Ceramic
A ceramic is a solid material comprising an inorganic compound of metal, non-metal or metalloid atoms held in ionic and covalent bonds. Common examples are earthenware and brick; the crystallinity of ceramic materials ranges from oriented to semi-crystalline and completely amorphous. Most fired ceramics are either vitrified or semi-vitrified as is the case with earthenware and porcelain. Varying crystallinity and electron composition in the ionic and covalent bonds cause most ceramic materials to be good thermal and electrical insulators. With such a large range of possible options for the composition/structure of a ceramic, the breadth of the subject is vast, identifiable attributes are difficult to specify for the group as a whole. General properties such as high melting temperature, high hardness, poor conductivity, high moduli of elasticity, chemical resistance and low ductility are the norm, with known exceptions to each of these rules. Many composites, such as fiberglass and carbon fiber, while containing ceramic materials, are not considered to be part of the ceramic family.
The earliest ceramics made by humans were pottery objects or figurines made from clay, either by itself or mixed with other materials like silica and sintered in fire. Ceramics were glazed and fired to create smooth, colored surfaces, decreasing porosity through the use of glassy, amorphous ceramic coatings on top of the crystalline ceramic substrates. Ceramics now include domestic and building products, as well as a wide range of ceramic art. In the 20th century, new ceramic materials were developed for use in advanced ceramic engineering, such as in semiconductors; the word "ceramic" comes from the Greek word κεραμικός, "of pottery" or "for pottery", from κέραμος, "potter's clay, pottery". The earliest known mention of the root "ceram-" is the Mycenaean Greek ke-ra-me-we, "workers of ceramics", written in Linear B syllabic script; the word "ceramic" may be used as an adjective to describe a material, product or process, or it may be used as a noun, either singular, or, more as the plural noun "ceramics".
A ceramic material is an inorganic, non-metallic crystalline oxide, nitride or carbide material. Some elements, such as carbon or silicon, may be considered ceramics. Ceramic materials are brittle, strong in compression, weak in shearing and tension, they withstand chemical erosion that occurs in other materials subjected to acidic or caustic environments. Ceramics can withstand high temperatures, ranging from 1,000 °C to 1,600 °C. Glass is not considered a ceramic because of its amorphous character. However, glassmaking involves several steps of the ceramic process, its mechanical properties are similar to ceramic materials. Traditional ceramic raw materials include clay minerals such as kaolinite, whereas more recent materials include aluminium oxide, more known as alumina; the modern ceramic materials, which are classified as advanced ceramics, include silicon carbide and tungsten carbide. Both are valued for their abrasion resistance and hence find use in applications such as the wear plates of crushing equipment in mining operations.
Advanced ceramics are used in the medicine, electronics industries and body armor. Crystalline ceramic materials are not amenable to a great range of processing. Methods for dealing with them tend to fall into one of two categories – either make the ceramic in the desired shape, by reaction in situ, or by "forming" powders into the desired shape, sintering to form a solid body. Ceramic forming techniques include shaping by hand, slip casting, tape casting, injection molding, dry pressing, other variations. Noncrystalline ceramics, being glass, tend to be formed from melts; the glass is shaped when either molten, by casting, or when in a state of toffee-like viscosity, by methods such as blowing into a mold. If heat treatments cause this glass to become crystalline, the resulting material is known as a glass-ceramic used as cook-tops and as a glass composite material for nuclear waste disposal; the physical properties of any ceramic substance are a direct result of its crystalline structure and chemical composition.
