Mosaic structure
The mosaic structure (also mosaicity ) is a property of single crystals that is very important for structural analysis by X-ray diffraction . While perfect three-dimensional translational symmetry is assumed for perfect single crystals, a mosaic structure is assumed for real crystals, i.e. H. the crystal is made up of very small crystallites (mosaic blocks), which have a size of approx. 100 nm and are slightly tilted and offset against each other . A crystal consists of hundreds or thousands of such blocks. The model of the mosaic structure goes back to the work of Charles Galton Darwin , which he published in 1914.
Emergence
The mosaic structure is created during crystal growth ( crystal growing ), but is also influenced by how the single crystal was treated before and during assembly on the single crystal diffractometer . There have been reports of protein crystals that briefly removing the nitrogen cooling ("annealing") improved the mosaic structure in some cases and worsened it in other cases.
impact
In the case of a perfect crystal, the scattering amplitudes would have to be added up over the entire crystal and would be so large that the Born approximation no longer applies. The reflections would be very sharp, but very numerous due to multiple scattering, making evaluation more difficult.
In the real crystal, only the elementary waves of one block interfere with each other, while the contributions of different blocks do not add up with their amplitudes, but with intensities. The mosaic structure can be explained in reciprocal space by the lattice point hkl not lying on a fixed node, but distributed around it. This distribution is often described by a Lorentz or Gaussian distribution . In many crystals, however, the mosaic structure is not isotropic, but anisotropic. Typical values for the mosaic distribution in crystals of small molecules and proteins are 0.2–1.0 °, but there are also reports of 0.01 ° for a protein. Such a small mosaic distribution is expected with inorganic compounds such as minerals or metals.
Measurement
Because the mosaic structure leads to the broadening of the X-ray reflexes, a mosaic distribution is often indirectly derived from the reflex profiles. A direct measurement is possible , for example, using the Renninger effect. This determines both the size of the mosaic blocks and the mosaic distribution.
literature
- RW James: The optical principles of the diffraction of X-rays (The Crystalline State, Vol. 2), G. Bell and Sons, London (1948), chapter 6.
- LA Aslanov, GV Fetisov, JAK Howard: Crystallographic instrumentation, Oxford University Press (1998), p. 235.