Physical phenomena explicitly associated with condensed matter surfaces have been studied since antiquity. Perhaps the oldest written record of experience in this area appears in Babylonian cuneiform dating from the time of Hammurabi (Tabor, 1980). A form of divination, known today as lecanomancy, involved an examination of the properties of oil poured into a bowl of water. The detailed behavior of the spreading oil film led the diviner, or baru, to prophesy the outcome of military campaigns and the course of illness.

In later years, many observers commented on the fact that choppy waves can be calmed by pouring oil into the sea. In particular, Pliny's account was known to Benjamin Franklin when he began his controlled experiments during one of his frequent visits to England. Franklin's apparatus consisted of a bamboo cane with a hollow upper joint for storage of the oil.

Introduction

The study of phase transitions plays a central role in modern condensed matter physics. Changes of phase often are very dramatic events and certainly one wants a good understanding of such transformations. However, the stature of this field derives mostly from the recognition that the fundamental concepts, language and methodology developed to attack the phase transition problem have far-reaching utility in other areas of physics. In this chapter, we take advantage of the successes in this branch of statistical physics as a part of a two-pronged program. On the one hand, we apply the phenomenological methods of the modern theory (which focus on notions such as symmetry and order) to highlight those aspects of surface phase transitions that do not depend on the details of the system. On the other hand, a few specific examples are examined in more depth to illustrate that an appreciation of these details can significantly deepen our understanding of surface processes. We begin with a brief review.

Phase transitions occur because all systems in thermodynamic equilibrium seek to minimize their free energy, F = U − TS. One phase will supplant another at a given temperature because different states (e.g., liquid/vapor, magnetic/non-magnetic, cubic/tetragonal) partition their free energy between the internal energy U(T) and the entropy S(T) in different ways. It is useful to characterize competing phases in terms of a so-called order parameter.

Introduction

Our account of adsorption to this point has been restricted largely to one particular, albeit important, special case: the situation where adsorbate–substrate interactions dominate adsorbate–adsorbate interactions. This is sufficient for discussion of the vast majority of interesting chemical processes that occur at surfaces. Important inter-adsorbate forces surely come into play – there would be no surface reactions otherwise – but what counts the most is just the fact that the species do in fact find themselves on a surface. This is what we mean by heterogeneous catalysis.

The rules of the game change somewhat when we consider the other major driving force for research into our subject: the microelectronics industry. Here, surface physics per se is not so crucial as the closely related field of interface physics. The interfaces in question typically involve the junction of two micron-sized wafers of metal, semiconductor, ceramic, etc. Since these junctions break translational invariance, it is unsurprising that certain ideas (such as interface localized electronic and vibrational states) reappear almost unchanged. But a great many new features enter which would carry us far outside the intended scope of this book. Luckily, there is one aspect of the problem which does fall within our purview: the concept of epitaxy and epitaxial growth.

Introduction

This chapter begins our exploration of the physics of dynamical processes at solid surfaces – adsorption, diffusion, reaction and desorption. To do so, we must leave the ground state problem and concentrate on the excited states of adsorbed atoms and molecules. One way to proceed focuses on the excitation spectrum. As we know, this spectrum comes in two parts: single particle excitations and collective excitations. Our earlier discussion for clean surfaces (Chapter 5) dwelt primarily with the latter and it is possible to duplicate that effort here. For example, Fig. 13.1 illustrates the calculated and measured (by EELS) dispersion of two types of collective excitations for two vastly different adsorbate/substrate combinations. The left panel pertains to vibrations localized in an oxygen adlayer on Ni(100), i.e. overlayer phonons. Theory and experiment are in good accord for this system. Both exhibit three dispersive branches. The low frequency acoustic excitation is the (oxygen-modified) Rayleigh mode of the nickel substrate.

A metallized adsorbate layer can support collective excitations of its charge density in addition to the more familiar phonon modes. The right panel of Fig. 13.1 compares theory and experiment for the dispersion of two-dimensional plasmons in an ordered potassium overlayer adsorbed on a dimerized Si(100)2 × 1 surface.

Introduction

The phenomenon of condensation is one of the most familiar properties of bulk matter and so has attracted the attention of physicists for decades. The basic questions are straightforward to pose but remarkably difficult to answer. In fact, a conceptual revolution was required before truly rapid progress was achieved (Wilson, 1979). As we have indicated earlier (Chapter 5), dimensionality plays a crucial role in this modern theory of phase transitions (Ma, 1976). It then is natural to ask how much (if any) of our common three-dimensional experience and intuition carry over to the two-dimensional problem. Typical questions might be: What is the nature of the adsorbate phase diagram? How does a surface species pass from an ordered crystallographic state to a disordered state? What microscopic mechanisms are involved? How does an overlayer freeze and/or melt? Are any properties unique to two dimensions?

