Metal-Catalysed Reactions of Hydrocarbons / 01-Metals and Alloys
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We may expect surface energy to be less for planes having the greater density of atoms, such as the fcc(111), because their creation by splitting a large crystal requires less work to be done than with more open planes such as the fcc (100). One important consequence of the skin effect is that bond lengths normal to the surface are usually shortened between the first and second layers, typically by a few percent, while there is expansion again between the second and third, and contraction again between the third and fourth layers. Contraction is greater the lower the co-ordination number of the surface atoms, i.e. the greater the surface energy, so that atoms at kinks are most noticeably affected, as are less densely packed planes in general.
The desire of a system to minimise its total energy determines that the surface energy should be as small as possible, so that where the potential benefit of changing from a high to a lower surface energy is sufficiently great the surface may reconstruct to achieve this saving. This may mean that the surface layer has to adopt a structure which is out of register with that of the underlying crystal; thus for example the (100) surfaces of iridium, platinum and gold are covered by a layer of (111) geometry, and the (110) surfaces can reconstruct to form more extended areas of (111) plane by ‘losing’ alternate rows.63,75−79 These types of reconstruction occur with clean surfaces only in the case of the Third Transition Series fcc metals, because they have higher heats of sublimation than the earlier metals (Figure 1.5), and therefore stand to gain more by forming closely-packed surfaces: this is a further manifestation of the relativistic effect.13,21 Ease of reconstruction depends on the density of packing the surface metal atoms; surfaces containing atoms of relatively low CN are most mobile, and reconstruct more easily than close-packed planes. With the surfaces of elements other than iridium, platinum and gold, reconstruction occurs only in the presence of a chemisorbed layer of atoms (e.g. carbon, oxygen, sulphur), which is able to mobilise the surface metal atoms by weakening their bonds to the atoms beneath. With molecular species that are strongly chemisorbed (e.g. ethylidyne, ethyne, see Chapter 4), a small group of metal atoms involved in the bonding may be drawn outwards; this process is sometimes described as extractive chemisorption, and the consequences of this disturbance may be felt by atoms even more remote.
The relative surface energies of different crystal planes determine the equilibrium shape of a metal crystal, and this can be predicted from knowledge of the energy terms by use of the Wulff construction.10 In this procedure the surface energies are drawn as vectors normal to the planes described by the indices, and these planes set at the tops of the vectors define the crystal shape.
The activation energies for surface self-diffusion are also much lower than sublimation energies, since here again only a limited number of bonds need to be broken to allow movement. Diffusion coefficients are not surprisingly much greater, and activation energies are lower, the more closely-packed the atoms in the plane: thus for example values of the latter for rhodium atom migration vary
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from 84 kJ mol−1 on the (100) plane, through 58 kJ mol−1 on the (110), to as little as 15 kJ mol−1 on the (111) surface.63
The work that has to be done to remove an electron from a metal into vacuum with zero kinetic energy at zero K is termed the work function,24,80 and this is the same as the ionisation potential, but is larger than that of the free atom because of the space charge or surface dipole that exists at the surface, due to the asymmetry of electron density. Work function is greatest at planes having a high concentration of atoms (i.e. generally low-index planes), and decreases with step density at stepped surfaces.63 Variation of work function with crystal plane underlies the technique of Field-Emission Microscopy (FEM).
This short survey suggests that, in the absence of a chemisorbed layer, atoms at the surface of massive metal are in a state of considerable agitation that belies the static impression that structural images convey.77,78 We shall see in the following chapters how this conclusion is affected by particle size and by adsorbed entities.
