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98-518: Invar , also known generically as FeNi36 ( 64FeNi in the US), is a nickel – iron alloy notable for its uniquely low coefficient of thermal expansion (CTE or α). The name Invar comes from the word invariable , referring to its relative lack of expansion or contraction with temperature changes, and is a registered trademark of ArcelorMittal . The discovery of the alloy was made in 1895 by Swiss physicist Charles Édouard Guillaume for which he received

196-491: A matte for further refining. Hydrometallurgical techniques are also used. Most sulfide deposits have traditionally been processed by concentration through a froth flotation process followed by pyrometallurgical extraction. The nickel matte is further processed with the Sherritt-Gordon process . First, copper is removed by adding hydrogen sulfide , leaving a concentrate of cobalt and nickel. Then, solvent extraction

294-404: A common edge. The next step is crucial: the search for an unfrustrated structure by allowing for curvature in the space , in order for the local configurations to propagate identically and without defects throughout the whole space. Twenty irregular tetrahedra pack with a common vertex in such a way that the twelve outer vertices form a regular icosahedron. Indeed, the icosahedron edge length l

392-423: A common vertex, but a gap remains between two edges. It is this kind of discrepancy which is called "geometric frustration". There is one way to overcome this difficulty. Let the surface to be tiled be free of any presupposed topology, and let us build the tiling with a strict application of the local interaction rule. In this simple example, we observe that the surface inherits the topology of a sphere and so receives

490-399: A compound, nickel has a number of niche chemical manufacturing uses, such as a catalyst for hydrogenation , cathodes for rechargeable batteries, pigments and metal surface treatments. Nickel is an essential nutrient for some microorganisms and plants that have enzymes with nickel as an active site . Nickel is a silvery-white metal with a slight golden tinge that takes a high polish. It

588-427: A curvature. The final structure, here a pentagonal dodecahedron, allows for a perfect propagation of the pentagonal order. It is called an "ideal" (defect-free) model for the considered structure. The stability of metals is a longstanding question of solid state physics, which can only be understood in the quantum mechanical framework by properly taking into account the interaction between the positively charged ions and

686-496: A non-monotonic angular dependence of the square lattice coercivity is found to be related to disorder in the artificial spin ice system. Another type of geometrical frustration arises from the propagation of a local order. A main question that a condensed matter physicist faces is to explain the stability of a solid. It is sometimes possible to establish some local rules, of chemical nature, which lead to low energy configurations and therefore govern structural and chemical order. This

784-401: A perfect tetrahedron, and try to add new spheres, while forming new tetrahedra. The next solution, with five balls, is trivially two tetrahedra sharing a common face; note that already with this solution, the fcc structure, which contains individual tetrahedral holes, does not show such a configuration (the tetrahedra share edges, not faces). With six balls, three regular tetrahedra are built, and

882-713: A public controversy regarding the problems of people with nickel allergy . An estimated 3.6 million tonnes (t) of nickel per year are mined worldwide; Indonesia (1,800,000 t), the Philippines (400,000 t), Russia (200,000 t), New Caledonia ( France ) (230,000 t), Canada (180,000 t) and Australia (160,000 t) are the largest producers as of 2023. The largest nickel deposits in non-Russian Europe are in Finland and Greece . Identified land-based sources averaging at least 1% nickel contain at least 130 million tonnes of nickel. About 60%

980-400: A range of temperatures, it does have a propensity to creep . Invar is used where high dimensional stability is required, such as precision instruments, clocks, seismic creep gauges, color-television tubes' shadow-mask frames, valves in engines and large aerostructure molds. One of its first applications was in watch balance wheels and pendulum rods for precision regulator clocks . At

1078-462: A study of the Ising model on a triangular lattice with nearest-neighbor spins coupled antiferromagnetically , by G. H. Wannier , published in 1950. Related features occur in magnets with competing interactions , where both ferromagnetic as well as antiferromagnetic couplings between pairs of spins or magnetic moments are present, with the type of interaction depending on the separation distance of

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1176-421: A sum over these products, summed over all plaquettes. The result for a single plaquette is either +1 or −1. In the last-mentioned case the plaquette is "geometrically frustrated". It can be shown that the result has a simple gauge invariance : it does not change – nor do other measurable quantities, e.g. the "total energy" H {\displaystyle {\mathcal {H}}} – even if locally

1274-474: A tetrahedron is not commensurable with 2 π ; consequently, a hole remains between two faces of neighboring tetrahedra. As a consequence, a perfect tiling of the Euclidean space R is impossible with regular tetrahedra. The frustration has a topological character: it is impossible to fill Euclidean space with tetrahedra, even severely distorted, if we impose that a constant number of tetrahedra (here five) share

