The metal of Mars gives us magnetism and life
Iron is best known as the metal that gave us weapons and tools, and whose ability by means of alloys and heat treatment to suit itself to every application makes it the primary metal of technology. The purpose of this article, however, is principally to explain in some detail two remarkable applications of iron, ferromagnetism and oxygen transport in the blood. The very similar cobalt and nickel will also be included.
Iron is the most freqently encountered metal in daily life, always in the form of manufactured objects, and usually covered with a protective coating or buried deep within the object. Concrete structures contain essential reinforcing iron; electrical machines, including transformers, depend on iron. Automobiles are mainly iron; "tin" cans are iron covered with thin coatings of tin or lacquer; fasteners, such as the nails and screws used in wooden construction, are usually iron. This list can easily be extended with a little thought.
Iron is an excellent and versatile material of construction--strong, tough, easily formed and worked, and, very importantly, cheap compared to the alternatives. Plastics give it competition, especially in products that must be manufactured at the lowest cost where strength and durability are not the primary concerns, such as modern American automobiles. Aluminium is a strong competitor where weight is a concern, as in aircraft. However, the versatility of iron-carbon alloys cannot be matched in any other material. Alloys with other metals, such as nickel, chromium and manganese, give further advantages. These steels can be tailored to nearly every demand, and are not significantly challenged as materials of construction.
The shortcomings of iron are its weight, and its propensity to rust. Both aluminium and plastics avoid these shortcomings, because their densities are much less than that of iron, and aluminium is protected by an adherent layer of oxide, and plastics by the inertness of the substance. The advantages of iron are so great, however, that these considerations prevail only in limited fields of application.
The three metals iron, cobalt and nickel are called the "iron family" and are very similar, so I shall discuss them together. A property of the iron family for which there is no substitute at an equivalent cost is that they can be induced to provide a strong magnetic field with only small excitation by an electric current. It is a very remarkable property, so an effort will be made to explain how it arises, and how it is used. Also, iron is important as a carrier of oxygen in blood, and how it does this will be explained.
In addition to these subjects, the physical and chemical properties of iron will be reviewed, and its curiosities examined, as usual. For some accounts and explanations, reference will be made to other articles where they appear, and will not be duplicated here. This is especially true of the application of iron as an engineering material, a very extensive subject.
Our word iron is cognate to the German Eisen, which in various forms is found in all the northern European languages, though not elsewhere. Why our pronunciation of the word is metathetical, "iorn" instead of "iron," I have not heard. In Gothic, it was eisarn, and in Old High German, isan. In Greek, iron is síderos and steel is chalybicón, stems that are encountered frequently in talking of iron, as in "siderurgy" and "chalybeate spring." "Sidereal time" is not iron time, however, but the "sider-" comes from the similar Latin sidera, "stars." Iron was very valuable when it came to the bronze-age Greeks from its inventors around the Pontus Euxinus, and was used for jewellery and prizes. It has been money in other places and times. The Latin for iron is ferrum, from which the word in most European languages has been derived, and which appears more commonly than any other stem in words dealing with iron, especially in chemical nomenclature.
Cobalt is from Kobold, an earth spirit, or a good house spirit. The kobold came surreptitiously and stole the silver from the ore, replacing it with base cobalt. There is a Greek word kobalos, meaning "rogue, trickster," but there is probably no connection with the German. Nickel is from Nickel, a water spirit, who took the copper from the ore and washed it away, replacing it with kupfernickel. A Nix is a male water spirit, a Nixe a female water spirit. These names were from miner's slang, not traditional names for the metals, which were unknown at the time. Many minerals resemble ores, but do not yield the expected metal, and this was confusing when their chemical natures were not known. Cobalt was recognized by Brandt in 1735 and nickel by Cronstadt in 1750, but their compounds were not carefully studied until the next century.
Iron is a shiny, bright white metal that is soft, malleable, ductile and strong. Its surface is usually discolored by corrosion, since it combines readily with the oxygen of the air in the presence of moisture. In absolutely dry air, it does not rust. The oxide that is produced is crumbly and soft, giving no protection to the base metal, which eventually rusts away. It is found in nature as the metal only in meteorites and in very rare circumstances where iron minerals have been reduced by environmental factors. Masses up to 25 tons in weight have been found in West Greenland. Practically, it is always obtained from ores that are usually the oxides, and occasionally the carbonate, as low in sulphur and phosphorus as possible. The plentiful iron pyrite, FeS2 is not an acceptable ore because sulphur is a deleterious impurity in iron, and expensive to remove in refining. Iron is the fourth most plentiful element in the earth's crust (4.6%), but is so widely disseminated that it can be obtained only from ores in which iron has been specially concentrated. Much of this concentration, incidentally, occurred very early in the earth's history when iron removed from the atmosphere the little oxygen that it then contained, possibly with the help of the earliest forms of life.
A clean surface of cobalt is tinged with pink, nickel with yellow. Neither rusts as vigorously as iron, since the oxide layers are more protective and adherent. Nickel displays a resistant bright surface that takes a high polish. It is generally used as an undercoat for chromium plating, since chromium is not suitable by itself on iron, as the electrodeposited film is not continuous.
Iron has atomic number 26, atomic weight 55.85, and stable isotopes 54 (5.9%), 56 (91.6%), 57 (2.2%) and 58 (0.33%). Its electron configuration is Ar3d64s2, and its first and second ionization potentials are 7.87V and 16.18V. With its neighbors cobalt (Z=27) and nickel (Z=28), it is one of the "iron triad" of similar metals. It is in the center of the periodic table, in the region of "transition metals" where a d-shell of electrons is being filled. The 4s electrons are actually more stable than the 3d electrons, so the d-electrons are actually on the outside of the atom. The d-shell can hold 10 electrons, and as it becomes nearly filled, drops below the 4s electrons in energy. All these atoms filling d-shells make metals that are very much alike; if the d-electrons were more inside, these metals would be even more alike than they are. More will be said in connection with magnetism, in which these electrons play leading roles.
