Introduction

The measurement of work functions or, more precisely, work function changes (surface potentials) has been widely used in the study of adsorption processes on metal surfaces. The technique has been used both on its own and in conjunction with other techniques such as LEED, infrared spectroscopy or flash desorption to elucidate the mechanism of surface reactions.

The measurement of the work function change or surface potential is useful in that it provides a relatively simple method of monitoring the state of the surface. Any adsorption on the surface will, in general, produce a change in the work function of the surface as will any further change in the state of the adsorbate and/or adsorbent. The method is very sensitive, since adsorption of a monolayer on a surface produces surface potentials which are usually in the range 0.1–1.5 V and, since surface potentials can be measured to within ±0.001 V, very small amounts of adsorption can be measured in a way which causes little or no disturbance to the surface.

A number of techniques are available for measuring surface potentials. In principle, any method which will measure work functions or Contact Potential Difference (CPD) may be used for measuring surface potentials, although some techniques may interfere with the adsorption process to a limited extent.

Introduction

The study of order in structures involving biomolecules divides naturally into two parts. On the one hand, one can consider ordered structures in vivo, and on the other hand in man-made systems. The obvious example of thin organic films in the former category is the cell plasma membrane (the term for the exterior membrane of a cell). In 1925 Gorter and Grendel suggested that the cell membrane consisted of a bilayer of lipid molecules with the hydrophilic ends facing outward and the hydrophobic ends facing one another in the interior of the membrane. (The structures of some common lipids are shown in Figure 8.1.) It was a long time before this postulate was definitely confirmed but it is now generally accepted that the plasma membrane is roughly of this general form. The main modifications of this picture are as follows.

1. (a) Many membrane-bound enzymes penetrate the plasma membrane and are stabilised by the fact that the surface of the enzyme consists of two hydrophilic end regions and an intermediate hydrophobic region. These enzymes take part in the transport of particular substances across the membrane and in various important processes in which energy is stored or interchanged by the medium of ion transport. This topic is returned to below.

2. (b) A number of glycoproteins are incorporated into the membrane and are involved in cell recognition processes.

3. […]

Introduction

The surface vibrations of adsorbates on crystal surfaces may be studied by Infrared Reflection—Absorption Spectroscopy (IRAS), Raman spectroscopy, High Resolution Electron Energy Loss Spectroscopy (HREELS) or molecular beam scattering. The last named is the subject of a separate chapter and will not be discussed further here. In all of these techniques, with the exception of molecular beam scattering, the inelastic process results from the same physical entity, the vibrating surface dipole, and to a certain extent similar selection rules apply for IRAS and HREELS; the selection rules for Raman activity complement those of IRAS.

One would expect that these techniques would yield much the same sort of structural information about adsorbed species on metal surfaces. This is generally true, though direct comparisons are not always possible since IRAS and Raman spectroscopy may be used at quite high pressures, akin to those encountered in catalytic systems, while HREELS may not. Balanced against this apparent disadvantage for HREELS is the fact that it can readily scan 1 eV, the whole infrared range, in one experiment. Unfortunately, until recently, the resolution obtained for HREELS did not exceed ∼ 5 meV; one must contrast this with the resolution attainable with IRAS, which is typically at least 0.05 meV.

Introduction

The name self-assembly is an unfortunate one as it implies the achievement of something approaching the synthesis of artificial life. However, this term has now been generally accepted and so will be used here. It has two distinct but related meanings. The majority of papers bearing this phrase in their titles concern monolayers of organic molecules adsorbed on solid inorganic surfaces. These rather simple systems can be studied and characterised at a level of detail and rigour which it is difficult to achieve with the other systems discussed in this book. They can also be formed using very simple apparatus. For both these reasons they have made a strong appeal to surface chemists. There exists, however, a more limited group of papers in which treatment of the initial organic layer by a succession of reagents has made it possible to build up ordered multilayers. In principle, this latter technique should make it possible to form the analogues of Langmuir–Blodgett Z-type multilayers and thus use relatively simple chemical methods to construct non-centrosymmetric systems of use in technology, as discussed, for example, in Chapter 5. So far such applications of this technique have not proved practicable and the difficulties involved will be discussed later in this chapter.

Monolayers formed from carboxylic acids

In recent years study of the absorption of small molecules on well characterised single crystal surfaces has attracted many research workers.