Solid-state chemistry reveals the fundamental connection between microstructure and properties such as localized density variations, grain size distribution, type of porosity and second-phase content, which can all be correlated with ceramic properties such as mechanical strength σ by the Hall-Petch equation, toughness, dielectric constant, the optical properties exhibited by transparent materials. Ceramography is the art and science of preparation and evaluation of ceramic microstructures. Evaluation and characterization of ceramic microstructures is implemented on similar spatial scales to that used in the emerging field of nanotechnology: from tens of angstroms to tens of micrometers; this is somewhere between the minimum wavelength of visible light and the resolution limit of the naked eye. The microstructure includes most grains, secondary phases, grain boundaries, micro-
Tin
Tin is a chemical element with the symbol Sn and atomic number 50. It is a post-transition metal in group 14 of the periodic table of elements, it is obtained chiefly from the mineral cassiterite, which contains stannic oxide, SnO2. Tin shows a chemical similarity to both of its neighbors in group 14, germanium and lead, has two main oxidation states, +2 and the more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table, thanks to its magic number of protons, it has two main allotropes: at room temperature, the stable allotrope is β-tin, a silvery-white, malleable metal, but at low temperatures it transforms into the less dense grey α-tin, which has the diamond cubic structure. Metallic tin does not oxidize in air; the first tin alloy used on a large scale was bronze, made of 1/8 tin and 7/8 copper, from as early as 3000 BC. After 600 BC, pure metallic tin was produced. Pewter, an alloy of 85–90% tin with the remainder consisting of copper and lead, was used for flatware from the Bronze Age until the 20th century.
In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are 60% or more tin, in the manufacture of transparent, electrically conducting films of indium tin oxide in optoelectronic applications. Another large application for tin is corrosion-resistant tin plating of steel; because of the low toxicity of inorganic tin, tin-plated steel is used for food packaging as tin cans. However, some organotin compounds can be as toxic as cyanide. Tin is a soft, malleable and crystalline silvery-white metal; when a bar of tin is bent, a crackling sound known as the "tin cry" can be heard from the twinning of the crystals. Tin melts at low temperatures of about 232 °C, the lowest in group 14; the melting point is further lowered to 177.3 °C for 11 nm particles. Β-tin, stable at and above room temperature, is malleable. In contrast, α-tin, stable below 13.2 °C, is brittle. Α-tin has a diamond cubic crystal structure, similar to silicon or germanium. Α-tin has no metallic properties at all because its atoms form a covalent structure in which electrons cannot move freely.
It is a dull-gray powdery material with no common uses other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C, impurities lower the transition temperature well below 0 °C and, on the addition of antimony or bismuth, the transformation might not occur at all, increasing the durability of the tin. Commercial grades of tin resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony and silver present as impurities. Alloying elements such as copper, bismuth and silver increase its hardness. Tin tends rather to form hard, brittle intermetallic phases, which are undesirable, it does not form wide solid solution ranges in other metals in general, few elements have appreciable solid solubility in tin.
Simple eutectic systems, occur with bismuth, lead and zinc. Tin was one of the first superconductors to be studied. Tin can be attacked by acids and alkalis. Tin can be polished and is used as a protective coat for other metals. A protective oxide layer prevents further oxidation, the same that forms on pewter and other tin alloys. Tin helps to accelerate the chemical reaction. Tin has ten stable isotopes, with atomic masses of 112, 114 through 120, 122 and 124, the greatest number of any element. Of these, the most abundant are 120Sn, 118Sn, 116Sn, while the least abundant is 115Sn; the isotopes with mass numbers have no nuclear spin, while those with odd have a spin of +1/2. Tin, with its three common isotopes 116Sn, 118Sn and 120Sn, is among the easiest elements to detect and analyze by NMR spectroscopy, its chemical shifts are referenced against SnMe4; this large number of stable isotopes is thought to be a direct result of the atomic number 50, a "magic number" in nuclear physics. Tin occurs in 29 unstable isotopes, encompassing all the remaining atomic masses from 99 to 137.