At room temperature, iron is in the form of ferrite, or α-iron, a body-centered cubic structure. The density of α-iron is 7.86 g/cc. At 910°C it changes to γ-iron, which is face-centered cubic and somewhat softer. At 1535°C iron melts, and boils at 3000°C. For more information on iron structures and the iron-carbon phase diagram, see Phase Rules!. Cobalt melts at 1480°C, nickel at 1455°C. The specific heat of any of the three metals is about 0.107 cal/g-K. The thermal conductivities of Fe, Co and Ni are 3.37, 3.81 and 4.19 cal/s-cm-K. Their electrical resistivities are 9.71, 6.24 and 6.84 μΩ-cm. These are "worse" than those of copper by factors of only 4 to 6, so the iron metals are very good conductors of electricity and heat. Comparing the numbers shows how similar these metals are in their physical properties. I have not heard whether cobalt and nickel make useful alloys with carbon, as iron does. They are much too expensive to use as structural metals, other than as alloying elements or coatings.
Iron occurs as the cations Fe++, ferrous iron, and Fe+++, ferric iron. Nickel and cobalt occur mainly as the dipositive ions, nickelous and cobaltous, but also in other oxidation states, usually in unstable compounds. A large number of important salts are formed with various anions. Fe++ will gladly donate an electron in an acid solution or in the presence of oxygen, so it is a reducing agent, oxidizing itself to Fe+++. In alkaline solution, this ion will gladly accept an electron, so it is an oxidizing agent, reducing itself to the ferrous state. In acid solution, Fe will reduce H+ to H2, since its electrode potential is -0.44V, well above hydrogen's. Iron is, in fact, an active element.
The oxides are ferrous oxide, FeO and ferric oxide, Fe2O3. Ferrous oxide is not stable against partial oxidation to Fe(II)(Fe(III)2O4), usually written Fe3O4 or FeO·Fe2O3. This hard, black substance is magnetite, an important ore of iron and a very interesting substance in its own right, which will be considered further in connection with magnetism, where its structure will be explained.
The ferrous ion is greenish in solution, while the ferric ion is a light violet. The distinct colors of iron compounds are due to the d-electrons, which can interact with light in many interesting ways. Ferrous oxide, as a mineral, is called hematite ("blood-stone") and is usually almost black. It leaves a red streak on unglazed porcelain, and in its usually finely-divided condition is a characteristic bright earthy red. In pure form, it is called rouge, good for reddening cheeks and polishing glass, or Venetian red, a red pigment. The red stains on concrete are ferric oxide, usually from reinforcement rods that are not properly protected from the weather. The red of Mars is ferric oxide, showing that the atmosphere once contained oxygen, the oxygen that is only liberated by life.
Ferrous sulphate, FeSO4 forms pale green crystals of the heptahydrate when a solution is evaporated. In air, these crystals will attract moisture and oxygen, and slowly become ferric. This salt is called copperas or green vitriol. In alkaline solution, gelatinous Fe(OH)2 precipitates, which likewise oxidizes in air through green, black and finally to red-brown ferric oxide. Ferrous tannate is obtained by mixing ferrous sulphate and tannic acid (from nut-galls, for example). This oxidizes in air to black ferric tannate, and so the solution is used as an ink. A dark-blue dye is generally added, since the ferrous tannate is almost colorless. By the time the dye has bleached in the light, the ferric tannate will be distinct. This kind of ink eventually rusts to ferric oxide, and is not nearly as permanent as India ink made from colloidal carbon. It is not as susceptible to clogging, however, and flows easily from the pen. It can be removed from fabrics with oxalic acid or ammonium oxalate, which dissove the iron. This was called "permanent ink" to distinguish it from "washable ink" that contained water-soluble dyes and was even less durable.
Anhydrous ferric chloride is a covalent compound FeCl3 that dissolves in organic solvents as well as in water. It forms bright-yellow crystals as the hexahydrate. Anhydrous ferric sulphate is colorless, but crystals of Fe2(SO4)3·9h2O are yellow. Ferric ammonium alum, FeNH4(SO4)2·12H2O is pale violet, the typical ferric color in solution. This is an "alum" without aluminium, the iron standing it for it. It is a mordant because of the gelatinous ferric hydroxide formed when a solution is make alkaline. There are also ferric potassium alum, also colorless or violet, and ferrous ammonium sulphate, which forms blue-green crystals of the hexahydrate.
The cyanide ion, CN-, and its relatives, accompany iron in many interesting compounds. The free cyanide ion is very poisonous, since it blocks nerve communications. This poison is purely in the structure, again, and there is nothing inherently poisonous about cyanide. Iron forms strong complexes with six cyanides, binding the carbon tightly and pointing the nitrogens to the vertices of an octahedron. If the iron is ferrous, the charge is -4, and if it is ferric, the charge is -3. This is the ferrocyanide or ferricyanide anion, which makes many salts in aqueous solution or ionic crystals. It even combines with iron, to form ferric ferrocyanide, ferric ferricyanide, ferrous ferrocyanide and ferrous ferricyanide, and often potassium joins in. Potassium ferrous ferricyanide is Prussian blue, ferrous ferricyanide is Turnbull's blue. Potassium ferrocyanide, also called potassium berlinate or potassium prussiate, is yellow, and can be obtained in the distillation of coal. Potassium ferricyanide is red. Solutions of ferrocyanide and ferricyanide show no evidence of either iron or cyanide, and are not poisonous. An Italian terrorist who plotted to poison with ferrocyanide was doomed to failure by his ignorance. Some colorless ferricyanides turn the urine blue, which was a typical prank among chemistry students. Prussian blue is now marketed as the prescription medicine Radiogardase, which aids elimination of thallium and caesium, beneficial when radioactive isotopes of these have been ingested, and also in cases of thallium poisoning, which is extremely serious. Caesium does not appear to be very poisonous. The new name would seem to denote an enzyme, which it is not, but at any rate allows sale at a much higher price.
