Metallic bond
Encyclopedia
Metallic bonding is the electrostatic attractive forces between the delocalized electron
s, called conduction electrons, gathered in an "electron sea", and the positively charged metal ions. Understood as the sharing of "free" electrons among a lattice
of positively charged ions (cations), metallic bonding is sometimes compared with that of molten salts; however, this simplistic view holds true for very few metals. In a more quantum-mechanical view, the conduction electrons divide their density equally over all atoms that function as neutral (non-charged) entities. Metallic bonding accounts for many physical properties of metals, such as strength
, malleability, ductility
, thermal
and electrical conductivity, opacity
, and luster
.
Although the term "metallic bond" is often used in contrast to the term "covalent bond
", it is preferable to use the term metallic bonding, because this type of bonding is collective in nature and a single "metallic bond" does not exist. Not all metals exhibit metallic bonding: one such example is the mercurous ion , which forms covalent metal-metal bonds.
As chemistry developed into a science it became clear that metals formed the large majority of the periodic table
of the elements and great progress was made in the description of the salts that can be formed in reactions with acids. With the advent of electrochemistry
it became clear that metals generally go into solution as positively charged ions and the oxidation reactions of the metals became well understood in the 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 more formal interpretation in the form of the free electron model
and its further extension, the nearly free electron model. In both of these models the electrons are seen as a gas traveling through the lattice 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
) should therefore be a sphere. In the nearly free correction of the model, box-like Brillouin zone
s are added to k-space by the periodic potential experienced from the (ionic) lattice.
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 the construction of phase diagram
s became accessible. Despite all this progress the nature of intermetallic compounds and alloys largely remained a mystery and their study was often 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 almost-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 his attempts were quite successful. Basically 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 indeed predicted a fairly large number of observed alloy compositions. Unfortunately, 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 at all, except perhaps in the case of caesium
. This reduced many of the conclusions to examples of how a wrong model can sometimes give a whole series of correct predictions.
The free-electron debacle showed researchers that the model assuming that the ions were in a sea of free electrons needed modification, and so a number of quantum mechanical models such as band structure calculations based on molecular orbitals or the density functional theory
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
s. Together with the electronic states, the vibrational states were also shown to form bands. Peierls 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 proved to be in the description of metallic bonding, it does have a drawback. It remains a one-electron approximation to a multitudinous 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 like 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
s to itinerant ones partaking in metallic bonding became more comprehensible.
— is most familiar from the example of benzene
C6H6, where six electrons from six carbon atoms are engaged in joint aromatic bonding
. The principle can easily be extended over larger aromatic molecules like naphthalene
, anthracene
, ovalene
, and so on, and, if the process is taken to its extreme, graphene
. The latter is an example of a system delocalized in two dimensions.
It interesting to note that there is an isoelectronic analog of benzene, B3N3H6 (borazine
), for which the same argument holds. It has very similar properties to benzene. When extended indefinitely, a layer of hexagonal boron nitride, BN, is obtained, with a structure identical to that of graphene apart from the alternation between boron and nitrogen in each ring. This material is a semiconductor
, exemplifying that delocalization is a necessary but not sufficient requirement for conductivity. Electrical conductivity does occur in graphene, because the π and π*-like bands overlap, making it a semimetal, with partly filled bands, fulfilling the other requirement for conductivity.
in metal clusters is another example of delocalization, this time often in three-dimensional entities. 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 intermolecular. 'Nonmolecular' would perhaps be a better term. Metallic bonding is mostly non-polar, because even in alloys there is little difference among the electronegativities
of the atom
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, therefore, and it describes the bonding only as present in a chunk of condensed matter, be it crystalline solid, liquid, or even glass. Metallic vapors by contrast are often atomic (Hg
) or at times contain molecules like Na2
held together by a more conventional covalent bond. This is why it is not correct to speak of a single 'metallic bond'.
The delocalization is most pronounced for s- and p-electrons. For caesium
it is so strong that the electrons are virtually free 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 too 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 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
s that retain their spin, adding interesting magnetic properties
to these metals.
s in their valence shells relative to their periods or energy level
s. They are electron 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 into a slightly different one. Thus, not only do they become delocalized, forming a sea of electrons permeating the lattice, but they are also able to migrate through the lattice when an external electrical field is imposed, leading to electrical conductivity. Without the field, there are electrons moving equally in all directions. Under the field, some will adjust their state slightly, adopting a different wave vector
. As a consequence, there will be more moving one way than the other and a net current will result.
