Experimental and calculated structure factors from a previous synchrotron diffraction measurement on synthetic fayalite have been converted by an inverse Fourier transformation to difference electron (deformation) densities (DED). These were processed in a revised 3D-display program giving hyperareas of DED floating in space around the iron positions M1 and M2 within the fayalite unit-cell and spanning a cluster size of 6 and 4 Å, respectively. These relatively wide limits are due to the different site symmetries and had been proposed by earlier DFT (density functional theory) calculations. From the different hyperareas the supposed charges were integrated in space and processed to electric field gradients (EFG) on M1 and M2 using a point-charge model. The two EFGs were compared with respect to the system of crystallographic axes with those obtained from published single-crystal Mössbauer measurements (experimental EFGs), yielding excellent agreement within ±5° and surpassing even the DFT results. This study reports the procedure and the conditions of success of the underlying semi-quantitative method, which is halfway between theory (DFT) and experiment (diffractometry) and is promising valuable results on many other compounds. The term “nanoscope” for the graphical representation may be justified due to its high spatial resolution.

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