Nonmetallic material

Last updated
Clay bird shaped ritual vessel archmus Heraklion, 2300-1900 BCE, one of the earlier uses of nonmetallic materials. Bird shaped ritual vessel archmus Heraklion.jpg
Clay bird shaped ritual vessel archmus Heraklion, 2300-1900 BCE, one of the earlier uses of nonmetallic materials.

Nonmetallic material, or in nontechnical terms a nonmetal, refers to materials which are not metals. Depending upon context it is used in slightly different ways. In everyday life it would be a generic term for those materials such as plastics, wood or ceramics which are not typical metals such as the iron alloys used in bridges. In some areas of chemistry, particularly the periodic table, it is used for just those chemical elements which are not metallic at standard temperature and pressure conditions. It is also sometimes used to describe broad classes of dopant atoms in materials. In general usage in science, it refers to materials which do not have electrons that can readily move around, more technically there are no available states at the Fermi energy, the equilibrium energy of electrons. For historical reasons there is a very different definition of metals in astronomy, with just hydrogen and helium as nonmetals. The term may also be used as a negative of the materials of interest such as in metallurgy or metalworking.

Contents

Variations in the environment, particularly temperature and pressure can change a nonmetal into a metal, and vica versa; this is always associated with some major change in the structure, a phase transition. Other external stimuli such as electric fields can also lead to a local nonmetal, for instance in certain semiconductor devices. There are also many physical phenomena which are only found in nonmetals such as piezoelectricity or flexoelectricity.

General definition

Filling of the electronic states in various types of materials at equilibrium. Here, height is energy while width is the density of available states for a certain energy in the material listed. The shade follows the Fermi-Dirac distribution (black: all states filled, white: no state filled). In metals and semimetals the Fermi level EF lies inside at least one band. In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes. "intrin." indicates intrinsic semiconductors. edit Band filling diagram.svg
Filling of the electronic states in various types of materials at equilibrium. Here, height is energy while width is the density of available states for a certain energy in the material listed. The shade follows the Fermi–Dirac distribution (black: all states filled, white: no state filled). In metals and semimetals the Fermi level EF lies inside at least one band.
In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes. "intrin." indicates intrinsic semiconductors.
edit

The original approach to conduction and nonmetals was a band-structure with delocalized electrons (i.e. spread out in space). In this approach a nonmetal has a gap in the energy levels of the electrons at the Fermi level. [1] : Chpt 8 & 19  In contrast, a metal would have at least one partially occupied band at the Fermi level; [1] in a semiconductor or insulator there are no delocalized states at the Fermi level, see for instance Ashcroft and Mermin. [1] These definitions are equivalent to stating that metals conduct electricity at absolute zero, as suggested by Nevill Francis Mott, [2] : 257  and the equivalent definition at other temperatures is also commonly used as in textbooks such as Chemistry of the Non-Metals by Ralf Steudel [3] and work on metal–insulator transitions. [4] [5]

In early work [6] [7] this band structure interpretation was based upon a single-electron approach with the Fermi level in the band gap as illustrated in the Figure, not including a complete picture of the many-body problem where both exchange and correlation terms can matter, as well as relativistic effects such as spin-orbit coupling. A key addition by Mott and Rudolf Peierls was that these could not be ignored. [8] For instance, nickel oxide would be a metal if a single-electron approach was used, but in fact has quite a large band gap. [9] As of 2024 it is more common to use an approach based upon density functional theory where the many-body terms are included. [10] [11] Rather than single electrons, the filling involves quasiparticles called orbitals, which are the single-particle like solutions for a system with hundreds to thousands of electrons. Although accurate calculations remain a challenge, reasonable results are now available in many cases. [12] [13]

Room temperature electrical resistivity of various materials. Room temperature electrical resistivity of various materials.jpg
Room temperature electrical resistivity of various materials.