Apart from 126Sn, with a half-life of 230,000 years, all the radioisotopes have a half-life of less than a year. The radioactive 100Sn, discovered in 1994, 132Sn are one of the few nuclides with a "doubly magic" nucleus: despite being unstable, having lopsided proton–neutron ratios, they represent endpoints beyond which stability drops off rapidly. Another 30 metastable isomers have been characterized for isotopes between 111 and 131, the most stable being 121mSn with a half-life of 43.9 years. The relative differences in the abundances of tin's stable isotopes can be explained by their different modes of formation in stellar nucleosynthesis. 116Sn through 120Sn inclusive are formed in the s-process in most stars and hence they are the most common isotopes, while 122Sn and 124Sn are only formed in the r-process (rapid neutr
Frank–Kasper phases
Topologically close pack phases known as Frank-Kasper phases, are one of the largest groups of intermetallic compounds, known for their complex crystallographic structure and physical properties. Owing to their combination of periodic and aperiodic structure, some TCP phases belong to the class of quasicrystals. Applications of TCP phases as high-temperature structural and superconducting materials have been highlighted, their complex and non-stoichiometric structure makes them good subjects for theoretical calculations. In 1958, Frank and Kasper, in their original work investigating many complex alloy structures, showed that non-icosahedral environments form an open-end network which they called the major skeleton, is now identified as the declination locus, they came up with the methodology to pack asymmetric icosahedra into crystals using other polyhedra with larger coordination number and atoms. These coordination polyhedra were constructed to maintain topological close packing. Based on the tetrahedral units, FK crystallographic structures are classified into low and high polyhedral groups denoted by their coordination numbers referring to the number of atom centering the polyhedron.
Some atoms have an icosahedral structure with low coordination, labeled CN12. Some others have higher coordination numbers of 14, 15 and 16, labeled CN14, CN15 and CN16, respectively; these atoms with higher coordination numbers form uninterrupted networks connected along the directions where the five-fold icosahedral symmetry is replaced by six-fold local symmetry. The most common members of a FK-phases family are: A15, Laves phases, σ, μ, M, P, R. A15 phases are intermetallic alloys with an average coordination number of 13.5 and eight A3B stoichiometry atoms per unit cell where two B atoms are surrounded by CN12 polyhedral, six A atoms are surrounded by CN14 polyhedral. Nb3Ge is a superconductor with A15 structure. Laves phases are intermetallic compounds composed of CN12 and CN16 polyhedra with AB2 stoichiometry seen in binary metal systems like MgZn2. Due to the small solubility of AB2 structures, Laves phases are line compounds, though sometimes they can have a wide homogeneity region.
The sigma phase is an intermetallic compound known as the one without definite stoichiometric composition and formed at the electron/atom ratio range of 6.2 to 7. It has a primitive tetragonal unit cell with 30 atoms. CrFe is a typical alloy crystallizing in the σ phase at the equiatomic composition. With physical properties adjustable based on its structural components, or its chemical composition provided a given structure; the μ phase has an ideal A6B7 stoichiometry, with its prototype W6Fe7, containing rhombohedral cell with 13 atoms. While many other Frank-Kasper alloy types have been identified, more continue to be found; the alloy Nb10Ni9Al3 is the prototype for the M phase. It has orthorhombic space group with 52 atoms per unit cell; the alloy Cr9Mo21Ni20 is the prototype for the P-phase. It has a primitive orthorhombic cell with 56 atoms; the alloy Co5Cr2Mo3 is the prototype for the R-phase which belongs to the rhombohedral space group with 53 atoms per cell. FK phase materials have been pointed out for their high-temperature structure and as superconducting materials.
Their complex and non-stoichiometric structure makes them good subjects for theoretical calculations. A15, Laves and σ are the most applicable FK structures with interesting fundamental properties; the A15 compounds are forming important intermetallic superconductor with major applications in materials used in wires for superconducting such as: Nb3Sn, Nb3Zr and Nb3Ti. A majority of superconducting magnets are constructed out of Nb3Ti alloy. Small extents of σ phase decreases the flexibility and impairment in erosion resistance. While addition of refractory elements like W, Mo or Re to FK phases helps to enhance the thermal properties in such alloys as steels or nickel-based superalloys, it increases the risk of unwanted precipitation in intermetallic compounds
Post-transition metal
Post-transition metals are a set of metallic elements in the periodic table located between the transition metals to their left, the metalloids to their right. Depending on where these adjacent groups are judged to begin and end, there are at least five competing proposals for which elements to include: the three most common contain six and thirteen elements, respectively. All proposals include gallium, tin, thallium and bismuth. Physically, post-transition metals are soft, have poor mechanical strength, have melting points lower than those of the transition metals. Being close to the metal-nonmetal border, their crystalline structures tend to show covalent or directional bonding effects, having greater complexity or fewer nearest neighbours than other metallic elements. Chemically, they are characterised—to varying degrees—by covalent bonding tendencies, acid-base amphoterism and the formation of anionic species such as aluminates and bismuthates, they can form Zintl phases. The name is universally used, but not sanctioned by any organization such as the IUPAC.
