What I have read is that the contents of the unit cell affect the intensities, but how? I am also unclear on why you need to know the symmetry of the unit cell, what is that used for? I understand segments of this topic (x-ray crystallography) but I am having trouble piecing all the segments together to make a complete picture. I've been spending hours every day on this on this, any help would be really appreciated!


1 Answer 1


Two questions here:

1) What does the symmetry of the crystal mean?

The symmetry of the unit cell is the symmetry of the crystal. Its really useful thing to know about the crystal in practice. You can always pretend that any crystal is space group P1 - with no internal symmetry. This implies half of the diffraction data is needed to get a complete set. Why half? The Laue symmetry of typical X-ray diffraction shows that the diffraction should be centrosymmetric I(hkl) = I(-h,-k,-l).

If you do this and the crystal has more symmetry than that you are collecting too many data. Here I take the example of a 2-fold axis. Along that axis the space group shows that the symmetry of the crystal should be 4 fold along the x axis (x axis is chosen by convention):

I(hkl) = I(-h,-k,-l) (as above) and I(hkl) = I(h,-k,-l)

This fact means we actually can collect less data and know the crystal diffraction pattern easily. In practice we collect from more than just the unique data, but the more diffraction data we take it also means that we can assume equivalence and have taken more measurements, giving us better experimental accuracy for the same effort. It also means that when we build a molecular model for structure in the crystal we have a simpler model - one only creates a model for the unique assymmetric unit of the crystal unit cell. Fewer atoms in the structure, fewer degrees of freedom and less error in our resulting model.

There's more... screw axes 2(1), 3(1) and non primitive lattices create systematic absences which helps us collect more accurate data and do refinement more easily in the same vein... but maybe this gives you an idea...

2) how does the unit cell contents reflect the diffraction intensities

X-ray scattering from crystals is the result of the photon causing an elastic scatter from atomic, inner shell electrons - Bragg scattering. By considering the crystal as a series of slits in 3 dimensions, it can be shown that the average positions of atoms in the crystal reinforce each other to give the reciprocal lattice that is diffraction data in 3D.

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In the picture above from Wikipedia you can see a beautiful protein crystal diffraction pattern. The rings of spots are a spherical section from a 3D orthorhombic lattice of spots.

Rather than digress into the reason the diffraction appears this way, back to your question: what causes the intensities to vary from spot to spot and crystal to crystal. The crystal lattice contains atoms which are in the same position in every unit cell which are creating the diffraction by Bragg scattering. As such, it is the positions, relative electrons in orbit that dictate the diffraction intensities measured.

The models built to model diffraction typically translate a set of atomic positions to the structure factors (square roots of the diffraction intensities), but this is an approximation that works pretty well - the full model is not atomic positions, but an electron density function in space.

There are other sorts of scattering methods, more that could be said about all these subjects, but I hope that gives you some help with your specific questions. If you want clarifications in this, I can edit the answer from comments...


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