From the thermodynamic point of view, we have learned that clean surface critical phenomena and melting do indeed both differ from their three-dimensional bulk counterparts. We further quantify this notion here and examine the universality hypothesis, which states that only symmetry considerations and (in some cases) the range of adsorbate interactions determine the intrinsic nature of overlayer phase changes on a Langmuir checkerboard. Both static and dynamic issues will receive attention.

Introduction

The interaction of light with the first few atomic layers of a solid is relevant to (at least) two rather different aspects of surface physics. First, the strength of the experimental signal for many of the spectroscopic tools at our disposal such as photoemission, electron scattering, Raman scattering, etc., depends crucially on the intensity of the electric and magnetic fields near the surface. One typically calculates these field amplitudes by use of the classical Fresnel formulae. It is important to inquire whether this approach is sufficient if one is interested in phenomena within an Ångström or two of the crystal surface. These considerations alone suggest that a thorough understanding of the nature of near-surface electromagnetic fields is of both practical and fundamental interest. A rather different motivation to study these fields comes from the realization that very long wavelength elementary excitations of the surface will couple directly to the ambient field. To account for this, we must generalize the results of the previous chapter beyond the static limit to include the finite propagation velocity of light. These excitations, known as surface polaritons, are coupled modes of the surface + electromagnetic field system. It is convenient to use the language of optics to discuss surface polaritons, although, in principle, no external driving field is needed to excite them.

Fundamentals

The weakest form of adsorption to a solid surface is called physical adsorption, or physisorption. It is characterized by the lack of a true chemical bond between adsorbate and substrate. If this is true, some other attractive force must exist that binds a gas phase species to a solid. One possibility that suggests itself is the ubiquitous van der Waals interaction. To see its origin, consider a closed shell atom that sits a distance, z, above a solid surface. We restrict our attention to distances z ≪ c/ωp (~ 1000 Å) so that the finite propagation velocity of light can be ignored. Even at these distances, a mutual attraction between the atom and the surface exists that arises from the interaction of the polarizable solid with dipolar quantum mechanical fluctuations of the atomic charge distribution. Put another way, the atomic electrons are attracted to their images in the solid.

A one-dimensional harmonic oscillator model of the hydrogen atom is sufficient to capture the essential physics of the van der Waals, or dispersion, force between an atom and a solid. Let the oscillator coordinate, r, represent the projection of the electron's orbital motion along the normal to the surface. Consider first the image system appropriate to a perfectly conducting substrate (Fig. 8.1).

Introduction

In this chapter we investigate the electronic properties of clean solid surfaces. Certainly this is a prerequisite to any fundamental understanding of the electrical behavior of surfaces and interfaces. However, it also is essential to a coherent view of other surface phenomena, viz., oxidation, heterogeneous catalysis, crystal growth, brittle fracture, etc. There is no question that applications such as these provide most of the impetus behind surface science research. Nevertheless, we restrict ourselves here to only the most basic physics questions. What is the charge density in the neighborhood of the vacuum interface? Are the electron states near the surface different from those in the bulk? How do chemical bonding states in the first few atomic planes rearrange themselves after cleavage? What is the electrostatic potential felt by surface atoms?

The principal experimental probe of these issues is photoelectron spectroscopy and we will have much to say about this technique below. It turns out that the relevant measurements are relatively easy to perform but that the interpretation of the data is not entirely straightforward. It is helpful to have some idea of what to expect. Therefore, we defer our account of the experimental situation and proceed with some rather general theoretical considerations.

The methods of surface electronic structure are the same as those used to analyze the corresponding bulk problem.

Introduction

The purpose of this chapter is to review the application of Mössbauer spectroscopy to the study of dynamics. The main emphasis will be on the new areas in which significant advances have been made in recent years, such as the study of diffusive processes, the influence of motion on lineshape, time-dependent studies and dynamics at phase transitions. Rather less attention will be devoted to areas such as f-factors in solids, the Goldanskii–Karyagin effect and temperature shift, which have been studied more extensively in the past. The trends towards future areas for this research will also be considered, together with an evaluation and comparison between Mössbauer spectroscopy and other methods for investigating these phenomena.

No attempt will be made to develop the formal theory of dynamics in this chapter. General physical arguments will be employed to describe the phenomena and the main theoretical results to be used in interpreting the experimental data will be summarised. Representative experimental data and results will be presented in the various sections.