It is also common to nuance somewhat the early definitions of Alan Herries Wilson and Mott. As discussed by both the chemist Peter Edwards and colleagues, [15] as well as Fumiko Yonezawa, [2] : 257–261 it is also important in practice to consider the temperatures at which both metals and nonmetals are used. Yonezawa provides a general definition: [2] : 260 

When a material 'conducts' and at the same time 'the temperature coefficient of the electric conductivity of that material is not positive under a certain environmental condition,' the material is metallic under that environmental condition. A material which does not satisfy these requirements is not metallic under that environmental condition.

Band structure definitions of metallicity are the most widely used, and apply both to single elements such as insulating boron [16] as well as compounds such as strontium titanate. [17] (There are many compounds which have states at the Fermi level and are metallic, for instance titanium nitride. [18] ) There are many experimental methods of checking for nonmetals by measuring the band gap, or by ab-initio quantum mechanical calculations. [19]

Functional definition

A turret lathe operator machining metallic parts for transport planes in the 1940s. WomanFactory1940s.jpg
A turret lathe operator machining metallic parts for transport planes in the 1940s.

An alternative in metallurgy is to consider various malleable alloys such as steel, aluminium alloys and similar as metals, and other materials as nonmetals; [20] fabricating metals is termed metalworking, [21] but there is no corresponding term for nonmetals. A loose definition such as this is often the common useage, but can also be inaccurate. For instance, in this useage plastics are nonmetals, but in fact there are (electrically) conducting polymers [22] [23] which should formally be described as metals. Similar, but slightly more complex, many materials which are (nonmetal) semiconductors behave like metals when they contain a high concentration of dopants, being called degenerate semiconductors. [24] A general introduction to much of this can be found in the 2017 book by Fumiko Yonezawa [2] : Chpt 1 

Periodic table elements

The periodic table Simple Periodic Table Chart-en.svg
The periodic table

The term nonmetal (chemistry) is also used for those elements which are not metallic in their normal ground state; compounds are sometimes excluded from consideration. Some textbooks use the term nonmetallic elements such as the Chemistry of the Non-Metals by Ralf Steudel, [25] : 4  which also uses the general definition in terms of conduction and the Fermi level. [25] : 154  The approach based upon the elements is often used in teaching to help students understand the periodic table of elements, [26] although it is a teaching oversimplification. [27] [28] Those elements towards the top right of the periodic table are nonmetals, those towards the center (transition metal and lanthanide) and the left are metallic. An intermediate designation metalloid is used for some elements.

The term is sometimes also used when describing dopants of specific elements types in compounds, alloys or combinations of materials, using the periodic table classification. For instance metalloids are often used in high-temperature alloys, [29] and nonmetals in precipitation hardening in steels and other alloys. [30] Here the description implicitly includes information on whether the dopants tend to be electron acceptors that lead to covalently bonded compounds rather than metallic bonding or electron acceptors.

Solar spectrum with Fraunhofer lines as it appears visually. Fraunhofer lines.svg
Solar spectrum with Fraunhofer lines as it appears visually.

Nonmetals in astronomy

A quite different approach is used in astronomy where the term metallicity is used for all elements heavier than helium, so the only nonmetals are hydrogen and helium. This is a historical anomaly. In 1802, William Hyde Wollaston [31] noted the appearance of a number of dark features in the solar spectrum. [32] In 1814, Joseph von Fraunhofer independently rediscovered the lines and began to systematically study and measure their wavelengths, and they are now called Fraunhofer lines. He mapped over 570 lines, designating the most prominent with the letters A through K and weaker lines with other letters. [33] [34] [35]

About 45 years later, Gustav Kirchhoff and Robert Bunsen [36] noticed that several Fraunhofer lines coincide with characteristic emission lines identifies in the spectra of heated chemical elements. [37] They inferred that dark lines in the solar spectrum are caused by absorption by chemical elements in the solar atmosphere. [38] Their observations [39] were in the visible range where the strongest lines come from metals such as Na, K, Fe. [40] In the early work on the chemical composition of the sun the only elements that were detected in spectra were hydrogen and various metals, [41] : 23–24  with the term metallic frequently used when describing them. [41] : Part 2  In contemporary usage all the extra elements beyond just hydrogen and helium are termed metallic.

