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Metallic bonding is a type of
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
ing that arises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of
delocalized electron In chemistry, delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or a covalent bond.IUPAC Gold Boo''delocalization''/ref> The term delocalization is general and can have slightly dif ...
s) and positively charged
metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
ions. It may be described as the sharing of ''free'' electrons among a
structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...
of positively charged ions (
cation An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
s). Metallic bonding accounts for many
physical properties A physical property is any property that is measurable, whose value describes a state of a physical system. The changes in the physical properties of a system can be used to describe its changes between momentary states. Physical properties are ...
of metals, such as strength,
ductility Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile str ...
,
thermal A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
and
electrical resistivity and conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
, opacity, and luster. Metallic bonding is not the only type of
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
ing a metal can exhibit, even as a pure substance. For example, elemental
gallium Gallium is a chemical element with the Symbol (chemistry), symbol Ga and atomic number 31. Discovered by France, French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in boron group, group 13 of the periodic table and is similar to ...
consists of covalently-bound pairs of atoms in both liquid and solid-state—these pairs form a
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pattern ...
with metallic bonding between them. Another example of a metal–metal covalent bond is the
mercurous ion Mercury polycations are polyatomic cations that contain only mercury atoms. The best known example is the ion, found in mercury(I) (mercurous) compounds. The existence of the metal–metal bond in Hg(I) compounds was established using X-ray stud ...
().


History

As chemistry developed into a science, it became clear that metals formed the majority of the
periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
of the elements, and great progress was made in the description of the salts that can be formed in reactions with
acids In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a ...
. With the advent of
electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an out ...
, 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 the
free electron model In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantu ...
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 k. In three-dimensional k-space, the set of points of the highest filled levels (the
Fermi surface In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crys ...
) should therefore be a sphere. In the nearly-free model, box-like
Brillouin zone In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice ...
s 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 X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
and
thermal analysis Thermal analysis is a branch of materials science where the properties of materials are studied as they change with temperature. Several methods are commonly used – these are distinguished from one another by the property which is measured: * ...
made it possible to study the structure of crystalline solids, including metals and their alloys; and
phase diagram A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous ...
s were developed. Despite all this progress, the nature of intermetallic compounds and alloys 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 laws 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 this field, notably Hume-Rothery, in an attempt to explain why certain 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 assumption that the balloon was spherical did not hold, except perhaps in the case of
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
. This finding reduced many of the conclusions to examples of how a model can sometimes give a whole series of correct predictions, yet still be wrong. The nearly-free electron debacle showed researchers that any model that assumed that ions were in a sea of free electrons needed modification. So, a number of quantum mechanical models—such as band structure calculations based on molecular orbitals or the
density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
—were developed. In these models, one either departs 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 education. The electronic band structure model became a major focus not only for the study of metals but even more so for the study of
semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way ...
s. Together with the electronic states, the vibrational states were also shown to form bands.
Rudolf Peierls Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allie ...
showed that, in the case of a one-dimensional row of metallic atoms—say, hydrogen—an instability had to arise that would lead to the breakup of such a chain into individual molecules. This sparked an interest in the general question: when is collective metallic bonding stable and when will a more localized form of bonding take its place? Much research went into the study of clustering of metal atoms. As powerful as the concept of the band structure model proved to be in describing metallic bonding, it has the drawback of remaining a one-electron approximation of a many-body problem. In other words, the energy states of each electron are described as if all the other electrons simply form a homogeneous background. Researchers such as Mott and Hubbard realized that this was perhaps appropriate for strongly delocalized s- and p-electrons; but for d-electrons, and even more for f-electrons, the interaction with electrons (and atomic displacements) in the local environment may become stronger than the delocalization that leads to broad bands. Thus, the transition from localized
unpaired electron In chemistry, an unpaired electron is an electron that occupies an orbital of an atom singly, rather than as part of an electron pair. Each atomic orbital of an atom (specified by the three quantum numbers n, l and m) has a capacity to contain ...
s to itinerant ones partaking in metallic bonding became more comprehensible.


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. The latter could be called electron deficiency.


