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The extraction, processing and study of metals and their alloys.

Historical formulation name; composition is identified by pharmacopoeial edition.

At sufficiently high temperature and density, forward and inverse nuclear reactions can balance so that abundances are determined by thermodynamic conditions, nuclear binding and conserved quantities. Silicon burning approaches such an equilibrium among iron-group nuclei. Weak reactions can separately change the electron fraction, so the favored mixture need not be pure iron.

The Mott two-current model treats the two spin populations as parallel conduction channels when spin-flip scattering is weak. Thus $\sigma ={\sigma }_{\uparrow }+{\sigma }_{\downarrow }$ and ${\rho }^{-1}={\rho }_{\uparrow }^{-1}+{\rho }_{\downarrow }^{-1}$. Light, broad-band carriers conduct efficiently; scattering into narrow $d$-like states relaxes their current. In a simple spin-conserving $s$–$d$ picture,In copper, the filled $d$ bands supply little final-state phase space at $E_F$, so both spin channels have low resistivity. In cobalt, the nearly filled majority $d$ band suppresses majority-channel scattering, while minority $d$ states remain available. The stated iron reversal corresponds to stronger scattering-weighted majority-channel phase space: its majority $d$ band is not closed as in cobalt. Band filling, exchange splitting, velocities and scattering matrix elements set this scattering-weighted spin-channel asymmetry; majority population alone does not select the better conductor. The given iron ordering is a material/scattering input, not a universal consequence of the two-current postulate. Different impurities and interfaces can change the asymmetry.^[ref]

RNA couples iron availability to the production of proteins that acquire, store, export and use iron. The clearest mammalian mechanism uses structured iron-responsive elements in untranslated regions and iron-regulated binding proteins. The RNA element encodes a regulatory address and its position determines the response; the main sensing machinery is protein-based, so this system should not be described as an autonomous iron-binding RNA riboswitch.

An iron-responsive element is a stem-loop with conserved sequence and structural features recognized by iron regulatory proteins. At low available iron, RNA-binding IRP1 and IRP2 are active. IRP1 is bifunctional: an iron–sulfur-cluster-containing form acts as cytosolic aconitase, whereas loss of the functional cluster permits high-affinity RNA binding. Biochemical disassembly of its cluster connected these two activities directly.^[ref] IRP2 does not use the same aconitase switch. Under iron- and oxygen-replete conditions, the FBXL5 ubiquitin-ligase pathway promotes IRP2 degradation; instability of the iron-sensitive FBXL5 regulator during iron depletion helps preserve IRP2.^[ref] Redox and oxygen conditions can therefore modify the relation between total cellular iron and RNA-binding activity.

The canonical 5′ example is ferritin mRNA. Binding of an IRP near the cap prevents efficient recruitment of the translation-initiation machinery, lowering ferritin synthesis when iron is scarce. This avoids committing a limited resource to storage. When iron is plentiful, reduced IRP occupancy releases repression, allowing more ferritin to store iron and limit its reactive pool. Deletion analysis and transfer of a synthetic ferritin element to another reporter established a cis-acting signal sufficient to confer iron-responsive biological translation.^[ref] This response can change biological translation before a major change in transcript abundance occurs.

At the 3′ end of transferrin receptor 1 mRNA, multiple IREs participate in a stability-control region. IRP binding during iron shortage protects the message from destabilization, increasing receptor production and iron uptake. At higher iron, loss of protection permits more rapid decay and reduces uptake. John L. Casey and colleagues showed that the transferrin-receptor 3′ region conferred iron-regulated RNA abundance and that isolated elements placed in a 5′ reporter context instead conferred translational control.^[ref] Thus similar recognition chemistry supports opposite outputs through different transcript positions and associated machinery.

The network also adjusts use and release. A 5′ IRE in erythroid ALAS2 mRNA couples synthesis of a haem-pathway enzyme to iron availability, helping limit production of porphyrin precursors when metal incorporation is restricted.^[ref] IRE-containing ferroportin transcripts can reduce iron export through translational repression during deficiency.^[ref] These are transcript-specific rules, not universal predictions from a gene name: alternative transcripts can lack an IRE, and ferroportin is also regulated at the protein level by systemic signals. The central RNA logic coordinates uptake with conservation, rather than simply maximizing the expression of every iron-related protein.

Regulation beyond the mammalian IRE system illustrates a broader eukaryotic principle. In budding yeast, iron deficiency induces the RNA-binding regulator Cth2, which recognizes AU-rich elements in selected 3′ regions and accelerates degradation of messages encoding iron-consuming metabolic functions. This remodels resource allocation rather than protecting an uptake message. Sergi Puig and colleagues combined expression and RNA-turnover analysis with RNA-element recognition to establish targeted degradation during deficiency.^[ref] It is therefore misleading to generalize that iron shortage always stabilizes iron-related RNA: the direction depends on the transcript and its physiological role.