The astrophysicst Carlos Jaschek, and the stellar astronomer and spectroscopist Mercedes Jaschek, in their book The Classification of Stars, observed that: [42]

Stellar interior specialists use 'metals' to designate any element other than hydrogen and helium, and in consequence ‘metal abundance’ implies all elements other than the first two. For spectroscopists this is very misleading, because they use the word in the chemical sense. On the other hand photometrists, who observe combined effects of all lines (i.e. without distinguishing the different elements) often use this word 'metal abundance', in which case it may also include the effect of the hydrogen lines.

Metal-insulator transition

Small changes in positions and d-levels lead to a metal-insulator transition in vanadium dioxide. VO2-MI.png
Small changes in positions and d-levels lead to a metal-insulator transition in vanadium dioxide.

There are many cases where an element or compound is metallic under certain circumstances, but a nonmetal in others. One example is metallic hydrogen which forms under very high pressures. [44] There are many other cases as discussed by Mott, [4] Inada et al [5] and more recently by Yonezawa. [2]

There can also be local transitions to a nonmetal, particularly in semiconductor devices. One example is a field-effect transistor where an electric field can lead to a region where there are no electrons at the Fermi energy (depletion zone). [45] [46]

Properties specific to nonmetals

A polarised dielectric material Capacitor schematic with dielectric.svg
A polarised dielectric material

Nonmetals have a wide range of properties, for instance the nonmetal diamond is the hardest known material, while the nonmetal molybdenum disulfide is a solid lubricants used in space. [47] There are some properties specific to them not having electrons at the Fermi energy. The main ones, for which more details are available in the links are: [1] : Chpt 27-29  [48]

See also


Related Research Articles

<span class="mw-page-title-main">Condensed matter physics</span> Branch of physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the properties of extremely large groups of atoms.

<span class="mw-page-title-main">Metal</span> Type of material

A metal is a material that, when polished or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. These properties are all associated with having electrons available at the Fermi level, as against nonmetallic materials which do not. Metals are typically ductile and malleable.

<span class="mw-page-title-main">Periodic table</span> Tabular arrangement of the chemical elements ordered by atomic number

The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows ("periods") and columns ("groups"). It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks. Elements in the same group tend to show similar chemical characteristics.

<span class="mw-page-title-main">Exciton</span> Quasiparticle which is a bound state of an electron and an electron hole

An electron and an electron hole that are attracted to each other by the Coulomb force can form a bound state called an exciton. It is an electrically neutral quasiparticle that exists mainly in condensed matter, including insulators, semiconductors, some metals, but also in certain atoms, molecules and liquids. The exciton is regarded as an elementary excitation that can transport energy without transporting net electric charge.

A metalloid is a chemical element which has a preponderance of properties in between, or that are a mixture of, those of metals and nonmetals. There is no standard definition of a metalloid and no complete agreement on which elements are metalloids. Despite the lack of specificity, the term remains in use in the literature.

<span class="mw-page-title-main">Nonmetal</span> Category of chemical elements

In the context of the periodic table a nonmetal is a chemical element that mostly lacks distinctive metallic properties. They range from colorless gases like hydrogen to shiny crystals like iodine. Physically, they are usually lighter than elements that form metals and are often poor conductors of heat and electricity. Chemically, nonmetals have relatively high electronegativity or usually attract electrons in a chemical bond with another element, and their oxides tend to be acidic.

<span class="mw-page-title-main">Band gap</span> Energy range in a solid where no electron states exist

In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron are free to move within the crystal lattice and serve as charge carriers to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band to the conduction band, then current can flow. Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances having large band gaps are generally insulators, those with small band gaps are semiconductor, and conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.