The freedom of conduction electrons to migrate also give 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 the deformation. This process does not affect the communal metallic bonding very much. This gives rise to metals' typical characteristic phenomena of malleability and ductility
. This is particularly true for pure elements. In the presence of dissolved impurities, the defects in the lattice that function as cleavage points may get blocked and the material becomes harder. Gold, for example, is very soft in pure form (24-karat
), which is why for jewellery alloys of 18-karat or lower are preferred.
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
s that travel through the solid as a wave, contribute strongly.
However, the latter also holds for a substance like diamond
. It conducts heat quite well but not electricity. The latter is not a consequence of the fact that delocalization is absent in diamond, but simply that carbon is not electron deficient. The position of carbon in the middle of its period in the Periodic Table makes that there are precisely enough electrons to fill the energy states. Under a field electrons are not able to adopt a different wave vector because there are no empty states to move into. This makes a current impossible in this wide band gap semiconductor
. However, as soon as charge carriers are introduced by doping the crystal with a suitable impurity, the resulting charge carriers are as mobile as in a metal, though far fewer in number. Even without doping, the vibrational motions (the phonons) are delocalized over the crystal explaining the heat conduction. Still the bonding in diamond is better described as covalent than as metallic if only because there is a very strong directional preference for tetrahedral stacking, producing a structure that is extremely hard to deform and by no means close packed.
The electron deficiency is an important point in distinguishing metallic from more conventional covalent bonding. Thus, we should amend the expression given above into: 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 so-called Goldschmidt correction, which converts the radii to the values the atoms would have if they were 12-coordinated. Since metallic radii are always biggest for the highest coordination number, correction for less dense coordinations involves dividing 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
who obtained the numerical values quoted above.
The radii follow general periodic trends
: they decrease across the period due to increase in the effective nuclear charge
, which is not offset by the increased number of valence electrons. The radii also decrease down the group due to increase in principal quantum number
. Between rows 3 and 4, the lanthanide contraction
is observed – there is very little increase of the radius down the group due to the presence of poorly shielding f orbitals.
(5828 K) being extremely high. A remarkable exception are the elements of the zinc group
: Zn, Cd, and Hg. Their electron configuration ends in ...ns2 and this comes to resemble a noble gas configuration like that of helium
more and more when going down in the periodic table because the energy distance to the empty np orbitals becomes larger. These metals are therefore relatively volatile, and are avoided in ultra-high vacuum systems.
Otherwise, metallic bonding can be very strong, even in the melt. Gallium
is a good example of that. Even though it melts by 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 latter also exemplifies that metallic bonding due to its delocalization in all directions is often not very particular about the directionality of the bonding. There is typically a preference for close packing of the atoms, such as face or body centered cubic arrangements, but in the case of liquid gallium the stacking is not regular, at least not at long range and bond angles are easily changed.
Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even in glasses with an amorphous structure.
Much biochemistry is mediated by the weak interaction of metal ions and biomolecules. Such interactions and their associated conformational change
has been measured using dual polarisation interferometry
.
, the alloys 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' is such cases and speak of phase
s instead. The study of such phases has traditionally been more the domain of metallurgy
than of chemistry
, although the two fields overlap considerably.
(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
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 like boron. Though it is electron deficient compared to carbon, it does not form a metal. Instead it has a number of complicated structures in which icosahedral
B12 clusters dominate. Charge density waves are a related phenomenon.
As these phenomena involve the movement of the atoms towards 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 cause a very different result at low temperatures, that of superconductivity
. Rather than blocking the mobility of the charge carriers by forming electron pair
s 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 are not able to penetrate very far into the metal and are typically reflected. They bounce off, although some may also be absorbed. This holds equally for all photons of 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 they are, although surface tarnish can obscure such observations. Silver, a very good 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 like indium tin oxide
(ITO) that are metallic conductors (actually degenerate semiconductor
s) for which this threshold is in the infrared
, which is why they are transparent in the visible, but good mirrors in the IR.
For silver
the limiting frequency is in the far UV, 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 still look like lustrous metals albeit with a dash of color. However, in colloidal gold
the metallic bonding is confined to a tiny metallic particle, preventing 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 beautiful purple-red color. Such colors are orders of magnitude more intense than ordinary absorptions seen in dyes and the like that involve individual electrons and their energy states.