The phenomenon of the recoil-free resonant absorption of gamma rays is the result of the special dynamics of nuclei in solids. This fact was recognised by Mössbauer, who interpreted his apparently anomalous observations in terms of lattice dynamics of a similar nature to those associated with neutron scattering (Mössbauer, 1958). He found that the recoil momentum of the recoiling nucleus is shared by many nuclei of the crystal and thus the recoil energy is extremely small.

Introduction

In this chapter the various kinds of time-dependent phenomena that can be studied by Mössbauer spectroscopy will be reviewed and the relationship between the data obtained by Mössbauer spectroscopy and that derived from other techniques will be assessed.

In many discussions on time-dependent or dynamical effects in Mössbauer spectroscopy the essential physical ideas get obscured by complicated theoretical formalism. The ideas, however, are quite simple and are capable of being appreciated at a qualitative level before embarking on detailed calculations. The present chapter is an attempt to fulfil this need and bring out the important concepts at a non-specialist level. Where necessary, the reader may refer to the original sources cited for more elaborate treatments. For these same reasons, only a few simple models have been chosen, which can be analysed without a detailed mathematical treatment.

As briefly outlined in Chapter 1, the Mössbauer effect concerns the resonant absorption of a gamma ray, of frequency ω0 and wavevector k, by a nucleus. If the absorbing nucleus is located at the position r, the electromagnetic field of the gamma ray at the nucleus can be represented by

where ΓN is the natural linewidth of the decaying nucleus in its excited state, which is given by 2π/τN, where τN is the mean lifetime of the nuclear excited state. In general, in this chapter, linewidths are expressed in terms of frequency, which must be multiplied by ħ, the Planck constant divided by 2π, in order to convert to an energy.

Introduction

The creation of a chemical bond involves the sharing of two or more electrons between a pair of atoms. If the atoms are identical, as in a homonuclear diatomic molecule, there is little change in the total electron density on each atom, but there may be a slight redistribution of electrons between the valence orbitals to achieve a more satisfactory hybridisation. If the atoms differ, the bond will be more or less polar, depending on the disparity in electronegativities: one atom will gain electron density at the expense of the other. This effect is at its most extreme in the formation of an ionic bond. When an atom forms more than one bond, considerable rehybridisation may take place, with or without gain or loss of electron density by the electronegativity effect. An examination of the distribution of electron density about a particular atom can therefore give considerable information about the bonds involving that atom.

Mössbauer spectroscopy is well suited to such a study, since two major parameters of a spectrum can be related directly to the populations and changes in population of the valence shell orbitals. The isomer shift relates to the total electron density on the atom, and the quadrupole splitting reflects any asymmetry in the distribution of electron density. Thus, each parameter is capable of giving information about bonding: from their combination, it is often possible to make quite detailed analyses.

Many techniques have developed in recent years which allow experimental scientists to extend their studies in new directions. An awareness of the scope, strengths, potential, and limitations of a particular technique is essential if it is to be utilised to the full. The aim of this book is to review the unique contribution that Mössbauer spectroscopy can make to the study of the bonding, structural, magnetic, time-dependent, and dynamical properties of various systems. Particular emphasis is given to the types of information which Mössbauer spectroscopy provides, as well as to a comparison with the information in these areas which can be obtained using other techniques.

In order to achieve the objectives outlined above, each of the main chapters relates to one aspect of the information which can be obtained by Mössbauer spectroscopy, and these chapters have been written by scientists with considerable experience in these different areas. We are particularly indebted to the authors of the individual chapters for embracing our overall philosophy for this book and the need to produce a coherent whole, while still reflecting their personal enthusiasm for their own particular area of interests, as well as the differences inherent in these different aspects.

One of the striking features of the growth of Mössbauer spectroscopy, following the discovery by Rudolf Mössbauer in 1957 of the effect which bears his name, was the rapidity with which the potential of the new technique was recognised and developed.

Introduction

The aim of this section is to begin with the most general and qualitative picture of the interactions of a Mössbauer nucleus with its environment. By developing and quantifying the treatment of these interactions, we seek to establish connections between the components of the environment and the energies of the nuclear levels and thus to build up an understanding of the features of the environment that shape the Mössbauer spectrum.

Classes of interaction

A schematic picture of the interactions that affect the energy levels of a Mössbauer nucleus is shown in Figure 4.1. In this representation it is seen that the Mössbauer nucleus senses its environment directly through atomic–nuclear interactions [1], solid–nuclear interactions [3] and the external field–nuclear interaction [5]. It is indirectly sensitive to the solid–atom interaction [2] and the external field–atom interaction [4], which are felt through their effect on the nucleus' own atom.

It is usual in magnetic solids for the main influence on the Mössbauer spectrum to be felt through the interactions [1] and [2]. That is, the nucleus senses its own atom and the state of the solid via the effect of the solid on that atom.