Metallic bonding is not the only type ofchemical bonding a metal can exhibit, even as a pure substance. For example, elementalgallium consists ofcovalently-bound pairs of atoms in both liquid and solid-state—these pairs form acrystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is themercurous ion (Hg2+ 2).
As chemistry developed into a science, it became clear that metals formed the majority of theperiodic table of the elements, and great progress was made in the description of the salts that can be formed in reactions withacids. With the advent ofelectrochemistry, it became clear that metals generally go into solution as positively charged ions, and the oxidation reactions of the metals became well understood in their electrochemical series. A picture emerged of metals as positive ions held together by an ocean of negative electrons.
With the advent of quantum mechanics, this picture was given a more formal interpretation in the form of thefree electron model and its further extension, thenearly free electron model. In both models, the electrons are seen as a gas traveling through the structure of the solid with an energy that is essentially isotropic, in that it depends on the square of themagnitude,not the direction of the momentum vectork. In three-dimensional k-space, the set of points of the highest filled levels (theFermi surface) should therefore be a sphere. In the nearly-free model, box-likeBrillouin zones are added to k-space by the periodic potential experienced from the (ionic) structure, thus mildly breaking the isotropy.
The advent ofX-ray diffraction andthermal analysis made it possible to study the structure of crystalline solids, including metals and their alloys; andphase diagrams were developed. Despite all this progress, the nature ofintermetallic compounds andalloys largely remained a mystery and their study was often merely empirical. Chemists generally steered away from anything that did not seem to follow Dalton'slaws of multiple proportions; and the problem was considered the domain of a different science, metallurgy.
The nearly-free electron model was eagerly taken up by some researchers in metallurgy, notablyHume-Rothery, in an attempt to explain why intermetallic alloys with certain compositions would form and others would not. Initially Hume-Rothery's attempts were quite successful. His idea was to add electrons to inflate the spherical Fermi-balloon inside the series of Brillouin-boxes and determine when a certain box would be full. This predicted a fairly large number of alloy compositions that were later observed. As soon ascyclotron resonance became available and the shape of the balloon could be determined, it was found that the balloon was not spherical as the Hume-Rothery believed, except perhaps in the case ofcaesium. This revealed how a model can sometimes give a whole series of correct predictions, yet still be wrong in its basic assumptions.
The nearly-free electron debacle compelled researchers to modify the assumpition that ions flowed in a sea of free electrons. A number of quantum mechanical models were developed, such as band structure calculations based on molecular orbitals, and thedensity functional theory. These models either depart from the atomic orbitals of neutral atoms that share their electrons, or (in the case of density functional theory) departs from the total electron density. The free-electron picture has, nevertheless, remained a dominant one in introductory courses on metallurgy.
The electronic band structure model became a major focus for the study of metals and even more ofsemiconductors. Together with the electronic states, the vibrational states were also shown to form bands.Rudolf Peierls showed that, in the case of a one-dimensional row of metallic atoms—say, hydrogen—an inevitable instability would break such a chain into individual molecules. This sparked an interest in the general question: when is collective metallic bonding stable, and when will a localized bonding take its place? Much research went into the study of clustering of metal atoms.
As powerful as the band structure model proved to be in describing metallic bonding, it remains a one-electron approximation of a many-body problem: the energy states of an individual electron are described as if all the other electrons form a homogeneous background. Researchers such as Mott and Hubbard realized that the one-electron treatment was perhaps appropriate for strongly delocalizeds- andp-electrons; but ford-electrons, and even more forf-electrons, the interaction with nearby individual electrons (and atomic displacements) may become stronger than the delocalized interaction that leads to broad bands. This gave a better explanation for the transition from localizedunpaired electrons to itinerant ones partaking in metallic bonding.
The nature of metallic bonding
The combination of two phenomena gives rise to metallic bonding:delocalization of electrons and the availability of a far larger number of delocalized energy states than of delocalized electrons.[clarification needed] The latter could be calledelectron deficiency.
Metal aromaticity inmetal clusters is another example of delocalization, this time often in three-dimensional arrangements. Metals take the delocalization principle to its extreme, and one could say that a crystal of a metal represents a single molecule over which all conduction electrons are delocalized in all three dimensions. This means that inside the metal one can generally not distinguish molecules, so that the metallic bonding is neither intra- nor inter-molecular. 'Nonmolecular' would perhaps be a better term. Metallic bonding is mostly non-polar, because even inalloys there is little difference among theelectronegativities of theatoms participating in the bonding interaction (and, in pure elemental metals, none at all). Thus, metallic bonding is an extremely delocalized communal form of covalent bonding. In a sense, metallic bonding is not a 'new' type of bonding at all. It describes the bonding only as present in achunk of condensed matter: be it crystalline solid, liquid, or even glass. Metallic vapors, in contrast, are often atomic (Hg) or at times contain molecules, such asNa2, held together by a more conventional covalent bond. This is why it is not correct to speak of a single 'metallic bond'.[clarification needed]
Delocalization is most pronounced fors- andp-electrons. Delocalization incaesium is so strong that the electrons are virtually freed from the caesium atoms to form a gas constrained only by the surface of the metal. For caesium, therefore, the picture of Cs+ ions held together by a negatively chargedelectron gas is very close to accurate (though not perfectly so).[a] For other elements the electrons are less free, in that they still experience the potential of the metal atoms, sometimes quite strongly. They require a more intricate quantum mechanical treatment (e.g.,tight binding) in which the atoms are viewed as neutral, much like the carbon atoms in benzene. Ford- and especiallyf-electrons the delocalization is not strong at all and this explains why these electrons are able to continue behaving asunpaired electrons that retain their spin, adding interestingmagnetic properties to these metals.