Introduction

In this chapter we turn to the study of LB films formed from polymers and LB films consisting of alternate layers of two different amphiphiles. In principle, of course, it would be possible to superimpose successive layers of three or more distinct amphiphiles but little has been done in this direction. However, a few examples of more complex alternating structures will be considered.

Polymer LB films naturally divide into the following categories.

1. Systems in which a multilayer structure is formed from molecules containing one or more double bonds and in which polymerisation is subsequently initiated by irradiation by γ-rays, ultraviolet light or an electron beam.

2. Systems similar to the above but in which the constituent monomers contain the diacetylene group.

3. Multilayers formed from polymers bearing both hydrophilic and hydrophobic side groups which are spread as polymers at the air/water interface and are subsequently deposited on a substrate by the LB technique.

4. Rigid rod polymers which have both hydrophilic and hydrophobic characteristics and which are capable of residing with the rod axis horizontal at the air/water interface and which can be deposited on a solid substrate by the LB technique.

Post-formed polymers made from monomers containing one or more double bonds

Studies of polymerisation at the air/water interface have been made repeatedly over the years and an account of early work in this field is given by Gaines. Here the discussion will be largely confined to polymerisation carried out after deposition.

Why surfaces?

The growth in the study of solid surfaces and in the number of techniques available for their study has been enormous since the early 1960s. At least one reason for this is the growing awareness of the importance of understanding surface properties and indeed the fact that work on surfaces has had an impact on this understanding and on specific applications in the ‘real world’. At a fundamental level surfaces are of great interest because they represent a rather special kind of defect in the solid state. Much of our understanding of solids is based on the fact that they are, in essence, perfectly periodic in three dimensions; the electronic and vibrational properties can be described in great detail using methods which rely on this periodicity. The introduction of a surface breaks this periodicity in one direction and can lead to structural changes as well as the introduction of localised electronic and vibrational states. Gaining a proper understanding of these effects is not only of academic interest, as there is growing interest in the properties of low-dimensional structures in semiconductor devices, and a free surface can represent the simplest case of such a structure.

Perhaps the most widely quoted motivation for modern surface studies is the goal of understanding heterogeneous catalysis.

Field emission

The field emission of electrons from a cold metallic cathode in the presence of a large surface electrical field was first reported by Wood (1899). Classical theory fails completely to describe field emission and it is to quantum mechanics that one must turn. Quantum mechanics were first applied to the field emission of electrons from a metal by Fowler & Nordheim (1928).

A simplified view of their result may be obtained by considering a potential energy diagram for electrons in a metal and the adjoining vacuum, in the presence and absence of an external electric field, fig. 6.1. The energy of the highest filled level in the metal, measured from the potential minimum in the metal, is called the Fermi energy EF, and is equal to the chemical potential of electrons in the metal. The energy difference between the Fermi level and the potential energy of electrons in the vacuum is the thermionic work function φ. (A more complete discussion of this is to be found in section 7.2.) The number of quantum states near the top of the Fermi sea is much larger than near the bottom, so that most electrons can be considered to be accommodated in energy levels near EF, and tunnelling can be assumed to take place largely from the Fermi level.

In the eight years since the first edition was prepared there has continued to be a high level of activity in the field of surface science, but there has been something of a change in character of the field. In particular, the rate of introduction of new techniques has slowed, and the rate of exploitation of existing methods, especially in the application of multiple methods to single scientific problems, has grown. This consolidation of the field has been a major benefit to the authors of this technique-based book, who found that the task of updating it was less of a hurdle than we might have anticipated when the first edition was published. Nevertheless, there have been some very important developments during the intervening period, and some major new sections have been introduced. For example, the whole field of atomic-scale scanning probe microscopy (particularly scanning tunnelling microscopy) is entering into the mainstream of the surface scientist's armoury. At the time of the first edition this technique could clearly be seen to be very elegant, but the scale of its impact was difficult to judge; even now there is much to be done (particularly on the theory) for it to achieve its full potential, but it has already progressed far beyond the novelty stage.

Definitions of order

In the last chapter we have used the word ‘order’ without giving it any precise meaning. Most definitions of order involve thermodynamic concepts. Thus, for example, one might say that the most ordered state of a system is the one to which the system tends as the temperature tends to absolute zero. This definition would, however, be of little service in the present context. Most of the systems which we will discuss are remote from thermodynamic equilibrium. This is true both of the films during their preparation and also of the ‘final’ prepared films. However, these prepared films are in states of metastable equilibrium which are likely to survive for periods long compared with the time taken to carry out experiments on them and, very often, for periods so long as to be, from a human point of view, infinite.