Metallic hydrogen is a phase of hydrogen in which it behaves like an electrical conductor. This phase was predicted in 1935 on theoretical grounds by Eugene Wigner and Hillard Bell Huntington.

<span class="mw-page-title-main">Semimetal</span> Metal with a small negative indirect band-gap

A semimetal is a material with a small energy overlap between the bottom of the conduction band and the top of the valence band, but they do not overlap in momentum space. According to electronic band theory, solids can be classified as insulators, semiconductors, semimetals, or metals. In insulators and semiconductors the filled valence band is separated from an empty conduction band by a band gap. For insulators, the magnitude of the band gap is larger than that of a semiconductor. Because of the slight overlap between the conduction and valence bands, semimetals have no band gap and a small density of states at the Fermi level. A metal, by contrast, has an appreciable density of states at the Fermi level because the conduction band is partially filled.

Organic semiconductors are solids whose building blocks are pi-bonded molecules or polymers made up by carbon and hydrogen atoms and – at times – heteroatoms such as nitrogen, sulfur and oxygen. They exist in the form of molecular crystals or amorphous thin films. In general, they are electrical insulators, but become semiconducting when charges are either injected from appropriate electrodes, upon doping or by photoexcitation.

<span class="mw-page-title-main">Dangling bond</span>

In chemistry, a dangling bond is an unsatisfied valence on an immobilized atom. An atom with a dangling bond is also referred to as an immobilized free radical or an immobilized radical, a reference to its structural and chemical similarity to a free radical.

<span class="mw-page-title-main">Mott insulator</span> Materials classically predicted to be conductors, that are actually insulators

Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators. These insulators fail to be correctly described by band theories of solids due to their strong electron–electron interactions, which are not considered in conventional band theory. A Mott transition is a transition from a metal to an insulator, driven by the strong interactions between electrons. One of the simplest models that can capture Mott transition is the Hubbard model.

<span class="mw-page-title-main">Electride</span> Ionic compound with electrons as the anion

An electride is an ionic compound in which an electron serves the role of the anion. Solutions of alkali metals in ammonia are electride salts. In the case of sodium, these blue solutions consist of [Na(NH3)6]+ and solvated electrons:

Metal–insulator transitions are transitions of a material from a metal to an insulator. These transitions can be achieved by tuning various ambient parameters such as temperature, pressure or, in case of a semiconductor, doping.

<span class="mw-page-title-main">Positron annihilation spectroscopy</span> Non-destructive spectroscopy

Positron annihilation spectroscopy (PAS) or sometimes specifically referred to as positron annihilation lifetime spectroscopy (PALS) is a non-destructive spectroscopy technique to study voids and defects in solids.

<span class="mw-page-title-main">Kondo insulator</span> Strongly correlated system with a narrow band gap at low temperatures

In solid-state physics, Kondo insulators are understood as materials with strongly correlated electrons, that open up a narrow band gap at low temperatures with the chemical potential lying in the gap, whereas in heavy fermion materials the chemical potential is located in the conduction band.

The chemical elements can be broadly divided into metals, metalloids, and nonmetals according to their shared physical and chemical properties. All elemental metals have a shiny appearance ; are good conductors of heat and electricity; form alloys with other metallic elements; and have at least one basic oxide. Metalloids are metallic-looking, often brittle solids that are either semiconductors or exist in semiconducting forms, and have amphoteric or weakly acidic oxides. Typical elemental nonmetals have a dull, coloured or colourless appearance; are often brittle when solid; are poor conductors of heat and electricity; and have acidic oxides. Most or some elements in each category share a range of other properties; a few elements have properties that are either anomalous given their category, or otherwise extraordinary.

<span class="mw-page-title-main">Samarium hexaboride</span> Chemical compound

Samarium hexaboride (SmB6) is an intermediate-valence compound where samarium is present both as Sm2+ and Sm3+ ions at the ratio 3:7. It is a Kondo insulator having a metallic surface state.