1372-504: Is Ni with 28 protons and 50 neutrons. Both are therefore unusually stable for nuclei with so large a proton–neutron imbalance . Nickel-63 is a contaminant found in the support structure of nuclear reactors. It is produced through neutron capture by nickel-62. Small amounts have also been found near nuclear weapon test sites in the South Pacific. Nickel ores are classified as oxides or sulfides. Oxides include laterite , where

1470-411: Is $ 0.045 (90% of the face value). In the 21st century, the high price of nickel has led to some replacement of the metal in coins around the world. Coins still made with nickel alloys include one- and two- euro coins , 5¢, 10¢, 25¢, 50¢, and $ 1 U.S. coins , and 20p, 50p, £1, and £2 UK coins . From 2012 on the nickel-alloy used for 5p and 10p UK coins was replaced with nickel-plated steel. This ignited

1568-427: Is a chemical element ; it has symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal . Pure nickel is chemically reactive, but large pieces are slow to react with air under standard conditions because a passivation layer of nickel oxide forms on the surface that prevents further corrosion. Even so, pure native nickel

1666-417: Is a 3d 4s energy level, specifically the 3d ( F) 4s F, J  = 4 level. However, each of these two configurations splits into several energy levels due to fine structure , and the two sets of energy levels overlap. The average energy of states with [Ar] 3d 4s is actually lower than the average energy of states with [Ar] 3d 4s . Therefore, the research literature on atomic calculations quotes

1764-725: Is a new nickel mine in Michigan's Upper Peninsula . Construction was completed in 2013, and operations began in the third quarter of 2014. In the first full year of operation, the Eagle Mine produced 18,000 t. Nickel is obtained through extractive metallurgy : it is extracted from ore by conventional roasting and reduction processes that yield metal of greater than 75% purity. In many stainless steel applications, 75% pure nickel can be used without further purification, depending on impurities. Traditionally, most sulfide ores are processed using pyrometallurgical techniques to produce

1862-501: Is a volatile, highly toxic liquid at room temperature. On heating, the complex decomposes back to nickel and carbon monoxide: This behavior is exploited in the Mond process for purifying nickel, as described above. The related nickel(0) complex bis(cyclooctadiene)nickel(0) is a useful catalyst in organonickel chemistry because the cyclooctadiene (or cod ) ligands are easily displaced. Nickel(I) complexes are uncommon, but one example

1960-400: Is also formed in nickel distillation as a by-product, but it decomposes to tetracobalt dodecacarbonyl at the reaction temperature to give a non-volatile solid. Geometrically frustrated magnet The term frustration , in the context of magnetic systems, has been introduced by Gerard Toulouse in 1977. Frustrated magnetic systems had been studied even before. Early work includes

2058-448: Is conceptually important for the following reason. The ideal models that have been introduced in the curved Space are three dimensional curved templates. They look locally as three dimensional Euclidean models. So, the {3,3,5} polytope, which is a tiling by tetrahedra, provides a very dense atomic structure if atoms are located on its vertices. It is therefore naturally used as a template for amorphous metals, but one should not forget that it

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2156-703: Is currently being set in place by the International Seabed Authority to ensure that these nodules are collected in an environmentally conscientious manner while adhering to the United Nations Sustainable Development Goals . The one place in the United States where nickel has been profitably mined is Riddle, Oregon , with several square miles of nickel-bearing garnierite surface deposits. The mine closed in 1987. The Eagle mine project

2254-433: Is dependent on the distance of the two magnetic ions. Due to the lattice disorder in the spin glass, one spin of interest and its nearest neighbors could be at different distances and have a different interaction property, which thus leads to different preferred alignment of the spin. With the help of lithography techniques, it is possible to fabricate sub-micrometer size magnetic islands whose geometric arrangement reproduces

2352-454: Is divided into two categories: the first corresponds to the spin glass , which has both disorder in structure and frustration in spin; the second is the geometrical frustration with an ordered lattice structure and frustration of spin. The frustration of a spin glass is understood within the framework of the RKKY model, in which the interaction property, either ferromagnetic or anti-ferromagnetic,

2450-762: Is exactly equivalent to having an antiferromagnetic interaction between each pair of spins, so in this case there is no geometrical frustration. With these axes, geometric frustration arises if there is a ferromagnetic interaction between neighbours, where energy is minimized by parallel spins. The best possible arrangement is shown in Figure 4, with two spins pointing towards the centre and two pointing away. The net magnetic moment points upwards, maximising ferromagnetic interactions in this direction, but left and right vectors cancel out (i.e. are antiferromagnetically aligned), as do forwards and backwards. There are three different equivalent arrangements with two spins out and two in, so

2548-601: Is found in Earth's crust only in tiny amounts, usually in ultramafic rocks , and in the interiors of larger nickel–iron meteorites that were not exposed to oxygen when outside Earth's atmosphere. Meteoric nickel is found in combination with iron , a reflection of the origin of those elements as major end products of supernova nucleosynthesis . An iron–nickel mixture is thought to compose Earth's outer and inner cores . Use of nickel (as natural meteoric nickel–iron alloy) has been traced as far back as 3500 BCE. Nickel