We thus need a different definition of order. Here it is suggested that we view the most ordered state as the one which corresponds most closely to some preconceived structure which we wish to bring about. From a practical point of view the extent to which we can tolerate disorder may vary widely depending on the context. Thus, for example, in a system analogous to a chain of DNA encoding the structure of a particular enzyme, a single defect may render the system useless.

Since the early 1960s or so there has been a virtual explosion in the level of research on solid surfaces. The importance of understanding surface processes in heterogeneous catalysis had been recognised since the early part of the twentieth century, but it was not until the 1960s, with the introduction and development of ultra-high-vacuum techniques, that real advances could be made, even using the ‘old’ techniques such as low energy electron diffraction (1927) and field emission (1936). The subsequent development of materials science and the growth of the semiconductor industry has added further surface problems for investigation while, at the same time, many new techniques have been introduced and exploited to study surfaces at the atomic level. For someone coming fresh to the field of surface physics or surface chemistry there seems to be a bewildering excess of different techniques, each commonly referred to by its acronym or unpronounceable string of initial letters. Much of the scientific literature in this field is occupied with technique-orientated studies of specific problems in which the strengths and limitations (particularly the latter!) of the technique or techniques used are rarely explained. Quite early in the development of surface science it became evident that surface problems should be tackled using a range of complementary techniques if a proper and complete understanding were to be obtained.

The scope of this book

The major scientific advances which have taken place since the Second World War have, in some cases, had little influence on everyday life while, in other cases, they have had the most profound effect on it. Thus, for example, particle physics and astronomy have revolutionised our basic concepts of the structure of matter but have had only minor effects on the life of the non-specialist. On the other hand there are two particular fields of study whose influence has affected the inhabitants of all civilised societies. One of those is solid state electronics and the computer revolution which it has given rise to. The other is the advance in biochemistry and organic chemistry which has provided the physician with a large range of effective drugs and has transformed medicine from an art to an applied science. It is thus not surprising that the idea has arisen that a synthesis of these two fields might bring about remarkable new advances. The name molecular electronics has been proposed for this concept though different people have rather different ideas as to what is meant by this expression.

To give effect to this concept it is necessary to design and construct molecules which have certain desired physical properties and then to learn how they can be assembled in particular well ordered ways. The first problem is the province of the chemist and here considerable progress has already been made.

Introduction

Although many techniques have been developed to study surface properties, most of these techniques are not fully surface-specific and yield information about the surface properties, entangled with information on the first few atom layers. An interaction which can be surface-specific is that between a gas atom or molecule and a surface. This interaction spans a range of phenomena, from diffraction through inelastic scattering to irreversible chemisorption, depending on the nature of the gas—surface potential. Gas atoms or molecules of low kinetic energy (<0.1 eV) act as very soft probes of the surface and, since they are physically unable to penetrate the solid, exhibit an extreme sensitivity to the outermost atomic layer, a sensitivity which surpasses that of LEED or AES. Indeed, one of the attendant difficulties in the development of atomic and molecular beam scattering from surfaces has been the problem of obtaining surfaces which are sufficiently clean to show, for example, any diffraction features which may be present. Surfaces which on examination by AES show no impurities and give sharp, well-defined LEED patterns may, nevertheless, be insufficiently clean for atomic or molecular beam studies. A good example of this sensitivity is provided by the work of Lapujoulade, Lejay & Papanicolaou (1979).

Introduction

In Chapters 6–10 we have dealt with the general structure of the linear response, kinetic theory and random-walk approaches to the calculation of the phenomenological coefficients and to the dielectric and anelastic response functions. We gave some straightforward examples of approximate results that can be obtained from the general expressions. The mathematical inter-relations between the three approaches demonstrated in those chapters allow the use of common techniques for the evaluation of the expressions for the transport coefficients of particular models.

In the present chapter, which, like Chapters 7–10, is concerned with dilute alloys and solid solutions, we first consider these techniques and then go on to present some results and applications of those results. It divides therefore into three more or less distinct parts. Techniques are the subject of §§11.2 and 11.3, the resulting transport coefficients are the subject of §§11.4–11.6 while various applications are reviewed in §§11.7–11.10.

