Allotropy

Allotropy or allotropism (from Ancient Greek ἄλλος (allos) 'other', and τρόπος (tropos) 'manner, form') is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the atoms of the element are bonded together in different manners.[1] For example, the allotropes of carbon include diamond (the carbon atoms are bonded together to form a cubic lattice of tetrahedra), graphite (the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets of graphite), and fullerenes (the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations).

Diamond and graphite are two allotropes of carbon: pure forms of the same element that differ in crystalline structure.

The term allotropy is used for elements only, not for compounds. The more general term, used for any compound, is polymorphism, although its use is usually restricted to solid materials such as crystals. Allotropy refers only to different forms of an element within the same physical phase (the state of matter, such as a solid, liquid or gas). The differences between these states of matter would not alone constitute examples of allotropy. Allotropes of chemical elements are frequently referred to as polymorphs or as phases of the element.

For some elements, allotropes have different molecular formulae or different crystalline structures, as well as a difference in physical phase; for example, two allotropes of oxygen (dioxygen, O₂, and ozone, O₃) can both exist in the solid, liquid and gaseous states. Other elements do not maintain distinct allotropes in different physical phases; for example, phosphorus has numerous solid allotropes, which all revert to the same P₄ form when melted to the liquid state.

History

The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius (1779–1848).[2][3] The term is derived from Greek άλλοτροπἱα (allotropia) 'variability, changeableness'.[4] After the acceptance of Avogadro's hypothesis in 1860, it was understood that elements could exist as polyatomic molecules, and two allotropes of oxygen were recognized as O₂ and O₃.[3] In the early 20th century, it was recognized that other cases such as carbon were due to differences in crystal structure.

By 1912, Ostwald noted that the allotropy of elements is just a special case of the phenomenon of polymorphism known for compounds, and proposed that the terms allotrope and allotropy be abandoned and replaced by polymorph and polymorphism.[5][3] Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.[6]

Differences in properties of an element's allotropes

Allotropes are different structural forms of the same element and can exhibit quite different physical properties and chemical behaviours. The change between allotropic forms is triggered by the same forces that affect other structures, i.e., pressure, light, and temperature. Therefore, the stability of the particular allotropes depends on particular conditions. For instance, iron changes from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C, and tin undergoes a modification known as tin pest from a metallic form to a semiconductor form below 13.2 °C (55.8 °F). As an example of allotropes having different chemical behaviour, ozone (O₃) is a much stronger oxidizing agent than dioxygen (O₂).

List of allotropes

Typically, elements capable of variable coordination number and/or oxidation states tend to exhibit greater numbers of allotropic forms. Another contributing factor is the ability of an element to catenate.

Examples of allotropes include:

Non-metals

Element	Allotropes
Carbon	Diamond – an extremely hard, transparent crystal, with the carbon atoms arranged in a tetrahedral lattice. A poor electrical conductor. An excellent thermal conductor. Lonsdaleite – also called hexagonal diamond. Graphene – is the basic structural element of other allotropes, nanotubes, charcoal, and fullerenes. Q-carbon – a ferromagnetic, tough, and brilliant crystal structure that is harder and brighter than diamonds. Graphite – a soft, black, flaky solid, a moderate electrical conductor. The C atoms are bonded in flat hexagonal lattices (graphene), which are then layered in sheets. Linear acetylenic carbon (carbyne) Amorphous carbon Fullerenes, including buckminsterfullerene, also known as "buckyballs", such as C₆₀. Carbon nanotubes – allotropes having a cylindrical nanostructure. Schwarzites Cyclocarbon Glassy carbon Superdense carbon allotropes – proposed allotropes
Nitrogen	Dinitrogen – by far the most common and stable form of nitrogen, found in the air. Hexazine Octaazacubane Tetranitrogen Trinitrogen Solid nitrogen
Phosphorus	White phosphorus – crystalline solid of tetraphosphorus (P₄) molecules Red phosphorus – amorphous polymeric solid Scarlet phosphorus Violet phosphorus with monoclinic crystalline structure Black phosphorus – semiconductor, analogous to graphite Diphosphorus – gaseous form composed of P₂ molecules, stable between 1200 °C and 2000 °C; created e.g. by dissociation of P₄ molecules of white phosphorus at around 827 °C
Oxygen	Dioxygen, O₂ – colorless (faint blue liquid and solid) Ozone, O₃ – blue Tetraoxygen, O₄ – metastable Octaoxygen, O₈ – red
Sulfur	Cyclo-Pentasulfur, Cyclo-S₅ Cyclo-Hexasulfur, Cyclo-S₆ Cyclo-Heptasulfur, Cyclo-S₇ Cyclo-Octasulfur, Cyclo-S₈
Selenium	"Red selenium", cyclo-Se₈ Gray selenium, polymeric Se Black selenium, irregular polymeric rings up to 1000 atoms long Monoclinic selenium, dark red transparent crystals