1.2.3. Theoretical Descriptions of the Metal Surface29
Our concern now is with the form of theoretical analysis appropriate to the extended metal surface; corresponding approaches suitable for small metal particles will receive attention in Chapter 2, although some of the concepts may apply there also. The literature is somewhat coy in dealing with this problem. We know that the necessary conditions for the Band Model cannot obtain at the surface, and indeed electrons emerging at near-grazing angles in X-ray photoelectron spectroscopy (XPS), and those stimulated by lower energy UV radiation (UPS), indicate bands narrower than those of the bulk, as well as additional features due to ‘surface states’, i.e. to electrons localised on surface atoms.63,81 It has to be accepted that the electronic structure of surface atoms, i.e. the extent to which their various energy levels or the bands in which they participate are occupied, will differ from that of atoms below the surface, and will be unique to each co-ordination number.82 Thus for example atoms at the tops of steps may have a lower density than those at the foot, and this may be the source of greater or even excessive activity in chemical process, although the evidence on this point is equivocal. Structure can be expressed as a local density of states (LDOS)83, which can now be calculated using the tight-binding approximation, and particular interest attaches to the LDOS at the Fermi surface (EF-LDOS) because it appears84 that electron density outside the surface (defined as the plane through the nuclei) comprises progressively more of these energetic electrons as distance increases. The EF-LDOS may well therefore determine surface reactivity in chemisorption and catalysis (see also Section 2.55).
The chemist’s mind may have some difficulty in grasping the concept of a band structure and LDOS for a single atom (e.g. at a kink site), but it may be helpful to remember that band width is a variable feast, increasing with the number of adjacent atoms of like type. There can therefore be all widths from the full width
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for bulk atoms to zero widths for isolated atoms, but this kind of information does not however seem to have been much applied to understanding and interpreting catalytic phenomena.
An alternative procedure is to attempt a molecular orbital description of surface atoms. It starts with the simple-minded view of an unrelaxed surface, such as would exist immediately after cleavage of a metal crystal.85 It was noticed some years ago86,87 that the arrangement of atoms in a metal of fcc structure, i.e. 12 near neighbours and 6 next-nearest neighbours, was precisely matched by the disposition of, respectively, t2g and eg orbital lobes of the d-electrons employed in octahedral complexes such as PtIICl62−. Bands may then be formed by a symmetryadapted linear combination of these atomic orbitals.24,88,89 It is a straightforward matter to map out how these orbital lobes project from any crystal plane85,90 (for an example, see Figure 1.15). The procedure has been criticised as overly simplistic,91 as indeed it is: it does not employ hybrid dsp-orbitals, as it should, although whatever the actual hybridisation it must generate orbitals sterically similar to those of the d-electrons. Furthermore, whatever the composition of the hybrid, the emerging orbitals must, according to this picture, be congruent with those that determine the bulk structure. Although such descriptions are unlikely to apply to the clean equilibrated (i.e. relaxed) surface, it is possible that a molecular orbital picture along the above lines may be appropriate when chemisorbed species have counteracted the relaxation. With all its imperfections, however, it has received some
Figure 1.15. The emergence of orbitals from the (100) face of an fcc metal. Filled arrows, eg orbitals in the plane of the paper: hatched arrows, t2g orbitals in the plane of the paper: open arrows, t2g orbitals emerging at 45◦ to the plane of the paper. The dashed circle shows the position of an atom in the next layer above the surface layer. In both the plan and the section an eg orbital emerges normal to the plane of the paper from each atom.
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support,59,88,89,92 especially from R.L. Augustine and his associates92−94 who have extended it to the various types of surface atom having a low CN, and have further adapted the Angular Overlay Model to predict the energies of their s-, p- and d-electrons. A more rigorous and theoretical respectable quantum mechanical treatment of emergent orbitals has been developed, and applied to hydrogen chemisorption (Chapter 3).
The original work85 and these further developments relate only to the fcc structure, which accounts for the most catalytically interesting and useful metals, but the concept can be extended to the bcc and cph structures using the orbital assignments given many years ago by Trost95 and others.40 In these cases however it is essential to use hybrid orbitals having d, s and p components.
Returning for a moment to the description of bonding inside the crystal,24 those d-orbitals whose interactions are responsible for bonding nearest neighbours (viz. the t2g family) will form a band which is broader than that formed by the eg family, since interactions between next-nearest neighbours are less strong. Extending this concept to surface atoms, we see on the (100) surface for example that the absence of atoms above the plane means that the overlap of dx z and dx y orbitals has decreased and their band is narrowed, while the dyz orbitals in the surface plane are unaffected, and their band remains broader. Similar but smaller effects will occur with the eg and s-orbitals. The modification of electronic structure of atoms at steps and kinks is then easily rationalised,96 and the story will be resumed in Chapter 2, where other concepts developed in the context of small metal particles will be considered.
