Metal-Catalysed Reactions of Hydrocarbons / 01-Metals and Alloys

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and so the lattice has to be regarded as a datum in the further development of the Theory.

A number of procedures have been devised for obtaining wave functions for the valence electrons.10 It is unnecessary to describe these in detail, as they are thoroughly expounded in texts on solid state chemistry.31,32 The first was the Cellular Method, due to Wigner and Seitz,34 in which the solid was notionally divided into cells, each containing one ion core. The Augmented Plane Wave Method35 used a muffin tin model of the crystal potential, in which the unit cell is divided into two regions by spheres drawn about each ion core. The potential inside the spheres is spherically symmetrical, and resembles that for the isolated atom, whereas outside the potential is constant, so that an electron here would behave as a plane wave. The KKR Method (Korringa,36 Kohn and Rostoker37) supposes that electrons as plane waves undergo diffraction as they encounter ion cores, in a way which permits the wave to be reconstructed so that it can proceed through the lattice. The wave functions derived from the latter two methods are virtually equivalent.

The theoretician is now in a position to calculate a density of states curve for any element, by selecting a method for formulating the wave function and applying it to the appropriate crystal potential. These choices are not always straightforward: it has been said that it is far easier to give descriptions than advice on how to choose them. Once the choices are made, however, solution of the wave equations leads to an energy band diagram, and hence by integration to a density of states curve.

It is unnecessary to provide details of the results of such calculations, or of their comparison with experimental determinations by for example soft X-ray spectroscopy:23,31,32 band structures for Transition Metals can adopt quite complex forms,10 so we must content ourselves with a few qualitative observations. For the metals of catalytic interest, the nd-electron band is narrow but has a high density of states (Figure 1.8), because these electrons are to some degree localised about each ion core, whereas the (n + 1)s band is broad with a much lower density of states because s-electrons extend further and interact more. On progressing from iron through to copper, the d-band occupancy increases quickly, and the level density at the Fermi surface falls. The extent of vacancy of the d -band is provided by the saturation moment of magnetisation; thus for example the electronic structure of metallic nickel is (Ar core) 3d9.44s0.6, and is said to have 0.6 ‘holes in the d-band’. There have been many attempts to correlate the outstanding chemisorptive and catalytic properties of the Groups 8-10 metals with the presence of an incomplete d-band or unfilled d-orbitals. According to the Band Theory, electrical conduction requires excitation to energy levels above the Fermi surface, so that substances that have only completely filled bands will be insulators. A metal such as magnesium for example is a good conductor because it possesses a partly filled hybrid sp band. By the same token, it is easier to carry a full bottle of mercury than a half-full one, because it doesn’t slop about so much.

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Figure 1.8. Schematic band structures for metals at the end of the First Transition Series according to the Rigid Band Model.

It needs to be stressed that models of the metallic state on which the Band Theory is based suppose an infinite three-dimensional array of ion cores, so that the band structure cannot be expected to persist unchanged to the surface. Moreover the ion cores must be precisely located before theoretical analysis starts, and we shall shortly see that interatomic distances and vibrational amplitudes in the surface differ somewhat from those in the interior. These factors certainly complicate the useful application of Band Theory to the properties of surfaces.

While the Band Theory is based on the concept of a free electron gas obeying the appropriate statistical mechanical rules, the Valence Bond Theory, due to Pauling,9,10,33,38,39 takes the view that the behaviour of metals is adequately described by essentially covalent bonds between neighbouring atoms. It distinguishes between those electrons which take part in cohesive binding, and those which are non-bonding and responsible for example for magnetic properties. Pauling’s model first recognises that d-electrons can participate in bonds between atoms; it then supposes that nd-electrons can be promoted into (n + 1)s and (n + 1) p orbitals, with the formation of hybrid d x spy -orbitals. From potassium to vanadium the number of bonding electrons increases from one to five, accounting for the increase in cohesive strength described above. Since the covalent bonds require electrons to be paired, these elements are neither ferromagnetic nor strongly paramagnetic despite the d-shell being incomplete.