Metalloids

Element	Allotropes
Boron	Amorphous boron – brown powder – B₁₂ regular icosahedra α-rhombohedral boron β-rhombohedral boron γ-orthorhombic boron α-tetragonal boron β-tetragonal boron High-pressure superconducting phase
Silicon	Amorphous silicon Crystalline silicon, diamond cubic structure Silicene, buckled planar single layer Silicon, similar to Graphene
Germanium	α-germanium – semimetallic, with the same structure as diamond β-germanium – metallic, with the same structure as beta-tin Germanene – Buckled planar Germanium, similar to graphene
Arsenic	Yellow arsenic – molecular non-metallic As₄, with the same structure as white phosphorus Gray arsenic, polymeric As (metalloid) Black arsenic – molecular and non-metallic, with the same structure as red phosphorus
Antimony	Blue-white antimony – stable form (metalloid), with the same structure as gray arsenic Yellow antimony (non-metallic) Black antimony (non-metallic) Explosive antimony
Tellurium	Amorphous tellurium – gray-black or brown powder[7] Crystalline tellurium – hexagonal crystalline structure (metalloid)

Metals

Among the metallic elements that occur in nature in significant quantities (56 up to U, without Tc and Pm), almost half (27) are allotropic at ambient pressure: Li, Be, Na, Ca, Ti, Mn, Fe, Co, Sr, Y, Zr, Sn, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Yb, Hf, Tl, Th, Pa and U. Some phase transitions between allotropic forms of technologically relevant metals are those of Ti at 882 °C, Fe at 912 °C and 1394 °C, Co at 422 °C, Zr at 863 °C, Sn at 13 °C and U at 668 °C and 776 °C.

Element	Phase name(s)	Space group	Pearson symbol	Structure type	Description
Lithium		R3m	hR9	α-Samarium structure	Forms below 70 K.[8]
		Im3m	cI2	Body-centered cubic	Stable at room temperature and pressure.
			cF4	Face centered cubic	Forms above 7GPa
			hR1		An intermediate phase formed ~40GPa.
			cI16		Forms above 40GPa.
Beryllium		P6₃/mmc	hP2	Hexagonal close packed	Stable at room temperature and pressure.
Beryllium		Im3m	cI2	Body centered cubic	Forms above 1255 °C.
Sodium		R3m	hR9	α-Samarium structure	Forms below 20 K.
		Im3m	cI2	Body centered cubic	Stable at room temperature and pressure.
		Fm3m	cF4	Face centered cubic	Forms at room temperature above 65 GPa.[9]
		I43d	cI16		Forms at room temperature, 108GPa.[10]
		Pnma	oP8		Forms at room temperature, 119GPa.[11]
Magnesium		P6₃/mmc	hP2	hexagonal close packed	Stable at room temperature and pressure.
Magnesium		Im3m	cI2	Body centered cubic	Forms above 50 GPa.[12]
Tin	α-tin, gray tin, tin pest	Fd3m	cF8	Diamond cubic	Stable below 13.2 °C.
	β-tin, white tin	I4₁/amd	tI4	β-Tin structure	Stable at room temperature and pressure.
	γ-tin, rhombic tin	I4/mmm		Body-centered tetragonal
	σ-Sn			Body-centered cubic	Forms at very high pressure.[13]
	Stanene
Iron	α-Fe, ferrite	Im3m	cI2	Body-centered cubic	Stable at room temperature and pressure. Ferromagnetic at T<770 °C, paramagnetic from T=770–912 °C.
	γ-iron, austenite	Fm3m	cF4	Face-centered cubic	Stable from 912 to 1,394 °C.
	δ-iron	Im3m	cI2	Body-centered cubic	Stable from 1,394 – 1,538 °C, same structure as α-Fe.
	ε-iron, Hexaferrum	P6₃/mmc	hP2	Hexagonal close-packed	Stable at high pressures.
Cobalt	α-Cobalt			simple cubic	Forms above 417 °C.
Cobalt	β-Cobalt			hexagonal close packed	Forms below 417 °C.
Polonium	α-Polonium			simple cubic
Polonium	β-Polonium			rhombohedral