The cyanate ion, CNO- and the thiocyante ion, CNS- are equally stable and nonpoisonous. Ferric thiocyanate, Fe(CNS)3, is blood-red and an analytical test for iron. It forms red, deliquescent crystals. When carbon monoxide is passed over warm Fe, Co or Ni powder, liquid carbonyls are formed, Fe(CO)5, Co(CO)4 and Ni(CO)4 the uncharged CO sticks to the Fe or Ni by "resonance" with states where various formal charges are assigned to the atoms, and a linear combination leads to a minimum energy. The carbons are adjacent to the central metal. A mixture of carbonyls can be fractionally distilled and the pure substances pyrolyzed to recover the metals. The Mond process for refining nickel is based on this property.
The usual ferrous sulphide, FeS, can add sulphur stochiometrically to form crystalline FeS2, known as the mineral pyrite. This is from the Greek pyrites, from pyr, "fire," and meaning something made of fire. When struck by iron, it will produce luminous sparks that can be used to ignite tinder to make fire. The wheellock was invented around 1500 for use in cavalry pistols. A spring-driven wheel pressed to a piece of pyrite threw a jet of sparks into the pan. Cavalrymen could not use the usual "slow match" of the time because the wind extinguished it. Pyrite gives excellent sparks, probably pieces of FeS2 heated by impact and burning in air, but is not as durable as flint. Such materials may be called spintharogenic. Good crystals of pyrite are an excellent brassy yellow color, leading fools to mistake it for gold. However, it is hard and light, not soft and heavy, so it is easily distinguished from gold. In small flakes, however, it could be deceiving, and especially because it is very often associated with gold.
Pyrite crystallizes in the cubic system, and its crystals are typically cubes and pyritohedrons. A pyritohedron has 12 pentagonal faces, but the pentagons are not regular, so the solid is not a dodecahedron. Crystals do not have 5-fold axes. The cube faces are usually striated, each face at right angles to the neighboring faces. Hardness, 6-6.5, and density 4.8-5.1 g/cc. When heated, sulphur is driven off and the iron oxidized to magnetite. Marcasite is orthorhombic instead of cubic, but the same substance. Marcasite is a whiter gold color. Pyrrhotite, a third sulphide, is closer to FeS. It is metallic bronze or brown-colored, softer (H = 3.5-4.5) and a bit lighter (4.40-4.65 g/cc) than pyrite. Notably, it is magnetic, probably ferrimagnetic. Its crystals are hexagonal. Pyrrhotite often contains nickel (as at Sudbury, Ontario) and is one of the most important ores of that metal.
Pyrite is a good source of sulphur, but not a good source of iron because of the sulphur, which ruins iron and is hard to separate from it. It has been used for the manufacture of sulphuric acid. Copperas, the sulphate, is obtained by its oxidation. Mineral copperas often accompanies pyrite as a weathering product. The "Sparta dollars" of southern Illinois are thin, round, radial pyrite crystals deposited in the bedding planes of shale. Pyrite is also found in coal, where it adds unwelcome sulphur to the fuel.
Magnetite may be the most important ore of iron. It is found at Kiruna, Sweden, and in other regions of ancient and metamorphic rocks. It (rarely) forms beautiful shiny black octahedral crystals, as well as rhombododecahedrons. It is hard, 5.5-6/5 and rather heavy, d = 5.18 g/cc. It dissolves in hydrochloric acid, and, of course, is strongly magnetic. Lodestone is a magnetized lump of magnetite that attracts iron. Lodestone is found at Magnet Cove, Arkansas, among other places.
Hematite and limonite are ferric oxide, Fe2O3. In massive form, hematite is black, but when finely divided, red. There is an earthy variety of hematite that is brick red and a good paint pigment. It was called reddle and used to paint distinguishing marks on sheep. Reniform hematite looks like beef kidney, with metallic lustre. It is usually the product of oxidation of other iron minerals, often with secondary enrichment. The exhausted rich hematite ores of the iron ranges of Minnesota, Wisconsin and Michigan were formed from iron silicates and and carbonates of early sedimentary origin. The Clinton iron bed of Alabama is also secondary hematite, as are the Brazilian ores.
Limonite is colloidal hydrated ferric oxide, yellow to brown in color. It is light, density 3.6-4.0 g/cc. Used as paint, limonite is known as ochre (see below). It is widely distributed, as in the Jurassic ores of eastern England (no longer exploited). It is a supergene concentration of iron from sedimentary rocks. Colloidal materials were long called amorphous, but they are actually microcrystalline. Goethite is crystalline hydrated ferric oxide, FeO(OH), much like limonite but crystalline (orthorhombic). It is brownish-black, yellowish or reddish. It was found in Cornwall, Alsace-Lorraine (the "minette" ores), Altenberg in Saxony, Lake Onega in Russia, and Jackson Iron mine, Michigan. Goethite was named in honor of the poet and scientist J. W. von Göthe (1749-1832).
Bog iron ore is limonite or goethite, deposited with the aid of iron bacteria in anaerobic swamps. The iron is carried in by waters containing CO2 as soluble bicarbonates. The organic matter reduces it to oxides, which make characteristic iridescent patches on the water, then precipitate on the bottom of the marsh to form an iron-rich layer. It was smelted at Lynn, Massachusetts with oyster shells and charcoal to be hammered into bars to be traded for slaves in Africa, which were sold in the Caribbean for sugar to be brought to New England for fermentation and distillation into rum to be sold to the Indians, making the fortunes of Boston and Providence. The Lynn ironworks have been reconstructed, but with questionable fidelity.
Ferric oxide is the basis for many pigments of earthy colors, generally through forms of the minerals hematite and limonite, but also through the weathering of sandstones containing an iron cement, or of ferruginous shales. The most familiar color is ochre, also known as raw sienna or oxide yellow. To me, it is a tan, not a bright yellow like cadmium yellow. Burnt sienna is darker and redder, perhaps a tuscan red. Raw umber is definitely brown, and burnt umber a dark brown that is called Vandyke brown. The color names are drawn from the ferruginous earths of Siena and Umbria. Ingredients other than ferric oxide, such as the manganese in sienna earth, may give characteristic shadings of color. Colors are notoriously difficult to name and describe, so a good color book is a great help.
