Surface energy and surface stress on vicinals Cu(1 1 n)

Abstract

The step energy and the step stresses are calculated as a function of the distance L between steps for vicinals Cu(1 1 n). In addition to the well-known Marchenko–Parshin model where the steps behave as dipole forces, we show that the steps are displaced in the direction parallel to the terrace with respect to the dipolar displacements. This results from the application at the step of a monopole force, Fb, whose modulus decreases as 1/L. The extra displacement due to Fb does not modify the step energy with respect to the MP model but is linked to the presence of the interaction term in the step stresses, that vary as 1/L. Because the step stress is calculated with respect to the nominal surface stress, we calculate the diagonal surface stresses in both the vicinal system (x, y, z) where z is normal to the vicinal and the projected system (x, b, c) where c is normal to the nominal terrace. Moreover, we calculate the surface stresses by using two methods: the first called the ‘Force’ method, from the surface pressure forces and the second called the ‘ΔE’ method, by homogeneously deforming the vicinal in the parallel direction, x or y, and by calculating the surface energy excess proportional to the applied strain. We confirm that the variation of the step stress in the tensor direction ‘xx’ is the same between the two methods while it is different in the direction ‘yy’. In the ‘Force’ method, the step stress in the direction ‘yy’ is the sum of the two step stresses in the directions ‘bb’ and ‘cc’. In the ‘ΔE’ method, the step stress in the direction ‘yy’ equals this calculated in the direction ‘bb’ (parallel to the terrace) in the ‘Force’ method, this in the normal direction ‘cc’ being excluded.