In both field ion microscopy and scanning tunneling microscopy, the preparation of sharp tips is crucial for carrying out observations with atomic resolution. The demands on the tip in scanning tunneling microscopy are not too rigorous; it has to have a sharp region of some kind in order to probe a surface with high resolution. For this task, tips are available commercially. In field ion microscopy, the tip is the surface to be studied, and therefore has to have a well-formed overall shape. As already pointed out in Chapter 2, there are fairly standard methods for preparing and polishing wire samples to the proper shape. We will give a few examples of how this can be accomplished. With the exception of the description for rhodium, these were all worked out by Liu, and with some minor changes taken directly from his thesis, but it should be noted that other recommendations are available.

Preparation of samples for field ion microscopy

“Three conditions have to be met for a good field emitter specimen: (a) The end of the specimen, that is the tip, has to be sharp enough so that strong electric fields can be attained at reasonable voltages; (b) The tapered section, or shank, has to be smooth and devoid of large defects or undercuts, so that the emitter can withstand field stresses; and (c) The whole shank and tip should be smooth and symmetric to avoid serious distortion of the image.

Single adatom diffusion on a variety of one- and two-dimensional surfaces has now been surveyed. However, events occurring at plane edges and other types of defects play an important role in affecting diffusion over the entire surface. There are also a huge number of indirect indications that impurities influence atom movement as well as other processes. The amount of direct information available for this field is not large, but we will examine it to gain at least some insight into such phenomena.

Near impurities

Some effort has been made to uncover the way in which atomic diffusion is affected by impurities in the substrate. A start was made by Cowan and Tsong in 1977, who explored the effect of rhenium atoms dissolved in tungsten on the surface diffusion of tungsten atoms on the (110) plane. This surface was prepared from W-3% Re alloy, and so had a number of rhenium substitutional atoms on the (110) plane. Tungsten atoms were then deposited on the surface, and the spatial distribution of places visited by atoms during their thermal movements was measured and compared with that for tungsten moving on the clean W(110), as shown in Fig. 6.1. Tungsten adatoms diffusing over a W-3% Re(110) surface were found to spend more time at a few sites on the surface, which the authors associated as most likely being next to interstitial rhenium atoms embedded in the surface.

So far we have concentrated on the behavior of single atoms. However, when several atoms are present on a plane and they diffuse, atoms may collide with each other and form a cluster. Such events are illustrated in Figs. 7.1, 7.2, and 7.3, where coalescence of two as well as three atoms is observed directly using the field ion microscope. These clusters are of considerable interest for the roles they play in the growth and dissolution of a crystal, as well as their effects on surface chemical reactions. Of primary concern here is the ability of atom clusters to diffuse over a crystal surface, and it is this aspect of cluster properties that we will emphasize. We will look at the conditions under which a cluster moves as a whole and also when parts of a cluster start moving independently. Different mechanisms of diffusion will be discussed in some detail.

In probing the diffusion of clusters, it is worthwhile to distinguish two different types of mechanisms – movement by single atom jumps, and by concerted atom displacements. In the first category, five types of movement have so far been identified, which are: 1. diffusion by sequential atom jumps (Fig. 7.4a), 2. peripheral displacements (Fig. 7.4b), 3. by the leapfrog mechanism (Fig. 7.4c), 4. by the correlated evaporation–condensation mechanism also known as detachment–attachment (Fig. 7.4d) or terrace limited diffusion, and 5. by the evaporation–condensation mechanism (Fig. 7.4e), in which one atom leaves a cluster and then a different atom from the terrace attaches to the cluster.

As is clear from the previous chapters, a considerable amount of information has become available about the diffusivity of metal atoms on metal surfaces. This knowledge will have an impact on understanding topics such as crystal growth and dissolution, annealing, sintering, as well as chemical surface reactions. We will not examine any of these important topics, but will instead focus on attempts to measure atomic surface interactions, as an example of effects which have become much clearer through gains in the knowledge of surface diffusion.

