Adsorption upon metal surfaces and catalytic activity are highly dependent on the arrangement of atoms exposed to the adsorbent. For example specific adsorption, discussed in the previous section, is dependent not only upon the identity of the solution species but also upon the arrangement of atoms at the electrode surface. This is because alignment of orbitals and bonding depend upon both these factors. Most prepared metals, although exhibiting a regular bulk structure, do not exhibit a regular surface structure. Their surfaces are made of a variety of sites, such as flat regions, steps and defects, which differ in their local atomic arrangement and have different electronic properties [52]. The local activity for a catalytic reaction may therefore vary over the whole surface as some areas may not have the ideal properties for catalysis. For the ORR catalyst in fuel cells such a scenario is a waste of platinum that could be more optimally used if the whole surface exhibited optimal activity. Therefore the relationship between particular surface atomic arrangements and ORR activity must be understood, as it is this fundamental understanding which informs which atomic arrangements have highest activity. Shape controlled nanoparticle catalysts may then be made which contain the maximum amount of these sites.
The metals used in this work have a face centred cubic (fcc) bulk structure. The surface structure reflects this underlying bulk structure. The identification of different surfaces shall be discussed in the following sections.
1.3.1 The Miller Index and Microfacet Notation Systems
Consider the face-centred cubic, fcc, structure below. One corner of this unit cell may be defined as the origin and the x, y and z axis are labelled. The unit cell dimension is the shortest distance between two corners of the cell and has units a. The distance from the origin to the next atom in the x, y or z axis is therefore 1a.
Figure 11. Face-centred cubic crystal lattice structure. Adapted from Wikimedia Commons image (http://commons.wikimedia.org/wiki/File:Face-centered_cubic_crystal_lattice.svg).
The fcc structure can be cut at any plane within the unit cell, creating an exposed surface with a unique atomic arrangement. This plane is defined by a series of three numbers, four in the case of a hexagonal close-packed (hcp) unit cell, collectively known its Miller index. The Miller index identifies the surface atomic structure that would be made from a cut at this plane. To determine the Miller index, firstly identify the x, y and z coordinates that the plane intercepts as fractions of the unit cell dimension, a. For example, let’s take a plane which intercepts at ½a in the x axis, 1a in the y axis and ∞a in the z (an ∞ intercept represents a plane running parallel to that axis and which therefore does not cross it). The next step (the final one in this case) in achieving the Miller index for the plane is to take the reciprocal of the numbers above; (1/[1/2], 1/1, 1/∞) = (2,1,0). The Miller index for this plane is therefore (210). [52]
If after the previous step the results are still fractions, then all the reciprocals must be multiplied by an appropriate number, as Miller indices must consist of whole numbers. For example, if after the reciprocals were taken the result (1, 1/2, 1/2) was achieved, then every number would be multiplied by 2 to give the Miller index (211). Likewise, if the index is not in its simplest form after taking the reciprocal, then every number must be divided by an appropriate number, as Miller indices are the simplest numeric representation of the plane. For example, the numbers of the index (842) would be halved to make the Miller index (421). If the plane intercepts at a negative point in one of the axis then a bar is placed above the relative value. For example, the index for the plane intercepting at ½, -1, ∞ would have the Miller index (21̅0) rather than (2,-1,0).
The three numbers in the Miller index plane are denoted generally by the letters h, k and l. With regards to notation, parenthesis, (), are used to denote a single plane whereas braces, {}, are used to denote a family of planes. A family of planes are those which are equivalent due to symmetry features of the unit cell. For example the planes (100), (010), (001), (1̅00), (01̅0) and (001̅) exhibit identical atomic arrangements and are recognised as a family of planes as {100}. If h, k and l in the Miller index are all either 1 or 0, then a cut through the crystal for that plane will form an atomically flat surface, with no steps or kinks. There are three such surfaces for fcc structures, {111}, {100} and {110}, illustrated below. The {111} plane exhibits a hexagonal atomic arrangement with 6 fold symmetry. The atoms of the {100} plane are packed in a cubic fashion with 4 fold symmetry and the {110} plane exhibits atoms packed rectangular, with 2 fold symmetry.
Figure 12. Base plane atomic arrangements of the fcc system. From left to right, (100), (110) and (111). Adapted from Wikimedia Commons image (http://commons.wikimedia.org/wiki/File:Face-
centered_cubic_crystal_lattice.svg).
Miller index planes with one or more numbers that are greater than 1 are known as high Miller index planes. As detailed above, these planes intercept at fractional values of the unit cell’s axis. These surfaces contain flat areas, which have an atomic arrangement of one of the three base planes. Flat areas of high index planes are known as terraces and are separated by monoatomic steps. The (13,1,1) surface for example contains terraces of (100) atoms separated by (111) steps.
Figure 13. Unit stereographic triangle of fcc single-crystal surfaces and their corresponding surface atomic arrangements. [70]
All the high Miller index planes may be represented on a triangle where the vertices (poles) represent the basal planes. This is known as the stereographic triangle of the fcc system. Stepped surfaces are represented along the sides of the triangle. The further away from the poles one travels, the shorter the terrace of a particular base plane and the higher the density of steps. Many high index surfaces also exhibit kinks in the steps. Kinked surfaces are represented by the area within the stereographic triangle.
Another notation system, useful for denoting stepped surfaces, is the microfacet system [71]. The (755) surface for instance contains (111) terraces that are 6 atoms wide separated by (100) steps, in microfacet notation this is written 6(111) x (100). This system can be helpful in visualising the surface. There are also rules for converting between the microfacet and Miller index notation systems for stepped surfaces. For example, the series of surfaces with microfacet notation n(111) x (100), where n is the number of atoms in the terrace, is written (n+1,n-1,n-1) in Miller index notation. The turning point of the zones occur where n=2 in their microfacet notation. This is the point where the length of terrace and step is equal (2 atoms). This is illustrated by the (311) surface, which in microfacet notation may be written as either 2(111) x (100) or 2(100) x (111).