In 2D

Graphene Graphene () is an allotrope of carbon consisting of a Single-layer materials, single layer of atoms arranged in a hexagonal lattice nanostructure.
is an example of two-dimensional metallic bonding. Its metallic bonds are similar to aromaticity, aromatic bonding in
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms ...
,
naphthalene Naphthalene is an organic compound with formula . It is the simplest polycyclic aromatic hydrocarbon, and is a white crystalline solid with a characteristic odor that is detectable at concentrations as low as 0.08  ppm by mass. As an aromat ...
,
anthracene Anthracene is a solid polycyclic aromatic hydrocarbon (PAH) of formula C14H10, consisting of three fused benzene rings. It is a component of coal tar. Anthracene is used in the production of the red dye alizarin and other dyes. Anthracene is co ...
, ovalene, etc.


In 3D

Metal aromaticity Metal aromaticity or metalloaromaticity is the concept of aromaticity, found in many organic compounds, extended to metals and metal-containing compounds. The first experimental evidence for the existence of aromaticity in metals was found in alum ...
in metal 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 in
alloys An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...
there is little difference among the
electronegativities Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the d ...
of the
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s 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 a ''chunk'' 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 as Na2, held together by a more conventional covalent bond. This is why it is not correct to speak of a single 'metallic bond'. Delocalization is most pronounced for s- and p-electrons. Delocalization in
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
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 not inaccurate. 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 solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at eac ...
) 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 electron In chemistry, an unpaired electron is an electron that occupies an orbital of an atom singly, rather than as part of an electron pair. Each atomic orbital of an atom (specified by the three quantum numbers n, l and m) has a capacity to contain ...
s that retain their spin, adding interesting
magnetic properties Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
to these metals.


Electron deficiency and mobility

Metal
atoms Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...
contain few
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
s in their valence shells relative to their periods or
energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...
s. They are
electron-deficient Electron deficiency (and electron-deficient) is jargon that is used in two contexts: species that violate the octet rule because they have too few valence electrons and species that happen to follow the octet rule but have electron-acceptor properti ...
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 different
wave vector In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
. 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' characteristic
malleability Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stres ...
and
ductility Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile str ...
. 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 The fineness of a precious metal object (coin, bar, jewelry, etc.) represents the weight of ''fine metal'' therein, in proportion to the total weight which includes alloying base metals and any impurities. Alloy metals are added to increase hardne ...
), 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
phonon In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechani ...
s that travel through the solid as a wave, are bigger contributors. However, a substance such as
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, b ...
, 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''.


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 the
coordination number In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central io ...
(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 by x, 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 after
Victor Goldschmidt Victor Moritz Goldschmidt (27 January 1888 in Zürich – 20 March 1947 in Oslo) was a Norwegian mineralogist considered (together with Vladimir Vernadsky) to be the founder of modern geochemistry and crystal chemistry, developer of the Golds ...
who obtained the numerical values quoted above. The radii follow general
periodic trends Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element. They were discovered by the Russian chemist Dmitri Mendeleev in the year 1863. Major periodic trends include atom ...
: they decrease across the period due to the increase in the
effective nuclear charge In atomic physics, the effective nuclear charge is the actual amount of positive (nuclear) charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevent ...
, 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 In quantum mechanics, the principal quantum number (symbolized ''n'') is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. A ...
. Between the 4d and 5d elements, the
lanthanide contraction The lanthanide contraction is the greater-than-expected decrease in atomic radii/ionic radii of the elements in the lanthanide series from atomic number 57, lanthanum, to 71, lutetium, which results in smaller than otherwise expected atomic radii ...
is observed—there is very little increase of the radius down the group due to the presence of poorly shielding f orbitals.