Of the five d-orbitals, it is assumed that only 2.56 are capable of bonding, the remaining 2.44 being localised atomic d-orbitals, which are non-bonding, and capable of receiving electrons with parallel spins as long as is permitted by Hund’s Rule. With chromium the sixth electron is divided as shown in Table 1.1. Now the dsp-hybrid orbital should in theory accommodate 6.56 electrons

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TABLE 1.1. Electronic Structures of Some First Row Transition Metals According to Valence Bond Theory

		Electrons in	Electrons in atomic
		hybrid	d-orbital					Saturation moment
Metal	Total electrons	dsp-orbital	Spin+	Spin−				Calc.	Obs.
Cr	6	5.78	0.22	0		0.22	0.22		—
Mn	7	5.78	1.22	0		1.22	1.22		—
Fe	8	5.78	2.22	0		2.22	2.22		2.2
Co	9	5.78	2.44	0.78		3.22	1.66		1.61
Ni	10	5.78	2.44	1.78		4.22	0.66		0.61

(i.e.1 + 3 + 2.56), but in fact it is necessary to assume that the maximum number is 5.78, the remaining 0.78 orbitals being metallic orbitals; these are said to be needed to effect the unrestricted synchronous resonance of the bonding orbitals. Although it may look as if the numbers are pulled like rabbits out of a hat, they are in fact selected to account for the saturation moments of magnetisation for iron, cobalt and nickel, as given by the number of unpaired electrons in the atomic d-orbital (Table 1.1). Their non-integral nature represents a time-average of an atom in one of two states.

Finally it is possible to calculate the fractional d-character of the covalent bonds for the Transition Series metals; these numbers were formerly much used by chemists to explain trends in catalytic activity, but are now little used. It is recognised that, while the model gives a qualitatively realistic picture of how the valence electrons are employed, it is an interpretation rather than an explanation, and its quantitative conclusions are unreliable. The role of the metallic orbitals is particularly mysterious: they are reminiscent of the Beaver who

. . . Paced on the deck,

Or sat making lace in the bow;

Who had often (the Captain said) saved them from wreck, But none of the sailors knew how.

A detailed critique of Pauling’s theory has been given in reference 10.

What is lacking in the theoretical analyses dealt with so far is any attempt to rationalise the regularity of changes in structure of the elements as one passes through the Transition Series (Section 1.1.1). It appears that this may be determined by the fraction of unpaired d-electrons in the hybrid dsp-bonding orbitals;33,40 this is thought to increase to a maximum in Group 7, and then to decrease. Metals in Groups 2, 9 and 10, where fraction is about 0.5 are fcc; in Groups 3, 4, 7 and 8, the fraction is about 0.7 and the structures are usually cph; and in Groups 5 and 6, the fraction is about 0.9 and structures are bcc. It is not however clear how the composition of the hybrid orbitals determines their direction in space and hence the crystal structure. The idea of the importance of bonding d-electrons in deciding

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structure has been further developed by Brewer41 and Engel42; the application of the concept to alloys and intermetallic compounds will be considered below.

One further theoretical approach deserves to be rescued from oblivion. In 1972, Johnson developed an Interstitial-Electron Theory for metals and alloys;43 it emphasises the spatial location of electrons, but also incorporates quantum mechanical aspects of bonding, such as electron correlation and spin. The interstices between the ion cores are the location of valence or itinerant electrons,11 and are thus ‘binding regions’, and the Hellmann-Feynman theorem provides a rigorous basis for analysing forces between electrons and ion cores in these regions.44 Electrons occupy interstices so that they provide maximum screening of positive ion cores, and suffer minimum electron-electron repulsions. In close-packed structures, there are only three interstices per ion core, and some vacant interstices are needed to account for metallic properties such as conductance. Thus before the number of valence electrons rises to six, some must be localised as d-states on the ion cores, while the rest remain itinerant. These latter act as ligands and determine the degeneracy of the localised electrons, and hence the magnetic properties.