The iron group are the only metals that fall from the sky. There is a lot of débris in space that enters the earth's atmosphere at 10-30 km/s relative velocity (much of this is the earth's orbital velocity of 30 km/s). These particles, mostly microscopic, cause the trail of a meteor. A lot of these are cometary particles, ices and dust, but these never reach the ground, burning up between 50 and 150 km altitude, roughly the domain of the ionosphere. A bright magnitude-0 meteor is less than 8 mm in diameter. Millions of meteors burn up in the atmosphere every day, mostly unseen. I make it that they add about 15 kg a year to the earth, but an astronomy text says 10,000 tons a year, which I believe is only enthusiasm and a missed decimal point. The odd large meteorite could put a spike in the average, of course. The larger lumps, of which there are few, reach the ground before burning or blowing up, and are called falls, or meteorites. Only Mrs. Hodges of Sylacauga, Alabama has been injured by one, on 30 November 1954. 92% of the falls are stony meteorites, 6% iron meterorites, and 2% stony-irons. The stony meteorites are mostly chondrites, which contain characteristic small glassy spheres. The rest are carbonaceous chondrites, containing volatile matter, and a few achondrites that seem to have been heated to a high temperature. The composition of stony meteorites is very much like that of olivine, 36 O, 23 Fe, 18 Si and 14 Mg. The remaining 9% is very miscellaneous. The average composition of olivine is 38 O, 28 Fe, 17 Si and 18 Mg.
Iron meteorites are nearly pure iron-group metals: 90.7 Fe, 8.5 Ni, 0.6 Co is an average composition. The remaining 0.2% is negligible. They are the most often picked up, since they have a distinctive appearance, unlike the stonies, which look just like stones. When sliced, polished and etched they show the Widmanstätten pattern that shows they cooled slowly. In studying them, Widmanstätten originated metallurgical microscopy. Meteorites are not cometary rubbish; astronomers say they look like the fragments of planetoids like asteroids. The composition of meteorites suggests the composition of the earth: a mantle of olivine covering a ball of iron group metals. The volume ratio of mantle:core is 82:17, not too far from the ratio of stony:iron falls of 92:6.
The magnetism of the iron group of metals is a rare and remarkable property. It is not due to any inherent magnetic propensities of the atoms, but to the structure of the metal. Other substances with similar structures also have similar magnetic properties. The properties that we will explain are called ferromagnetism, antiferromagnetism and ferrimagnetism. All three are basically similar, but have different external expressions.
A magnetic field H is created by electric currents. It exerts forces on a moving charge q given by F = (q/c)v x H. Here the charge q is in esu, c is the speed of light, about 3 x 1010 cm/s, and the magnitude of the magnetic field H is in oersted, which is numerically equal to the magnetic flux density in gauss. In space, there is no difference between field and flux density. Wherever there is a magnetic field, there must be moving charge somewhere to produce it.
An electron moving as in a Bohr atom around a nucleus represents such a current, which produces a magnetic field. If q is the charge, and v is its orbital velocity, then the average current in an orbit of radius r is qv/2πrc. The product of the current and the area of its orbit is called the magnetic moment μ of the current. Hence, μ = qvr/2c = q(mvr)/2mc = (q/2mc)(mvr) = (q/2mc)j, where j is the angular momentum of the mass m. This is quite a general result, and the quantity in parentheses is called the gyromagnetic ratio. The orbital motion of the electron causes a magnetic moment μ = -(e/2mc)j antiparallel to the angular momentum.
The deBroglie wavelength associated with a momentum p is λ = p/h, where the dimensions of Planck's Constant h work out to erg-sec. The circumference of an orbit of radius r is 2πr, so if an integral number of wavelengths is to fit into it, 2πr/λ = n, an integer. This demands that the angular momentum be an integral multiple of h/2&pi: j = n(h/2π). This means that the magnetic moment will be quantized in multiples of eh/4πmc, which is called the Bohr magneton, μB, about 0.927 x 10-20 emu.
A magnetic moment μ in a magnetic field H is acted upon by a torque tending to turn it in the direction of the field. The energy function that yields this torque on differentiation with respect to the angle is U = -μ·H. The energy differences resulting for various orientations of the atomic magnetic moments should appear in measurements of the wavelengths emitted and absorbed by the atoms, and indeed it does, especially in observations of the Zeeman Effect, when an external magnetic field H is applied.
These measurements (and others) revealed a surprising fact: the electron itself must be regarded as possessing a magnetic moment that interacts with the orbital magnetic moment, as well as an angular momentum. These facts are not consistent with the view of an electron as a point particle, but show that it must have internal structure. Dirac's relativistic theory of the electron showed how this occurs. The electron has an angular momentum, or spin of one-half unit, j = h/4π, and a magnetic moment of one Bohr magneton. Therefore, the electron is twice as effective in turning angular momentum into magnetic moment. The factor 2 is called the electron g-factor. Actually, it is very slightly different from 2, and the tiny difference was exactly explained by the theory of quantum electrodynamics, showing that we really do know a lot of what is going on. The spin and g-factor of the electron have no classical analogues.
Closed subshells of electrons have zero angular momentum, hence zero magnetic moment. All the magnetic moment of an atom is due to the electrons in unfilled subshells. The transition metals usually have an unfilled d-shell, so they usually have magnetic moments. The orbital angular momentum of an electron that takes part in bonding, as in metals, is usually quenched, meaning that it vanishes, along with any magnetic moment, in the quantum-mechanical state. The other electrons may have a magnetic moment. In a crystalline solid, each atom then has a magnetic moment that can rotate freely. When an external field is applied, the moments tend to line up with it, and this is opposed by thermal agitation. The result is paramagnetism, seen in many substances. The net magnetic moment is proportional to the field, M = χH. The magnetic susceptibility χ is always quite small. Gases behave in a similar manner; oxygen is paramagnetic. If the atom has no magnetic moment, the application of an external field produces a small magnetization in the opposite direction, called diamagnetism, which is even smaller than paramagnetism.