Interactions can be divided into two categories, direct, for example van der Waals, dipolar, as well as electronic interactions, and indirect, which are mediated by the substrate, such as coupling by electronic states, elastic effects, or vibrational coupling. In Chapters 8 and 9 we described the movement of clusters created mostly by direct interactions of adatoms. In this chapter we will concentrate on the second type of interactions, mediated by the lattice – indirect interactions. The theory of interactions between adsorbed atoms has been nicely reviewed by Einstein, so here we just want to point out that with two atoms in the gas phase, the wave function for a higher state will be confined to the vicinity of the core. Placed on a metal surface, however, quantum interference of wave functions enters and adatom waves combine with metal wave functions from the lattice. The contributions from two atoms may overlap, as shown in Fig. 10.1.

In this chapter, we continue the task started in the last one: we will list diffusion characteristics determined on a variety of two-dimensional surfaces. For better orientation, ball models of fcc(111) and (100) planes have already been shown in Fig. 3.3, together with the (110), (100), and (111) planes of the bcc lattice in Fig. 3.4. In experiments it has been observed that on fcc(111) planes there are two types of adsorption sites: fcc (sometimes called bulk or stacking) and hcp (also referred to as surface or fault sites); these sites, indicated in Fig. 3.3b, can have quite different energetic properties. Two types of adsorption sites also exist on bcc(111) and hcp(0001) structures. However, on bcc(110) as well as on bcc(100) and fcc(100) planes, only one type of adsorption site has so far been observed, which makes it easier to follow adsorption on these surfaces.

Aluminum: Al(100)

Experimental work on two-dimensional surfaces of aluminum was long in coming, and was preceded by considerable theoretical work, with which we therefore begin here. The first effort, by Feibelman in 1987, was devoted to the Al(100) surface, and relied on local-density-functional theory (LDA–DFT). The primary aim of the work was to examine the binding energy of atom pairs, but he also estimated a barrier of 0.80 eV for the diffusive hopping of Al adatoms. Two years later, Feibelman investigated surface diffusion which takes place on Al(100) by exchange of an adatom with one from the substrate.

In the previous chapter we presented possible mechanisms which can contribute to cluster diffusion; in this chapter, we will concentrate on the energetics of cluster movement, mostly the movement of the center of mass. Early studies of cluster diffusion were all done on tungsten surfaces using FIM, but as techniques other than field ion microscopy were applied to learning more about this subject, other surfaces came under scrutiny. The biggest change in the level of activity, however, was made by theoretical calculations. These now dominate the field and have usually covered several surfaces of different materials in one examination. The number of experimental studies of cluster behavior decreased markedly as computational efforts reached new intensities. Unfortunately, theoretical investigations still are quite uncertain and experiments are urgently needed for comparison and verification. Nevertheless we will try to arrange our comments chronologically in the description of each material, but with experiments and theoretical calculations separated.

Early investigations

Experiments

Work on the diffusion of single adatoms on a metal surface had been going on for just a few years when Bassett began to look at clusters formed by association of several atoms. In 1969 he noted that after depositing several atoms on the (211) and (321) planes of tungsten, clusters formed, with a mobility smaller than that of single atoms, provided that deposition took place with the atoms in the same channel. On these planes, clusters moved in only one dimension, along the channels of the planes.

With background information about the kinetic and experimental aspects of surface diffusion in hand we will now turn our attention to the atomistics of diffusion about which much has been learned through modern instrumentation. The usual picture of surface diffusion, which seems to agree at least qualitatively with experiments on diffusivities, is that atoms carry out random jumps between nearest-neighbor sites. Is this picture correct? Has it been tested in reasonable experiments? What can be said about the jumps which move an atom in surface diffusion? What is the nature of the sites at which atoms are bound? These are among the topics that will be considered at length now.

In these matters the geometry of the various surfaces studied plays an important role, and at the very start we therefore show hard-sphere models of planes that will emerge as significant. Presented first are channeled surfaces, bcc (211) and (321) in Fig. 3.1, as well as fcc(110), (311), and (331) in Fig. 3.2. These are followed in Fig. 3.3 by fcc(100) and (111) and bcc(100), (110), and (111) planes in Fig. 3.4. Their structures are sometimes quite similar, but their diffusion behavior may be quite different.

Adatom binding sites

Location

Where on a surface are metal adatoms bonded? That is an important question for understanding how atoms progress over a surface in diffusion. LEED has been very important in providing information about the geometry of adsorbed layers.