Delocalized electron
In chemistry, delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or one covalent bond....
s, called conduction electrons, gathered in an "electron sea", and the positively charged metal ions. Understood as the sharing of "free" electrons among a lattice
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
of positively charged ions (cations), metallic bonding is sometimes compared with that of molten salts; however, this simplistic view holds true for very few metals. In a more quantum-mechanical view, the conduction electrons divide their density equally over all atoms that function as neutral (non-charged) entities. Metallic bonding accounts for many physical properties of metals, such as strength
Strength of materials
In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...
, malleability, ductility
Ductility
In materials science, ductility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. Malleability, a similar property, is a material's ability to deform under compressive stress; this is often characterized...
, thermal
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
and electrical conductivity, opacity
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...
, and luster
Lustre (mineralogy)
Lustre is a description of the way light interacts with the surface of a crystal, rock, or mineral. The word lustre traces its origins back to the Latin word lux, meaning "light", and generally implies radiance, gloss, or brilliance....
.
Although the term "metallic bond" is often used in contrast to the term "covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
", it is preferable to use the term metallic bonding, because this type of bonding is collective in nature and a single "metallic bond" does not exist. Not all metals exhibit metallic bonding: one such example is the mercurous ion , which forms covalent metal-metal bonds.
History
The nature of metals has fascinated humankind for many centuries, because these materials provided people with tools of unsurpassed properties both in war and in their preparation and processing.As chemistry developed into a science it became clear that metals formed the large majority of the periodic table
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
of the elements and great progress was made in the description of the salts that can be formed in reactions with acids. With the advent of electrochemistry
Electrochemistry
Electrochemistry is a branch of chemistry that studies chemical reactions which take place in a solution at the interface of an electron conductor and an ionic conductor , and which involve electron transfer between the electrode and the electrolyte or species in solution.If a chemical reaction is...
it became clear that metals generally go into solution as positively charged ions and the oxidation reactions of the metals became well understood in the 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 more formal interpretation in the form of the free electron model
Free electron model
In solid-state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid. It was developed principally by Arnold Sommerfeld who combined the classical Drude model with quantum mechanical Fermi-Dirac statistics and hence it...
and its further extension, the nearly free electron model. In both of these models the electrons are seen as a gas traveling through the lattice 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
Wave vector
In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...
. In three-dimensional k-space, the set of points of the highest filled levels (the Fermi surface
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
) should therefore be a sphere. In the nearly free correction of the model, box-like Brillouin zone
Brillouin zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. The boundaries of this cell are given by planes related to points on the reciprocal lattice. It is found by the same method as for the Wigner–Seitz cell in the Bravais lattice...
s are added to k-space by the periodic potential experienced from the (ionic) lattice.
The advent of X-ray diffraction and thermal analysis
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 the construction of phase diagram
Phase diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium...
s became accessible. Despite all this progress the nature of intermetallic compounds and alloys largely remained a mystery and their study was often 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 almost-free electron model was eagerly taken up by some researchers in this field, notably Hume-Rothery
William Hume-Rothery
William Hume-Rothery OBE was a British metallurgist who studied the constitution of alloys.- Career :Hume-Rothery was born the son of lawyer Joseph Hume-Rothery in Worcester Park, Surrey but spent his youth in Cheltenham and was educated at Cheltenham College. In 1917 he was made totally deaf by a...
in an attempt to explain why certain intermetallic alloys with certain compositions would form and others would not. Initially his attempts were quite successful. Basically 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 indeed predicted a fairly large number of observed alloy compositions. Unfortunately, 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 at all, except perhaps in the case of caesium
Caesium
Caesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of 28 °C , which makes it one of only five elemental metals that are liquid at room temperature...
. This reduced many of the conclusions to examples of how a wrong model can sometimes give a whole series of correct predictions.
The free-electron debacle showed researchers that the model assuming that the ions were in a sea of free electrons needed modification, and so a number of quantum mechanical models such as band structure calculations based on molecular orbitals or the density functional theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
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
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
) 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
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
s. Together with the electronic states, the vibrational states were also shown to form bands. Peierls 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 proved to be in the description of metallic bonding, it does have a drawback. It remains a one-electron approximation to a multitudinous 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 like 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
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. As the formation of electron pairs is often energetically favourable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively...
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
Delocalization — bonding that involves more than one pair of atoms held together by one pair of electronsElectron pair
In chemistry, an electron pair consists of two electrons that occupy the same orbital but have opposite spins.Because electrons are fermions, the Pauli exclusion principle forbids these particles from having exactly the same quantum numbers. Therefore the only way to occupy the same orbital, i.e....
— is most familiar from the example of benzene
Benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....