The Interstitial-Electron Theory has been applied to the structure of metals, alloys and interstitial compounds, to their magnetic and superconducting properties, as well as to a range of surface phenomena.45 This work has seemingly not come to the attention of the wider scientific community perhaps because it was published only in Japanese journals. It merits wider recognition and a critical evaluation.

The reader may be confused by the number of different theoretical models that have been advanced to explain the properties of metals. Each type of approach has concentrated on a limited aspect. Electron Band Theory looks at the collective properties of electrons, especially their energy; the prediction of structure is not a prime target, and the location of electrons in the energy dimension is thought to be more important than finding where they are in real space. It is possible to gain the impression that theoreticians with a leaning to physics regard the existence of atoms as a complication if not a positive nuisance. The more chemically-oriented theories are less worried about electron energies, and cannot yield density of states curves, but they provide a generally satisfying qualitative picture of the behaviour of metals, which if not derived from fundamental theory is nevertheless useful to the practising chemist.

1.2. THE METALLIC SURFACE10,33,46

1.2.1. Methods of Preparation

Very many different forms of metals are used as catalysts: the size of the assembly of metal atoms varies from the single crystal, which may contain an appreciable fraction of a mole of the metal, to the tiniest particle containing only

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5 to 10 atoms. For practical catalysis it is usually desirable for the metal to be in a such highly divided form, exposing a large surface are to the reactants; however, the smaller the particle the more unstable it becomes, and special measures need to be adopted to prevent loss of area by aggregation or sintering. The best way of doing this is to form the particles on a support, but the subject of supported metal catalysts is of such importance and size that a large part of the next chapter is devoted to them. There are however other means of making and using quite small metal particles, without the assistance of a support; these are briefly described in this section, but their characterisation and properties will be considered in Section 2.2, alongside supported metal particles.

For fundamental studies there is much to be said for using the metal in a massive form;47,48 the disadvantage is the very limited surface areas that are obtained. Historically, polycrystalline wires, foils and granules were used,10,33 and indeed these forms still find application in major processes, such as ammonia oxidation and oxidative dehydrogenation of methanol, which are not within the scope of this work. A major advance in the formation of clean metal surfaces for catalysis research was the introduction of evaporated metal films49−51 (more properly called condensed metal films). First used in the 1930’s, Otto Beeck and his associates subsequently developed them,52−55 and they were quickly adopted by other scientists. By conductive heating of a wire of the catalytic metal, or of a fragment of the metal attached to an inert wire, in an evacuated vessel, atoms of the metal evaporated and then condensed on the walls of the vessel, forming first islands and later a continuous film. A major strength of the technique was the ability to apply a range of techniques to the study of chemisorption on the film; these included calorimetry, electrical conductance, work function measurement and changes in magnetisation.51 We shall refer below to important results obtained on hydrocarbon reactions using metal films, although they are however no longer much employed.

The more recently favoured form for fundamental research is the single crystal, made by slowly cooling the molten metal. By judicious cutting, an area of about 1cm2 of a well-defined crystal surface is exposed, and when placed within a UHV chamber it can be heated and cleaned by ion bombardment.56 A particular danger with some metals is the slow emergence at the surface of dissolved impurities, particularly sulphur; this is a problem that has been recognised since the early 1970s.57

Two other forms of massive metal deserve a mention. Extremely fine metal tips have been used for Field-Emission Micrpscopy (FEM) and Field-Ion Microscopy (FIM);58 by the latter technique, atomic resolution of the various planes near the tip can be obtained,59 and the process of surface migration closely can be studied.

Considerable interest has been shown in the recent past in amorphous or glassy metals,10,60,61 made by extremely rapid cooling of the molten metal; the product lacks long-range order, and it was believed that their study would reveal the importance of crystallinity in catalysis. However, pure metals are difficult to make in the amorphous state, because of the ease with which they recrystallise.

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The tendency is much less with binary alloys and intermetallic compounds, but catalytic activity is generally low before ‘activation’, which roughens or otherwise disturbs the surface. Interest in their use seems to be declining.