<span class="mw-page-title-main">Fulleride</span> Chemical compound

Fullerides are chemical compounds containing fullerene anions. Common fullerides are derivatives of the most common fullerenes, i.e. C60 and C70. The scope of the area is large because multiple charges are possible, i.e., [C60]n− (n = 1, 2...6), and all fullerenes can be converted to fullerides. The suffix "-ide" implies their negatively charged nature.

<span class="mw-page-title-main">Thomas Maurice Rice</span> Theoretical physicist and professor

Thomas Maurice Rice, known professionally as Maurice Rice, is an Irish theoretical physicist specializing in condensed matter physics.

References

  1. 1 2 3 4 5 Ashcroft, Neil W.; Mermin, N. David (1976). Solid state physics. Fort Worth Philadelphia San Diego [etc.]: Saunders college publ. ISBN   978-0-03-083993-1.
  2. 1 2 3 4 5 Yonezawa, Fumiko (2017). Physics of metal-nonmetal transitions. Washington, DC: IOS Press. ISBN   978-1-61499-786-3.
  3. ↑ Steudel, Ralf (2020). Chemistry of the Non-Metals: Syntheses - Structures - Bonding - Applications. De Gruyter. p. 154. doi:10.1515/9783110578065. ISBN   978-3-11-057806-5.
  4. 1 2 Mott, N. F. (1968). "Metal-Insulator Transition". Reviews of Modern Physics. 40 (4): 677–683. Bibcode:1968RvMP...40..677M. doi:10.1103/RevModPhys.40.677. ISSN   0034-6861.
  5. 1 2 Imada, Masatoshi; Fujimori, Atsushi; Tokura, Yoshinori (1998). "Metal-insulator transitions". Reviews of Modern Physics. 70 (4): 1039–1263. Bibcode:1998RvMP...70.1039I. doi:10.1103/RevModPhys.70.1039. ISSN   0034-6861.
  6. ↑ Wilson, A. H. (1931). "The theory of electronic semi-conductors". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 133 (822): 458–491. Bibcode:1931RSPSA.133..458W. doi: 10.1098/rspa.1931.0162 . ISSN   0950-1207.
  7. ↑ Wilson, A. H. (1931). "The theory of electronic semi-conductors. - II". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 134 (823): 277–287. Bibcode:1931RSPSA.134..277W. doi: 10.1098/rspa.1931.0196 . ISSN   0950-1207.
  8. ↑ Mott, N F; Peierls, R (1937). "Discussion of the paper by de Boer and Verwey". Proceedings of the Physical Society. 49 (4S): 72–73. Bibcode:1937PPS....49...72M. doi:10.1088/0959-5309/49/4S/308. ISSN   0959-5309.
  9. ↑ Boer, J H de; Verwey, E J W (1937). "Semi-conductors with partially and with completely filled 3 d -lattice bands". Proceedings of the Physical Society. 49 (4S): 59–71. Bibcode:1937PPS....49...59B. doi:10.1088/0959-5309/49/4S/307. ISSN   0959-5309.
  10. ↑ Burke, Kieron (2007). "The ABC of DFT" (PDF).
  11. ↑ Gross, Eberhard K. U.; Dreizler, Reiner M. (2013). Density Functional Theory. Springer Science & Business Media. ISBN   978-1-4757-9975-0.
  12. ↑ Ferreira, Luiz G.; Marques, Marcelo; Teles, Lara K. (2008). "Approximation to density functional theory for the calculation of band gaps of semiconductors". Physical Review B. 78 (12): 125116. arXiv: 0808.0729 . Bibcode:2008PhRvB..78l5116F. doi:10.1103/PhysRevB.78.125116. ISSN   1098-0121.
  13. ↑ Tran, Fabien; Blaha, Peter (2017). "Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory". The Journal of Physical Chemistry A. 121 (17): 3318–3325. Bibcode:2017JPCA..121.3318T. doi:10.1021/acs.jpca.7b02882. ISSN   1089-5639. PMC   5423078 . PMID   28402113.
