The Metallic State

The number of atoms required to describe “the metallic state” depends on which properties of the metal we wish to describe. Groups, or clusters, of metal atoms M_m with values of m in the range of 40 to 60 would be quite valuable for the assessment of the nature and energy distribution of orbitals, as well as in discussion of local bonding arrangements. In contrast, such values would be quite inadequate for any consideration of effects associated with the Fermi surface of a metal. Recent calculations have been taken to suggest that metal aggregates containing as few as four noble metal atoms have gross electronic structures that can be related to the bulk metal electronic structures. Against this other calculations would indicate that, in the ground state, the equilibrium bond-lengths of molecules (M₂) at the beginning and end of the 3d transition series are less than nearest neighbour distances in bulk metals especially at the right-hand side of the series where

From a structural point of view the relative numbers of edge and face atoms vary widely for metal particles with sizes in the range 10 to 50 Å. Below 10 Å the crystallites have only edge atoms. Beyond 50 Å more than 90 per cent of the surface atoms are regular face atoms. This effect is demonstrated for rhodium metal clusters in Table I. The chemist, who rightly associates changes in reactivity with changes in co-ordination number, orbital vacancies and electron distribution, will expect the greatest change in reactivity within this range of particle sizes. Such effects will tend to level out beyond that region. It is for particle sizes falling between 10 and 50 Å that the chemist, who is specially interested in the catalytic behaviour of the platinum metals, has been able to obtain considerable information about the interaction of commercially important molecules such as olefins, alkynes, carbon monoxide and hydrogen with small metal aggregates from studies of the co-ordination chemistry of metal clusters M_mL_n(m ≥ 3); L = ligand.

In general two questions are being asked:

Here we define a metal, as did Nyholm, as an element which, in one or more of its forms, is a good conductor of electricity and whose specific resistance (p ) is proportioned to the absolute temperature, T°K.

The second question is not so easily answered. In the past there has been a tendency among chemists to assume that when a stable metal aggregate is under construction atom by atom the growth sequence will follow a path to either a hexagonal close-packed (h.c.p.) or a cubic close-packed form (c.c.p.). In the main, work on transition-metal clusters has tended to support this view, most clusters forming fragments of these common close-packed arrangements. The Rh₁₃ skeleton in [Rh₁₃(CO)₂₄H_5−n]ⁿ⁻ (n = 2, 3 or 4) forms a piece of regular h.c.p. lattice and the Rh₁₄ skeleton in [Rh₁₄(CO)₂₅]⁴⁻-possesses essentially a body centred cubic (b.c.c.) type of structure. Of special interest is the Rh₁₅ cluster [Rh₁₅(CO)₂₇]³⁻ which possesses a structure that is an intermediate structure between the h.c.p. and the b.c.c. forms. The structural relationship between these three structures may be seen in Figure 1.

Another point of interest in connection with the structures of transition metal clusters is the sequence of structures adopted by the osmium compounds [Os₆(CO)₁₈]²⁻, Os₇(CO)₂₁, [Os₈(CO)₂₂]²⁻ and [Os₁₀C(CO)₂₄]²⁻. These progress from the O_h-octahedron, through the mono- and bicapped forms until at [Os₁₀C(CO)₂₄]²⁻ a tetracapped octahedral arrangement of metal atoms is observed. The latter is clearly a fragment of c.c.p. (Figure 2). Of further interest, the carbido-atom in this dianion resides in an octahedral interstitial site.

Cluster compounds, exemplified by these osmium and rhodium compounds, which, in contrast to the metals themselves, are easily studied by the usual physico-chemical techniques, would appear to fill the gap between simple molecular compounds and infinite metallic lattices—at least from a structural point of view.

However, as may be seen from Table II the structures of these small clusters are different from those of the pure metals. Polymorphism is common to the transition metals and structural changes which are sensitive to external influences (for example, ligands such as CO) are not, therefore, too surprising. This is apparent from the work carried out on the Rh₁₃, Rh₁₄ and Rh₁₅ clusters referred to earlier in the text.

 

Table II

Metallic Structures of the Platinum Metals

 

 

 

 

 

 

Ruthenium	Rhodium	Palladium
h.c.p.	c.c.p.	c.c.p.
Osmium	Iridium	Platinum
h.c.p.	c.c.p.	c.c.p.

Recent calculations on the stability of small aggregates of platinum metals, using both the Lennard-Jones and the Morse potential, showed that polytetrahedral aggregates are more stable than the face centred cubic (f.c.c.) or h.c.p. types. Polytetrahedral packing may be carried out atom by atom according to three different growth sequences as shown in the Scheme, opposite. It would appear that for clusters with more than 70 atoms (∼10Å) the more stable aggregates are expected to form regular f.c.c. types. Examples of tetrahedral growth patterns have been found in cluster co-ordination chemistry. Commonly found for gold, such icosahedral forms are not related to the more common close-packed arrangements. Again, cluster chemistry provides examples of pentagonal symmetries in, for example, the Pt₁₉(CO)₂₂]⁴ anion, which provides an especially attractive example (Figure 3) and in Os₆(CO)₁₈ which has the triple tetrahedron structure (Figure 4).