It would be logical at this stage to consider the techniques9,47,58,62−64 that can be used to characterise the metal forms and their surfaces listed above. The problems we face may be classified as follows. (i) With any metal form, it is desirable to establish the surface cleanliness: this is best done by techniques such as X-ray photoelectron spectroscopy (XPS) and the associated Auger spectroscopy (AES), or most sensitively by secondary-ion mass spectrometry (SIMS) or ion-scattering spectroscopy (ISS). These methods9,10,62−64 necessitate placing the material in vacuo, where one hopes it remains stable and unaffected by the radiation used; they are not often applied to the unsupported forms such as blacks or powders.65 (ii) With the more dispersed forms, it is useful to know the size, size distribution and shape of the particles; many of the techniques that are appropriate here are also applied to the study of supported metal catalysts, and will therefore be treated in Chapter 2. (iii) The structure of metal surfaces at the atomic level can only really be examined using single crystals; the predominant method is lowenergy electron diffraction (LEED), which can give surface structures, at least for those areas where the atoms experience long-range order.10,62−64 Other methods capable of providing atomic resolution include scanning-tunnelling microscopy (STM) and atomic force microscopy (AFM)10,64,66, use of which is becoming more popular.

1.2.2. Structure of Metallic Surfaces30,67

Certain things are easy to define, and we have already met a few; other things are more easily recognised than defined. Someone once remarked: I cannot define an elephant, but I’m sure if I saw one I should recognise it. It is much the same with surfaces. It is simple to say that the surface of a solid is the interface between the bulk and the surrounding fluid phase or vacuum; it is also straightforward, if somewhat more complicated, to assign thermodynamic properties to the ‘surface phase’. It is however when one starts to examine a metal surface at atomic resolution that the problems start.

A plane occupied by atoms or ions within a crystal, or at its surface, is defined by its Miller index, which consists of integers that are the reciprocals of the intersections of that plane with the system of axes appropriate to the crystal symmetry.63,68,69 The procedure was not in fact devised by Miller, but by Whewell (1825) and Grossman (1829), and only popularised by Miller in his textbook on crystallography (1829)68: it served to characterise visually observable crystal planes at surfaces long before their atomic structure was known. Consider the three low-Miller-index planes of an fcc metal (Figure 1.9). In the (111) plane, the atoms are close-packed and have a co-ordination number (CN) of nine; while these atoms

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Figure 1.9. Arrangements of atoms in low-index planes for the fcc structure.

are undoubtedly in the surface, some of the properties of atoms in parallel planes beneath the surface plane are not quite the same as those truly in the bulk, but the effect of the interface dies away, usually quite rapidly, as one moves towards the interior. The problem of defining the surface is seen even more clearly with the (100) and (110) planes (Figure 1.9). With the former, atoms in the top plane have CN of 8, and the atoms of the next layer form the bottom of the octahedral holes in the surface and peep through the gap. Yet more obviously, with the (110) surface the atoms actually forming the plane (CN7) are separated by rows of atoms in the next plane down (CN10) which are readily accessible from above. This plane can in fact be represented as a highly stepped (111) surface in which both types of atom participate. Certainly any atom that does not have the full quota of 12 nearest neighbours has to be regarded as part of the surface; the lower its CN the greater is its contribution to it.

Most attention is usually paid to the surfaces of metals of fcc structure because this group contains the best catalysts. The problem of identifying surfaces is greater

¯	¯
with the cph structure, where the (1010) and (1120) planes have second layer atoms
	¯	70	are
that are almost totally exposed (Figure 1.10): the (0001) and (3034) planes

Figure 1.10. Arrangements of atoms in low-index planes for the cph structure.

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Figure 1.11. Arrangements of atoms in the low-index planes of the bcc structure.

however respectively the same as the (111) and (100) planes of the fcc structure. The (100) and (211) planes of the bcc structure also contain second-layer atoms that are substantially exposed (Figure 1.11). Thus, except for the close-packed planes of the fcc and cph structures having hexagonal or cubic symmetry, all other surfaces contain atoms of different CN.

