Surface atoms have fewer interatomic bonds than those in the bulk that they often relax and reconstruct on extended two-dimensional surfaces. Far less is known about the surface structures of nanocrystals. Here, we show that coherent diffraction patterns recorded from individual nanocrystals are very sensitive to the atomic structure of nanocrystal surfaces. Nanocrystals of Au of 3-5nm in diameter were studied by examining diffraction intensity oscillations around the Bragg peaks. Both results obtained from modelling the experimental data and molecular dynamics simulations strongly suggest inhomogeneous relaxations, involving large out-of-plane bond length contractions for the edge atoms (similar to 0.2 angstrom); a significant contraction (similar to 0.13 angstrom) for {100} surface atoms; and a much smaller contraction (similar to 0.05 angstrom) for atoms in the middle of the {111} facets. These results denote a coordination/facet dependence that markedly differentiates the structural dynamics of nanocrystals from bulk crystalline surfaces.