We should note that the ductility, malleability and softness of pure metals depend at least to some extent, on the ease with which adjacent planes and rows of atoms can glide over one another. This in turn depends upon the ability of the metal atom to reorganise its bonding requirements. In a cubic close-packed crystal there is a greater possibility of gliding because there are four equivalent sets of parallel close-packed planes whereas in hexagonal close-packed crystal there is only one such plane. Thus palladium and platinum are ductile and malleable by comparison with ruthenium and osmium, see Table II. Crystals with pentagonal symmetries (D_5h etc.) might be expected to be quite hard and brittle, similar to boron in fact.

Bonding

Put simply, the properties of metals—good conductors whose specific resistance (ρ ) is proportional to the absolute temperature T°K—arise because metals have a (relatively) small number of available valence electrons in comparison with the larger number of low-lying (molecular) bonding orbitals. Thus, metals display multicentre, electron-deficient bonding. The view that the bonding in metals may be described as involving “positive metal ions in a sea of electrons” is misleading, emphasising as it does an ionic nature within the metal. Metals are best regarded as covalent with bonding delocalised throughout the metal lattice, allowing the easy movement of electrons through the lattice.

This easy movement of valence electrons between the atoms of the metallic lattice is responsible essentially—although not exclusively—for the transport of electric current. A small part of the current may be due to the motion of metallic ions. It is worth remembering, however, that at high current densities it is often possible with alloys to observe a change in the concentration of alloy components as a consequence of the passage of current. This effect may be correlated with large differences in the coefficient of electronegativities. It can also be shown that the geometric arrangement of metal atoms within limits does not unduly affect orbital overlap, thus allowing easy movement of metal atoms with respect to each other without breaking the lattice. The activation energy for such movement is small (∼0.5 kJ/mol) compared to usual chemical processes (80 to 160 kJ/mol) or fluxional behaviour (20 to 80 kJ/mol). Metal atoms may, therefore, be displaced very easily. This explains, at least to some extent, their malleability and ductility and the ease of polishing of, for example, palladium and platinum. To some degree it may also account for their catalytic properties.

The ability of the metallic surface to undergo structural rearrangement to accommodate the incoming substrate is clearly of importance. It has also been argued that the catalytic activity of the platinum metals is related to the anomalous co-ordination numbers and site deficiencies exhibited by the surface even within regular lattice types. However, it is significant that the importance of the so-called non-lattice symmetries (as in the tetrahedral growth patterns outlined in the scheme and often found for microcrystallites of the platinum metals) in catalysis has been recognised, and it is interesting to record that such geometries are observed with platinum metal cluster compounds, for example Os₆ and Pt₁₉.

However, this description of bonding is far too simple. The chemical bond in metals is far less well defined than in simple molecular species. Unlike simple molecules, the atomic orbitals within a metal do not so easily form a sound basis for discussing the electronic properties of metals. Within the metal the density of orbitals is so high that atomic orbital overlap occurs far beyond the first coordination sphere, (next nearest neighbours). It is, therefore, difficult to assign any special chemical significance to the overlap of atomic orbitals on nearest neighbours though it is just this overlap which is used to give a quantum mechanical meaning to the idea of the chemical bond.

Apart from the advantages stemming from high co-ordination numbers and close-packing, little is known of the basis of geometric arrangement as a source of structural stability—apart from transition metal cluster compounds with up to about six metal atoms. It appears that close-packed structures occur when the concentration of electrons is low (∼2 electrons per atom) whereas for higher concentrations (∼2 to 4) directed chemical bonds play a role in the structural arrangement—hence more success with molecular cluster compounds—and structures are no longer close-packed. A major problem in assessing the importance of geometric effects is the lack of any precise knowledge of the suitable sizes of metal atoms. This point is clearly emphasised by the range of metal-metal distances found in cluster compounds. In metals the atoms frequently have vacant orbitals in addition to those containing electrons; in addition they are generally surrounded by far more neighbours than can be bonded by simple electron pair bonds. As a consequence atoms are generally separated by distances considerably greater than those expected for a bond order of one. It follows that there is a considerable latitude in how closely any particular pair of atoms may approach each other without generating a strongly repulsive interaction. For this reason many different interatomic distances are found in the structures of metals, alloys and cluster compounds. Any relationship between bond length and bond order is thus not readily developed for such systems. The compression of atoms may occur in order to produce high coordination numbers, the total summation of bond energies outweighing any energy penalty created. A bond shortening should not, therefore be necessarily interpreted as the result of increased bonding in these directions, since it may arise merely in order to allow more effective contacts between atoms in other directions. In the case of metals it is for this reason that the concept of atomic volume is more meaningful than that of interatomic distance. It follows from these arguments that the more strongly electronegative ligands such as Cl⁻ cause a contraction in interatomic distance, whereas more strongly electron donating ligands such as CO cause interatomic expansion in metallic clusters such as Pt₆Cl₁₂ and Os₆(CO)₁₈, respectively.