2646-470: Is greater than both Fe and Fe , more abundant nuclides often incorrectly cited as having the highest binding energy. Though this would seem to predict nickel as the most abundant heavy element in the universe, the high rate of photodisintegration of nickel in stellar interiors causes iron to be by far the most abundant. Nickel-60 is the daughter product of the extinct radionuclide Fe (half-life 2.6 million years). Due to

2744-426: Is impossible to have all interactions favourable, and the system is frustrated. Geometrical frustration is also possible if the spins are arranged in a non- collinear way. If we consider a tetrahedron with a spin on each vertex pointing along the easy axis (that is, directly towards or away from the centre of the tetrahedron), then it is possible to arrange the four spins so that there is no net spin (Figure 3). This

2842-498: Is in amazing agreement with the missing entropy measured by Giauque and Stout. Although Pauling's calculation neglected both the global constraint on the number of protons and the local constraint arising from closed loops on the Wurtzite lattice, the estimate was subsequently shown to be of excellent accuracy. A mathematically analogous situation to the degeneracy in water ice is found in the spin ices . A common spin ice structure

2940-575: Is in laterites and 40% is in sulfide deposits. Also, extensive nickel sources are found in the depths of the Pacific Ocean , especially in an area called the Clarion Clipperton Zone in the form of polymetallic nodules peppering the seafloor at 3.5–6 km below sea level . These nodules are composed of numerous rare-earth metals and are estimated to be 1.7% nickel. With advances in science and engineering , regulation

3038-504: Is not generally the case and often the local order defined by local interactions cannot propagate freely, leading to geometric frustration. A common feature of all these systems is that, even with simple local rules, they present a large set of, often complex, structural realizations. Geometric frustration plays a role in fields of condensed matter, ranging from clusters and amorphous solids to complex fluids. The general method of approach to resolve these complications follows two steps. First,

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3136-455: Is now Syria have been found to contain as much as 2% nickel. Some ancient Chinese manuscripts suggest that "white copper" ( cupronickel , known as baitong ) was used there in 1700–1400 BCE. This Paktong white copper was exported to Britain as early as the 17th century, but the nickel content of this alloy was not discovered until 1822. Coins of nickel-copper alloy were minted by Bactrian kings Agathocles , Euthydemus II , and Pantaleon in

3234-434: Is now known as the mineral nickeline (formerly niccolite ), a nickel arsenide . In 1751, Baron Axel Fredrik Cronstedt tried to extract copper from kupfernickel at a cobalt mine in the village of Los, Sweden , and instead produced a white metal that he named nickel after the spirit that had given its name to the mineral. In modern German, Kupfernickel or Kupfer-Nickel designates the alloy cupronickel . Originally,

3332-412: Is one of only four elements that are ferromagnetic at or near room temperature; the others are iron, cobalt and gadolinium . Its Curie temperature is 355 °C (671 °F), meaning that bulk nickel is non-magnetic above this temperature. The unit cell of nickel is a face-centered cube ; it has lattice parameter of 0.352 nm, giving an atomic radius of 0.124 nm. This crystal structure

3430-591: Is only one subdivision of frustrated systems. The word frustration was initially introduced to describe a system's inability to simultaneously minimize the competing interaction energy between its components. In general frustration is caused either by competing interactions due to site disorder (see also the Villain model ) or by lattice structure such as in the triangular , face-centered cubic (fcc), hexagonal-close-packed , tetrahedron , pyrochlore and kagome lattices with antiferromagnetic interaction. So frustration

3528-469: Is produced by the silicon burning process and later set free in large amounts in type Ia supernovae . The shape of the light curve of these supernovae at intermediate to late-times corresponds to the decay via electron capture of Ni to cobalt -56 and ultimately to iron-56. Nickel-59 is a long-lived cosmogenic radionuclide ; half-life 76,000 years. Ni has found many applications in isotope geology . Ni has been used to date

3626-414: Is shown in Figure 6 in the cubic pyrochlore structure with one magnetic atom or ion residing on each of the four corners. Due to the strong crystal field in the material, each of the magnetic ions can be represented by an Ising ground state doublet with a large moment. This suggests a picture of Ising spins residing on the corner-sharing tetrahedral lattice with spins fixed along the local quantization axis,

3724-504: Is slightly longer than the circumsphere radius r ( l  ≈ 1.05 r ). There is a solution with regular tetrahedra if the space is not Euclidean, but spherical. It is the polytope {3,3,5}, using the Schläfli notation, also known as the 600-cell . There are one hundred and twenty vertices which all belong to the hypersphere S with radius equal to the golden ratio ( φ  =  ⁠ 1 + √ 5 / 2 ⁠ ) if