If there are lots of magnetic moments, then when a magnetization is created in a certain direction, there is a field at any lattice point due to all the magnetic moments at other lattice points. If the crystal is cubic, or if the moments are at random points, as in a gas, then this extra field is (4π/3)M. Since it is in the direction of M, it acts to strengthen the magnetization. Should it be strong enough, it will cause all the moments to snap over into a single direction spontaneously, without the application of any external field. Alas, it is never strong enough to do this in any paramagnetic substance.
In iron metal, there is a similar interaction that is strong enough to cause all the moments to snap into a single direction. The same occurs in cobalt and nickel. This cannot be the polarizing field we have just mentioned, since it is not strong enough. What happens is that the same electrons that produce the magnetic moments are involved in the metallic binding, and the orientation of the spins of the electrons affect the binding energy of the metal. This is a much stronger interaction than the magnetic interaction of the moments, so it can bring about the desired result. The phenomenon of magnetostriction is evidence for this; when iron is magnetized, its shape and size may change slightly because of the coupling of the electron spins and the binding.
In iron, each atom has five d-orbitals which must accommodate six electrons. Linear combinations of the atomic orbitals are used to generate the crystal orbitals, and then the states are filled in order of energy. Some of these orbitals are the metallic binding electrons, and some are more or less located on the ions. In iron, 0.72 electron is devoted to the delocalized metallic binding on the average. To see how the spins affect the energy as electrons are added to the other orbitals, we can look at the helium atom. The two electrons are in the first approximation assigned to hydrogen-like orbitals in an average potential, as if they did not repel one another. Then, the energy of the actual states is found by perturbation theory, using two-electron product states that have been properly antisymmetrized. It is a requirement that any multi-electron state must change signs if the coordinates of the two electrons are interchanged. If the two orbital states are the same, then this can be done if the spins are opposite. If the spins are the same, the state vanishes when an attempt is made to antisymmetrize it, since the states are identical and no linear combination of them can be made to be antisymmetrical. This is called the Pauli Principle, and is a consequence of the exact identity of electrons.
In helium, the electrostatic interaction energy between the electrons is e2/r12, where r12 is the distance between the electrons. If the electrons are farther from each other, then the energy is lower. Grinding through the perturbation theory, the resulting energies depend on integrals like J = ∫ f(1)g(2)(e2/r12)f*(1)g*(2) dv1dv2 and K = ∫ f(1)g(2)(e2/r12)f*(2)g*(1)dv1dv2. There is no trick here; these are just the usual "matrix elements" used in perturbation theory. J is called a coulomb integral and K is called an exchange integral. It should be clear that there are no physical exchanges either going on or implied; it is just the way it works out with antisymmetric states made of products of one-electron states. This assignment of electrons to orbitals results in two states, one of which has the electron spins opposite and energy J + K, the other of which has the electron spins the same and energy J - K. The energy is lower in the second case because the electrons are farther apart on the average than in the first case. This makes triplet states lower in helium, parallel spin states lower in iron.
The parallel spin states are lower in energy because of the effect on the electrostatic energy, not from any magnetic interactions of the spins. This is a very common result, and holds because the electrostatic interaction is very much stronger than the magnetic. Before this was explained on the basis of quantum mechanics, Weiss postulated a fictitious magnetic field that became known as the Weiss field that would cause the magnetic moments to lock into parallelism. There is no such field, of course, and we have just explained why it looked as if one existed.
The saturation magnetization of iron at 0K is 1752 emu (22,000 gauss). In a cubic centimeter of iron, there are 6.02 x 1023(7.86/55.85) iron atoms. The magnetic moment per atom is found by dividing the total moment by the number of atoms, or 2.23 x 10-20 emu. This is just a little more than two Bohr magnetons, so it appears that about two electrons are effectively unpaired at each atom. For cobalt, the number is 1.72, and for nickel 0.61. If we start with six electrons and five d-orbitals, then two electrons are paired in the lowest crystal d-orbital, two electrons are parallel in the two highest crystal d-orbitals that give the crystal binding and no net magnetic moment, leaving the two middle d-orbitals for one electron each. The fractional numbers quoted above show that there is no integral correspondence of electrons and atom orbitals, so the complete picture must be more complicated. The next atom after nickel, copper, will have no unpaired electrons and cannot be ferromagnetic. There is also no trace of ferromagnetism in the palladium and platinum groups of metals in the next two periods, so we see what a fluke it is to be ferromagnetic.
It can happen that the exchange integral is negative. In this case, the two states reverse their energy order, and the moments are antiparallel in the stable case. This often occurs in oxides, such as FeO, CoO, NiO and MnO. These are face-centered cubic lattices, which can be divided into two sublattices, such that every member of lattice A is surrounded only by members of lattice B, and vice versa. Exchange integrals can be written for A-A, B-B and A-B interactions. The A-B interactions are usually much stronger than the A-A and B-B, and this causes the minimum energy to occur when the magnetic moments on both the A atoms and the B atoms are all in the same direction, but in opposite directions on the A and B atoms. The net moment depends on the difference of the moments on A and B, which is zero, and we have antiferromagnetism.
If the A and B atoms have different moments, then there will still be a net moment when they are antiparallel, and the material will be spontaneously magnetized. This is called ferrimagnetism. Ferrimagnetic materials often crystallize in the spinel structure. Spinel is MgAl2O4, consisting of Al-O octahedra with Mg in the tetrahedral voids between the octahedra. Each Al is surrounded by four O's in a plane, of which it has a quarter interest in each, and one above and below, in which it has a half interest, so the unit is AlO2-. In the general spinel structure, the place of the Al is taken by a trivalent ion, and the place of the Mg by a divalent ion. If the trivalent ion is Fe+++, we have a ferrite. Ferrites are spontaneously magnetized, like a ferromagnetic material, but have no metallic binding and low electrical conductivity. This means that they can be used at high frequencies, where eddy currents make the use of iron impossible. In their applications, they act just like a ferromagnetic material.