Properties of Metals

A chemist’s role is to seek general relationship covering a group of elements or compounds and then to look for an explanation of similarities and differences. We will adopt this attitude and seek correlations between the properties of the metal and platinum fundamental atomic parameters. Given that metals are essentially covalent, it is not unreasonable to ask how far one can go in correlating the properties of solid metals with a simple model based on a diatomic molecule.

Physical Properties

For a diatomic molecule (M₂), the vibration frequency (ν ) and the force constant (k′) are related by the expression

where μ is reduced mass given by the equation

Physical properties which are dependent on the stretching of M–M bonds should be dependent on k′ and hence proportional to Mν ².

Using this very simple model most of the physical properties may be understood in terms of:

The metal is regarded as an assembly of n metal atoms, each of mass m, oscillating in simple harmonic motion with a range of frequencies which at low temperatures range from ν ₀, ν ₁, ν ₂ up to ν _max. As the temperature is raised the mean frequency (and amplitude) of vibration of individual atoms increases. At temperatures near to, or above, θ (the so-called Debye temperature) it is assumed that most atoms are vibrating with a frequency ν _max, provided that θ is not too large compared with room temperature, and the expression

may be used.

For a particle of mass m vibrating in simple harmonic motion the kinetic energy is given by mean square of the amplitude of vibration), which may be rewritten as CMθ ²(X²) (C = constant), and since the energy is proportional to T°K then

Thus, properties dependent on X² should be proportional to T°K. Within this class fall melting point, electrical conductivity and thermal conductivity.

This information is classified in Table III.

Properties dependent on (a), namely multicentre bonding and the ability to undergo structural rearrangement, will be electrical conductivity, malleability, ductility, ease of polishing, and polymorphism. Those properties which will also be dependent on (b) and (c), the mass of the metal atom (M) and the vibration frequency (max ν ) will include elasticity, the thermal coefficient of expansion and hardness. Finally there are those properties which will depend not only on (a), (b) and (c) but also on (d), the amplitude of vibration (X²). Since X² is proportional to T°K these will include melting point, electrical conductivity and thermal conductivity.

Chemical Properties

For an understanding of the chemical properties of metals knowledge of four further parameters is necessary. These parameters are:

at 298°K and one atmosphere pressure.

Essentially it may be taken as a measure of the M−M bond strength (E_M−M). The manner in which ▵H°_at (and thus (E_M−M) varies within the transition metal block is shown in Figure 5. Some of the highest values are found for the platinum metals although the values for palladium, silver, and gold are smaller than those for several first row elements. A plot of the boiling points against ▵H°_at values is roughly linear, suggesting that the boiling point of a metal is largely dependent on E_M−M. It would appear that there is very little disruption of the metallic bonding when the crystal melts, and nearly all metallic bond strength is conserved until the metal boils.

(ii) The ionisation energy for the formation of the appropriate ion Mⁿ⁺ (I.P.).

The ionisation energies (and potentials) for the platinum metals are given in Table IV.

Among the platinum metals the third row elements, osmium, iridium and platinum, exhibit very high first ionisation energies. However, as elsewhere in the transition metal block, values for some members of the second row are less than those of the first row, for example Ru < Fe < Os, Rh < Co < Ir and Ag < Cu < Au, but a revision occurs in the nickel triad Ni < Pd < Pt. The very high values of ▵H°_at and ionisation energies for the members of the third row are clearly responsible for the relative inertness of these metals. The high values of ▵H°_at for osmium, iridium and platinum must also be largely responsible for the tendency that these metals have to form cluster compounds. It may be argued that by forming such clusters the energy required is a fraction of that necessary to produce individual atoms. Furthermore, one of the consequences of the multicentre bonding approach—or broadening of the energy levels containing the valence electrons into an energy band—is that the minimum energy required to remove an electron from the bulk metal is much less than the ionisation energy of the free atoms. This so-called work function may be determined from photoelectric measurements. It follows that the energy required to remove an electron from a small cluster of atoms will also be less than the ionisation energy, although certainly more than the work function. Hence both ▵H°_at and ionisation energies favour cluster formation as opposed to the formation of simple monometal compounds.

Values of electronegativity coefficients, as derived by Pauling, are given in Table V. Metals with the largest electronegativity values include the noble metals with coefficients in the range 1.9 (silver) to 2.4 (gold). These values may be compared to those of the more electropositive metals rubidium (0.8) and caesium (0.7). As listed above a pure metal has essentially covalent multicentre bonding and replacement of one metal by another of a similar kind produces an alloy with similar bonding. In contrast, if two metals of widely differing electronegativities are employed then an ionic compound results. Such is the case with caesium and gold giving Cs⁺Au⁻. As such, gold may be regarded as a quasi halide. It is worth remembering in any discussion of this sort that electronegativity values are dependent on their source. The Pauling values, derived from bond energies of chemical compounds, tend to be larger than those of Mulliken given by (I.P. + E.A.)/2.

Conclusion

Any simplistic approach such as that offered here can at best offer only a limited guide to the behaviour, both physical and chemical, of the platinum metals. Nevertheless, such a simple model is not without its attractions. Certainly it can act as a useful guide and can offer some understanding of the multitude of factors responsible for the so-called metallic properties.