3822-572: Is stable to pressures of at least 70 GPa. Nickel is hard, malleable and ductile , and has a relatively high electrical and thermal conductivity for transition metals. The high compressive strength of 34 GPa, predicted for ideal crystals, is never obtained in the real bulk material due to formation and movement of dislocations . However, it has been reached in Ni nanoparticles . Nickel has two atomic electron configurations , [Ar] 3d 4s and [Ar] 3d 4s , which are very close in energy; [Ar] denotes

3920-446: Is the tetrahedral complex NiBr(PPh 3 ) 3 . Many nickel(I) complexes have Ni–Ni bonding, such as the dark red diamagnetic K 4 [Ni 2 (CN) 6 ] prepared by reduction of K 2 [Ni 2 (CN) 6 ] with sodium amalgam . This compound is oxidized in water, liberating H 2 . It is thought that the nickel(I) oxidation state is important to nickel-containing enzymes, such as [NiFe]-hydrogenase , which catalyzes

4018-479: Is used as the cathode in many rechargeable batteries , including nickel–cadmium , nickel–iron , nickel–hydrogen , and nickel–metal hydride , and used by certain manufacturers in Li-ion batteries . Ni(IV) remains a rare oxidation state and very few compounds are known. Ni(IV) occurs in the mixed oxide BaNiO 3 . Unintentional use of nickel can be traced back as far as 3500 BCE. Bronzes from what

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4116-455: Is used chiefly in alloys and corrosion-resistant plating. About 68% of world production is used in stainless steel . A further 10% is used for nickel-based and copper-based alloys, 9% for plating, 7% for alloy steels, 3% in foundries, and 4% in other applications such as in rechargeable batteries, including those in electric vehicles (EVs). Nickel is widely used in coins , though nickel-plated objects sometimes provoke nickel allergy . As

4214-579: Is used to facilitate the manufacture of parts to extremely tight tolerances. In the astronomical field, Invar is used as the structural components that support dimension-sensitive optics of astronomical telescopes. Superior dimensional stability of Invar allows the astronomical telescopes to significantly improve the observation precision and accuracy. There are variations of the original Invar material that have slightly different coefficient of thermal expansion such as: A detailed explanation of Invar's anomalously low CTE has proven elusive for physicists. All

4312-412: Is used to separate the cobalt and nickel, with the final nickel content greater than 86%. A second common refining process is leaching the metal matte into a nickel salt solution, followed by electrowinning the nickel from solution by plating it onto a cathode as electrolytic nickel. The purest metal is obtained from nickel oxide by the Mond process , which gives a purity of over 99.99%. The process

4410-440: Is well modeled by a close packing of tetrahedra, leading to an imperfect icosahedral order. A regular tetrahedron is the densest configuration for the packing of four equal spheres. The dense random packing of hard spheres problem can thus be mapped on the tetrahedral packing problem . It is a practical exercise to try to pack table tennis balls in order to form only tetrahedral configurations. One starts with four balls arranged as

4508-505: The <111> cubic axes , which coincide with the lines connecting each tetrahedral vertex to the center. Every tetrahedral cell must have two spins pointing in and two pointing out in order to minimize the energy. Currently the spin ice model has been approximately realized by real materials, most notably the rare earth pyrochlores Ho 2 Ti 2 O 7 , Dy 2 Ti 2 O 7 , and Ho 2 Sn 2 O 7 . These materials all show nonzero residual entropy at low temperature. The spin ice model

4606-520: The Nobel Prize in Physics in 1920. It enabled improvements in scientific instruments. Like other nickel/iron compositions, Invar is a solid solution ; that is, it is a single-phase alloy . In one commercial grade called Invar 36 it consists of approximately 36% nickel and 64% iron, has a melting point of 1427C, a density of 8.05 g/cm3 and a resistivity of 8.2 x 10-5 Ω·cm. The invar range

4704-467: The arsenide niccolite . Identified land-based resources throughout the world averaging 1% nickel or greater comprise at least 130 million tons of nickel (about the double of known reserves). About 60% is in laterites and 40% in sulfide deposits. On geophysical evidence, most of the nickel on Earth is believed to be in Earth's outer and inner cores . Kamacite and taenite are naturally occurring alloys of iron and nickel. For kamacite,

4802-484: The metal aquo complex [Ni(H 2 O) 6 ] . The four halides form nickel compounds, which are solids with molecules with octahedral Ni centres. Nickel(II) chloride is most common, and its behavior is illustrative of the other halides. Nickel(II) chloride is made by dissolving nickel or its oxide in hydrochloric acid . It is usually found as the green hexahydrate, whose formula is usually written NiCl 2 ·6H 2 O . When dissolved in water, this salt forms

4900-479: The metal aquo complex [Ni(H 2 O) 6 ] . Dehydration of NiCl 2 ·6H 2 O gives yellow anhydrous NiCl 2 . Some tetracoordinate nickel(II) complexes, e.g. bis(triphenylphosphine)nickel chloride , exist both in tetrahedral and square planar geometries. The tetrahedral complexes are paramagnetic ; the square planar complexes are diamagnetic . In having properties of magnetic equilibrium and formation of octahedral complexes, they contrast with