C6H6, where six electrons from six carbon atoms are engaged in joint aromatic bonding
Aromaticity
In organic chemistry, Aromaticity is a chemical property in which a conjugated ring of unsaturated bonds, lone pairs, or empty orbitals exhibit a stabilization stronger than would be expected by the stabilization of conjugation alone. The earliest use of the term was in an article by August...
. The principle can easily be extended over larger aromatic molecules like naphthalene
Naphthalene
Naphthalene is an organic compound with formula . It is a white crystalline solid with a characteristic odor that is detectable at concentrations as low as 0.08 ppm by mass. As an aromatic hydrocarbon, naphthalene's structure consists of a fused pair of benzene rings...
, anthracene
Anthracene
Anthracene is a solid polycyclic aromatic hydrocarbon 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...
, ovalene
Ovalene
Ovalene is a polycyclic aromatic hydrocarbon with the formula C32H14, which consists of ten peri-fused six-membered rings. It is very similar to coronene....
, and so on, and, if the process is taken to its extreme, graphene
Graphene
Graphene is an allotrope of carbon, whose structure is one-atom-thick planar sheets of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. The term graphene was coined as a combination of graphite and the suffix -ene by Hanns-Peter Boehm, who described single-layer...
. The latter is an example of a system delocalized in two dimensions.
It interesting to note that there is an isoelectronic analog of benzene, B3N3H6 (borazine
Borazine
Borazine is an inorganic compound with the chemical formula 33. In this cyclic compound, the three BH units and three NH units alternate. The compound is isoelectronic and isostructural with benzene...
), for which the same argument holds. It has very similar properties to benzene. When extended indefinitely, a layer of hexagonal boron nitride, BN, is obtained, with a structure identical to that of graphene apart from the alternation between boron and nitrogen in each ring. This material is a semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
, exemplifying that delocalization is a necessary but not sufficient requirement for conductivity. Electrical conductivity does occur in graphene, because the π and π*-like bands overlap, making it a semimetal, with partly filled bands, fulfilling the other requirement for conductivity.
In 3D
Metal aromaticityMetal aromaticity
In metal aromaticity the concept of aromaticity found in many hydrocarbons is extended to metals. The first experimental evidence for the existence of aromaticity in metals was found in aluminium cluster compounds of the type MAl4- where M stands for lithium, sodium or copper...
in metal clusters is another example of delocalization, this time often in three-dimensional entities. 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 intermolecular. 'Nonmolecular' would perhaps be a better term. Metallic bonding is mostly non-polar, because even in alloys there is little difference among the electronegativities
Electronegativity
Electronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...
of the atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
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, therefore, and it describes the bonding only as present in a chunk of condensed matter, be it crystalline solid, liquid, or even glass. Metallic vapors by contrast are often atomic (Hg
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
) or at times contain molecules like Na2
Sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...
held together by a more conventional covalent bond. This is why it is not correct to speak of a single 'metallic bond'.
The delocalization is most pronounced for s- and p-electrons. For caesium
Caesium
Caesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of 28 °C , which makes it one of only five elemental metals that are liquid at room temperature...
it is so strong that the electrons are virtually free 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
Nearly-free electron model
In solid-state physics, the nearly-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual Empty Lattice Approximation...
is not too 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 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
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. As the formation of electron pairs is often energetically favourable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively...
s that retain their spin, adding interesting magnetic properties
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...
to these metals.
Electron deficiency and mobility
Metal atoms contain few electronElectron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in their valence shells relative to their periods or energy level
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
s. They are electron deficient
Electron deficiency
Electron deficiency occurs when a compound has too few valence electrons for the connections between atoms to be described as covalent bonds. Electron deficient bonds are often better described as 3-center-2-electron bonds...
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 into a slightly different one. Thus, not only do they become delocalized, forming a sea of electrons permeating the lattice, but they are also able to migrate through the lattice when an external electrical field is imposed, leading to electrical conductivity. Without the field, there are electrons moving equally in all directions. Under the field, some will adjust their state slightly, adopting a different wave vector
Wave vector
In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...
. As a consequence, there will be more moving one way than the other and a net current will result.
The freedom of conduction electrons to migrate also give 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 the deformation. This process does not affect the communal metallic bonding very much. This gives rise to metals' typical characteristic phenomena of malleability and ductility
Ductility
In materials science, ductility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. Malleability, a similar property, is a material's ability to deform under compressive stress; this is often characterized...
