Networks of Steps on Crystal Surfaces

Abstract

Scanning tunneling microscopy observations show that steps on vicinal surfaces near (110) missingrow reconstructed surfaces of metals such as Au and Pt tend to form networks. A simple microscopic model introduced here shows that these networks are unstable (or metastable) against faceting. This leads to the formation of ridges between rounded areas and of angles in the equilibrium shape of the (110) The free energy per unit of area of a crystal surface depends rather strongly on the surface orientation. Typically, especially at low temperatures, certain orientations corresponding to high symmetry directions in the crystal lattice have low free energies and appear as large flat areas (facets) in the equilibrium crystal shape (ECS).Orientations tilted over a small angle with respect to a facet are called vicinals and consist of steps separated by large terraces. The free energy of a vicinal is typically expressed as an expansion in the step density p ͑p ø 1͒.In this Letter we investigate the surface free energies of certain vicinals of missing-row (MR) reconstructed ͑110͒ facets of metals such as Au and Pt. We will show that these orientations are, in fact, not stable which leads to faceting, or in other words to the presence of sharp edges in the ECS [1]. Figure 1 shows a typical pattern of steps found on vicinal orientations of Au and Pt͑110͒ surfaces [2,3] (areas of equal contrast denote terraces of the same height). Instead of an array of parallel steps, as found ordinarily on such surfaces, one sees a pattern of zigzagging steps, which repeatedly touch each other at a collection of contact points. We call this pattern a network of steps, since we can think of it as two arrays of roughly parallel steps, making on average angles f and 2f, with the vertical direction in Fig. 1.Why is the surface forming this pattern? The explanation [3] is related to the large energy difference between two different types of steps which can be generated on the surface: the clockwise (CW) steps and the anticlockwise (ACW) steps, illustrated in the examples of Fig. 2. Scanning tunneling microscopy (STM) observations at room temperature show that ACW steps appear very rarely on the surface and CW steps, which cost lower energy, prevail [2,3]. In Fig. 2(a) we show two possibilities for the microscopic configurations of steps: on the left side the typical crossing pattern as observed in STM experiments; on the right side two pieces of isolated steps, coming close to each other in the given example. Figure 2(b) shows the cross section of the surface along the segment AB: going from A to B one meets a CW up step and a CW down step, with a change in the reconstruction state as shown in the figure. In the configuration on the right side of Fig. 2(a), the points C and D belong to the same terrace, and therefore belong to the same reconstructed state. Only a combination of a CW and an ACW step matches this requirement [ Fig. 2(c)]. The situation where four terraces meet in a single point is favored, since only

Anomalous Shape and Decay of Islands on Au(110)

“…Our observations confirm the recent prediction of a peculiar island shape on this surface, which features two sharp corners [2]. We show that the missing-row reconstruction (MRR), which is responsible for this shape, also modifies the decay of the islands, making the layer below a disappearing island break up into two separate regions.…”

“…This is because the meandering would introduce both (111) and (331) regions along the step, and the latter are high in energy. Under the assumption that (331) steps cannot be formed, so that steps along [001] can be only straight, Carlon and van Beijeren have computed the orientation-dependent free energy of steps on Au(110) [2]. They find that the steps indeed exhibit a distinct maximum in the free energy along [001] and that this orientation plus a (temperature dependent) range of step orientations around it is expelled from the equilibrium island shape.…”

Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type

“…the minimum of (11) corresponds to α = γ = 0 and the orientation p = q = 0 is unreconstructed, with free energy given by (14), which is negative as expected. So for this orientation our mean field theory predicts a phase transition where the reconstruction order parameters (α and γ) jump from ±1 to zero and the step free energy vanishes with a mean-field exponent 1/2 as can be seen from the free energies (22) and (27).…”

“…One finds: (54) which is valid to lowest order in an expansion around the (011) facet where q = p = 1. Comparing (54) with (14) one concludes that the mean field free energy reproduces the exact surface free energy in the neighborhood of the (011) facet to linear order in the step density.…”

“…Applying Eqs. (31) and (14) for p, q → 1 one finds that z = δ − 2C(β). Equating this to zero one obtains the so-called edge rounding temperature T ER from…”