4998-460: The 16 possible configurations associated with each oxygen, only 6 are energetically favorable, maintaining the H 2 O molecule constraint. Then an upper bound of the numbers that the ground state can take is estimated as Ω  < 2 ( ⁠ 6 / 16 ⁠ ) . Correspondingly the configurational entropy S 0  = k B ln( Ω ) = Nk B ln( ⁠ 3 / 2 ⁠ ) = 0.81 cal/(K·mol) = 3.4 J/(mol·K)

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5096-418: The 1930s. In land surveying , when first-order (high-precision) elevation leveling is to be performed, the level staff (leveling rod) used is made of Invar, instead of wood, fiberglass, or other metals. Invar struts were used in some pistons to limit their thermal expansion inside their cylinders. In the manufacture of large composite material structures for aerospace carbon fibre layup molds , Invar

5194-577: The 1970s, in the context of spin glasses and spatially modulated magnetic superstructures. In spin glasses, frustration is augmented by stochastic disorder in the interactions, as may occur experimentally in non- stoichiometric magnetic alloys . Carefully analyzed spin models with frustration include the Sherrington–Kirkpatrick model , describing spin glasses, and the ANNNI model , describing commensurability magnetic superstructures. Recently,

5292-543: The 2nd century BCE, possibly out of the Chinese cupronickel. In medieval Germany, a metallic yellow mineral was found in the Ore Mountains that resembled copper ore. But when miners were unable to get any copper from it, they blamed a mischievous sprite of German mythology, Nickel (similar to Old Nick ), for besetting the copper. They called this ore Kupfernickel from German Kupfer 'copper'. This ore

5390-579: The Third Law of Thermodynamics. Heat Capacity of Ice from 15 K to 273 K , reporting calorimeter measurements on water through the freezing and vaporization transitions up to the high temperature gas phase. The entropy was calculated by integrating the heat capacity and adding the latent heat contributions; the low temperature measurements were extrapolated to zero, using Debye's then recently derived formula. The resulting entropy, S 1  = 44.28 cal/(K·mol) = 185.3 J/(mol·K)

5488-504: The United States, the term "nickel" or "nick" originally applied to the copper-nickel Flying Eagle cent , which replaced copper with 12% nickel 1857–58, then the Indian Head cent of the same alloy from 1859 to 1864. Still later, in 1865, the term designated the three-cent nickel , with nickel increased to 25%. In 1866, the five-cent shield nickel (25% nickel, 75% copper) appropriated the designation, which has been used ever since for

5586-501: The alloy is usually in the proportion of 90:10 to 95:5, though impurities (such as cobalt or carbon ) may be present. Taenite is 20% to 65% nickel. Kamacite and taenite are also found in nickel iron meteorites . Nickel is commonly found in iron meteorites as the alloys kamacite and taenite . Nickel in meteorites was first detected in 1799 by Joseph-Louis Proust , a French chemist who then worked in Spain. Proust analyzed samples of

5684-446: The cluster is incompatible with all compact crystalline structures (fcc and hcp). Adding a seventh sphere gives a new cluster consisting in two "axial" balls touching each other and five others touching the latter two balls, the outer shape being an almost regular pentagonal bi-pyramid. However, we are facing now a real packing problem, analogous to the one encountered above with the pentagonal tiling in two dimensions. The dihedral angle of

5782-469: The complete argon core structure. There is some disagreement on which configuration has the lower energy. Chemistry textbooks quote nickel's electron configuration as [Ar] 4s 3d , also written [Ar] 3d 4s . This configuration agrees with the Madelung energy ordering rule , which predicts that 4s is filled before 3d. It is supported by the experimental fact that the lowest energy state of the nickel atom

5880-453: The concept of frustration has been used in brain network analysis to identify the non-trivial assemblage of neural connections and highlight the adjustable elements of the brain. Geometrical frustration is an important feature in magnetism , where it stems from the relative arrangement of spins . A simple 2D example is shown in Figure 1. Three magnetic ions reside on the corners of a triangle with antiferromagnetic interactions between them;

5978-476: The configurational disorder intrinsic to the protons in ice. In the hexagonal or cubic ice phase the oxygen ions form a tetrahedral structure with an O–O bond length 2.76  Å (276  pm ), while the O–H bond length measures only 0.96 Å (96 pm). Every oxygen (white) ion is surrounded by four hydrogen ions (black) and each hydrogen ion is surrounded by 2 oxygen ions, as shown in Figure 5. Maintaining

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6076-409: The constraint of perfect space-filling is relaxed by allowing for space curvature. An ideal, unfrustrated, structure is defined in this curved space. Then, specific distortions are applied to this ideal template in order to embed it into three dimensional Euclidean space. The final structure is a mixture of ordered regions, where the local order is similar to that of the template, and defects arising from

