Metallic bonding: Difference between revisions

'''Metallic bonding''' is a type of [[chemical bond]]ing that arises from the electrostatic attractive force between [[conduction electrons]] (in the form of an electron cloud of [[delocalized electron]]s) and positively charged [[metal]] [[ion]]s. It may be described as the sharing of ''free'' electrons among a [[crystal structure|structure]] of positively charged ions ([[cation]]s). Metallic bonding accounts for many [[physical property|physical properties]] of metals, such as [[Strength of materials|strength]], [[ductility]], [[thermal conductivity|thermal]] and [[electrical resistivity and conductivity]], [[Opacity (optics)|opacity]], and [[lustre (mineralogy)|lusterlustre]].<ref>[http://www.chemguide.co.uk/atoms/bonding/metallic.html Metallic bonding]. chemguide.co.uk</ref><ref>[http://www.chemguide.co.uk/atoms/structures/metals.html Metal structures]. chemguide.co.uk</ref><ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Chemical Bonds]. chemguide.co.uk</ref><ref>[https://web.archive.org/web/19991018204506/http://www.physics.ohio-state.edu/%7Eaubrecht/physics133.html "Physics 133 Lecture Notes" Spring, 2004. Marion Campus]. physics.ohio-state.edu</ref>

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 [[phase diagram]]s were developed. Despite all this progress, the nature of [[Intermetallic|intermetallic compounds]] and [[Alloy|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 [[Law of multiple proportions#Law 3: Law of Multiple Proportions|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 fieldmetallurgy, notably [[William Hume-Rothery|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 not spherical didas notthe holdHume-Rothery believed, except perhaps in the case of [[caesium]]. This finding reduced many of the conclusions to examples ofrevealed how a model can sometimes give a whole series of correct predictions, yet still be wrong in its basic assumptions.

The nearly-free electron debacle showedcompelled researchers thatto anymodify modelthe that assumedassumpition that ions wereflowed in a sea of free electrons needed modification. So, aA number of quantum mechanical models—suchmodels were developed, such as band structure calculations based on molecular orbitals, orand the [[density functional theory]]—were developed. In theseThese models, one either departsdepart 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 educationintroductory courses on metallurgy.

The electronic band structure model became a major focus not only for the study of metals butand even more so for the study of [[semiconductor]]s. Together with the electronic states, the vibrational states were also shown to form bands. [[Rudolf Peierls]] showed that, in the case of a one-dimensional row of metallic atoms—say, hydrogen—an inevitable instability had to arise that would lead to the breakup ofbreak 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 remainingremains a one-electron approximation of a many-body problem. In other words,: the energy states of eachan individual electron are described as if all the other electrons simply form a homogeneous background. Researchers such as Mott and Hubbard realized that thisthe one-electron treatment was perhaps appropriate for strongly delocalized [[azimuthal quantum number|'''s'''- and '''p'''-electrons]]; but for '''d'''-electrons, and even more for '''f'''-electrons, the interaction with nearby individual electrons (and atomic displacements) in the local environment may become stronger than the delocalizationdelocalized interaction that leads to broad bands. Thus,This gave a better explanation for the transition from localized [[unpaired electron]]s to itinerant ones partaking in metallic bonding became more comprehensible.

Delocalization is most pronounced for '''s'''- and '''p'''-electrons. Delocalization in [[caesium]] is so strong that the electrons are virtually freed from the caesium atoms to form a gas constrained only by the surface of the metal. For caesium, therefore, the picture of Cs⁺ ions held together by a negatively charged [[nearly-free electron model|electron gas]] is very close to accurate (though not inaccurateperfectly so).{{efn|If the electrons were truly ''free'', their energy would only depend on the magnitude of their [[wave vector]] '''k''', not its direction. That is, in [[momentum space|'''k'''-space]], the Fermi level should form a perfect [[sphere]]. The [[Fermi surface|shape of the Fermi level]] can be measured by [[cyclotron resonance]] and is never a sphere, not even for caesium.<ref>{{cite journal|title=The Fermi Surface of Caesium|author1=Okumura, K. |author2=Templeton, I. M. |name-list-style=amp |journal=Proceedings of the Royal Society of London A|issue=1408 |year=1965|pages=89–104|jstor=2415064|doi=10.1098/rspa.1965.0170|volume=287|bibcode = 1965RSPSA.287...89O|s2cid=123127614 }}</ref>}} 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 [[magnetism|magnetic properties]] to these metals.

As these phenomena involve the movement of the atoms toward or away from each other, they can be interpreted as the coupling between the electronic and the vibrational states (i.e. the phonons) of the material. A different such electron-phonon interaction is thought to lead to a very different result at low temperatures, that of [[superconductivity]]. Rather than blocking the mobility of the charge carriers by forming [[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 cannot penetrate very far into the metal and are typically reflected, although some may also be absorbed. This holds equally for all photons in the visible spectrum, which is why metals are often silvery white or grayish with the characteristic specular reflection of metallic [[lustre (mineralogy)|lusterlustre]]. The balance between reflection and absorption determines how white or how gray a metal is, although surface tarnish can obscure the lusterlustre. Silver, a metal with high conductivity, is one of the whitest.