Lanthanides and actinides

Phase diagram of the actinide elements.

Cerium, samarium, dysprosium and ytterbium have three allotropes.
Praseodymium, neodymium, gadolinium and terbium have two allotropes.
Plutonium has six distinct solid allotropes under "normal" pressures. Their densities vary within a ratio of some 4:3, which vastly complicates all kinds of work with the metal (particularly casting, machining, and storage). A seventh plutonium allotrope exists at very high pressures. The transuranium metals Np, Am, and Cm are also allotropic.
Promethium, americium, berkelium and californium have three allotropes each.[14]

Nanoallotropes

In 2017, the concept of nanoallotropy was proposed by Rafal Klajn of the Organic Chemistry Department of the Weizmann Institute of Science.[15] Nanoallotropes, or allotropes of nanomaterials, are nanoporous materials that have the same chemical composition (e.g., Au), but differ in their architecture at the nanoscale (that is, on a scale 10 to 100 times the dimensions of individual atoms).[16] Such nanoallotropes may help create ultra-small electronic devices and find other industrial applications.[16] The different nanoscale architectures translate into different properties, as was demonstrated for surface-enhanced Raman scattering performed on several different nanoallotropes of gold.[15] A two-step method for generating nanoallotropes was also created.[16]

Notes

IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Allotrope". doi:10.1351/goldbook.A00243
See:
- Berzelius, Jac. (1841). Årsberättelse om Framstegen i Fysik och Kemi afgifven den 31 Mars 1840. Första delen [Annual Report on Progress in Physics and Chemistry submitted March 31, 1840. First part.] (in Swedish). Stockholm, Sweden: P.A. Norstedt & Söner. p. 14. From p. 14: "Om det ock passar väl för att uttrycka förhållandet emellan myrsyrad ethyloxid och ättiksyrad methyloxid, så är det icke passande för de olika tillstånd hos de enkla kropparne, hvari dessa blifva af skiljaktiga egenskaper, och torde för dem böra ersättas af en bättre vald benämning, t. ex. Allotropi (af αλλότροπος, som betyder: af olika beskaffenhet) eller allotropiskt tillstånd." (If it [i.e., the word isomer] is also well suited to express the relation between formic acid ethyl oxide [i.e., ethyl formate] and acetic acid methyloxide [i.e., methyl acetate], then it [i.e., the word isomers] is not suitable for different conditions of simple substances, where these [substances] transform to have different properties, and [therefore the word isomers] should be replaced, in their case, by a better chosen name; for example, Allotropy (from αλλότροπος, which means: of different nature) or allotropic condition.)
- Republished in German: Berzelius, Jacob; Wöhler, F., trans. (1841). "Jahres-Bericht über die Fortschritte der physischen Wissenschaften" [Annual Report on Progress of the Physical Sciences]. Jahres Bericht Über die Fortschritte der Physischen Wissenschaften (in German). Tübingen, (Germany): Laupp'schen Buchhandlung. 20: 13.{{cite journal}}: CS1 maint: multiple names: authors list (link) From p. 13: "Wenn es sich auch noch gut eignet, um das Verhältniss zwischen ameisensaurem Äthyloxyd und essigsaurem Methyloxyd auszudrücken, so ist es nicht passend für ungleiche Zustände bei Körpern, in welchen diese verschiedene Eigenschaften annehmen, und dürfte für diese durch eine besser gewählte Benennung zu ersetzen sein, z. B. durch Allotropie (von αλλότροπος, welches bedeutet: von ungleicher Beschaffenheit), oder durch allotropischen Zustand." (Even if it [i.e., the word isomer] is still well suited to express the relation between ethyl formate and methyl acetate, then it is not appropriate for the distinct conditions in the case of substances where these [substances] assume different properties, and for these, [the word isomer] may be replaced with a better chosen designation, e.g., with Allotropy (from αλλότροπος, which means: of distinct character), or with allotropic condition.)