1.3. ALLOYS96
1.3.1. The Formation of Alloys11,23,31,41,50,97
This section is not primarily concerned with the mechanics of making alloys, but rather with the physical chemistry that determines whether they are formed or not. The term ‘alloy’ has been used indiscriminately in the literature,10 but we shall restrict its meaning to a material containing two or more elements in the zero-valent state that are mixed at the atomic level. What happens when two metals are brought together depends on the thermodynamic functions that describe their interaction, and on temperature; the former depends on their relative sizes and electronic structures.
We consider first bimetallic substitutional alloys, where atoms of either kind can occupy the same lattice site. Now an ideal solution is one for which the enthalpy of mixing is zero, and the process of alloy formation is purely entropy-driven;
Smix = R[x ln x + (1 − x ) ln (l − x )] |
(1.5) |
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where x is the mole fraction of one component. Deviations from ideal behaviour are expressed by excess functions. Near-ideal solid solutions are formed between metals having the same crystal structure, their atoms being of almost the same size and having similar electronic structures; this usually means they have to be in the same or adjacent Groups of the Periodic Table. Such pairs have complete mutual solubility and are described as monophasic. There are many examples of this class, for example, alloys formed between silver and gold or between palladium and silver. For solutions formed endothermically (i.e. Hmix is positive), there is a limit to the solubility of each in the other even if both have the same structure, and there is a range of composition where the alloy comprises various amounts of two phases of constant composition: such alloys are said to be biphasic. The nickel-copper system is of this type10,49,98 and it has been very thoroughly studied. The free energy of mixing at 473 K has been calculated from the excess functions (Figure 1.16), and the two minima define the limits of the two-phase region in which there is a physical mixture of alloy phases containing respectively 3 and 85% copper. Thus a mixture containing equal numbers of nickel and copper atoms will have 40% of the copper-rich alloy and 60% of the nickel rich alloy. If temperature is increased, the entropy term −T Smix becomes more important,
Gmixbecomes more negative, and the two-phase region contracts, until the critical solution temperature is reached, above which the components are miscible in all proportions. The platinum-gold system is also of this type.
For alloys that are formed endothermically or only slightly exothermically, there are many indications of a mutual perturbation of the electronic structure. As attractive interaction increases and the process becomes more exothermic,99 random arrangements are replaced at certain compositions by ordered superlattices
Figure 1.16. Free energy of formation of nickel-copper alloys at 473 K as a function of composition.
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(or superstructures) such as are formed in the platinum-copper and gold-copper systems (e.g. Cu3Pt, Cu3Au). Other examples occur in the platinum-tin system (Pt3Sn, Pt2Sn) and in the aluminium alloys used for making Raney metals.100 Even stronger interaction leads to the very exothermic formation of intermetallic compounds101,102 between quite unlike elements (e.g. HfIr3, Ce2Ni, CeRh3, ZrPd3). Compositions used for forming amorphous alloys by melt spinning are often of this type.61 The terminus of this progression is of course the formation of recognisable compounds such as oxides and sulfides.
Interstitial alloys101 are formed between metals and non-metallic or semimetallic elements such as boron, phosphorus, carbon and nitrogen: the latter occupy holes in the metal structure, which may however have to expand or re-arrange to accommodate them.2,7 Carbides and nitrides of metals of the first Transition Series form spontaneously during catalytic reactions where the reactants contain these atoms, and are themselves catalytically active.101,103 They do not exist as stable compounds of the noble metals of Groups 8 to 10.
Many of the physical properties of monophasic alloys are intermediate between those of the pure components. Lattice parameters, readily determined by X-ray diffraction and constituting a sensitive means of checking alloy composition, often show only slight deviations from Vegard’s Law, which states that they should be linear functions of composition. The silver-gold system is unusual in that the lattice parameter passes through a maximum, but the two metals are of almost the same size. Certain binary alloys exhibit a number of intermediate phases differing in structure as well as composition; according to the Hume-Rothery Rules,23,31 the structure depends on the ratio of valence electrons to atoms, and such alloys (occurring for example in the Cu-Zn (brass) system) are termed electron compounds. The systematic alteration of structure that is independent of the atomic mass of the metal is reminiscent of that found on passing through the Transition Series metals, but the explanation cannot be the same.