. This is particularly true for pure elements. In the presence of dissolved impurities, the defects in the lattice that function as cleavage points may get blocked and the material becomes harder. Gold, for example, is very soft in pure form (24-karat
Carat (purity)
The karat or carat is a unit of purity for gold alloys.- Measure :Karat purity is measured as 24 times the purity by mass:where...
), which is why for jewellery alloys of 18-karat or lower are preferred.
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
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
s that travel through the solid as a wave, contribute strongly.
However, the latter also holds for a substance like diamond
Diamond
In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...
. It conducts heat quite well but not electricity. The latter is not a consequence of the fact that delocalization is absent in diamond, but simply that carbon is not electron deficient. The position of carbon in the middle of its period in the Periodic Table makes that there are precisely enough electrons to fill the energy states. Under a field electrons are not able to adopt a different wave vector because there are no empty states to move into. This makes a current impossible in this wide band gap semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
. However, as soon as charge carriers are introduced by doping the crystal with a suitable impurity, the resulting charge carriers are as mobile as in a metal, though far fewer in number. Even without doping, the vibrational motions (the phonons) are delocalized over the crystal explaining the heat conduction. Still the bonding in diamond is better described as covalent than as metallic if only because there is a very strong directional preference for tetrahedral stacking, producing a structure that is extremely hard to deform and by no means close packed.
The electron deficiency is an important point in distinguishing metallic from more conventional covalent bonding. Thus, we should amend the expression given above into: Metallic bonding is an extremely delocalized communal form of electron deficient covalent bonding.
Metallic radius
Metallic radius is defined as one-half of the distance between neighbouring atoms in the metal solid. This radius depends on the nature of the atom as well as its environment, to be specific on the coordination 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 so-called Goldschmidt correction, which converts the radii to the values the atoms would have if they were 12-coordinated. Since metallic radii are always biggest for the highest coordination number, correction for less dense coordinations involves dividing 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 Goldschmidt
Victor Moritz Goldschmidt was a mineralogist considered to be the founder of modern geochemistry and crystal chemistry, developer of the Goldschmidt Classification of elements.-Early life & career:Goldschmidt was born in Zürich...
who obtained the numerical values quoted above.
The radii follow general periodic trends
Periodic trends
In Chemistry, periodic trends are the tendencies of certain elemental characteristics to increase or decrease as one progresses along a row or column of the periodic table of elements.-Atomic radius:...
: they decrease across the period due to increase in the effective nuclear charge
Effective nuclear charge
The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge by the repelling effect...
, which is not offset by the increased number of valence electrons. The radii also decrease down the group due to increase in principal quantum number
Principal quantum number
In atomic physics, the principal quantum symbolized as n is the firstof a set of quantum numbers of an atomic orbital. The principal quantum number can only have positive integer values...
. Between rows 3 and 4, the lanthanide contraction
Lanthanide contraction
Lanthanide contraction is a term used in chemistry to describe the decrease in ionic radii of the elements in the lanthanide series from atomic number 58, Cerium to 71, Lutetium, which results in smaller than otherwise expected ionic radii for the subsequent elements starting with 72, Hafnium...
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 tungstenTungsten
Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...
(5828 K) being extremely high. A remarkable exception are the elements of the zinc group
Group 12 element
A group 12 element is one of the elements in group 12 in the periodic table. This includes zinc , cadmium and mercury . The further inclusion of copernicium in group 12 is supported by recent experiments on individual Cn atoms...
: Zn, Cd, and Hg. Their electron configuration ends in ...ns2 and this comes to resemble a noble gas configuration like that of helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
more and more when going down in the periodic table because the energy distance to the empty np orbitals becomes larger. These metals are therefore relatively volatile, and are avoided in ultra-high vacuum systems.
Otherwise, metallic bonding can be very strong, even in the melt. Gallium
Gallium
Gallium is a chemical element that has the symbol Ga and atomic number 31. Elemental gallium does not occur in nature, but as the gallium salt in trace amounts in bauxite and zinc ores. A soft silvery metallic poor metal, elemental gallium is a brittle solid at low temperatures. As it liquefies...
is a good example of that. Even though it melts by 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 latter also exemplifies that metallic bonding due to its delocalization in all directions is often not very particular about the directionality of the bonding. There is typically a preference for close packing of the atoms, such as face or body centered cubic arrangements, but in the case of liquid gallium the stacking is not regular, at least not at long range and bond angles are easily changed.
Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even in glasses with an amorphous structure.