- Merriam-Webster online dictionary: Allotropy
Jensen, W. B. (2006), "The Origin of the Term Allotrope", J. Chem. Educ., 83 (6): 838–39, Bibcode:2006JChEd..83..838J, doi:10.1021/ed083p838.
"allotropy", A New English Dictionary on Historical Principles, vol. 1, Oxford University Press, 1888, p. 238.
Ostwald, Wilhelm; Taylor, W.W., trans. (1912). Outlines of General Chemistry (3rd ed.). London, England: Macmillan and Co., Ltd. p. 104.{{cite book}}: CS1 maint: multiple names: authors list (link) From p. 104: "Substances are known which exist not only in two, but even in three, four or five different solid forms; no limitation to the number is known to exist. Such substances are called polymorphous. The name allotropy is commonly employed in the same connexion, especially when the substance is an element. There is no real reason for making this distinction, and it is preferable to allow the second less common name to die out."
Jensen 2006, citing Addison, W. E. The Allotropy of the Elements (Elsevier 1964) that many have repeated this advice.
Raj, G. Advanced Inorganic Chemistry Vol-1. Krishna Prakashan. p. 1327. ISBN 9788187224037. Retrieved January 6, 2017.
Overhauser, A. W. (1984-07-02). "Crystal Structure of Lithium at 4.2 K". Physical Review Letters. American Physical Society (APS). 53 (1): 64–65. Bibcode:1984PhRvL..53...64O. doi:10.1103/physrevlett.53.64. ISSN 0031-9007.
Hanfland, M.; Loa, I.; Syassen, K. (2002-05-13). "Sodium under pressure: bcc to fcc structural transition and pressure-volume relation to 100 GPa". Physical Review B. American Physical Society (APS). 65 (18): 184109. Bibcode:2002PhRvB..65r4109H. doi:10.1103/physrevb.65.184109. ISSN 0163-1829.
McMahon, M. I.; Gregoryanz, E.; Lundegaard, L. F.; Loa, I.; Guillaume, C.; Nelmes, R. J.; Kleppe, A. K.; Amboage, M.; Wilhelm, H.; Jephcoat, A. P. (2007-10-18). "Structure of sodium above 100 GPa by single-crystal x-ray diffraction". Proceedings of the National Academy of Sciences. 104 (44): 17297–17299. Bibcode:2007PNAS..10417297M. doi:10.1073/pnas.0709309104. ISSN 0027-8424. PMC 2077250. PMID 17947379.
Gregoryanz, E.; Lundegaard, L. F.; McMahon, M. I.; Guillaume, C.; Nelmes, R. J.; Mezouar, M. (2008-05-23). "Structural Diversity of Sodium". Science. American Association for the Advancement of Science (AAAS). 320 (5879): 1054–1057. Bibcode:2008Sci...320.1054G. doi:10.1126/science.1155715. ISSN 0036-8075. PMID 18497293. S2CID 29596632.
Olijnyk, H.; Holzapfel, W. B. (1985-04-01). "High-pressure structural phase transition in Mg". Physical Review B. American Physical Society (APS). 31 (7): 4682–4683. Bibcode:1985PhRvB..31.4682O. doi:10.1103/physrevb.31.4682. ISSN 0163-1829. PMID 9936412.
Molodets, A. M.; Nabatov, S. S. (2000). "Thermodynamic Potentials, Diagram of State, and Phase Transitions of Tin on Shock Compression". High Temperature. 38 (5): 715–721. doi:10.1007/BF02755923. S2CID 120417927.
Benedict, U.; Haire, R. G.; Peterson, J. R.; Itie, J. P. (1985). "Delocalisation of 5f electrons in curium metal under high pressure". Journal of Physics F: Metal Physics. 15 (2): L29–L35. Bibcode:1985JPhF...15L..29B. doi:10.1088/0305-4608/15/2/002.
Udayabhaskararao, Thumu; Altantzis, Thomas; Houben, Lothar; Coronado-Puchau, Marc; Langer, Judith; Popovitz-Biro, Ronit; Liz-Marzán, Luis M.; Vuković, Lela; Král, Petr (2017-10-27). "Tunable porous nanoallotropes prepared by post-assembly etching of binary nanoparticle superlattices". Science. 358 (6362): 514–518. Bibcode:2017Sci...358..514U. doi:10.1126/science.aan6046. hdl:10067/1472420151162165141. ISSN 0036-8075. PMID 29074773.
"Materials That Don't Exist in Nature Might Lead to New Fabrication Techniques". israelbds.org. Archived from the original on 2017-12-09. Retrieved 2017-12-08.