6174-409: The disks in the densest way as possible. The best arrangement for three disks is trivially an equilateral triangle with the disk centers located at the triangle vertices. The study of the long range structure can therefore be reduced to that of plane tilings with equilateral triangles. A well known solution is provided by the triangular tiling with a total compatibility between the local and global rules:

6272-484: The divalent complexes of the heavier group 10 metals, palladium(II) and platinum(II), which form only square-planar geometry. Nickelocene has an electron count of 20. Many chemical reactions of nickelocene tend to yield 18-electron products. Many Ni(III) compounds are known. Ni(III) forms simple salts with fluoride or oxide ions. Ni(III) can be stabilized by σ-donor ligands such as thiols and organophosphines . Ni(III) occurs in nickel oxide hydroxide , which

6370-701: The earth's crust exists as oxides, economically more important nickel ores are sulfides, especially pentlandite . Major production sites include the Sudbury region , Canada (which is thought to be of meteoric origin), New Caledonia in the Pacific , Western Australia , and Norilsk , Russia. Nickel is one of four elements (the others are iron , cobalt , and gadolinium ) that are ferromagnetic at about room temperature. Alnico permanent magnets based partly on nickel are of intermediate strength between iron-based permanent magnets and rare-earth magnets . The metal

6468-427: The edges are of unit length. The six hundred cells are regular tetrahedra grouped by five around a common edge and by twenty around a common vertex. This structure is called a polytope (see Coxeter ) which is the general name in higher dimension in the series containing polygons and polyhedra. Even if this structure is embedded in four dimensions, it has been considered as a three dimensional (curved) manifold. This point

6566-437: The embedding. Among the possible defects, disclinations play an important role. Two-dimensional examples are helpful in order to get some understanding about the origin of the competition between local rules and geometry in the large. Consider first an arrangement of identical discs (a model for a hypothetical two-dimensional metal) on a plane; we suppose that the interaction between discs is isotropic and locally tends to arrange

6664-399: The energy is minimized when each spin is aligned opposite to neighbors. Once the first two spins align antiparallel, the third one is frustrated because its two possible orientations, up and down, give the same energy. The third spin cannot simultaneously minimize its interactions with both of the other two. Since this effect occurs for each spin, the ground state is sixfold degenerate . Only

6762-418: The energy units considered) assume the values ±1 (mathematically, this is a signed graph ), while the S k ν · S k μ are inner products of scalar or vectorial spins or pseudo-spins. If the graph G has quadratic or triangular faces P , the so-called "plaquette variables" P W , "loop-products" of the following kind, appear: which are also called "frustration products". One has to perform

6860-409: The exchange integrals and the spins are simultaneously modified as follows: Here the numbers ε i and ε k are arbitrary signs, i.e. +1 or −1, so that the modified structure may look totally random. Although most previous and current research on frustration focuses on spin systems, the phenomenon was first studied in ordinary ice . In 1936 Giauque and Stout published The Entropy of Water and

6958-440: The far position and two of them in the near position, so-called ‘ ice rules ’. Pauling proposed that the open tetrahedral structure of ice affords many equivalent states satisfying the ice rules. Pauling went on to compute the configurational entropy in the following way: consider one mole of ice, consisting of N O and 2 N protons. Each O–O bond has two positions for a proton, leading to 2 possible configurations. However, among

7056-446: The frustration found in naturally occurring spin ice materials. Recently R. F. Wang et al. reported the discovery of an artificial geometrically frustrated magnet composed of arrays of lithographically fabricated single-domain ferromagnetic islands. These islands are manually arranged to create a two-dimensional analog to spin ice. The magnetic moments of the ordered ‘spin’ islands were imaged with magnetic force microscopy (MFM) and then

7154-479: The ground state configuration as [Ar] 3d 4s . The isotopes of nickel range in atomic weight from 48  u ( Ni ) to 82 u ( Ni ). Natural nickel is composed of five stable isotopes , Ni , Ni , Ni , Ni and Ni , of which Ni is the most abundant (68.077% natural abundance ). Nickel-62 has the highest binding energy per nucleon of any nuclide : 8.7946 MeV/nucleon. Its binding energy

7252-408: The ground state is three-fold degenerate. The mathematical definition is simple (and analogous to the so-called Wilson loop in quantum chromodynamics ): One considers for example expressions ("total energies" or "Hamiltonians") of the form where G is the graph considered, whereas the quantities I k ν , k μ are the so-called "exchange energies" between nearest-neighbours, which (in

7350-449: The internal H 2 O molecule structure, the minimum energy position of a proton is not half-way between two adjacent oxygen ions. There are two equivalent positions a hydrogen may occupy on the line of the O–O bond, a far and a near position. Thus a rule leads to the frustration of positions of the proton for a ground state configuration: for each oxygen two of the neighboring protons must reside in