The origin of the term is unclear: one early use was in 1940 in a chemistry text. Alternate names for this group are B-subgroup metals, other metals, p-block metals. Included in this category are the group 13–15 metals in periods 4–6: gallium and thallium. Other elements sometimes included are the group 11 metals copper and gold. Astatine, classified as a nonmetal or a metalloid, has been predicted to have a metallic crystalline structure. If so, it would be a post-transition metal. Elements 112–118 may be post-transition metals. Which elements start to be counted as post-transition metals depends, in periodic table terms, on where the transition metals are taken to end. In the 1950s, most inorganic chemistry textbooks defined transition elements as finishing at group 10, therefore excluding group 11, group 12. A survey of chemistry books in 2003 showed that the transition metals ended at either group 11 or group 12 with equal frequency. Where the post-transition metals end depends on where the metalloids or nonmetals start.
Boron, germanium, arsenic and tellurium are recognised as metalloids. The diminished metallic nature of the post-transition metals is attributable to the increase in nuclear charge going across the periodic table, from left to right; the increase in nuclear charge is offset by an increasing number of electrons but as these are spatially distributed each extra electron does not screen each successive increase in nuclear charge, the latter therefore dominates. With some irregularities, atomic radii contract, ionisation energies increase, fewer electrons become available for metallic bonding, "ions smaller and more polarizing and more prone to covalency." This phenomenon is more evident in period 4–6 post-transition metals, due to inefficient screening of their nuclear charges by their d10 and f14 electron configurations. The reductions in atomic size due to the interjection of the d- and f-blocks are referred to as the'scandide' or'd-block contraction', the'lanthanide contraction'. Relativistic effects "increase the binding energy", hence ionisation energy, of the electrons in "the 6s shell in gold and mercury, the 6p shell in subsequent elements of period 6."
The origin of the term post-transition metal is unclear. An early usage is recorded in 1940, in his well-known book Fundamental Chemistry, he treated the transition metals as finishing at group 10. He referred to the ensuing elements in periods 4 to 6 of the periodic table —in view of their underlying d10 electronic configurations—as post-transition metals; this section outlines relevant physical and chemical properties of the elements or sometimes classified as post-transition metals. For complete profiles, including history, specific uses, biological roles and precautions, see the main article for each element. Abbreviations: MH—Mohs hardness; the group 11 metals are categorised as transition metals given they can form ions with incomplete d-shells. Physically, they have the low melting points and high electronegativity values associated with post-transition metals. "The filled d subshell and free s electron of Cu, Ag, Au contribute to their high electrical and thermal conductivity. Transition metals to the left of group 11 experience interactions between s electrons and the filled d subshell that lower electron mobility."
Chemically, the group 11 metals in their +1 valenc
Nitride
In chemistry, a nitride is a compound of nitrogen where nitrogen has a formal oxidation state of −3. Nitrides are a large class of compounds with a wide range of applications; the nitride ion, N3−, is never encountered in protic solution because it is so basic that it would be protonated immediately. Its ionic radius is estimated to be 140 pm. Like carbides, nitrides are refractory materials owing to their high lattice energy which reflects the strong attraction of "N3−" for the metal cation. Thus, titanium nitride and silicon nitride are used as cutting hard coatings. Hexagonal boron nitride, which adopts a layered structure, is a useful high-temperature lubricant akin to molybdenum disulfide. Nitride compounds have large band gaps, thus nitrides are insulators or wide bandgap semiconductors; the wide band gap material gallium nitride is prized for emitting blue light in LEDs. Like some oxides, nitrides can absorb hydrogen and have been discussed in the context of hydrogen storage, e.g. lithium nitride.
