Disorder determines how easy it is to locate atoms in 3D

Recent advances in electron microscopy, and particularly electron tomography, have suggested the possibility of locating the atoms that make up solids in three-dimensions with picometre precision. However, the only experimental reports so far have been on thin crystalline materials. In this paper, we explain using an information theoretical approach why it is relatively easier to reconstruct atoms in crystals by electron tomography than to reconstruct atoms in amorphous materials. The ordering of atomic columns in crystals specifically sets up imaging conditions at critical orientations of the crystal where the most important information about the positions of the atoms is pronounced. These special orientations are not found in amorphous materials due to the disordered arrangement of the atoms. As a result, the recovery of all atom positions in an amorphous material poses significantly greater challenges, though our modelling results indicate it may be  easible provided the atoms remained fixed at their positions throughout an experiment.

Figure: Atomic-resolution atom positions of model structures reconstructed using electron tomography used to exemplify key properties of the newly presented interpretive theory.