  14. ↑ Edwards, P. P.; Lodge, M. T. J.; Hensel, F.; Redmer, R. (2010). "'… a metal conducts and a non-metal doesn't'". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 368 (1914): 941–965. Bibcode:2010RSPTA.368..941E. doi:10.1098/rsta.2009.0282. ISSN   1364-503X. PMC   3263814 . PMID   20123742.
  15. ↑ Edwards, P. P.; Lodge, M. T. J.; Hensel, F.; Redmer, R. (2010). "'… a metal conducts and a non-metal doesn't'". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 368 (1914): 941–965. Bibcode:2010RSPTA.368..941E. doi:10.1098/rsta.2009.0282. ISSN   1364-503X. PMC   3263814 . PMID   20123742.
  16. ↑ Ogitsu, Tadashi; Schwegler, Eric; Galli, Giulia (2013). "β-Rhombohedral Boron: At the Crossroads of the Chemistry of Boron and the Physics of Frustration". Chemical Reviews. 113 (5): 3425–3449. doi:10.1021/cr300356t. ISSN   0009-2665. OSTI   1227014. PMID   23472640.
  17. ↑ Reihl, B.; Bednorz, J. G.; Müller, K. A.; Jugnet, Y.; Landgren, G.; Morar, J. F. (1984). "Electronic structure of strontium titanate". Physical Review B. 30 (2): 803–806. Bibcode:1984PhRvB..30..803R. doi:10.1103/PhysRevB.30.803. ISSN   0163-1829.
  18. ↑ Höchst, H.; Bringans, R. D.; Steiner, P.; Wolf, Th. (1982). "Photoemission study of the electronic structure of stoichiometric and substoichiometric TiN and ZrN". Physical Review B. 25 (12): 7183–7191. Bibcode:1982PhRvB..25.7183H. doi:10.1103/PhysRevB.25.7183. ISSN   0163-1829.
  19. ↑ Kim, Sangtae; Lee, Miso; Hong, Changho; Yoon, Youngchae; An, Hyungmin; Lee, Dongheon; Jeong, Wonseok; Yoo, Dongsun; Kang, Youngho; Youn, Yong; Han, Seungwu (2020). "A band-gap database for semiconducting inorganic materials calculated with hybrid functional". Scientific Data. 7 (1): 387. Bibcode:2020NatSD...7..387K. doi:10.1038/s41597-020-00723-8. ISSN   2052-4463. PMC   7658987 . PMID   33177500.
  20. ↑ Cottrell, Alan (1985). An introduction to metallurgy: SI units (2. ed., repr ed.). London: Arnold. ISBN   978-0-7131-2510-8.
  21. ↑ DeGarmo, E. Paul, ed. (2003). Materials and processes in manufacturing (9th ed.). Hoboken, N.J: Wiley. ISBN   978-0-471-65653-1.
  22. ↑ Waltman, R. J.; Bargon, J. (1986). "Electrically conducting polymers: a review of the electropolymerization reaction, of the effects of chemical structure on polymer film properties, and of applications towards technology". Canadian Journal of Chemistry. 64 (1): 76–95. doi:10.1139/v86-015. ISSN   0008-4042.
  23. ↑ Das, Tapan K.; Prusty, Smita (2012). "Review on Conducting Polymers and Their Applications". Polymer-Plastics Technology and Engineering. 51 (14): 1487–1500. doi:10.1080/03602559.2012.710697. ISSN   0360-2559.
  24. ↑ Wolff, P. A. (1962). "Theory of the Band Structure of Very Degenerate Semiconductors". Physical Review. 126 (2): 405–412. Bibcode:1962PhRv..126..405W. doi:10.1103/PhysRev.126.405. ISSN   0031-899X.
  25. 1 2 Steudel, Ralf (2020). Chemistry of the Non-Metals: Syntheses - Structures - Bonding - Applications. De Gruyter. p. 4. doi:10.1515/9783110578065. ISBN   978-3-11-057806-5.