References

Chisholm, Hugh, ed. (1911). "Allotropy" . Encyclopædia Britannica (11th ed.). Cambridge University Press.

External links

Nigel Bunce and Jim Hunt. "The Science Corner: Allotropes". Archived from the original on January 31, 2008. Retrieved January 6, 2017.
Allotropes – Chemistry Encyclopedia

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[1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Allotrope". doi:10.1351/goldbook.A00243

[2] See:
Berzelius, Jac. (1841). Årsberättelse om Framstegen i Fysik och Kemi afgifven den 31 Mars 1840. Första delen [Annual Report on Progress in Physics and Chemistry submitted March 31, 1840. First part.] (in Swedish). Stockholm, Sweden: P.A. Norstedt & Söner. p. 14. From p. 14: "Om det ock passar väl för att uttrycka förhållandet emellan myrsyrad ethyloxid och ättiksyrad methyloxid, så är det icke passande för de olika tillstånd hos de enkla kropparne, hvari dessa blifva af skiljaktiga egenskaper, och torde för dem böra ersättas af en bättre vald benämning, t. ex. Allotropi (af αλλότροπος, som betyder: af olika beskaffenhet) eller allotropiskt tillstånd." (If it [i.e., the word isomer] is also well suited to express the relation between formic acid ethyl oxide [i.e., ethyl formate] and acetic acid methyloxide [i.e., methyl acetate], then it [i.e., the word isomers] is not suitable for different conditions of simple substances, where these [substances] transform to have different properties, and [therefore the word isomers] should be replaced, in their case, by a better chosen name; for example, Allotropy (from αλλότροπος, which means: of different nature) or allotropic condition.)

Republished in German: Berzelius, Jacob; Wöhler, F., trans. (1841). "Jahres-Bericht über die Fortschritte der physischen Wissenschaften" [Annual Report on Progress of the Physical Sciences]. Jahres Bericht Über die Fortschritte der Physischen Wissenschaften (in German). Tübingen, (Germany): Laupp'schen Buchhandlung. 20: 13.{{cite journal}}: CS1 maint: multiple names: authors list (link) From p. 13: "Wenn es sich auch noch gut eignet, um das Verhältniss zwischen ameisensaurem Äthyloxyd und essigsaurem Methyloxyd auszudrücken, so ist es nicht passend für ungleiche Zustände bei Körpern, in welchen diese verschiedene Eigenschaften annehmen, und dürfte für diese durch eine besser gewählte Benennung zu ersetzen sein, z. B. durch Allotropie (von αλλότροπος, welches bedeutet: von ungleicher Beschaffenheit), oder durch allotropischen Zustand." (Even if it [i.e., the word isomer] is still well suited to express the relation between ethyl formate and methyl acetate, then it is not appropriate for the distinct conditions in the case of substances where these [substances] assume different properties, and for these, [the word isomer] may be replaced with a better chosen designation, e.g., with Allotropy (from αλλότροπος, which means: of distinct character), or with allotropic condition.)