Electronic properties such as electrical conductance, magnetic behaviour and band structure typically show dramatic changes with alloy composition, especially where the electronic structures of the pure components differ greatly, as happens for example when the d-shell is filled. Alloys of this type (Ni-Cu, Pd-Ag, Pd-Au) were the subject of intensive research in the period 1945-1970, as it was believed that the presence of an incompletely-filled d-shell was an important feature in determining catalytic activity, and that filling would occur at some composition that could be deduced from electronic properties. The experimental results and the theoretical models that form our present state of understanding of the behaviour of electrons in alloys will be considered in the following section.
One quite new way of making alloys suitable for fundamental study is to condense atoms of one metal onto the surface of a single crystal of the other: there results a ‘two-dimensional alloy’. The surface composition is easily changed, the problem of surface segregation (see following text) is avoided, and bimetallic
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systems having little or no mutual bulk solubility (e.g. Ru-Ag) are available for study. Extensive information is now available on how metals interact when brought together in this way,10 and on the way in which atoms of the second metal agglomerate as their coverage is increased.10 One surface which has received much attention is the isotropic Ru(0001) (Figure 1.10); the coinage metals have all been deposited on it to give bimetallic catalysts simulating the dispersed forms which have also proved of great catalytic interest (see Chapter 2). However the film of the deposited metal may suffer strain through mismatch of atomic sizes, with consequential effects on its physical properties.104
1.3.2. Electronic Properties of Alloys and Theoretical Models105
The paramagnetism or ferromagnetism shown by the metals of Group 10 is progressively lost on alloying with a metal of Group 11. Nickel, which has a saturation magnetic moment of 0.606 Bohr magnetons, was thought to have about 0.54 d-band holes per atom, these two numbers being in fair agreement, and on addition of copper the magnetic moment falls linearly to a minimum value at 60% copper. Parallel changes were observed23,106 with the low-temperature electronic specific heat coefficient and with the Curie temperature (at which ferromagnetic elements become paramagnetic), and analogous changes were seen with other Group 10-Group 11 alloys.10,33 It was therefore perfectly logical to suppose that the s-electrons of the Group 11 metal atoms entered and filled the d-band of the Group 10 metal: this simple and satisfying picture, first advanced by Mott and Jones,106 came to be called the Rigid Band Model, because it was assumed that the band shape of the Group 10 metal was unaltered by alloying. The valence electrons were thought to share a common band system, and the metals to lose their identity, except in regard of their nuclear charge. Unfortunately, as Oscar Wilde said, The truth is rarely pure and never simple: this model proved to be incorrect. Errare humanum est.
Early work on electron band structure by soft X-ray spectroscopy was concentrated on pure metals,23 and it was not until the advent of photoelectron spectroscopies that alloys started to be examined. It soon became clear that small additions of nickel to copper resulted in the appearance of electrons having energies close to the Fermi value; there was no common d-band, but each component exhibited its own band structure10,58 (Figure 1.17). Many other kinds of physical measurement confirmed this, and corresponding behaviour was observed with the palladium-silver system (Figure 1.18). It became necessary to find a new and better theory.
The heart of the problem is this: a copper atom in a nickel matrix does not wish to lose its 4s electron totally, nor does a nickel atom wish to accept, it as this would be tantamount to forming an ionic bond Ni−Cu+. While electrostatic bonding can contribute to the stability of some intermetallic compounds, as in the
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Figure 1.17. Band structures of (A) nickel, (B) copper and (C) a nickel-copper alloy as revealed by the intensity of photoemission current as a function of energy.
Cs+Au− type of compound, which we have already met, it is not a suitable basis for explaining the formation of alloys. An early attempt to solve at least part of the problem involved looking at a nickel atom in a copper matrix. The 3d electrons of the nickel atom occupied highly localised energy levels around it,107 but they were broadened by resonant interaction with the 4s electrons of copper.108 The width of the d-band should increase with nickel concentration as the d-electrons
Figure 1.18. Valence band spectra for (A) silver, (B) palladium + silver and (C) palladium supported on silica.