To establish these mechanisms experimentally, compare iron chelation with iron restoration, measuring available iron, IRP–RNA binding, transcript half-life and newly synthesized protein separately. Match reporter transcription and mutate recognition features without inadvertently changing general RNA stability. For a stem-loop, a compensatory paired mutation helps distinguish loss of structure from loss of a specific sequence contact. Electrophoretic binding assays with purified protein, cellular crosslinking and rescue with functional versus binding-defective IRP variants connect recognition to regulation. RNA-abundance measurements alone cannot establish translational repression, and chelators can cause broad stress, so unrelated control reporters and viability measurements are needed. The decisive principle is position-dependent RNA control: low iron can repress storage and export biological translation while preserving uptake RNA and reducing expendable iron-consuming programmes.

The terminal nitrosyls are linear in both proposed electron-precise structures; the formal M–M bond orders are V–V double and Fe–Fe single. Use three-electron terminal linear NO donors, three-electron ${\mu }_2$-NO bridges, and five-electron neutral Cp donors in covalent counting.

For the vanadium dimer the two metal fragments together containA metal–metal bond of order $b$ adds $b$ to each local count, so $32+2b=36$ gives $b=2$ and 18 electrons per V. For an ionic cross-check, Cp is $-1$, each linear terminal NO is conventionally NO${}^{+}$, and each bridge is represented as NO${}^{-}$. ThusEach V then has $4+6_{\mathrm{Cp}}+2_{\mathrm{terminal}\mathrm{NO}}+4_{\mathrm{two}\mathrm{bridges}}+2_{\mathrm{V}=\mathrm{V}}=18$ electrons.

The iron species is monoanionic, and ${\mathrm{L}}^{-}$ is a pyrazolate bridge binding through its two nitrogens. This is a four-electron donor overall in ionic counting, or three overall in neutral counting. The carbonyl bridge supplies two electrons overall. The covalent fragment total is consequentlyTherefore $34+2b=36$ gives $b=1$. In the formal NO${}^{+}$ description,Each Fe receives $10+4_{\mathrm{two}\mathrm{NO}}+2_{\mathrm{pyrazolate}\mathrm{N}}+1_{\mu \mathrm{CO}}+1_{\mathrm{Fe}-\mathrm{Fe}}=18$ electrons. The negative formal oxidation state follows from the chosen nitrosyl assignment and the overall charge; omitting that charge would change the count.

Bent terminal NO ligands would supply fewer neutral-count electrons and demand much higher formal M–M bond orders to attain 18-electron counts. The linear assignments give the ordinary double and single bond solutions. Since NO is a non-innocent ligand, these oxidation states are formal bookkeeping limits, not measured metal charges; actual nitrosyl bending and M–M bond strengths require structural and spectroscopic evidence.^[ref]

For the doubly bridged tetracarbonyl, each iron has one terminal carbonyl ligand, two bridging carbonyl ligands and one cyclopentadienyl ligand. Neutral electron counting gives $8+5+2+2=17$ before direct bonding, so a single Fe–Fe bond gives 18 at each iron. For the triply bridged tricarbonyl, each iron instead has $8+5+3=16$ before direct bonding; formal completion to 18 requires a double Fe–Fe bond. Equivalently, the total fragment counts before metal–metal bonding are 34 and 32 respectively.The increased direct bond order explains the substantial contraction. The pentamethylcyclopentadienyl ligands also alter steric and electronic effects, and bridge geometry changes, so this is not a controlled measurement of bond order alone. Nevertheless, the markedly shorter distance in the less carbonyl-saturated dimer is consistent with stronger direct Fe–Fe bonding. The isolated triply bridged compound was characterized structurally and magnetically in the primary work.^[ref]

iron remains Fe(II), $d^6$, in both states; the change is a spin crossover, rather than a change in oxidation state. At the higher temperature the high-spin complex has $t_{2g}^4{e}_g^2$: four unpaired electrons, $S=2$, andThis matches the observed moment. At low temperature a low-spin complex with $t_{2g}^6{e}_g^0$ has $S=0$ and shows diamagnetism. Cooling switches high-spin $d^6$ to low-spin $d^6$. Emptying the metal–ligand antibonding $e_g$ orbitals strengthens and shortens the Fe–N bonds, accounting for the contraction by roughly $0.2\text{A˚}$.