Ordered arrays of atoms of low CN can be produced by cutting a single crystal at a slight angle to a low-index plane;63,71 this will produce (at least in theory) a series of single atom steps separated by plateaux the width of which depends on the angle selected (Figure 1.12). In a further elaboration of this concept, cutting at a slight angle to two low-index planes produces a surface that is both stepped and kinked (Figure 1.13); atoms of unusually low CN are then exposed. The structure of such surfaces may be defined by the Miller index of the plane formed by the atoms at the steps or kinks, or more simply by the indices of the plateau and at the step, together with the number of atoms between the steps (e.g. 5(111) × (100)). This procedure, conceived and exploited by G.A. Somorjai,63 has helped to reveal

Figure 1.12. Representation of stepped crystal surface (fcc (755)).63

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Figure 1.13. Representation of a kinked crystal surface fcc (10,8,7).63

the role of low CN atoms in chemisorption and catalysis, and in a way it models the characteristics of small metal particles. However, unless the steps are quite close together, the contribution of the atoms in the plane defined by the Miller indices will be swamped by that of the low-index plateaux. Incidentally, scanning-tunnelling microscopy (STM) has shown that even surfaces giving a seemingly perfect LEED pattern for a low-index plane may nevertheless have quite a high density of steps and other defects.62 Kink sites lack symmetry when step lengths and faces on either side are unequal; their mirror images are therefore not superimposable, and they possess the quality of chirality.72,73 Representations of many normal and stepped surfaces are to be found in Masel’s book.30

Surface atoms, being defined as having a CN less than the bulk value, are said to be co-ordinatively unsaturated, and, lacking neighbours above them, they experience a net inward force: this effect is equivalent to the more readily sensed surface tension of liquid surfaces, and may be thought of as due either to multiple bonding between atoms in the surface layer, using the surface free valencies, or to a wish to maximise interatomic bonding. It is expressed quantitatively as the surface tension γ, which is the energy needed to create an extra unit of surface area:11,63,70,74 its units are therefore J m−2. It is a periodic function of atomic number (Figure 1.14), following closely the pattern set by sublimation heat (Figure 1.5). For a single-component system at constant temperature and pressure,

γ = Gs

(1.3)

where Gs is the specific surface free energy. Conventional thermodynamic formulae can be applied to give the enthalpy, entropy and heat capacity of the surface layer.63

Even when surface atoms have found their stable places, they will oscillate about their mean positions with a frequency which increases with temperature: thus the signals given by techniques such as LEED, EXAFS and Mossbauer¨

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Figure 1.14. Periodic variation of the surface tension (specific surface work) at 0 K for metals of Groups 1 to 14 (see Figure 1.4 for meaning of points).

spectroscopy weaken as temperature rises, as fewer and fewer atoms are to be found at their exact lattice sites.24,58,63 Surface atoms experience a greater vibrational amplitude than those in the bulk, since they have no neighbours above them to restrain them. Atoms at step and kinks, having fewest neighbours, vibrate most freely, and rising temperature affects surface atoms more than bulk atoms; in this way surface phenomena can sometimes be distinguished from things happening in the bulk. It also follows that the surface is a weaker scatterer of radiation than the bulk.

These concepts may be quantified as follows. A quantum of lattice vibration is termed a phonon, and the mean deviation of an atom from its lattice position is the mean-square displacement u2 . Phonons are detected by vibrational spectroscopy by absorption peaks below 500 cm−1. According to the Debye model, atoms vibrate as harmonic oscillators with a distribution of frequencies, the highest of which is ωD : then the Debye temperature θD is defined as

kθD = hωD /2π

(1.4)

A high θD betokens a rigid lattice, and vice versa: it will be lower for surface atoms than for bulk atoms by a factor of 1/3 to 2/3. It can be measured for bulk atoms by XRD, EXAFS and by the scattering of neutrons or high-energy electrons, and for surface atoms by varying the energy of electrons in LEED to obtain by extrapolation the scattering characteristic of zero energy. By the Lindemann criterion, melting bgins when u2 exceeds a quarter of the interatomic distance: surface melting therefore precedes melting of the bulk.