Much biochemistry is mediated by the weak interaction of metal ions and biomolecules. Such interactions and their associated conformational change
Conformational change
A macromolecule is usually flexible and dynamic. It can change its shape in response to changes in its environment or other factors; each possible shape is called a conformation, and a transition between them is called a conformational change...
has been measured using dual polarisation interferometry
Dual Polarisation Interferometry
Dual polarization interferometry is an analytical technique that can probe molecular scale layers adsorbed to the surface of a waveguide by using the evanescent wave of a laser beam confined to the waveguide...
.
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, as in the case of electrumElectrum
Electrum is a naturally occurring alloy of gold and silver, with trace amounts of copper and other metals. It has also been produced artificially. The ancient Greeks called it 'gold' or 'white gold', as opposed to 'refined gold'. Its color ranges from pale to bright yellow, depending on the...
, the alloys 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
Intermetallics
Intermetallics or intermetallic compounds is a term that is used in a number of different ways. Most commonly it refers to solid-state phases involving metals. There is a "research definition" adhered to generally in scientific publications, and a wider "common use" term...
, but, because materials with metallic bonding are typically not molecular, Dalton's law of integral proportions
Law of definite proportions
In chemistry, the law of definite proportions, sometimes called Proust's Law, states that a chemical compound always contains exactly the same proportion of elements by mass. An equivalent statement is the law of constant composition, which states that all samples of a given chemical compound have...
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' is such cases and speak of phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
s instead. The study of such phases has traditionally been more the domain of metallurgy
Metallurgy
Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. It is also the technology of metals: the way in which science is applied to their practical use...
than of chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, although the two fields overlap considerably.
Localization and clustering: from bonding to bonds
The metallic bonding in complicated compounds does not necessarily involve all constituent elements equally. It is quite possible to have an element or more 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 spectroscopyX-ray photoelectron spectroscopy
X-ray photoelectron spectroscopy is a quantitative spectroscopic technique that measures the elemental composition, empirical formula, chemical state and electronic state of the elements that exist within a material...
(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
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
is an extreme example of this form of condensation. At high pressures it is a metal
Metallic hydrogen
Metallic hydrogen is a state of hydrogen which results when it is sufficiently compressed and undergoes a phase transition; it is an example of degenerate matter. Solid metallic hydrogen is predicted to consist of a crystal lattice of hydrogen nuclei , with a spacing which is significantly smaller...
. The core of the planet Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
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 like boron. Though it is electron deficient compared to carbon, it does not form a metal. Instead it has a number of complicated structures in which icosahedral
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
B12 clusters dominate. Charge density waves are a related phenomenon.
As these phenomena involve the movement of the atoms towards 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 cause a very different result at low temperatures, that of superconductivity
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
. Rather than blocking the mobility of the charge carriers by forming electron pair
Electron pair
In chemistry, an electron pair consists of two electrons that occupy the same orbital but have opposite spins.Because electrons are fermions, the Pauli exclusion principle forbids these particles from having exactly the same quantum numbers. Therefore the only way to occupy the same orbital, i.e....
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 of metals. They 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
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
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 are not able to penetrate very far into the metal and are typically reflected. They bounce off, although some may also be absorbed. This holds equally for all photons of 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 they are, although surface tarnish can obscure such observations. Silver, a very good 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 like indium tin oxide
Indium tin oxide
Indium tin oxide is a solid solution of indium oxide and tin oxide , typically 90% In2O3, 10% SnO2 by weight. It is transparent and colorless in thin layers while in bulk form it is yellowish to grey...
(ITO) that are metallic conductors (actually degenerate semiconductor
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....
s) for which this threshold is in the infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
, which is why they are transparent in the visible, but good mirrors in the IR.
For silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...
the limiting frequency is in the far UV, 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
Surface plasmon resonance
The excitation of surface plasmons by light is denoted as a surface plasmon resonance for planar surfaces or localized surface plasmon resonance for nanometer-sized metallic structures....
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
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
to set the ripple in motion. Therefore, plasmons are hard to excite on a bulk metal. This is why gold and copper still look like lustrous metals albeit with a dash of color. However, in colloidal gold
Colloidal gold
Colloidal gold is a suspension of sub-micrometre-sized particles of gold in a fluid — usually water. The liquid is usually either an intense red colour , or a dirty yellowish colour ....
the metallic bonding is confined to a tiny metallic particle, preventing 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 beautiful purple-red color. Such colors are orders of magnitude more intense than ordinary absorptions seen in dyes and the like that involve individual electrons and their energy states.