The most interesting ferrite is magnetite, Fe3O4. Half of the ferric iron is on the tetrahedral interstices of the spinel structure, the other half of the ferric iron and all the ferrous iron in the octahedral interstices. The moments of the ferric iron, 5 μB, cancel, leaving the 4 μB of the ferrous ions. Here we can count the electrons and states, since there are no crystal orbitals. Each unit cell contains 8 ferrous ions, so the moment per unit cell will be 8 x 4 Bohr magnetons. The experimental result is 8 x 4.07, so the agreement is excellent.
The earliest experiences with magnetism involved the lodestone, which was magnetite, named for its ability to attract bits of iron. Therefore, magnetism began with ferrites!
Now we must explain how a spontaneously magnetized substance exhibits the magnetic properties familiar to us. If all the moments in a macroscopic sample were aligned, a very strong external magnetic field would be produced. This magnetic field represents a great deal of energy. If the moments were rearranged to reduce this external field, then the overall free energy would be reduced and the state more stable. This could be done, for example, by dividing the sample into two equal parts magnetized in opposite directions. To do this, a boundary between the two regions is required, where the moments reverse directions, and this boundary must absorb some energy. Therefore, the region will tend to divide into regions of different directions of magnetization so long as the net energy saving, field-boundaries is positive. The regions of uniform magnetization are called domains, and the boundaries domain walls or Bloch walls. An individual crystallite may be a single domain or, more usually, several. The domains are arranged to reduce the external magnetic field to as low a value as possible, as shown in the diagram. Normally, no magnetic field can be detected around the sample.
When we apply an external magnetic field, those domains magnetized in the direction of the field are energy-favored over those magnetized in the opposite direction. The favored domains then expand and the expense of the unfavored, and a net magnetization results. The domains can expand by elastic movements of the domain walls at first, then as the field is increased they may jump over obstacles caused by crystal imperfections, and when the domain walls have moved as far as they can, the magnetization directions of the domains are forced into the direction of the applied field. The result is the familiar S-shaped magnetization curve of flux (H + 4πM in gauss) against magnetizing field (H in oersted). If the external field is removed, the domain magnetization returns to easy directions, and the domain walls spring back as well as they can. The magnetization decreases to the remanence, and the sample has become a permanent magnet. If now an external field is applied in the reverse direction, the magnetization is reduced to zero when the field has the value of the coercive force, then increases in the reverse direction as it originally did in the other direction. We are tracing the hysteresis curve of the iron. The material does not return to the unmagnetized state except by careful manipulation. All the magnetic applications of the material depend on this behavior. The permeability, the ratio of a change in flux to a change in H, is not constant, but may be a thousand times greater than the permeability of space, which is unity.
Permanent magnet materials are designed to offer as many pinning sites for the domain walls as possible. Once magnetized, the domain walls cannot move and the magnetization persists. Alnico V, 8 Al, 14 Ni, 24 Co, 3 Cu, with the remainder iron, is a traditional permanent magnet material. It has a saturation flux density of 12,500 gauss and a coercive force of 550 oersted. Neodymium Iron Boron and Samarium Cobalt are modern sintered materials with excellent properties, except that they cannot stand high temperatures. Sintered magnets can easily be made in odd shapes.
"Soft" magnetic materials, where the domain walls can move easily, ideally make the magnetization a single-valued function of the magnetizing field, so that there is no hysteresis loss when the field reverses repeatedly. These materials are required for transformers and rotating machines. Crystals of pure iron have few pinning sites, so pure iron is magnetically "soft." Pure iron has a saturation flux density of 21,500 gauss and a coercive force of 0.05 oersted. Its maximum permeability is 180,000. Other alloys are designed to have as large a permeability as possible, so that only a small magnetizing field will saturate them. "Mu-metal," 18 Fe, 75 Ni, 2 Cr, 5 Cu, has a saturation flux density of 6,500 gauss, a coercive force of 0.05 oersted, and a maximum permeability of 100,000. It is used for magnetic shielding. "Supermalloy," 15.7 Fe, 79 Ni, 5 Mo, 0.3 Mn, has a saturation flux density of 8,000 gauss, a coercive force of 0.002 oersted, and a maximum permeability of 800,000.
Silicon iron as a magnetic material was developed by Sir Robert Hadfield in England, and was introduced to the United States by the Allegheny Steel Company in 1903. As silicon is added, the iron becomes a better and better magnetic material as its electrical resistivity increases, but it also becomes brittle and difficult to work. At 4.25% silicon, its resistivity is about 60 μΩ-cm, more than 7 times that of pure iron, without impairment of its magnetic qualities. The aim is to produce a steel with the lowest total core loss, eddy currents plus hysteresis. The ultimate strength of this iron is 97.9 ksi, with 5% elongation in the tensile test. At 3.25%, the elongation is still 29%, so this last percent of silicon comes at a price. The saturation flux density of the 4.25% steel is 19,700 gauss. The remanent flux density from 10,000 gauss is 8100 gauss, and the coercive force 0.4 oersted. The maximum permeability is about 7600. This represents an average working condition for the steel used in transformers. Allegheny Steel Company introduced mumetal in 1934. Silicon steel is much less expensive than the exotic alloys.
To reduce eddy current losses, magnetic cores are made of thin laminations, insulated from each other. The currents would flow normal to the laminations, so their paths are made to be of high resistance by this means. Eddy currents are, of course, just the currents that flow in conducting materials as the result of electric fields created by changing magnetic fields, according to Faraday's Law. For direct current excitation, there are no eddy currents. Transformer steel is furnished in thin sheets, from which the laminations are punched, and then assembled to form the magnetic cores.
