Sublimation-induced shape evolution of silver cubes.

Surface free energy is a criterion usually employed to identify the stability of a solid surface. Nanoparticles of face-centered cubic (fcc) noble metals are usually enclosed by the lowerenergy surfaces such as {111} and {100}, because these surfaces are believed to have the lowest energy, typically following g{111}<g{100}<g{110}. This criterion is proposed based on the assumption that the surface free energy is largely determined by the coordination number of the surface atoms at the top layer, which in general can explain the formation of various metal nanoparticles such as Au, Pt, and Ag. However, one of the simple manifestations of the presence of a surface is the relaxation of atoms located at the first, second, and even deeper surface layers, either inwards or outwards with respect to bulk terminated positions, which can contribute to the surface free energy in a realistic situation. As a result of surface relaxation that may sensitively depend on temperature, the surface free energy could be dramatically minimized. Due to the high density of surface atoms and their relatively high coordination numbers, both experiments and theoretical calculations manifest that relaxations of metal {111} surfaces at room temperature are expected to be minimal. Lowenergy electron diffraction (LEED) and high-energy ionscattering (HEIS) studies found that oscillatory relaxation of the interlayer spaces occurred in {110} surfaces. With the increase of temperature, the contribution of the lattice vibration to the surface free energy increases. As we know, the creation of a crystal surface means breaking of bulk translational symmetry, which implies that an anharmonic behavior of the restoring forces should be expected. Such anharmonic effects become increasingly crucial to the surface stability when the temperature is close to the melting point,