Editing Metal (section)

===Electrical and thermal===
[[File:Band filling diagram.svg|thumb|{{{1|right}}}|300px|

The energy states available to electrons in different kinds of solids at [[thermodynamic equilibrium]].
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Here, height is energy while width is the [[density of states|density of available states]] for a certain energy in the material listed. The shading follows the [[Fermi–Dirac statistics|Fermi–Dirac distribution]] ('''black'''=all states filled, '''white'''=no state filled).
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The [[Fermi level]] ''E''<sub>F</sub> is the energy level at which the electrons are in a position to interact with energy levels above them. In metals and [[semimetal]]s the [[Fermi level]] ''E''<sub>F</sub> lies inside at least one band of energy states.
<div style="height:6px;font-size:1px;">&nbsp;</div>
In [[insulator (electricity)|insulators]] and [[semiconductor]]s the Fermi level is inside a [[band gap]]; however, in semiconductors the bands are near enough to the Fermi level to be [[Fermi–Dirac statistics|thermally populated]] with electrons or [[electron hole|holes]].
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The electronic structure of metals makes them good [[electrical conductivity|conductors of electricity]]. In general, electrons in a material all have different [[Momentum|momenta]], which average to zero when there is no external [[voltage]]. In metals, when a voltage is applied, some electrons shift to states with slightly higher momentum in the direction of the electric field, while others slow down slightly. This creates a net [[drift velocity]] that leads to an electric current.<ref name="Kittel-2018" /><ref name="Ashcroft-1976" /><ref name="h887">{{cite book |last=Simon |first=Steven H. |title=The Oxford Solid State Basics |date=2013-06-21 |publisher=OUP Oxford |isbn=978-0-19-150210-1 |publication-place=Oxford |pages=173-174}}</ref> This involves small changes in which [[Quantum state|wavefunctions]] the electrons are in, changing to those with the higher momenta. According to the [[Pauli exclusion principle]], no two electrons can occupy the same quantum state.<ref>{{Cite book |last=Schiff |first=Leonard |author-link=Leonard I. Schiff |url=https://ia601609.us.archive.org/11/items/ost-physics-schiff-quantummechanics/Schiff-QuantumMechanics.pdf |title=Quantum Mechanics |publisher=[[McGraw-Hill]] |year=1959}}</ref> Therefore, for the electrons to shift to higher-momentum states, such states must be unoccupied. In metals, these empty [[Delocalized electron|delocalized electron states]] are available at energies near the highest occupied levels, as shown in the Figure.

By contrast, semiconductors like silicon and nonmetals like [[strontium titanate]] have an [[Band gap|energy gap]] between the highest filled electron states (the valence band) and the lowest empty states (the conduction band). A small electric field is insufficient to excite electrons across this gap, making these materials poor electrical conductors.<ref name="h887" /> However, semiconductors can carry some current when [[Doping (semiconductor)|doped]] with elements that introduce additional partially occupied energy states, or when thermal excitation enables electrons to cross the energy gap.<ref name="Solymar-2004">{{Cite book |last1=Solymar |first1=L. |title=Electrical properties of materials |last2=Walsh |first2=D. |date=2004 |publisher=Oxford University Press |isbn=978-0-19-926793-4 |edition=7th |location=Oxford; New York}}</ref>

