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This is a very strong statement, and whilst it may not be true in all possible cases, to a large extent it is. Over the last century there have been enormous developments in the ability to determine the structure of materials, both in terms of average structures as well as localized structures at the nanoscale. However, almost all of these have focused on finding the positions of the atoms and the more important problem of experimental determination of the positions of the (ground state) electrons is much less well developed. It has been known for many years that accurate x-ray diffraction intensities contain information about the charge density; after correction for a number of well-understood experimental phenomena, the measured structure factors are the moduli of the Fourier transform of the charge density. The cross-sections for high energy electron diffraction (energies 100-400kV) are about 10⁴ times larger than those for x-rays, so one can obtain very good signal-to-noise intensity measurements in a Transmission Electron Microscope (TEM).

We therefore pose a Grand Challenge, namely experimental determination of local charge density in materials at the nanoscale. If one could do this it would open up substantial new areas of science in many diverse fields. We believe the time has come to attack this problem due in large part to the recent revolution in TEM with aberration-corrected instruments giving both much higher spatial resolution as well as substantially improved signal-to-noise in the data. The time has also come to tackle this problem for surfaces and defects, where recent results have shown that one can start to obtain this information.

Our strategy has several parts:

• Very careful studies using High-Resolution Electron Microscopy. Here we want to image the charge density changes in a material. While at the moment we are focussing on model systems such as Andalusite, the larger picture is to move beyond this, for instance to image charge density effects at bulk defecs such as dislocations.
• Very careful studies using techniques such as precession electron diffraction. This approach is more appropriate for changes averaged over larger regions of a few nm.
• Very careful studies of charge density changes at surface

Much of this work is done in collaboration with Professor Kirkland and Dr Castell at Oxford University, as well as others such as Professor Feidenhans'l in Denmark and Robinson in London

1. Diffraction refinement of localized antibonding at the Si (111) 7x7 surface
   J. Ciston, A. Suramanian, I. K. Robinson, and L. D. Marks, Physical Review B, 79, 193302 (2009)
   
2. Charge defects glowing in the dark
   B. Deng, L.D. Marks, and J.M. Rondinelli, Ultramicroscopy 107(4-5): p. 374-381, 2007
   
3. Experimental surface charge density of the Si (100)-2x1H surface
   Ciston J, Marks LD, Feidenhans'l R, Bunk O, Falkenberg G, Lauridsen EM, Physical Review B 74 (8): Art. No. 085401 AUG 2006
   
4. Structure of the SrTiO3 (110) 3x1 surface Enterkin, J., A. Subramanian, M. Castell, K.R. Poeppelmeier, and L.D. Marks, Nature Materials, 2010 doi:10.1038/nmat2636