Merriam-Webster online dictionary: Allotropy

[3] Berzelius, Jac. (1841). Årsberättelse om Framstegen i Fysik och Kemi afgifven den 31 Mars 1840. Första delen [Annual Report on Progress in Physics and Chemistry submitted March 31, 1840. First part.] (in Swedish). Stockholm, Sweden: P.A. Norstedt & Söner. p. 14. From p. 14: "Om det ock passar väl för att uttrycka förhållandet emellan myrsyrad ethyloxid och ättiksyrad methyloxid, så är det icke passande för de olika tillstånd hos de enkla kropparne, hvari dessa blifva af skiljaktiga egenskaper, och torde för dem böra ersättas af en bättre vald benämning, t. ex. Allotropi (af αλλότροπος, som betyder: af olika beskaffenhet) eller allotropiskt tillstånd." (If it [i.e., the word isomer] is also well suited to express the relation between formic acid ethyl oxide [i.e., ethyl formate] and acetic acid methyloxide [i.e., methyl acetate], then it [i.e., the word isomers] is not suitable for different conditions of simple substances, where these [substances] transform to have different properties, and [therefore the word isomers] should be replaced, in their case, by a better chosen name; for example, Allotropy (from αλλότροπος, which means: of different nature) or allotropic condition.)

[4] Republished in German: Berzelius, Jacob; Wöhler, F., trans. (1841). "Jahres-Bericht über die Fortschritte der physischen Wissenschaften" [Annual Report on Progress of the Physical Sciences]. Jahres Bericht Über die Fortschritte der Physischen Wissenschaften (in German). Tübingen, (Germany): Laupp'schen Buchhandlung. 20: 13.{{cite journal}}: CS1 maint: multiple names: authors list (link) From p. 13: "Wenn es sich auch noch gut eignet, um das Verhältniss zwischen ameisensaurem Äthyloxyd und essigsaurem Methyloxyd auszudrücken, so ist es nicht passend für ungleiche Zustände bei Körpern, in welchen diese verschiedene Eigenschaften annehmen, und dürfte für diese durch eine besser gewählte Benennung zu ersetzen sein, z. B. durch Allotropie (von αλλότροπος, welches bedeutet: von ungleicher Beschaffenheit), oder durch allotropischen Zustand." (Even if it [i.e., the word isomer] is still well suited to express the relation between ethyl formate and methyl acetate, then it is not appropriate for the distinct conditions in the case of substances where these [substances] assume different properties, and for these, [the word isomer] may be replaced with a better chosen designation, e.g., with Allotropy (from αλλότροπος, which means: of distinct character), or with allotropic condition.)

[5] Merriam-Webster online dictionary: Allotropy

[Jensen-3] Jensen, W. B. (2006), "The Origin of the Term Allotrope", J. Chem. Educ., 83 (6): 838–39, Bibcode:2006JChEd..83..838J, doi:10.1021/ed083p838.

[4] "allotropy", A New English Dictionary on Historical Principles, vol. 1, Oxford University Press, 1888, p. 238.

[5] Ostwald, Wilhelm; Taylor, W.W., trans. (1912). Outlines of General Chemistry (3rd ed.). London, England: Macmillan and Co., Ltd. p. 104.{{cite book}}: CS1 maint: multiple names: authors list (link) From p. 104: "Substances are known which exist not only in two, but even in three, four or five different solid forms; no limitation to the number is known to exist. Such substances are called polymorphous. The name allotropy is commonly employed in the same connexion, especially when the substance is an element. There is no real reason for making this distinction, and it is preferable to allow the second less common name to die out."