In Chapters 7 and 8 general expressions were derived for the phenomenological coefficients and response functions from kinetic and linear response theories while consistent expressions for diffusion coefficients were obtained from random walk theory in Chapter 10. The techniques for the evaluation of these expressions are reviewed here in §§11.2 and 11.3. In the first of these sections the techniques are limited to calculations for which, in the terminology introduced in Chapter 10, only one type of jump occurs in the formal analysis. Important examples of such calculations are furnished by evaluations of the three independent phenomenological coefficients LAA, LAB, LBB for dilute binary alloys of cubic structure with transport by single vacancies, simple interstitials or dumb-bell interstitials.

Introduction

In the preceding Chapters 6–12 we have dealt with the general structure of the various statistical theories of atomic transport in solids and with the relations between them. However, in obtaining analytical results for specific classes of model the emphasis has been mostly on dilute alloys and solid solutions containing only low concentrations of defects. The theory of such systems is made easier because we need to retain only the lower-order terms in defect and solute concentrations. In this chapter we turn to theories of so-called lattice-gas models which give physically simplified representations of both concentrated alloys and systems containing high concentrations of defects. In such systems the concentrations of the components are not useful expansion parameters. As a result, and as is usual in statistical mechanics, an accurate theory is much more difficult to formulate in these circumstances.

The rather broad range of systems of current interest includes (i) ideal or random alloys and solid solutions (such as were discussed in §§5.6 and 10.8), (ii) alloys displaying short-range or long-range order and (iii) various systems where the number of mobile atoms is significantly less than the number of sites available to them. In this third group these sites are commonly interstitial sites within a structure formed by relatively immobile atoms. Examples are provided by the β-aluminas and other fast ion conductors (Laskar and Chandra, 1989), metals containing interstitial hydrogen or deuterium atoms and various other interstitial solid solutions (e.g. the tungsten ‘bronzes’; Cox, 1992). We shall refer to the sublattice of interstitial sites in these systems simply as the lattice.

Introduction

In Chapter 1 we briefly introduced the extended macroscopic equations of atomic transport that are provided by non-equilibrium thermodynamics. In this chapter and the next we expand this description, in this chapter in general terms and then in the next by a series of applications. The objectives are (i) to show how to use the description provided by non-equilibrium thermodynamics and (ii) to focus attention on the corresponding transport coefficients (denoted by Lij) and the expressions of various practical transport coefficients in terms of them. By working in terms of these basic L-coefficients we obtain a better understanding of the relations among the various practical coefficients and we provide a more sharply defined objective for the statistical atomic theories to be developed later.

The subject of non-equilibrium thermodynamics is now supported by a considerable body of statistical mechanical theory. Since our interest in this book lies primarily with the use of this formalism and with the calculation of the quantities appearing in it, it is not appropriate to go into this body of general theory widely. For this purpose we refer the reader to the books by de Groot and Mazur (1962) and by Haase (1969) for wide-ranging treatments, especially of the use of the macroscopic formulation, and to Kreuzer (1981) for a more recent account which emphasizes the general statistical mechanical foundations of this formalism. Here, a less extensive review will be given of those aspects pertinent to our interest in atomic transport in solids.

As we have already pointed out in §1.4 the immediately obvious features of the formalism are threefold: …

Introduction

The theory presented in the last chapter has already provided important general insight into atomic transport coefficients, as well as specific results which define routes to the evaluation of these coefficients for particular systems, both dilute and concentrated. We could therefore go straight to these evaluations. However, there are good reasons for delaying the matter. One is that there are alternative approaches to dilute systems which convey particular insights into the processes of atomic transport and which define additional quantities of experimental interest, most notably the so-called correlation factor (Chapters 8 and 10). Two of the most important of these alternative approaches are the kinetic and random-walk theories: the former are the subject of this and the next chapter while the latter are dealt with in Chapters 9–10. Although these theories are very different in appearance we shall show that in the end they can lead to the same expressions for measurable quantities in terms of specific atomic features of the system under study. Ultimately therefore they may use the same techniques for the evaluation of these expressions (as we shall show in Chapter 11 especially).

Although we shall henceforth be much more concerned with the physical details of the systems of interest, both approaches relate rather closely to what we have presented in Chapter 6. We shall take kinetic theory first because it offers a rather direct representation of many of the basic equations of Chapter 6 together with a number of easily obtained approximate results for particular systems. At the same time some of its notions are useful in the development of the random-walk theories.