Chapter 1
Surface Electrochemistry with Pt Single-Crystal Electrodes

Victor Climent and Juan M. Feliu

1.1 Introduction

The sensitivity of electrochemical processes to the crystallographic structure of the electrode surface is now a well-established fact demonstrated for numerous reactions. Except for outer sphere processes, the majority of electrochemical reactions involve the formation of adsorbed intermediates. In fact, the concepts underneath the electrocatalytic phenomena are intimately linked to the existence of strong interactions of reacting species and the electrode surface [1]. In this case, adsorption energies are very sensitive to the geometries of the adsorption sites, strongly affecting the energetic pathway from reactants to products and, in consequence, the rate of the reaction.

In addition, the properties of the interphase are affected by the crystallographic structure of the electrode. Considering that the electron transfer has to take place in the narrow region that separates the metal from the solution, it is easy to understand that the interfacial properties will also have strong effect on the rate of most reactions. Anion-specific adsorption, distribution of charges at the interphase, and even interaction of water with the metal surface are aspects of the interphase that need to be considered in order to get the complete picture about the influence of the structure on the electrochemical reactivity.

In this sense, the approach of interfacial electrochemistry has been proved as very convenient (and inexpensive) to study the interaction of molecules and ions with metal surfaces. An iconic moment in the development of electrochemistry as a surface-sensitive approach is the introduction of the flame annealing methodology by the French scientist Jean Clavilier [2, 3]. Earlier attempts to obtain a surface-sensitive electrochemical response with well-defined metal surfaces resulted in dissimilar and contradictory results [4-8]. The flame annealing technique not only offered a much simpler method in comparison with the more complex approaches based on ultrahigh-vacuum (UHV) preparation of the surface but also offered the opportunity to perform the experiments in many different laboratories across the world, soon proving the reproducibility of the results. Immediately after the introduction of this methodology, some controversy arose because it revealed aspects of the electrochemical behavior of platinum not previously reported (the so-called unusual adsorption states) [9-11]. This initial controversy was soon resolved, and now the correct electrochemistry of platinum single crystals is well established and understood [11, 12].

The knowledge gained about the electrochemical reactivity of platinum from the studies using well-defined electrode surfaces has resulted in very useful understanding of the behavior of more complex electrode structures, such as polycrystalline materials and nanoparticles.

Figure 1.1 2D representation of the process of cutting a crystal through a plane, resulting on a stepped surface.

1.2 Concepts of Surface Crystallography

An atomically flat surface is generated by cutting a single crystal in a desired orientation with respect to the crystallographic axis of the crystal. The ideal surface that is obtained by such process can be understood as the result of removing all the atoms whose center lies on one side of the cutting plane and keeping all the atoms lying on the other side. Because the cutting plane does not necessarily pass through the center of all of the atoms, the resulting surface is not perfectly flat, and, in the more general case, the atomic centers of the atoms will define a regular distribution of terraces separated with steps which may also contain some corners or kinks. This process is illustrated in Figure 1.1 for the two-dimensional (2D) situation.

Each of these surfaces is designated with a set of three numbers (four for crystal in the hexagonal close-packed system) called Miller indices [13-15]. Miller indices are three integer numbers proportional to the reciprocal of the intersections of the mathematical plane used for defining the surface with the crystallographic axis of the crystal. This is illustrated in Figure 1.2.

Figure 1.2 Illustration showing the definition of Miller indices of a surface as three integer numbers proportional to the reciprocal of the intercepts of the plane defining the surface with the three crystallographic axes.

For cubic crystals, Miller indices define a vector that is perpendicular to the surface. This is very convenient, since it allows using vector calculus to easily obtain angles between surfaces and between the surface and given directions in space.

Surfaces on a crystal are conveniently depicted in a stereographic projection [15, 16]. To briefly describe this, we imagine the crystal in the center of a sphere, and we draw radii perpendicular to each surface from the center of the crystal until the sphere is intercepted (for cubic crystals, these radii will follow the direction of the vector defined by the three Miller indices of each surface). In this way, each surface is projected as a pole on the surface of the sphere. Finally, the poles on the surface of the sphere are projected onto a plane following the strategy illustrated in Figure 1.3. Imagine we put the sphere tangent to a plane at its north pole and we put a light source on the south pole. Then, poles on the sphere will cast shadows on the plane: these are their stereographic projections. The equator of the sphere will define a circle on the plane. Poles on the northern hemisphere of the sphere will cast their shadows inside this circle, while the projection of the poles in the southern hemisphere will lie outside this circle, with their projection being further apart from the circle as the poles are closer to the south pole of the sphere. To avoid this situation, it is customary to interchange the position of the plane and the light to project the poles on the southern hemisphere, so all poles are projected inside the circle defined by the equator of the sphere. Figure 1.3b shows the procedure for the projection from a side view for a pole with x = 0. From this view, it can be easily realized that it is equivalent to project the poles on the plane tangent to the sphere, as described earlier, or on the circle defined by the equator of the sphere. The side view allows getting the following relationship between the vector that defines the pole and the x´ and y´ coordinates of its projection:

where x´ and y´ are the coordinates of the point in the projection and x, y, z are the coordinates of the pole on the 3D sphere. A rotation of the three axes might be necessary to calculate x, y, and z if the crystallographic axes are not aligned with the Cartesian axis in space.

Figure 1.3 Schematic diagrams illustrating the procedure for obtaining the stereographic projection of the faces of a crystal. (a) 3D representation showing the reference sphere and the projection for a general pole with three coordinates x, y, z. (b) Side view and projection of a pole with x = 0.

In what follows, we assume that the crystal belongs to the face-centered cubic system, since this is the system of the most electrocatalytic metals used in electrochemistry (Pt, Rh, Pd, Ag, Ir, etc.). Figure 1.4 shows a stereographic projection of several characteristic surfaces in a cubic crystal. As is evident, the large symmetry in this family of crystals is also translated into the stereographic projection. In fact, the stereographic triangle depicted in Figure 1.4b contains a minimum set of surfaces in such a way that all other surfaces can be obtained from those in the chosen stereographic triangle by symmetry operations. In other words, any surface outside the triangle is equivalent, by symmetry operations, to another surface inside the triangle.

Figure 1.4 (a) Stereographic projection of the main poles for a cubic crystal. The (001) axis has been oriented perpendicular to the plane of the paper. (b) Enlargement of the crystal model, showing the crystallographic axis. The crystal has been slightly tilted to show the (100), (110), and (010) faces, which would be otherwise perpendicular to the paper. (c) Stereographic triangle containing a representative subset of surfaces. All other surfaces can be obtained from those in the triangle by symmetry operations.

Figure 1.5 Atomic structure of basal planes for an fcc crystal.

This is reflected in the Miller indices. Any surface of the crystal with Miller indices (hkl) can be translated inside the triangle by simple permutation of the three Miller indices and some sign changes. For instance, surface (714) will be equivalent to surface (147) inside the selected stereographic triangle. Surfaces transformed in this way will be either identical or mirror images of each other, depending on the symmetry operations that have been used to bring the surface into the stereographic triangle.

Corners of the stereographic triangle are called basal planes and are the simplest surfaces that can be obtained. In this case, the centers of the atoms on the surface define a perfect 2D flat plane, without steps or kinks. Figure 1.5 shows the relationship between the...