7448-446: The iron-rich face-centered cubic Fe–Ni alloys show Invar anomalies in their measured thermal and magnetic properties that evolve continuously in intensity with varying alloy composition. Scientists had once proposed that Invar's behavior was a direct consequence of a high-magnetic-moment to low-magnetic-moment transition occurring in the face centered cubic Fe–Ni series (and that gives rise to the mineral antitaenite ); however, this theory

7546-750: The large deposits in the Sudbury Basin in Canada in 1883, in Norilsk -Talnakh in Russia in 1920, and in the Merensky Reef in South Africa in 1924 made large-scale nickel production possible. Aside from the aforementioned Bactrian coins, nickel was not a component of coins until the mid-19th century. 99.9% nickel five-cent coins were struck in Canada (the world's largest nickel producer at

7644-672: The local accommodation of frustration was thoroughly studied. In their previous work on a square lattice of frustrated magnets, they observed both ice-like short-range correlations and the absence of long-range correlations, just like in the spin ice at low temperature. These results solidify the uncharted ground on which the real physics of frustration can be visualized and modeled by these artificial geometrically frustrated magnets, and inspires further research activity. These artificially frustrated ferromagnets can exhibit unique magnetic properties when studying their global response to an external field using Magneto-Optical Kerr Effect. In particular,

7742-784: The long half-life of Fe , its persistence in materials in the Solar System may generate observable variations in the isotopic composition of Ni . Therefore, the abundance of Ni in extraterrestrial material may give insight into the origin of the Solar System and its early history. At least 26 nickel radioisotopes have been characterized; the most stable are Ni with half-life 76,000 years, Ni (100 years), and Ni (6 days). All other radioisotopes have half-lives less than 60 hours and most these have half-lives less than 30 seconds. This element also has one meta state . Radioactive nickel-56

7840-416: The metals at a profit. The United States Mint , anticipating this practice, implemented new interim rules on December 14, 2006, subject to public comment for 30 days, which criminalized the melting and export of cents and nickels. Violators can be punished with a fine of up to $ 10,000 and/or a maximum of five years in prison. As of September 19, 2013, the melt value of a US nickel (copper and nickel included)

7938-446: The meteorite from Campo del Cielo (Argentina), which had been obtained in 1783 by Miguel Rubín de Celis, discovering the presence in them of nickel (about 10%) along with iron. The most common oxidation state of nickel is +2, but compounds of Ni , Ni , and Ni are well known, and the exotic oxidation states Ni and Ni have been characterized. Nickel tetracarbonyl (Ni(CO) 4 ), discovered by Ludwig Mond ,

8036-509: The only source for nickel was the rare Kupfernickel. Beginning in 1824, nickel was obtained as a byproduct of cobalt blue production. The first large-scale smelting of nickel began in Norway in 1848 from nickel-rich pyrrhotite . The introduction of nickel in steel production in 1889 increased the demand for nickel; the nickel deposits of New Caledonia , discovered in 1865, provided most of the world's supply between 1875 and 1915. The discovery of

8134-407: The principal mineral mixtures are nickeliferous limonite , (Fe,Ni)O(OH), and garnierite (a mixture of various hydrous nickel and nickel-rich silicates). Nickel sulfides commonly exist as solid solutions with iron in minerals such as pentlandite and pyrrhotite with the formula Fe 9-x Ni x S 8 and Fe 7-x Ni x S 6 , respectively. Other common Ni-containing minerals are millerite and

8232-477: The reversible reduction of protons to H 2 . Nickel(II) forms compounds with all common anions, including sulfide , sulfate , carbonate, hydroxide, carboxylates, and halides. Nickel(II) sulfate is produced in large amounts by dissolving nickel metal or oxides in sulfuric acid , forming both a hexa- and heptahydrate useful for electroplating nickel. Common salts of nickel, such as chloride, nitrate, and sulfate, dissolve in water to give green solutions of

8330-520: The spin-flipping configurations (SFCs) in Fe 3 Pt with the free energies of FM and SFCs predicted from first-principles calculations and were able to predict the temperature ranges of negative thermal expansion under various pressures. It was shown that all individual FM and SFCs have positive thermal expansion, and the negative thermal expansion originates from the increasing populations of SFCs with smaller volumes than that of FM. Nickel Nickel

8428-400: The spins. In that case commensurability , such as helical spin arrangements may result, as had been discussed originally, especially, by A. Yoshimori, T. A. Kaplan, R. J. Elliott , and others, starting in 1959, to describe experimental findings on rare-earth metals. A renewed interest in such spin systems with frustrated or competing interactions arose about two decades later, beginning in