Living cells oxidize glucose with atmospheric oxygen, and release carbon dioxide as a result. A cell bathed in water can easily dispose of the carbon dioxide, since it diffuses through the cell wall to the water in which it is very soluble, 1800 cc per litre of water. Oxygen diffuses into the cell from the water where it dissolves to the extent of 50 cc per litre. This is a small, but sufficient concentration. More oxygen would probably be deleterious. A small cell is a colloid, dominated by surface area, not volume. A cell must be small for this strategy to be successful, so most cells and simple organisms are microscopic.
When cells associate in a multicellular organism, the support of respiration by provision of oxygen and carrying-away of carbon dioxide must be arranged. Coelenterata, with an inside and an outside and specialized cells, set up a flow of water through their body that brings in oxygen, and nutrients, with the fresh water, and discharges carbon dioxide and other waste product with the efflux.
More complex organisms, such as ourselves, consist of a large assembly of cells that must respire, though out of water and packed tightly against each other. To supply oxygen and eliminate carbon dioxide, a circulatory system is required where a fluid transports the substances between the working cells and organs that communicate with the atmosphere, the lungs. In the atmosphere, the partial pressure of carbon dioxide is very low (0.3 torr), and the partial pressure of oxygen is high, 152 torr. If water is circulated, the soluble carbon dioxide would be transferred very well, since it would dissolve easily near the cell, and would evaporate easily when a thin layer were exposed to the air. Oxygen, however, is a different story. Because of its low solubility, an insufficient amount would dissolve across the limited lung area to supply all the cells, who would require an absorbing area equal to their total surface area. Some vehicle is necessary that would absorb oxygen in the required amount in the lungs, and then when carried to the cells, would release it for their use. This is not a simple matter. Something that absorbed oxygen in the lungs would hold on to it at the other end as well. It is necessary to make the vehicle hungry for oxygen in the lungs, and disgusted with it in the tissues, to transport sufficient oxygen for the hosts of cells in the body.
A very intricate and wonderful mechanism has evolved to handle this job. It involves a protein, globin, and a prosthetic group, heme. A protein is a chain of amino acids linked by peptide groups that folds intricately in the presence of water to carry out a chemical task, using its ensemble of amino acid side chains and its structure to that end. The purpose of globin is to hold and manage heme groups that are the actual oxygen carriers. A simple globin is myoglobin, in which the ingenious mechanism of the heme group is used to store oxygen in muscles, for instant release when needed. The transporter is hemoglobin, which consists of four myoglobin-like units carefully arranged and mechanically connected. This protein is allosteric, meaning that changes occurring at one point in the molecule have effects at distant points.
The purpose of the allosterism is to make binding of one oxygen at one of the four heme groups help the bonding of additional oxygen at the other heme groups. Oxygen bonds to hemoglobin cooperatively. This mechanism works in reverse when the oxygen is released. Hemoglobin with oxygen bound to its four heme groups is oxyhemoglobin, and without oxygen, it is deoxyhemoglobin. Hemoglobin not only carries oxygen, but also carbon dioxide and hydrogen ion, H+, so it responds to the pH of its environment and the CO2 concentration as well as to the partial pressure of oxygen.
In the lungs, the partial pressure of oxygen is high, the partial pressure of carbon dioxide is low, and the pH is relatively alkaline. All these factors encourage deoxyhemoglobin to become oxyhemoglobin. The hemoglobin is contained in erythrocytes, red blood cells, that communicate readily through their cell walls with the blood plasma. They are in constant circulation through the body, reaching the most distant cells. Activity of a cell, especially muscle cells that are hungry for oxygen, produces carbon dioxide and acids, such as lactic acid, which make the pH acidic. The hemoglobin adds CO2 and responds to the increased acidity and low partial pressure of oxygen by actively dumping its oxygen. The release of one oxygen makes the release of the others easier, and the oxygen pressure in the region is restored, so oxygen diffuses to all the cells in the vicinity. The whole procedure is quite automatic, and generally works very well indeed. The sensitivity of hemoglobin to CO2 and H+ is called the Bohr effect, after Christian Bohr, who discovered it in 1904.
Free hemoglobin does not have these properties; its oxygen affinity is like that of myoglobin. Within an erythrocyte, it is provided with BPG, 2,3 biphosphoglycerate, which lowers the partial pressure of oxygen at which half the hemoglobin is oxyhemoglobin from 1 torr to 26 torr. This means that a lowering of the oxygen partial pressure to 26 torr will release half the oxygen from oxyhemoglobin, so the cells will not have to gasp for air. The effect of BPG was discovered by Reinhold and Ruth Benesch in 1967. Fetal hemoglobin, hemoglobin F, has a higher oxygen affinity than hemoglobin A. This enables the fetus to receive oxygen across the placenta. At birth, it is replaced by hemoglobin A for normal respiration through the lungs. Hemoglobin F has less affinity for BPG, and so more affinity for oxygen, than hemoglobin A.
A very wonderful thing is that all of this is now understood in detail, even the mechanism of the Bohr effect, since the structure of proteins can be worked out by X-ray scattering. John Kendrew worked out myoglobin in 1957, and Max Perutz hemoglobin in 1959, after 23 years of effort. Myoglobin is 4.5 x 3.5 x 2.5 nm and contains about 141 amino acids and one heme group. Hemoglobin is about 5.5 nm in diameter, and contains about 574 amino acids. The methods of protein synthesis are now known as well. An enzyme travels down a DNA double helix and makes a single-strand messenger RNA. Another enzyme starts like a zipper at one end, and travels down the mRNA, making a protein as it goes like a strip from a labeling machine. This protein then curls up, grabbing a heme group, and associates with three others to make hemoglobin. This takes place in bone marrow. There are several different kinds of chains, which make a variety of hemoglobins. The predominant adult human hemoglobin is hemoglobin A. Errors in the DNA that make defective protein chains cause recognizable diseases, like sickle-cell anemia, when the hemoglobin does not function as intended.