Electron deficiency and mobility
Metalatoms contain fewelectrons in theirvalence shells relative to their periods orenergy levels. They areelectron-deficient elements and the communal sharing does not change that. There remain far more available energy states than there are shared electrons. Both requirements for conductivity are therefore fulfilled: strong delocalization and partly filled energy bands. Such electrons can therefore easily change from one energy state to a slightly different one. Thus, not only do they become delocalized, forming a sea of electrons permeating the structure, but they are also able to migrate through the structure when an external electrical field is applied, leading to electrical conductivity. Without the field, there are electrons moving equally in all directions. Within such a field, some electrons will adjust their state slightly, adopting a differentwave vector. Consequently, there will be more moving one way than another and a net current will result.
The freedom of electrons to migrate also gives metal atoms, or layers of them, the capacity to slide past each other. Locally, bonds can easily be broken and replaced by new ones after a deformation. This process does not affect the communal metallic bonding very much, which gives rise to metals' characteristicmalleability andductility. This is particularly true for pure elements. In the presence of dissolved impurities, the normally easily formed cleavages may be blocked and the material become harder. Gold, for example, is very soft in pure form (24-karat), which is why alloys are preferred in jewelry.
Metals are typically also good conductors of heat, but the conduction electrons only contribute partly to this phenomenon. Collective (i.e., delocalized) vibrations of the atoms, known asphonons that travel through the solid as a wave, are bigger contributors.
However, a substance such asdiamond, which conducts heat quite well, is not an electrical conductor. This is not a consequence of delocalization being absent in diamond, but simply that carbon is not electron deficient.
Electron deficiency is important in distinguishing metallic from more conventional covalent bonding. Thus, we should amend the expression given above to:Metallic bonding is an extremely delocalized communal form of electron-deficient[b] covalent bonding.
Metallic radius
The metallic radius is defined as one-half of the distance between the two adjacent metal ions in the metallic structure. This radius depends on the nature of the atom as well as its environment—specifically, on thecoordination number (CN), which in turn depends on the temperature and applied pressure.
When comparing periodic trends in the size of atoms it is often desirable to apply the so-called Goldschmidt correction, which converts atomic radii to the values the atoms would have if they were 12-coordinated. Since metallic radii are largest for the highest coordination number, correction for less dense coordinations involves multiplying byx, where 0 <x < 1. Specifically, for CN = 4,x = 0.88; for CN = 6,x = 0.96, and for CN = 8,x = 0.97. The correction is named afterVictor Goldschmidt who obtained the numerical values quoted above.[6]
The atoms in metals have a strong attractive force between them. Much energy is required to overcome it. Therefore, metals often have high boiling points, withtungsten (5828 K) being extremely high. A remarkable exception is the elements of thezinc group: Zn, Cd, and Hg. Their electron configurations end in ...ns2, which resembles a noble gas configuration, like that ofhelium, more and more when going down the periodic table, because the energy differential to the empty np orbitals becomes larger. These metals are therefore relatively volatile, and are avoided inultra-high vacuum systems.
Otherwise, metallic bonding can be very strong, even in molten metals, such asgallium. Even though gallium will melt from the heat of one's hand just above room temperature, its boiling point is not far from that of copper. Molten gallium is, therefore, a very nonvolatile liquid, thanks to its strong metallic bonding.
The strong bonding of metals in liquid form demonstrates that the energy of a metallic bond is not highly dependent on the direction of the bond; this lack of bond directionality is a direct consequence of electron delocalization, and is best understood in contrast to the directional bonding of covalent bonds. The energy of a metallic bond is thus mostly a function of the number of electrons which surround the metallic atom, as exemplified by theembedded atom model.[7] This typically results in metals assuming relatively simple,close-packed crystal structures, such as FCC, BCC, and HCP.
Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even inglasses, which have amorphous structures.
Metals are insoluble in water or organic solvents, unless they undergo a reaction with them. Typically, this is an oxidation reaction that robs the metal atoms of their itinerant electrons, destroying the metallic bonding. However metals are often readily soluble in each other while retaining the metallic character of their bonding. Gold, for example, dissolves easily in mercury, even at room temperature. Even in solid metals, the solubility can be extensive. If the structures of the two metals are the same, there can even be complete solidsolubility, as in the case ofelectrum, an alloy of silver and gold. At times, however, two metals will form alloys with different structures than either of the two parents. One could call these materialsmetal compounds. But, because materials with metallic bonding are typically not molecular, Dalton'slaw of integral proportions is not valid; and often a range of stoichiometric ratios can be achieved. It is better to abandon such concepts as 'pure substance' or 'solute' in such cases and speak ofphases instead. The study of such phases has traditionally been more the domain ofmetallurgy than ofchemistry, although the two fields overlap considerably.