8526-468: The subsequent 5-cent pieces. This alloy proportion is not ferromagnetic . The US nickel coin contains 0.04 ounces (1.1 g) of nickel, which at the April 2007 price was worth 6.5 cents, along with 3.75 grams of copper worth about 3 cents, with a total metal value of more than 9 cents. Since the face value of a nickel is 5 cents, this made it an attractive target for melting by people wanting to sell

8624-470: The system is said to be "unfrustrated". But now, the interaction energy is supposed to be at a minimum when atoms sit on the vertices of a regular pentagon . Trying to propagate in the long range a packing of these pentagons sharing edges (atomic bonds) and vertices (atoms) is impossible. This is due to the impossibility of tiling a plane with regular pentagons, simply because the pentagon vertex angle does not divide 2 π . Three such pentagons can easily fit at

8722-399: The terrestrial age of meteorites and to determine abundances of extraterrestrial dust in ice and sediment . Nickel-78, with a half-life of 110 milliseconds, is believed an important isotope in supernova nucleosynthesis of elements heavier than iron. Ni, discovered in 1999, is the most proton-rich heavy element isotope known. With 28 protons and 20 neutrons , Ni is " doubly magic ", as

8820-442: The time it was invented, the pendulum clock was the world's most precise timekeeper, and the limit to timekeeping accuracy was due to thermal variations in length of clock pendulums. The Riefler regulator clock developed in 1898 by Clemens Riefler, the first clock to use an Invar pendulum, had an accuracy of 10 milliseconds per day, and served as the primary time standard in naval observatories and for national time services until

8918-563: The time) during non-war years from 1922 to 1981; the metal content made these coins magnetic. During the war years 1942–1945, most or all nickel was removed from Canadian and US coins to save it for making armor. Canada used 99.9% nickel from 1968 in its higher-value coins until 2000. Coins of nearly pure nickel were first used in 1881 in Switzerland. Birmingham forged nickel coins in c.  1833 for trading in Malaysia. In

9016-520: The two states where all spins are up or down have more energy. Similarly in three dimensions, four spins arranged in a tetrahedron (Figure 2) may experience geometric frustration. If there is an antiferromagnetic interaction between spins, then it is not possible to arrange the spins so that all interactions between spins are antiparallel. There are six nearest-neighbor interactions, four of which are antiparallel and thus favourable, but two of which (between 1 and 2, and between 3 and 4) are unfavourable. It

9114-523: The valence and conduction electrons. It is nevertheless possible to use a very simplified picture of metallic bonding and only keeps an isotropic type of interactions, leading to structures which can be represented as densely packed spheres. And indeed the crystalline simple metal structures are often either close packed face-centered cubic (fcc) or hexagonal close packing (hcp) lattices. Up to some extent amorphous metals and quasicrystals can also be modeled by close packing of spheres. The local atomic order

9212-472: Was compared to the theoretical result from statistical mechanics of an ideal gas, S 2  = 45.10 cal/(K·mol) = 188.7 J/(mol·K). The two values differ by S 0  = 0.82 ± 0.05 cal/(K·mol) = 3.4 J/(mol·K). This result was then explained by Linus Pauling to an excellent approximation, who showed that ice possesses a finite entropy (estimated as 0.81 cal/(K·mol) or 3.4 J/(mol·K)) at zero temperature due to

9310-551: Was described by Westinghouse scientists in 1961 as "30–45 atom per cent nickel". Common grades of Invar have a coefficient of thermal expansion (denoted α , and measured between 20 °C and 100 °C) of about 1.2 × 10  K (1.2  ppm /°C), while ordinary steels have values of around 11–15 ppm/°C. Extra-pure grades (<0.1% Co ) can readily produce values as low as 0.62–0.65 ppm/°C. Some formulations display negative thermal expansion (NTE) characteristics. Though it displays high dimensional stability over

9408-462: Was first isolated and classified as an element in 1751 by Axel Fredrik Cronstedt , who initially mistook the ore for a copper mineral , in the cobalt mines of Los, Hälsingland, Sweden . The element's name comes from a mischievous sprite of German miner mythology, Nickel (similar to Old Nick ). Nickel minerals can be green, like copper ores, and were known as kupfernickel – Nickel's copper – because they produced no copper. Although most nickel in

9506-429: Was patented by Ludwig Mond and has been in industrial use since before the beginning of the 20th century. In this process, nickel is treated with carbon monoxide in the presence of a sulfur catalyst at around 40–80 °C to form nickel carbonyl . In a similar reaction with iron, iron pentacarbonyl can form, though this reaction is slow. If necessary, the nickel may be separated by distillation. Dicobalt octacarbonyl

9604-467: Was proven incorrect. Instead, it appears that the low-moment/high-moment transition is preceded by a high-magnetic-moment frustrated ferromagnetic state in which the Fe–Fe magnetic exchange bonds have a large magneto-volume effect of the right sign and magnitude to create the observed thermal expansion anomaly. Wang et al. considered the statistical mixture between the fully ferromagnetic (FM) configuration and

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