Dear Dr Duax,

In your editorial on holography with X-rays, you state that the homometric solution belongs in the same category as the Loch Ness monster and the Abominable Snowman. If you write to any major museum of natural history, I am sure that a request for even the thinnest slice of the mentioned species will bring you a negative reply. So why not ask for a sample of the mineral tapiolite FeTa₂O₆ instead? The structure of this mineral is simply a three-fold superstructure of the rutile type and tapiolites with partial cation disorder appear to exhibit homometry [Acta Cryst. (1995), A51, 514-519]. Our results on tapiolite can probably be extended to other three-fold superstructures caused by cation ordering, of which there are many known examples among minerals and ceramic materials. Even if homometric structures turn out to be so rare that X-ray crystallographers need not really worry, I think that little is gained by pretending they do not exist at all.

Dear Staffan,

My remarks with respect to homometric solutions were made in reference to the undue emphasis placed upon the phenomenon by early opponents of direct methods who believed the work of Hauptman and Karle was the heretical ravings of upstart mathematicians and physicists with little understanding of chemistry and the laws of crystallography. The fearful specter raised was that direct methods would lead to an incorrect solution, that was chemical nonsense but mathematically indistinguishable from a correct one and that correct solutions would be missed. As I understand it your "homometric structures" are partially disordered atomic arrangements that satisfy the same diffraction pattern. I believe our understanding of what "homometric" means is colored by our experience.