The elemental metals have electrical conductivity values of from 6.9 × 10<sup>3</sup> [[Siemens (unit)|S]]/cm for [[manganese]] to 6.3 × 10<sup>5</sup> S/cm for [[silver]]. In contrast, a [[semiconductor|semiconducting]] metalloid such as [[boron]] has an electrical conductivity 1.5 × 10<sup>−6</sup> S/cm. Typically, the electrical conductivity of metals decreases with heating because the increased thermal motion of the atoms makes it harder for electrons to flow.<ref>{{Cite book |title=Springer Handbook of Electronic and Photonic Materials |date=2017 |publisher=Springer International Publishing : Imprint: Springer |isbn=978-3-319-48933-9 |editor-last=Capper |editor-first=Peter |edition=2nd ed. 2017 |series=Springer Handbooks |location=Cham |pages=23 |editor-last2=Kasap |editor-first2=Safa}}</ref> Exceptionally, [[plutonium]]'s electrical conductivity increases when heated in the temperature range of around −175 to +125&nbsp;°C, with anomalously large thermal expansion coefficient and a phase change from monoclinic to face-centered cubic near 100&nbsp;°C.<ref name="HeckerPlutonium">{{Cite journal |last=Hecker |first=Siegfried S. |date=2000 |title=Plutonium and its alloys: from atoms to microstructure |url=https://fas.org/sgp/othergov/doe/lanl/pubs/00818035.pdf |url-status=live |journal=Los Alamos Science |volume=26 |pages=290–335 |archive-url=https://web.archive.org/web/20090224204042/http://www.fas.org/sgp/othergov/doe/lanl/pubs/00818035.pdf |archive-date=February 24, 2009 |access-date=February 15, 2009}}</ref> This behavior, along with similar phenomena observed in other transuranic elements, is attributed to more complex relativistic and spin interactions which are not captured in simple models.<ref>{{Cite journal |last1=Tsiovkin |first1=Yu. Yu. |last2=Lukoyanov |first2=A. V. |last3=Shorikov |first3=A. O. |last4=Tsiovkina |first4=L. Yu. |last5=Dyachenko |first5=A. A. |last6=Bystrushkin |first6=V. B. |last7=Korotin |first7=M. A. |last8=Anisimov |first8=V. I. |last9=Dremov |first9=V. V. |date=2011 |title=Electrical resistivity of pure transuranium metals under pressure |url=https://linkinghub.elsevier.com/retrieve/pii/S0022311511003369 |journal=Journal of Nuclear Materials |volume=413 |issue=1 |pages=41–46 |doi=10.1016/j.jnucmat.2011.03.053 |bibcode=2011JNuM..413...41T |issn=0022-3115|url-access=subscription }}</ref>
[[File:TiN_DOS.tif|thumb|Density of states of TiN, with the occupied states shaded in blue and the Fermi level at the x origin. All the states, as well as those associated with the Ti and N atoms are shown.|left|250x250px]]
All of the metallic alloys as well as conducting ceramics and polymers are metals by the same definition; for instance [[titanium nitride]] has delocalized states at the Fermi level. They have electrical conductivities similar to those of elemental metals. Liquid forms are also metallic conductors or electricity, for instance [[Mercury (element)|mercury]]. In normal conditions no gases are metallic conductors. However, a [[plasma (physics)|plasma]] is a metallic conductor and the charged particles in a plasma have many properties in common with those of electrons in elemental metals, particularly for white dwarf stars.<ref>{{Cite journal |last1=Koester |first1=D |last2=Chanmugam |first2=G |date=1990 |title=Physics of white dwarf stars |url=https://iopscience.iop.org/article/10.1088/0034-4885/53/7/001 |journal=Reports on Progress in Physics |volume=53 |issue=7 |pages=837–915 |doi=10.1088/0034-4885/53/7/001 |issn=0034-4885|url-access=subscription }}</ref>

Metals are relatively good [[thermal conductivity|conductors of heat]], which in metals is transported mainly by the conduction electrons.<ref name=bassani>{{cite book | last=Skośkiewicz | first=T. | title=Encyclopedia of Condensed Matter Physics | chapter=Thermal Conductivity at Low Temperatures | publisher=Elsevier | date=2005 | pages=159–164 | isbn=978-0-12-369401-0 | doi=10.1016/b0-12-369401-9/01168-2}}</ref> At higher temperatures the electrons can occupy slightly higher energy levels given by [[Fermi–Dirac statistics]].<ref name="Ashcroft-1976" /><ref name="Solymar-2004" /> These have slightly higher momenta ([[kinetic energy]]) and can pass on thermal energy. The empirical [[Wiedemann–Franz law]] states that in many metals the ratio between thermal and electrical conductivities is proportional to temperature, with a proportionality constant that is roughly the same for all metals.<ref name="Ashcroft-1976" />
[[File:Battery Demonstration Unit - DPLA (cropped).jpg|alt=Battery demonstration unit for conducting polymers built by nobel laureate Alan MacDiarmid|thumb|Battery demonstration unit for conducting polymers built by nobel laureate [[Alan MacDiarmid]]<ref>{{Cite web |title=The Nobel Prize in Chemistry 2000 |url=https://www.nobelprize.org/prizes/chemistry/2000/summary/ |access-date=2024-07-23 |website=NobelPrize.org |language=en-US}}</ref>]]
The contribution of a metal's electrons to its heat capacity and thermal conductivity, and the electrical conductivity of the metal itself can be approximately calculated from the [[free electron model]].<ref name="Ashcroft-1976" /> However, this does not take into account the detailed structure of the metal's ion lattice. Taking into account the positive potential caused by the arrangement of the ion cores enables consideration of the [[electronic band structure]] and [[binding energy]] of a metal. Various models are applicable, the simplest being the [[nearly free electron model]].<ref name="Ashcroft-1976" /> Modern methods such as [[density functional theory]] are typically used.<ref>{{Cite web |last=Burke |first=Kieron |date=2007 |title=The ABC of DFT |url=https://dft.uci.edu/doc/g1.pdf}}</ref><ref>{{Cite book |last1=Gross |first1=Eberhard K. U. |url=https://books.google.com/books?id=aG4ECAAAQBAJ&q=density+functional+theory |title=Density Functional Theory |last2=Dreizler |first2=Reiner M. |date=2013 |publisher=Springer Science & Business Media |isbn=978-1-4757-9975-0 |language=en}}</ref>