  26. ↑ "1.8: Introduction to the Periodic Table". Chemistry LibreTexts. 2015. Retrieved 2024-06-16.
  27. ↑ Worstall, Tim (2015). "'The Scientific Method' Is A Myth, Long Live The Scientific Method". Forbes . Archived from the original on 2015-11-12. Retrieved 2024-06-27.
  28. ↑ Worstall, Tim (2015). "To Prove Econ 101 Is Wrong You Do Need To Understand Econ 101". Forbes. Retrieved 2024-06-27.
  29. ↑ Perepezko, John H. (2009). "The Hotter the Engine, the Better". Science. 326 (5956): 1068–1069. Bibcode:2009Sci...326.1068P. doi:10.1126/science.1179327. ISSN   0036-8075. PMID   19965415.
  30. ↑ Ardell, A. J. (1985). "Precipitation hardening". Metallurgical Transactions A. 16 (12): 2131–2165. Bibcode:1985MTA....16.2131A. doi:10.1007/BF02670416. ISSN   0360-2133.
  31. ↑ Melvyn C. Usselman: William Hyde Wollaston Encyclopædia Britannica, retrieved 31 March 2013
  32. ↑ William Hyde Wollaston (1802) "A method of examining refractive and dispersive powers, by prismatic reflection," Philosophical Transactions of the Royal Society, 92: 365–380; see especially p. 378.
  33. ↑ Hearnshaw, J.B. (1986). The analysis of starlight. Cambridge: Cambridge University Press. p. 27. ISBN   978-0-521-39916-6.
  34. ↑ Joseph Fraunhofer (1814 - 1815) "Bestimmung des Brechungs- und des Farben-Zerstreuungs - Vermögens verschiedener Glasarten, in Bezug auf die Vervollkommnung achromatischer Fernröhre" (Determination of the refractive and color-dispersing power of different types of glass, in relation to the improvement of achromatic telescopes), Denkschriften der Königlichen Akademie der Wissenschaften zu München (Memoirs of the Royal Academy of Sciences in Munich), 5: 193–226; see especially pages 202–205 and the plate following page 226.
  35. ↑ Jenkins, Francis A.; White, Harvey E. (1981). Fundamentals of Optics (4th ed.). McGraw-Hill. p.  18. ISBN   978-0-07-256191-3.
  36. ↑ See:
    • Gustav Kirchhoff (1859) "Ueber die Fraunhofer'schen Linien" (On Fraunhofer's lines), Monatsbericht der Königlichen Preussische Akademie der Wissenschaften zu Berlin (Monthly report of the Royal Prussian Academy of Sciences in Berlin), 662–665.
    • Gustav Kirchhoff (1859) "Ueber das Sonnenspektrum" (On the sun's spectrum), Verhandlungen des naturhistorisch-medizinischen Vereins zu Heidelberg (Proceedings of the Natural History / Medical Association in Heidelberg), 1 (7) : 251–255.
  37. ↑ G. Kirchhoff (1860). "Ueber die Fraunhofer'schen Linien". Annalen der Physik. 185 (1): 148–150. Bibcode:1860AnP...185..148K. doi:10.1002/andp.18601850115.
  38. ↑ G. Kirchhoff (1860). "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht" [On the relation between the emissive power and the absorptive power of bodies towards heat and light]. Annalen der Physik. 185 (2): 275–301. Bibcode:1860AnP...185..275K. doi: 10.1002/andp.18601850205 .
  39. ↑ "Kirchhoff and Bunsen on Spectroscopy". www.chemteam.info. Retrieved 2024-07-02.
  40. ↑ "Spectrum analysis in its aqplication to terrestrial substances and the physical constitution of the heavenly bodies : familiarly explained / by H. Schellen ..." HathiTrust. hdl:2027/hvd.hn3317 . Retrieved 2024-07-02.