The structure of heme is shown at the right. The ferrous ion is at the center, and is the active ingredient. Only ferrohemoglobin can bind oxygen; ferrihemoglobin cannot. The double bonds give rigidity, since there is no free rotation about them. The central part, formed of four pyrrole rings with the nitrogens holding the iron loosely, is a rigid disc. Each of the side chains can rotate about a single bond, and have rigid "hooks" that can lock them into the globin that holds the heme. Oxyhemoglobin is transparent to light of wavelength greater than 580 nm, so it appears bright red, while deoxyhemoglobin absorbs a little in this band, appearing darker red. Both absorb strongly everything of less than 580 nanometer wavelength.
When the globin winds around the heme, it places a histidine next to the iron on one side that bonds to it. The amino acid histidine is shown at the right. An H has come off the COOH carboxyl group typical of an organic acid and attached itself to the N, as usually occurs in solution. This end is part of the globin chain. On the other side there is a second histidine, but it does not bond to the iron. When the iron moves in and out slightly from its position, the motion is transmitted to the histidine bound to it, which moves a section of the protein that interacts with the other proteins of the hemoglobin to make the bonding of oxygen more or less favorable. This is the mechanism of the allosteric effect. The iron ion is a little on the bound histidine side of the heme disc in dexoyhemoglobin. When it bonds to an O2 molecule, it moves into the plane, producing the allosteric effect. The axis of the oxygen molecule is at an angle (it binds to one of the lone-pair electrons of the oxygen). This is shown in the diagram to the right.
The iron also bonds strongly to CO, and prefers to be end-on, where all the electrons are. The body has an internal problem with CO, since it is formed by the recycling of heme at the end of the 120-day life span of an erythrocyte. There is enough CO formed to block all the hemoglobin in the blood after a while, so something must be done. The other histidine, the one not bound to the oxygen, stands just above the iron ion, and will not allow CO to bind end-on, but forces it to the side. This reduces the problem enough that only about 1% of the hemoglobin is blocked by endogenic CO. Oxygen normally binds at an angle, so the histidine does not bother it. Once CO has bonded with hemoglobin, it is very difficult to pry it off. Fortunately, few other molecules will bind to the heme.
A heme group is also present in cytochromes, proteins which transfer electrons to O2 in metabolism, converting them to H2O as one of the end products of oxidizing food. This heme is slightly different than that in hemoglobin. Cytochrome oxidase, the enzyme catalyzing this reaction, also contains a heme, called heme A.
Chlorophyll has a structure very similar to heme, except that the metal held by the four nitrogens is magnesium, and one of the attached chains is rather long. This molecule absorbs in the blue and red, so is green by transmitted light, the familiar green of photosynthetic plants. It is located in small bodies called chloroplasts, relics of once-independent cells, where it absorbs the energy of light to supply the energy necessary for making carbohydrates out of carbon dioxide and water, supporting all the life on earth.
Another similar molecule is vitamin B12 or cobalamin, in which the heme-like molecule corrin binds a cobalt atom with the four nitrogens. This is the business site of coenzyme B12, which is necessary in purine synthesis and other duties. In coenzyme B12, one of the cobalt bonds is directly to a carbon, the only example of a carbon-metal bond in all biochemistry. Cobalamin can be synthesized only by microorganisms, typically anaerobic bacteria. It must be obtained in the diet, or from intestinal bacteria. Only about 10 μg/day is required by a human. It is so widely available that a deficiency is rare. The body takes special care to make chemicals that aid its absorption in the small intestine. If these chemicals are lacking, the result is serious pernicious anemia, from the resulting scarcity of coenzyme B12. The cobalt atom can be in a +1, +2 or +3 oxidation state, and all are important in the actions of vitamin B12. The cobalt in cobalamin is successively reduced to +2 and then +1, when it combines with ATP to form 5'-deoxyadenosylcobalamin, which is the coenzyme B12 essential for cell chemistry.
Iron also appears in the iron-sulphur proteins which are essential to aerobic life. The enzyme aconitase occurs in the citric acid cycle that oxidizes carbon to CO2 in mitochondria, rearranging the citrate to isocitrate at the beginning of the cycle so it can be further processed. The prosthetic group in aconitase is the iron-sulphur group shown in the diagram at the left, composed of interpenetrating iron and sulphur tetrahedra. It is bound tetrahedrally to four cysteine residues in the enzyme. Iron-sulphur proteins also play a role in nitrogen fixation.
Iron and cobalt, therefore, are essential to life, and especially for animals with red blood. It is curious that molybdenum is also essential for the fixation of atmospheric nitrogen by bacteria, since it plays a role in a necessary protein. This protein is an enzyme converting N2 to NH4+. Very little is required, but it is required. Such trace nutrients need not be supplied in any quantity greater than the need, and are usually amply available to plants and animals in their normal surroundings. The "supplements" filling the shelves in health stores and supermarkets are surplus to requirements and totally useless, the result of a combination of ignorance of nutrition with thirst for money. In fact, too much of a trace nutrient, especially metals, may be toxic. Some nonmetals, such as iodine to support thyroid function, fluorine to strengthen tooth enamel, or boron for plant growth are necessary in small amounts, but in larger amounts are also toxic. Unlike the trace metals, they may actually be deficient in the environment, and require supplementation. Iron, of course, is more than a trace nutrient, but is effectively recycled by the body and only needs to be topped up.
C. Kittel, Introduction to Solid State Physics, 2nd ed. (New York: John Wiley & Sons, 1956. Chapter 15.
L. Pauling, General Chemistry, 3rd ed. (New York: Dover, 1988). pp. 578-589, pp. 678-693.
L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics (New York: McGraw-Hill, 1935). pp. 210-221. The helium atom and exchange integrals.
L. Stryer, Biochemistry, 3rd ed. (New York: W. H. Freeman, 1988). Chapter 7. Myoglobin and hemoglobin.
Composed by J. B. Calvert
Created 13 December 2002
Last revised 6 December 2003