Classification of such a varied group of compounds is somewhat arbitrary. Compounds where nitrogen is not assigned −3 oxidation state are not included, such as nitrogen trichloride where the oxidation state is +3. Only one alkali metal nitride is stable, the purple-reddish lithium nitride, which forms when lithium burns in an atmosphere of N2. Sodium nitride remains a laboratory curiosity; the nitrides of the alkaline earth metals have the formula. Examples include Be3N2, Mg3N2, Ca3N2, Sr3N2; the nitrides of electropositive metals hydrolyze upon contact with water, including the moisture in the air: Mg3N2 + 6 H2O → 3 Mg2 + 2 NH3 Boron nitride exists as several forms. Nitrides of silicon and phosphorus are known, but only the former is commercially important; the nitrides of aluminium and indium adopt diamond-like wurtzite structure in which each atom occupies tetrahedral sites. For example, in aluminium nitride, each aluminium atom has four neighboring nitrogen atoms at the corners of a tetrahedron and each nitrogen atom has four neighboring aluminium atoms at the corners of a tetrahedron.
This structure is like hexagonal diamond. Thallium nitride, Tl3N is known, but thallium nitride, TlN, is not. For the group 3 metals, ScN and YN are both known. Group 4, 5, 6 transition metals, the titanium and chromium groups all form nitrides, they are chemically stable. Representative is titanium nitride. Sometimes these materials are called "interstitial nitrides." Nitrides of the Group 7 and 8 transition metals decompose readily. For example, iron nitride, Fe2N decomposes at 200 °C. Platinum nitride and osmium nitride may contain N2 units, as such should not be called nitrides. Nitrides of heavier members from group 11 and 12 are less stable than copper nitride, Cu3N and Zn3N2: dry silver nitride is a contact explosive which may detonate from the slightest touch a falling water droplet. Many metals form molecular nitrido complexes; the main group elements form some molecular nitrides. Cyanogen and tetrasulfur tetranitride are rare examples of a molecular binary nitrides, they dissolve in nonpolar solvents.
Both undergo polymerization. S4N4 is unstable with respect to the elements, but less so that the isostructural Se4N4. Heating S4N4 gives a polymer, a variety of molecular sulfur nitride anions and cations are known. Related to but distinct from nitride is pernitride, N2−2
Magnetism
Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments; the most familiar effects occur in ferromagnetic materials, which are attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4. Although ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, all other materials are influenced to some extent by a magnetic field, by several other types of magnetism. Paramagnetic substances such as aluminum and oxygen are weakly attracted to an applied magnetic field; the force of a magnet on paramagnetic and antiferromagnetic materials is too weak to be felt, can be detected only by laboratory instruments, so in everyday life these substances are described as non-magnetic.
The magnetic state of a material depends on temperature and other variables such as pressure and the applied magnetic field. A material may exhibit more than one form of magnetism as these variables change; as with magnetising a magnet, demagnetising a magnet is possible. "Passing an alternate current, or hitting a heated magnet in an east west direction are ways of demagnetising a magnet", quotes Sreekethav. Magnetism was first discovered in the ancient world, when people noticed that lodestones magnetized pieces of the mineral magnetite, could attract iron; the word magnet comes from the Greek term μαγνῆτις λίθος magnētis lithos, "the Magnesian stone, lodestone." In ancient Greece, Aristotle attributed the first of what could be called a scientific discussion of magnetism to the philosopher Thales of Miletus, who lived from about 625 BC to about 545 BC. The ancient Indian medical text Sushruta Samhita describes using magnetite to remove arrows embedded in a person's body. In ancient China, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, The Sage of Ghost Valley.