  41. 1 2 Meadows, A. J. (Arthur Jack) (1970). Early solar physics. Internet Archive. Oxford, New York, Pergamon Press. ISBN   978-0-08-006653-0.
  42. ↑ Jaschek, C; Jascheck, M (1990). The Classification of Stars. Cambridge: Cambridge University Press. p. 22. ISBN   978-0-521-26773-1.
  43. ↑ Shao, Zewei; Cao, Xun; Luo, Hongjie; Jin, Ping (2018). "Recent progress in the phase-transition mechanism and modulation of vanadium dioxide materials". NPG Asia Materials. 10 (7): 581–605. Bibcode:2018npgAM..10..581S. doi: 10.1038/s41427-018-0061-2 . ISSN   1884-4049.
  44. ↑ Wigner, E.; Huntington, H. B. (1935). "On the Possibility of a Metallic Modification of Hydrogen". The Journal of Chemical Physics. 3 (12): 764–770. Bibcode:1935JChPh...3..764W. doi:10.1063/1.1749590. ISSN   0021-9606.
  45. ↑ Kushwah, D. S. (1975). "Field Effect Transistors-A review of their growth and the state of the art". IETE Journal of Education. 16 (3): 126–132. doi:10.1080/09747338.1975.11450118. ISSN   0974-7338.
  46. ↑ Zhang, Shubo (2020). "Review of Modern Field Effect Transistor Technologies for Scaling". Journal of Physics: Conference Series. 1617 (1): 012054. Bibcode:2020JPhCS1617a2054Z. doi: 10.1088/1742-6596/1617/1/012054 . ISSN   1742-6588.
  47. ↑ Vazirisereshk, Mohammad R.; Martini, Ashlie; Strubbe, David A.; Baykara, Mehmet Z. (2019). "Solid Lubrication with MoS2: A Review". Lubricants. 7 (7): 57. arXiv: 1906.05854 . doi: 10.3390/lubricants7070057 . ISSN   2075-4442.
  48. ↑ Griffiths, David J. (2017). Introduction to Electrodynamics (4 ed.). Cambridge University Press. doi:10.1017/9781108333511.008. ISBN   978-1-108-33351-1.
  49. ↑ "Dielectric | Definition, Properties, & Polarization | Britannica". 2021. Archived from the original on 2021-04-27. Retrieved 2024-06-16.
  50. 1 2 "Electrostriction | Piezoelectricity, Ferroelectricity, Magnetostriction | Britannica". www.britannica.com. Retrieved 2024-06-16.
  51. ↑ Zubko, Pavlo; Catalan, Gustau; Tagantsev, Alexander K. (2013). "Flexoelectric Effect in Solids". Annual Review of Materials Research. 43 (1): 387–421. Bibcode:2013AnRMS..43..387Z. doi:10.1146/annurev-matsci-071312-121634. hdl: 10261/99362 . ISSN   1531-7331.
  52. ↑ Mizzi, C. A.; Lin, A. Y. W.; Marks, L. D. (2019). "Does Flexoelectricity Drive Triboelectricity?". Physical Review Letters. 123 (11): 116103. arXiv: 1904.10383 . Bibcode:2019PhRvL.123k6103M. doi:10.1103/PhysRevLett.123.116103. ISSN   0031-9007. PMID   31573269.
  53. ↑ Kasap, Safa; Koughia, Cyril; Ruda, Harry E. (2017), Kasap, Safa; Capper, Peter (eds.), "Electrical Conduction in Metals and Semiconductors", Springer Handbook of Electronic and Photonic Materials, Cham: Springer International Publishing, p. 1, doi:10.1007/978-3-319-48933-9_2, ISBN   978-3-319-48933-9 , retrieved 2024-06-30
  54. ↑ Rogers, Alan (2009). Essentials of Photonics (2nd ed.). CRC Press. doi:10.1201/9781315222042. ISBN   9781315222042.
  55. ↑ Jackson, John David (2009). Classical electrodynamics (3rd ed.). Hoboken, NY: Wiley. ISBN   978-0-471-30932-1.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.