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Metallic bonding is a type of that arises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal . It may be described as the sharing of free electrons among a structure of positively charged ions (). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and lustre. Metallic bonding. chemguide.co.uk Metal structures. chemguide.co.uk Chemical Bonds. chemguide.co.uk "Physics 133 Lecture Notes" Spring, 2004. Marion Campus. physics.ohio-state.edu
Metallic bonding is not the only type of a metal can exhibit, even as a pure substance. For example, elemental gallium consists of covalent bond pairs of atoms in both liquid and solid-state—these pairs form a crystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is the mercurous ion ().
With the advent of quantum mechanics, this picture was given a more formal interpretation in the form of the free electron model and its further extension, the nearly 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 the magnitude, not the direction of the momentum vector wave vector. In three-dimensional k-space, the set of points of the highest filled levels (the Fermi surface) should therefore be a sphere. In the nearly-free model, box-like are added to k-space by the periodic potential experienced from the (ionic) structure, thus mildly breaking the isotropy.
The advent of X-ray diffraction and thermal analysis made it possible to study the structure of crystalline solids, including metals and their alloys; and were developed. Despite all this progress, the nature of Intermetallic and Alloy largely remained a mystery and their study was often merely empirical. Chemists generally steered away from anything that did not seem to follow Dalton's ; 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, notably Hume-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 as cyclotron 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 of caesium. 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 the density 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 of . 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 delocalized s- and p-electrons; but for d-electrons, and even more for f-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 localized unpaired electrons to itinerant ones partaking in metallic bonding.
Delocalization is most pronounced for s- and p-electrons. Delocalization in caesium 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 charged electron gas is very close to accurate (though not perfectly so). 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. For d- and especially f-electrons the delocalization is not strong at all and this explains why these electrons are able to continue behaving as unpaired electrons that retain their spin, adding interesting magnetism to these metals.
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' characteristic malleability and ductility. 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 as that travel through the solid as a wave, are bigger contributors.
However, a substance such as diamond, 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 covalent bonding.
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 by , where 0 < < 1. Specifically, for CN = 4, = 0.88; for CN = 6, = 0.96, and for CN = 8, = 0.97. The correction is named after Victor Goldschmidt who obtained the numerical values quoted above.
The radii follow general periodic trends: they decrease across the period due to the increase in the effective nuclear charge, which is not offset by the increased number of valence electrons; but the radii increase down the group due to an increase in the principal quantum number. Between the 4 d and 5 d elements, the lanthanide contraction is observed—there is very little increase of the radius down the group due to the presence of poorly shielding atomic orbitals.
Otherwise, metallic bonding can be very strong, even in molten metals, such as gallium. 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 the embedded atom model. 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 in metallic glass, which have amorphous structures.
Much biochemistry is mediated by the weak interaction of metal ions and biomolecules. Such interactions, and their associated conformational changes, have been measured using dual polarisation interferometry.
Some intermetallic materials, e.g., do exhibit 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 pressures it is a metal. The core of the planet Jupiter 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 which icosahedron 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 of superconductivity. Rather than blocking the mobility of the charge carriers by forming in localized bonds, Cooper pairs are formed that no longer experience any resistance to their mobility.
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 metallic lustre. 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: the plasmon frequency. At the plasmon frequency, the frequency-dependent dielectric function of the free 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 as indium tin oxide (ITO), that are metallic conductors (actually degenerate semiconductors) for which this threshold is in the infrared, which is why they are transparent in the visible, but good reflectors in the infrared.
For silver 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 as surface 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 enough momentum 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, in colloidal 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.
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