Thermal expansion near plane and stepped surfaces

A theory of the thermal expansion of the plane and (11n) stepped surfaces of fcc crystals is presented. The temperature dependent relaxations arise from cubic anharmonic terms in the crystal potential energy. We show that the thermal expansion depends on the positions of the atoms with respect to the steps and is greatest for the atom of the upper corner. The knowledge of these new atomic positions at each temperature allows us to calculate new atomic force constants and then new vibrational properties at this temperature. The application is made for a Ni crystal for which we give the corrections, due to the thermal expansion, on the mean square displacements of stepped surface atoms. The variation with temperature of the optical modes due to a light monolayer is also presented.