated precisely in order to clearly see the limits of the method.

Atoms have a spherical electronic distribution. This assumption is reflected in the tables giving the atomic scattering factor. We know that X-rays interact with electrons: in a way, they count the electrons of the different atoms and we obtain the barycenter of the electronic cloud of each atom. This point has no reason to coincide with the nucleus; however, the higher the atom's atomic number, the smaller the deviation. Under these conditions, the distances measured between light atoms, Li and H for example, even if the method gives them with an accuracy of 0.001Å (1Å = 0.1 nm), cannot be considered without a certain amount of discernment.

Note that neutrons ignore this difficulty because they interact with nuclei.

Thermal vibrations of atoms are considered centrosymmetrical, but not necessarily isotropic. In fact, the observation time is very long compared with the vibration period, so that the observed electron density is a time average. Static disorder is linked, for example, to the occupation of the same crystallographic site by two atoms with similar dimensions but different atomic numbers; dynamic disorder is that of a rapidly moving group of atoms in the crystal, for example a CH ₃ group rotating around its ternary axis.

Atoms are thought to vibrate independently of one another. Infrared spectrometry tells us that this is not true. Attempts have been made, at great mathematical cost, to get a closer look at reality. It doesn't seem worth the effort. Sometimes, when studying a molecule whose bond organization gives it a particularly rigid character, such as camphor, we can implement a model where the molecule is taken as a single rigid block.

Finally, the model assumes a perfect infinite crystal. The crystal under examination is necessarily finite, at most 2 mm at its largest dimension. In fact, the crystal has a so-called mosaic structure, it is said to be ideally imperfect; it is made up of micrometer-sized parcels that are disoriented from their neighbors by a few seconds of arc. The average orientation of these blocks corresponds to the orientation of the crystal. Each block is perfect and diffracts independently of its neighbors. This particular situation makes it possible to apply kinematic theory, which states that the intensity diffracted by a plane is proportional to the square of the modulus of the structure factor.