[6] Jensen 2006, citing Addison, W. E. The Allotropy of the Elements (Elsevier 1964) that many have repeated this advice.

[google-7] Raj, G. Advanced Inorganic Chemistry Vol-1. Krishna Prakashan. p. 1327. ISBN 9788187224037. Retrieved January 6, 2017.

[8] Overhauser, A. W. (1984-07-02). "Crystal Structure of Lithium at 4.2 K". Physical Review Letters. American Physical Society (APS). 53 (1): 64–65. Bibcode:1984PhRvL..53...64O. doi:10.1103/physrevlett.53.64. ISSN 0031-9007.

[9] Hanfland, M.; Loa, I.; Syassen, K. (2002-05-13). "Sodium under pressure: bcc to fcc structural transition and pressure-volume relation to 100 GPa". Physical Review B. American Physical Society (APS). 65 (18): 184109. Bibcode:2002PhRvB..65r4109H. doi:10.1103/physrevb.65.184109. ISSN 0163-1829.

[10] McMahon, M. I.; Gregoryanz, E.; Lundegaard, L. F.; Loa, I.; Guillaume, C.; Nelmes, R. J.; Kleppe, A. K.; Amboage, M.; Wilhelm, H.; Jephcoat, A. P. (2007-10-18). "Structure of sodium above 100 GPa by single-crystal x-ray diffraction". Proceedings of the National Academy of Sciences. 104 (44): 17297–17299. Bibcode:2007PNAS..10417297M. doi:10.1073/pnas.0709309104. ISSN 0027-8424. PMC 2077250. PMID 17947379.

[11] Gregoryanz, E.; Lundegaard, L. F.; McMahon, M. I.; Guillaume, C.; Nelmes, R. J.; Mezouar, M. (2008-05-23). "Structural Diversity of Sodium". Science. American Association for the Advancement of Science (AAAS). 320 (5879): 1054–1057. Bibcode:2008Sci...320.1054G. doi:10.1126/science.1155715. ISSN 0036-8075. PMID 18497293. S2CID 29596632.

[12] Olijnyk, H.; Holzapfel, W. B. (1985-04-01). "High-pressure structural phase transition in Mg". Physical Review B. American Physical Society (APS). 31 (7): 4682–4683. Bibcode:1985PhRvB..31.4682O. doi:10.1103/physrevb.31.4682. ISSN 0163-1829. PMID 9936412.

[13] Molodets, A. M.; Nabatov, S. S. (2000). "Thermodynamic Potentials, Diagram of State, and Phase Transitions of Tin on Shock Compression". High Temperature. 38 (5): 715–721. doi:10.1007/BF02755923. S2CID 120417927.

[14] Benedict, U.; Haire, R. G.; Peterson, J. R.; Itie, J. P. (1985). "Delocalisation of 5f electrons in curium metal under high pressure". Journal of Physics F: Metal Physics. 15 (2): L29–L35. Bibcode:1985JPhF...15L..29B. doi:10.1088/0305-4608/15/2/002.

[:0-15] Udayabhaskararao, Thumu; Altantzis, Thomas; Houben, Lothar; Coronado-Puchau, Marc; Langer, Judith; Popovitz-Biro, Ronit; Liz-Marzán, Luis M.; Vuković, Lela; Král, Petr (2017-10-27). "Tunable porous nanoallotropes prepared by post-assembly etching of binary nanoparticle superlattices". Science. 358 (6362): 514–518. Bibcode:2017Sci...358..514U. doi:10.1126/science.aan6046. hdl:10067/1472420151162165141. ISSN 0036-8075. PMID 29074773.

[:1-16] "Materials That Don't Exist in Nature Might Lead to New Fabrication Techniques". israelbds.org. Archived from the original on 2017-12-09. Retrieved 2017-12-08.