The reconstruction matrix has area multiplier . A bulk-terminated monatomic surface would therefore contain atoms in that projected cell, whereas the reconstructed top layer contains . Its density increases byThe denser layer can reduce the large tensile surface stress and improve the outermost layer's preferred metallic bonding, at the expense of registry/domain-boundary and elastic costs. Surface atoms need not prefer exactly the same equilibrium spacing as bulk-coordinated atoms.
Close-packed layers occupy one of three lateral registries, conventionally A, B and C. Hexagonal close packing has ABAB stacking, while face-centered cubic stacking is ABCABC. On a bulk-terminated (111) terrace the two kinds of threefold hollow differ by subsurface registry: an hcp hollow places an atom above a second-layer atom, while an fcc hollow continues the ABC sequence.
Compressing the top Au layer makes its registry drift relative to the unreconstructed layers. Parts of the cell occupy fcc hollows, others hcp hollows, and transition strips pass through less favorable bridge-like positions. Those registry changes are associated with partial-dislocation/domain boundaries. Varying local coordination and repulsion from the substrate cause vertical relaxation, producing the observed corrugation rather than an entirely flat shifted sheet.
The Au(111) surface has three equivalent in-plane directions related by rotations. A reconstruction that contracts along only one direction creates anisotropic stress. Periodically changing boundary direction among equivalent orientations redistributes that strain and lowers its long-range elastic cost, while boundary formation and bending carry their own energy cost.
The resulting compromise produces the characteristic herringbone arrangement. Threefold symmetry explains the equivalent turning directions; a balance of elastic relaxation and boundary costs, rather than symmetry alone, sets the finite repeat distance.
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