In 1998 I had the following e-mail question from a course member:

Chaper 7 of our book speaks of anomalous dispersion saying, "... the technique is too sophisticated to discuss here". After learning and experiencing the things that we have thus far in the course, I can no longer be satisfied with such an answer, especially out of a textbook. I think this is the same technique you mentioned today in class and I am interested in knowing how it works.

This is definitely NOT something you need to know for Chem 125. But it is admirable that you want to know, so here is the problem and its answer, and a connection with Prelog:

As we discussed, when two atoms are scattering an x-ray wave, and they are not in a common plane normal to the "scattering direction", their scattered waves can be more or less out of phase with one another, giving a resulting wave that depends in intensity on the distance between the atoms measured along the "scattering direction", on the scattering angle, and on the wavelength of the x-rays. Unfortunately the resulting intensity does not depend on which atom is in front. That is, the size of the resulting wave depends on the distance between the atoms, but not on its sign. You might imagine that with a large set of atoms and the choice of many scattering directions to sample, it would be possible to resolve this ambiguity, but this is not so. No matter how many scattering directions you study, the differences in "geometric" phases, and thus the scattered intensity, will always be the same for the object studied as for the one that would have all three coordinates of each atom changed in sign. (Changing an odd number of signs generates an enantiomer).

Thus it would seem impossible to distinguish by diffraction between an object and its enantiomer.

We talked about the electron being driven to vibrate by the x-ray wave and reemiting radiation. Careful consideration shows that there is a change of phase between the driving wave and the scattered wave. If this phase change is the same for all atoms, it makes no difference in how the scattered waves from each atom reinforce one another in generating a net scattered wave, and for many purposes it may be ignored.

BUT, if different atoms in the sample have different amounts of phase change between the driving x-ray wave and the driven electrons, then this contribution must be added to the amount of phase difference that is due to their relative geometric positions. When one atom is in front, the overall phase difference influencing the amplitude of the scattered wave will be a little greater than when the other one is in front. Thus if you turned the sample over to scatter from the other side of the same set of planes, you would change which atom is in front, and by comparing the scattered intensity, you could tell the sign of the distance between the atoms, and thus the handedness of the system. Usually this difference is small and requires very careful measurement. Atoms of elements that are close in the periodic table to the metal used in generating the x-rays can be substantially different from atoms of normal elements (like C, N, O, etc.). This is why Bijvoet used the Rb salt of tartaric acid.

If all the atoms in the sample were Rb, there would again be no difference in relative phase after flopping the sample over. Using anomalous dispersion requires having DIFFERENT kinds of atoms so you can tell which is in front. A difference as subtle as between O and C has been used, but this requires very careful work. Because the relative phase change for given atoms depends on x-ray wavelength, it is possible by changing the x-rays to make a given system easier to work with. When Bijvoet used Rb, he generated the x-rays using a zirconium target in the x-ray tube. Since Zr is only three elements beyond Rb in the periodic table the phase is particularly anomalous.

For a good, brief treatment of this subject see J.M. Bijvoet, A.F. Peerdeman, and A.J. van Bommel, Nature, 1951, 168, 271-272; for a really complete, satisfying treatment see J.D. Dunitz, X-Ray Analysis and the Structure of Organic Molecules, (Cornell, 1979) pp.129-148.

There is no ambiguity in the x-ray structure of a racemic crystal, where both the molecule and its mirror image are present so that for every atom with coordinates x,y,z in one molecule there is an atom in the enantiomer with the same magnitude of the coordinates, but in which an odd number of signs have been changed, e.g. x,y,-z, or -x,-y,-z. It is clear from x-ray which enantiomer is oriented which way with respect to the faces of the macroscopic crystal. Let's define the handedness of the crystals surfaces by saying that the right-handed enantiomer is oriented toward "right-handed surface" of the crystal, while its enantiomer is oriented toward the opposite "left-handed surface".

If you now take some third molecule which is chiral and resolved, it should adsorb more tightly on one of these faces than on the other, because it matches better in structure with the portion of the molecules that are exposed on that face than on the mirror-image face. If you are confident that you know the mechanism of adsorption, you can predict whether adsorption should be tighter between the right-handed crystal surface and the right-handed version of the third molecule or between the left-handed crystal surface and the right-handed version of the third molecule. For example, on the surface of a racemic amino acid crystal that exposes the hydrogen, ammonium, and carboxylate groups linked to right-handed carbons (but exposes the other substituent, the R group, of the left-handed molecules), it is plausible that one could bind the complementary hydrogen, ammonium, and carboxylate groups attached to the left-handed carbon of a different amino acid (to give a packing that is closely analogous to the interface between enantiomeric layers in the pure racemic crystal), but not the R' group of the enantiomer of the different amino acid, which doesn't look at all like the R groups in the pure crystal.

Suppose you are sure that association should be tighter between the left-handed surface of the crystal and the right-handed version of the foreign amino acid, but you observe that the foreign molecule is adsorbed on the right-handed face of the crystal. The obvious conclusion is that the foreign molecule is left-handed. Thus the x-ray structure of a racemic crystal may be used together with determination of selective molecular adsorption to establish the handedness of the adsorbed molecule.

Preferential absorption of the foreign molecule can be detected either by its ability to retard growth on that crystal facet (because, when it is present on the surface, it will be difficult to add the next layer of normal "host" molecules), or by cleaving the resulting crystal and analyzing the two halves to find which has included the foreign molecule.  (There are other ways as well, for example the foreign molecule might be colored and dye only one crystal face.)

By this approach one could have established absolute configurations decades before Bijvoet's work with anomalous scattering. Of course you would have had to be confident about predicting adsorption, but you would have been confident if one part of the adsorbed molecule were very similar in structure to the corresponding part of one enantiomer of the host crystal, as in the case of amino acids.

A really imaginative, clever group of Israeli chemists devised this technique and used it in 1982 to determine the absolute configuration of several amino acids by their ability to adsorb on crystals of racemic glutamic acid or glycine. They measured solute absorption by its tendency to inhibit normal growth of a crystal facet in a supersaturated solution. Their work confirmed results based on anomalous x-ray scattering. (see Addadi, Berkovitch-Yellin, Weissbuch, Lahav, and Leiserowitz, "A link between macroscopic phenomena and molecular chirality: crystals as probes for the direct assignment of absolute configuration of chiral molecules", Topics in Stereochemistry, 1986, 16, 1-87)

As in the cases of van't Hoff and Koerner, their imagination was necessary in part for seeing exactly how to do the experiment, but even more importantly for seeing that it might in principle be doable. Almost everyone else had swallowed the facile dogma that it would be impossible to determine absolute configurations using normal x-ray structures and macroscopic chemical observations.  When Leiserowitz presented this work for the first time to a gathering of the world's experts on stereochemistry at an international meeting in Switzerland, they thought he was presenting this outlandish concept with the intention of pulling their legs (since the annual program traditionally included one such "joke" lecture).

Notice that this was not so long ago. Plenty of analogous dogmas must still be circulating unrecognized. Keep your eyes and your mind open.