The 2nd-century BC annals, Lüshi Chunqiu notes: "The lodestone makes iron approach, or it attracts it." The earliest mention of the attraction of a needle is in a 1st-century work Lunheng: "A lodestone attracts a needle." The 11th-century Chinese scientist Shen Kuo was the first person to write—in the Dream Pool Essays—of the magnetic needle compass and that it improved the accuracy of navigation by employing the astronomical concept of true north. By the 12th century the Chinese were known to use the lodestone compass for navigation, they sculpted a directional spoon from lodestone in such a way that the handle of the spoon always pointed south. Alexander Neckam, by 1187, was the first in Europe to describe the compass and its use for navigation. In 1269, Peter Peregrinus de Maricourt wrote the Epistola de magnete, the first extant treatise describing the properties of magnets. In 1282, the properties of magnets and the dry compasses were discussed by Al-Ashraf, a Yemeni physicist and geographer.
In 1600, William Gilbert published his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure. In this work he describes many of his experiments with his model earth called the terrella. From his experiments, he concluded that the Earth was itself magnetic and that this was the reason compasses pointed north. An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Ørsted, a professor at the University of Copenhagen, who discovered by the accidental twitching of a compass needle near a wire that an electric current could create a magnetic field; this landmark experiment is known as Ørsted's Experiment. Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity and optics into the field of electromagnetism.
In 1905, Einstein used these laws in motivating his theory of special relativity, requiring that the laws held true in all inertial reference frames. Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, the standard model. Magnetism, at its root, arises from two sources: Electric current. Spin magnetic moments of elementary particles; the magnetic properties of materials are due to the magnetic moments of their atoms' orbiting electrons. The magnetic moments of the nuclei of atoms are thousands of times smaller than the electro
Superconductivity
Superconductivity is a phenomenon of zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 1911, in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon, it is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor during its transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood as the idealization of perfect conductivity in classical physics; the electrical resistance of a metallic conductor decreases as temperature is lowered. In ordinary conductors, such as copper or silver, this decrease is limited by impurities and other defects. Near absolute zero, a real sample of a normal conductor shows some resistance.
In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current through a loop of superconducting wire can persist indefinitely with no power source. In 1986, it was discovered that some cuprate-perovskite ceramic materials have a critical temperature above 90 K; such a high transition temperature is theoretically impossible for a conventional superconductor, leading the materials to be termed high-temperature superconductors. The cheaply-available coolant liquid nitrogen boils at 77 K, thus superconduction at higher temperatures than this facilitates many experiments and applications that are less practical at lower temperatures. There are many criteria; the most common are: A superconductor can be Type I, meaning it has a single critical field, above which all superconductivity is lost and below which the magnetic field is expelled from the superconductor. These points are called vortices. Furthermore, in multicomponent superconductors it is possible to have combination of the two behaviours.
In that case the superconductor is of Type-1.5. It is conventional if it can be explained by the BCS theory or its derivatives, or unconventional, otherwise. A superconductor is considered high-temperature if it reaches a superconducting state when cooled using liquid nitrogen – that is, at only Tc > 77 K) – or low-temperature if more aggressive cooling techniques are required to reach its critical temperature. Superconductor material classes include chemical elements, ceramics, superconducting pnictides or organic superconductors. Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature, critical field, critical current density at which superconductivity is destroyed. On the other hand, there is a class of properties. For instance, all superconductors have zero resistivity to low applied currents when there is no magnetic field present or if the applied field does not exceed a critical value; the existence of these "universal" properties implies that superconductivity is a thermodynamic phase, thus possesses certain distinguishing properties which are independent of microscopic details.
The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V / I. If the voltage is zero, this means. Superconductors are able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature. In practice, currents injected in superconducting coils have persisted for more than 23 years in superconducting gravimeters. In such instruments, the measurement principle is based on the monitoring of the levitation of a superconducting niobium sphere with a mass of 4 grams.
In a normal conductor, an electric current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are colliding with the ions in the lattice, during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat, the vibrational kinetic energy of the lattice ions; as a result, the energy carried by the current is being dissipated. This is the phenomenon of electrical Joule heating; the situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons known as Cooper pairs; this pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectr