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start to interact; this is what is observed experimentally. The d-electrons thus occupy a virtual bound state, this being the name applied to the model, which is associated with the names of Friedel and Anderson.109 The d-band holes (about 0.6 of them on average), remain associated with the nickel atoms,110 and alloys are paramagnetic up to the highest copper contents. XANES measurements (Section 2.42) on nickel-copper powders using LII and LIII absorption edges have confirmed that the number of d-states on nickel atoms decreases only slowly with increasing copper content, and at Ni5Cu95 is still 95% of that in pure nickel. However, even at Ni15Cu85, nickel atoms start to form clusters, which show superparamagentism: these start to overlap at about Ni40Cu60 and ferromagnetism appears. In going from this composition to pure nickel the overlap increases, giving a linear dependence of ferromagnetic saturation moment on nickel content.106 It was this that misled early workers into thinking that copper’s electrons filled the d-band holes in nickel. Short-range ordering is slight in this system, but increases in importance as Periodic Group separation of the elements forming the alloy becomes greater.
Proper quantum mechanical approaches to understanding the properties of alloys encounter a real difficulty at the start, because of the inhomogeneous potential field through which the electron waves must move. The random arrangement of ion cores of different nuclear and electronic charge density causes the electron waves to suffer multiple scattering, which causes electrical conductance to increase: the essence of the theoretical problem lies in how to tackle this. One quite successful method10,111 is to suppose that the electron wave moves through a uniform or coherent potential, and is affected only by a single selected scatterer. The effective medium is chosen self-consistently, and the Coherent Potential Approximation results from the self-consistent solution to a multiple-scattering version of the Schrodinger¨ equation within a single site approximation. Density of states curves and other physical properties are well described by this theory.10
We now have to think how the chemical interaction of the components of the alloy when at the surface affects their ability in chemisorption. Before we can look at this, however, we must address the problem of surface segregation.
1.3.3. The Composition of Alloy Surfaces74,99
In general the ratio of the two components of a bimetallic alloy is not the same in the surface layer (or layers, see preceding section) as in the bulk. The reason for this is that at equilibrium the configuration is adopted which minimises the total energy, and, since this includes surface energy, that component having the lower surface energy will tend to concentrate in the surface. If it does not, it is because diffusion normal to the surface is slow, and the system is not at equilibrium. To a first approximation, therefore, we may use values of surface tension (specific surface work) or heat of sublimation to predict which partner will segregate at the surface.
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The formalism used for liquid solutions can also be applied to solids.74 For an ideal solution, the enthalpy of mixing is zero, and by application of the Gibbs equation we can deduce that the ratio of the mol fractions of the two components
in the surface x1s /x2s is given by |
|
x1s/x2s = x1b/x2b exp[(γ2 − γ1)a/RT] |
(1.6) |
where superscript b stands for bulk and a is the molar area of component 2. This equation permits the surface composition to be estimated if the surface tensions of the two components are known. We may note that the extent of segregation will decrease with rising temperature. The next refinement is to allow for non-ideality by introducing the regular solution parameter , which is in the nature of an excess heat and may be defined as
= Hmix/x1 x2 |
(1.7) |
When is positive, bonds between unlike atoms are preferred and greater enrichment occurs at low bulk concentrations, but if it is negative bonds between like atoms are preferred and greater enrichment occurs at high bulk concentrations. The somewhat complex equations10 which describe surface enrichment for real solutions, i.e. when is not zero, can also predict concentration differences in second, third and fourth layers.
For example, when is negative, weak enrichment of one component in the surface is accompanied by an increased amount of the other in the second layer. We have already considered the difficulty of deciding which atoms are actually in the surface layer. With ideal solid solutions, it is only the concentration in the first layer that differs from that of the bulk.
There are several other factors that deserve mention before this subject is left. First, the surface tensions of different crystal planes may vary quite considerably; the value is greater for less densely packed planes (e.g. for fcc(100) it is less than for fcc(111), Figure 1.9) because of the smaller number of bonds that need to be broken to create new surface. Preferential segregation at these planes therefore minimises the system’s energy, and by extension of this principle atoms of unusually low CN, such as occur at steps and kinks, are particularly favoured sites for segregated atoms. The reader wishing to explore further the question of surface enrichment in binary alloys should consult the classic paper by Williams and Nason.112
Amongst the main experimental techniques that have been deployed to determine the composition and structure of binary alloy surfaces, Auger electron spectroscopy (AES), XPS, LEED and ISS feature most prominently. There is now a very large literature describing the results obtained, which, after some early inconsistencies had been resolved, are now generally in line with theoretical