Strength of the bond

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, with
tungsten Tungsten, or wolfram, is a chemical element with the symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identified as a new element in 1781 and first isol ...
(5828 K) being extremely high. A remarkable exception is the elements of the zinc group: Zn, Cd, and Hg. Their electron configurations end in ...ns2, which resembles a noble gas configuration, like that of
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
, 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 in
ultra-high vacuum Ultra-high vacuum (UHV) is the vacuum regime characterised by pressures lower than about . UHV conditions are created by pumping the gas out of a UHV chamber. At these low pressures the mean free path of a gas molecule is greater than approximatel ...
systems. Otherwise, metallic bonding can be very strong, even in molten metals, such as
gallium Gallium is a chemical element with the Symbol (chemistry), symbol Ga and atomic number 31. Discovered by France, French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in boron group, group 13 of the periodic table and is similar to ...
. 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 In computational chemistry and computational physics, the embedded atom model, embedded-atom method or EAM, is an approximation describing the energy between atoms and is a type of interatomic potential. The energy is a function of a sum of functio ...
. 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
glasses Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples ...
, which have amorphous structures. Much biochemistry is mediated by the weak interaction of metal ions and biomolecules. Such interactions, and their associated
conformational change In biochemistry, a conformational change is a change in the shape of a macromolecule, often induced by environmental factors. A macromolecule is usually flexible and dynamic. Its shape can change in response to changes in its environment or oth ...
s, have been measured using dual polarisation interferometry.


Solubility and compound formation

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 solid
solubility In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
, as in the case of
electrum Electrum is a naturally occurring alloy of gold and silver, with trace amounts of copper and other metals. Its color ranges from pale to bright yellow, depending on the proportions of gold and silver. It has been produced artificially, and ...
, 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 materials metal compounds. But, because materials with metallic bonding are typically not molecular, Dalton's law 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 of phases instead. The study of such phases has traditionally been more the domain of
metallurgy Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the sc ...
than of
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, 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 an
X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy (XPS) is a surface-sensitive quantitative spectroscopic technique based on the photoelectric effect that can identify the elements that exist within a material (elemental composition) or are covering its surface, ...
(XPS) spectrum. If an element partakes, its peaks tend to be skewed. Some intermetallic materials, e.g., do exhibit metal 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 Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
is an extreme example of this form of condensation. At high pressures it is a metal. The core of the planet
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...
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 icosahedral 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 Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
. Rather than blocking the mobility of the charge carriers by forming
electron pair In chemistry, an electron pair or Lewis pair consists of two electrons that occupy the same molecular orbital but have opposite spins. Gilbert N. Lewis introduced the concepts of both the electron pair and the covalent bond in a landmark paper he ...
s 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 the
optical properties The optical properties of a material define how it interacts with light. The optical properties of matter are studied in optical physics, a subfield of optics. The optical properties of matter include: * Refractive index *Dispersion * Transmittan ...
of metals, which can only be understood by considering the electrons as a ''collective'', rather than considering the states of individual electrons involved in more conventional covalent bonds.
Light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
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 luster. The balance between reflection and absorption determines how white or how gray a metal is, although surface tarnish can obscure the luster. 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 Free electron in physics may refer to: *Electron, as a free particle *Solvated electron *Charge carrier, as carriers of electric charge *Valence electron, as an outer shell electron that is associated with an atom *Valence and conduction bands, as a ...
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 Indium tin oxide (ITO) is a ternary composition of indium, tin and oxygen in varying proportions. Depending on the oxygen content, it can be described as either a ceramic or an alloy. Indium tin oxide is typically encountered as an oxygen-saturated ...
(ITO), that are metallic conductors (actually
degenerate semiconductor A degenerate semiconductor is a semiconductor with such a high level of doping that the material starts to act more like a metal than as a semiconductor. Unlike non-degenerate semiconductors, these kind of semiconductor do not obey law of mass ac ...
s) for which this threshold is in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...
, which is why they are transparent in the visible, but good reflectors in the infrared. For
silver Silver is a chemical element with the symbol Ag (from the Latin ', derived from the Proto-Indo-European ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical ...
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 In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
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 Colloidal gold is a sol or colloidal suspension of nanoparticles of gold in a fluid, usually water. The colloid is usually either wine-red coloured (for spherical particles less than 100  nm) or blue/purple (for larger spherical particl ...
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.


See also

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Notes


References

{{DEFAULTSORT:Metallic Bond Chemical bonding Metals