Pascal Hecquet

Step interactions and surface stability for Cu vicinals

Abstract The surface energies are computed for vicinals of Cu(100), Cu(110) and Cu(111) using a molecular dynamics technique modified to minimize the surface energy at zero temperature. The steps are simple, double or triple. A many-body, semi-empirical potential derived from tight-binding models is used. The step energy and the step-step interaction are deduced. The energy of multiple steps is found to be roughly proportional to the step height, except for vicinals of (111) with (111)-type step edges. On Cu(115) the energy for displacing a single step is found to be very small. As a general rule, the energy of perturbed configurations cannot be deduced from the surface energy of macroscopic facets.

Temperature dependence of the atomic relaxations and vibrations on a stepped surface: a molecular dynamics study of Cu(1,1,19)

We have studied the relaxations and vibrations of atoms near the surface of a (1,1,19) copper crystal. For this purpose, we have performed molecular dynamics simulations using a semi-empirical many-body potential derived from tight binding models. The total displacement field can be described as the sum of a mean surface relaxation and a specific contribution of the steps, which is maximal for step edge atoms (0.08 A) and corner atoms (0.06 A). Whereas step edge atoms relax towards the inner terrace and towards the bulk, corner atoms relax in the opposite direction, leading to vortex-like structures in the displacement field. We demonstrate that, as predicted by continuous elasticity, the displacement field induced by steps is equivalent to the one created by a line of dipoles on a flat surface. In the particular case studied here, the equivalent dipole density is 3.3×10−10 N. The specific relaxations of kink atoms have been calculated. We have also studied the variation of the relaxations as a function of temperature (T). A strong effect is predicted for inner terrace atoms: when increasing T, the contraction of the first interplanar distance, with respect to the bulk value, progressively cancels and turns to an expansion at high T. This is not the case for the specific contraction of step edge atoms that is nearly temperature independent. This latter behaviour is related to very strong longitudinal correlation between vibrations of the step edge atom and of its nearest neighbour inside the terrace. In the same time, whereas the vibrations of inner terrace atoms are found to be isotropic, the ones of step edge atoms are anisotropic, with a larger component along the direction parallel to the terrace plane and perpendicular to the step edge, the other components being the same as for inner terrace atoms.

Stress on vicinal surfaces

Abstract We develop an understanding of the variation of the surface stress tensor with facet orientation within the framework of elasticity theory. The surface stress behaves very differently from the surface energy. It is known that the elastic repulsion between steps behaves as d −2 and contributes a tan 3 θ term to the surface energy, with d the step–step distance and θ the vicinal angle. We show that the presence of steps induces a strong tan 2 θ term in the surface stress. Atomistic calculations confirm this behavior.

Energetics of surface defects: towards a simplified model

The energetics of some surface defects for the (111), (100) and (110) surfaces of Cu are calculated using a many-body potential. These formation energies allow a lattice-gas model to be defined, which is very useful in performing large-scale Monte Carlo simulations in order to study the morphology of surfaces within realistic energetic models. We show that some defects are very sensitive to the curvature of the site energy as a function of the coordination number, α. In the case of the potential used for Cu in the present study, the site energy is an almost linear function of the coordination number in a wide range of values of α, allowing an easy and accurate determination of the formation energy of surface defects.

A possible re-entrant phase transition at the (001) surface in L12 structure

Abstract The relative stability of the different terminations of the (001) surface of A3B compounds with the L12 structure is investigated as a function of both the temperature and the relevant energetic parameters. This is performed using the Ising model and a mean-field approximation. For a strong tendency to A surface segregation, the termination of the A3B compound is an almost pure A surface plane in the whole range of temperatures corresponding to the bulk ordered state. Conversely, for a large tendency to B segregation, the stability of the mixed AB termination is predicted. However, between these two domains, a complex behavior is predicted. One or even two transitions, leading to a re-entrant behavior, can occur as a function of the temperature between the pure A and the mixed AB termination, all these transitions being located in the bulk ordered state. It is suggested that Ir3V is a good candidate to exhibit such a rather surprising behavior. We also investigate the influence of some deviation with respect to the stoichiometry. A transition from the mixed AB to the pure A termination is predicted when the bulk concentration in A element increases.