 Solution

The reconstruction matrix has area multiplier $|\det M|=44$. A bulk-terminated monatomic surface would therefore contain $44$ atoms in that projected cell, whereas the reconstructed top layer contains $46$. 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.