Localization and clustering: from bonding to bonds
The metallic bonding in complex compounds does not necessarily involve all constituent elements equally. It is quite possible to have one or more elements that do not partake at all. One could picture the conduction electrons flowing around them like a river around an island or a big rock. It is possible to observe which elements do partake: e.g., by looking at the core levels in anX-ray photoelectron spectroscopy (XPS) spectrum. If an element partakes, its peaks tend to be skewed.
Some intermetallic materials, e.g., do exhibitmetal clusters reminiscent of molecules; and these compounds are more a topic of chemistry than of metallurgy. The formation of the clusters could be seen as a way to 'condense out' (localize) the electron-deficient bonding into bonds of a more localized nature.Hydrogen is an extreme example of this form of condensation. At high pressuresit is a metal. The core of the planetJupiter could be said to be held together by a combination of metallic bonding and high pressure induced by gravity. At lower pressures, however, the bonding becomes entirely localized into a regular covalent bond. The localization is so complete that the (more familiar) H2 gas results. A similar argument holds for an element such as boron. Though it is electron-deficient compared to carbon, it does not form a metal. Instead it has a number of complex structures in whichicosahedral B12 clusters dominate.Charge density waves are a related phenomenon.
As these phenomena involve the movement of the atoms toward or away from each other, they can be interpreted as the coupling between the electronic and the vibrational states (i.e. the phonons) of the material. A different such electron-phonon interaction is thought to lead to a very different result at low temperatures, that ofsuperconductivity. Rather than blocking the mobility of the charge carriers by formingelectron pairs in localized bonds,Cooper pairs are formed that no longer experience any resistance to their mobility.
Optical properties
The presence of an ocean of mobile charge carriers has profound effects on theoptical properties of metals, which can only be understood by considering the electrons as acollective, rather than considering the states of individual electrons involved in more conventional covalent bonds.
Light consists of a combination of an electrical and a magnetic field. The electrical field is usually able to excite an elastic response from the electrons involved in the metallic bonding. The result is that photons cannot penetrate very far into the metal and are typically reflected, although some may also be absorbed. This holds equally for all photons in the visible spectrum, which is why metals are often silvery white or grayish with the characteristic specular reflection of metalliclustre. The balance between reflection and absorption determines how white or how gray a metal is, although surface tarnish can obscure the lustre. Silver, a metal with high conductivity, is one of the whitest.
Notable exceptions are reddish copper and yellowish gold. The reason for their color is that there is an upper limit to the frequency of the light that metallic electrons can readily respond to: theplasmon frequency. At the plasmon frequency, the frequency-dependent dielectric function of thefree electron gas goes from negative (reflecting) to positive (transmitting); higher frequency photons are not reflected at the surface, and do not contribute to the color of the metal. There are some materials, such asindium tin oxide (ITO), that are metallic conductors (actuallydegenerate semiconductors) for which this threshold is in theinfrared,[8] which is why they are transparent in the visible, but good reflectors in the infrared.
Forsilver the limiting frequency is in the far ultraviolet, but for copper and gold it is closer to the visible. This explains the colors of these two metals. At the surface of a metal, resonance effects known assurface plasmons can result. They are collective oscillations of the conduction electrons, like a ripple in the electronic ocean. However, even if photons have enough energy, they usually do not have enoughmomentum to set the ripple in motion. Therefore, plasmons are hard to excite on a bulk metal. This is why gold and copper look like lustrous metals albeit with a dash of color. However, incolloidal gold the metallic bonding is confined to a tiny metallic particle, which prevents the oscillation wave of the plasmon from 'running away'. The momentum selection rule is therefore broken, and the plasmon resonance causes an extremely intense absorption in the green, with a resulting purple-red color. Such colors are orders of magnitude more intense than ordinary absorptions seen in dyes and the like, which involve individual electrons and their energy states.
^If the electrons were trulyfree, their energy would only depend on the magnitude of theirwave vectork, not its direction. That is, ink-space, the Fermi level should form a perfectsphere. Theshape of the Fermi level can be measured bycyclotron resonance and is never a sphere, not even for caesium.[5]
^Electron deficiency is a relative term: it means fewer than half of the electrons needed to complete thenext noble gas configuration. For example, lithium is electron deficient with respect toneon, but electron-rich with respect to the previous noble gas,helium.
^Brewer, Scott H.; Franzen, Stefan (2002). "Indium Tin Oxide Plasma Frequency Dependence on Sheet Resistance and Surface Adlayers Determined by Reflectance FTIR Spectroscopy".The Journal of Physical Chemistry B.106 (50):12986–12992.doi:10.1021/jp026600x.
