Quantitative analysis of surface atom positions in a thick crystal as determined by a reconstructed exit wave

Atomic structures of an Au (110) 2 x 1 reconstructed surface were analysed quantitatively using an exit wave reconstructed by the three-dimensional Fourier filtering method in high-resolution transmission electron microscopy. To reconstruct the exit wave in a relatively thick crystal, a practical criterion was proposed in the present analysis. In the 'pseudo-exit wave' obtained by the proposed criterion, relaxation of surface atoms was clearly visible in the top three layers. The atoms' displacement was measured to be about 5-20 pm. For quantitative analysis of the atom column positions, image contrast calculations were performed using a structural model of the Au (110) reconstructed surface. Calculations confirmed that the reconstructed pseudo-exit wave could represent the atom column positions directly with an accuracy of several pm, even for a relaxed surface, provided the sample thickness was <7 nm.