Modelling of transition and noble metal vicinal surfaces: energetics, vibrations and stability

Abstract

The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces, i.e., surface energy, step energy, kink energy and electronic interactions between steps, is studied at 0K from electronic structure calculations in the tight-binding approximation using a s, p and d valence orbital basis set. Then, the surface phonon spectra of copper are investigated in the harmonic approximation with the help of a semi-empirical inter-atomic potential. This allows to derive the contribution of phonons at finite temperatures to the step free energy and to the interactions between steps. The last part is devoted to the stability of vicinal surfaces relative to faceting with special attention to the domain of orientations (100)-(111). Semi-empirical potentials are shown to be not realistic enough to give a reliable answer to this problem. The results derived from electronic structure calculations predict a variety of behaviors and, in particular, a possible faceting into two other vicinal orientations. Finally, temperature effects are discussed. Comparisons are made with other theoretical works and available experiments.

Energy of Step Defects on the TiO2 Rutile (110) Surface: An ab initio DFT Methodology

“…In Section 1 of the Supporting Information, we elaborate further on this issue and provide a detailed discussion of why linear fitting approaches to surface energy estimation should be avoided in materials like TiO 2 rutile where surface-surface interactions are strong. Alongside this obvious practical limitation, we also argue that using a linear fitting approach in this context has some questionable underlying assumptions because it fails to properly recognize surface energy oscillations in TiO 2 rutile as a non-random, 44 , and direct extraction of step energies from vicinal slabs 45,46 , where, in all cases, it was ensured that total surface energies were fully converged at the slab thicknesses used. The difficulty with systems like TiO 2 rutile is that linear fitting techniques do not work, and neither does the "brute force" approach of using arbitrarily large slabs because of the very long-ranged nature of surface-surface interactions.…”

All-electron first-principles investigations of the energetics of vicinal Cu surfaces

“…26 The numbers n s ͑p͒ and n s ͑ϱ͒ are the total number of bonds in the sth coordination sphere broken by the vicinal and flat surfaces, respectively. Due to the short range of the EPP parameters, n step,s becomes a constant as soon as p overcomes a value p ϱ , which is usually very small: most often, according to Vitos et al, 21 p ϱ = 2.…”

“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] For example, Methfessel et al, 11 employing the full-potential linear muffin-tin orbital ͑FP-LMTO͒ method, found a roughly parabolic behavior for the surface energy of the low-Miller-index ͑flat͒ surfaces across the 4d transition-metal series, which was explained in terms of the d-band occupation. Almost at the same time, Skriver and Rosengaard, 12 employing a Green's-function technique based on the LMTO method, discussed the trends exhibited by the surface energies of flat surfaces of the alkali, alkaline earth, divalent rare-earth, 3d, 4d, and 5d transition and noble metals, as derived from the surface tension of liquid metals.…”

Elastic relaxations and interactions on metallic vicinal surfaces: Testing the dipole model

“…When the steps are close together, the number of allowed configurations are reduced, and this reduction of entropy is equivalent to a step repulsion. Steps interact also electronically through the modification of the density of states 3,4 , electrostatic ally due to the presence of electrostatic dipoles at the steps 5,6 , and thermally through the modification of their vibrational free energy 7 . They also interact elastically through the long range relaxation fields generated by local atomic relaxations at the steps 8 .…”