AN INVERT SOLUTION TO AN INVERSE PROBLEM

Amorphous materials — found in solar panels and DVDs, spectacles and shells — all share one thing in common: their structures have no-long range order. And because of this, crystallography is powerless to work out where the atoms are.

Or so one might think. It has been known for some decades that total scattering experiments can be used to measure the pair distribution function (PDF), even for amorphous materials. The PDF reveals the distribution of inter-atomic separations in a material, but contains no direct information about the orientations of atoms in three dimensions. A long-standing question in the amorphous materials community has been whether there might actually be enough information in the PDF to determine the structure of amorphous materials. A classic inverse problem.

The problem is that quite different structures can give rise to essentially identical PDFs. At face value, this should put to rest any hopes of inverting the PDF data.

But what we have now shown is that the missing piece of the puzzle is knowing the number of unique atomic environments in the material  — precisely the information readily obtained from NMR experiments. We call the technique  — perhaps more than a little cheesily — the INVariant Environment Refinement Technique (INVERT). Try and refine a model using PDF data alone, and things fail often spectacularly; demand that only a specific number of atomic environments evolve, and the solution seems to fall into place.

Early days so far, but INVERT seems to work surprisingly well on nanostructured materials and network glasses alike, even with more than one unique environment. Some animations showing the structure solution of C60 and S12 from PDF data are available for download.

Structure determination of disordered materials from diffraction data. Phys Rev Lett 104, 125501 (2010)

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