The octahedral splitting and electron pairing energy must be sufficiently close for both states to be accessible. The low-spin state gains electronic energy, while the high-spin state has greater spin degeneracy and usually greater vibrational entropy because of its softer bonds. The resulting Gibbs free energy balance favors high spin at higher temperature. The two endpoint observations do not by themselves specify hysteresis or transition cooperativity; those require a temperature series. Coupled structural and magnetic measurements distinguish this explanation from a mere bond-length anomaly.

Replace the two chlorides on one ring phosphorus $P_1$ with the two ends of the diiron unit. $D$ has a spiro $P_1\mathrm{F}{\mathrm{e}}_2$ triangle, with an Fe–Fe bond, a $P_1$–Fe bond to each metal and four terminal CO ligands on each Fe. The other two phosphorus atoms retain their $\mathrm{PC}{\mathrm{l}}_2$ groups. Its composition is ${\mathrm{N}}_3{\mathrm{P}}_3\mathrm{C}{\mathrm{l}}_4\mathrm{F}{\mathrm{e}}_2(\mathrm{CO}{)}_8$. In neutral electron counting, each metal has $8_{\mathrm{Fe}}+8_{4\mathrm{CO}}+1_{\mathrm{Fe}-\mathrm{P}}+1_{\mathrm{Fe}-\mathrm{Fe}}=18$.

$E$ has a triangular Fe${}_3$ cluster, one bridging CO, and an adjacent ring N$\to$Fe bond. The two original metals remain bonded to $P_1$ and to one another, and each bonds to the added third Fe. Each Fe bears three terminal CO ligands; one additional bridging carbonyl ligand spans the original Fe–Fe edge. A nitrogen directly adjacent to $P_1$ donates its lone pair to the third Fe. The formula is therefore ${\mathrm{N}}_3{\mathrm{P}}_3\mathrm{C}{\mathrm{l}}_4\mathrm{F}{\mathrm{e}}_3(\mathrm{CO}{)}_{10}$, satisfying $8+5-3=10$ retained CO ligands. The original diagram above gives all metal–metal and metal–ring connections.

The counts are an especially useful structural check. Each original Fe has $8+6_{3\mathrm{CO}}+1_{\mu \mathrm{CO}}+1_{\mathrm{P}}+2_{2\mathrm{Fe}-\mathrm{Fe}}=18$. The added Fe has $8+6_{3\mathrm{CO}}+2_{\mathrm{N}}+2_{2\mathrm{Fe}-\mathrm{Fe}}=18$. Omitting nitrogen coordination leaves the third Fe two electrons short; omitting the bridging CO leaves both original metals one electron short.

In $D$, the two untouched phosphorus sites are equivalent: an $A_{2}X$ phosphorus-31 nuclear magnetic resonance system gives their doublet with integral 2, and the unique $P_1$ triplet with integral 1. The two equivalent nuclei do not split each other. In $E$, coordination of one adjacent nitrogen distinguishes the two sides of the ring, producing three inequivalent phosphorus sites. Each couples to the other two and gives a doublet of doublets in the first-order limit; equal couplings or strong coupling could distort this simple pattern.

The high-frequency infrared spectroscopy bands belong to terminal carbonyl stretching modes. The extra low-frequency band is diagnostic of a strongly backbonded bridging carbonyl ligand. The number of IR bands counts allowed, possibly overlapping normal modes, not individual CO ligands. Formula, 18-electron rule, NMR equivalence and IR together select this model; the historical experimental work independently established diiron spiro rings and triiron products containing both P–Fe and N–Fe bonds.^[ref]

The two remaining partial pressures sum to $200-160=40$ bar. Their ratio therefore gives $p_{{\mathrm{N}}_2}=10$ bar and $p_{\mathrm{N}{\mathrm{H}}_3}=30$ bar. With the ideal-gas activity approximation $a_i=p_i/p^{\circ }$ and $p^{\circ }=1$ bar,The equilibrium constant is dimensionless: pressures enter as ratios to the standard pressure. Blindly substituting pressures in pascals into an unnormalized expression would give a different, incorrect thermodynamic $K$.

The standard reaction enthalpy is $2(-45.90)=-91.80\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ per mole of reaction as written, because the elements are in their reference states. ThusThis calculation uses the supplied constant-enthalpy simplification. At 200 bar, an accurate thermodynamic treatment would use chemical fugacities rather than ideal partial pressures; no chemical fugacity coefficients are supplied. The iron catalyst changes the approach to equilibrium, not its thermodynamic value.

The wording places both dicarbollide cages on the same iron, leaving the second iron outside the cages. The corresponding proposal is $[L_2\mathrm{Fe}\to \mathrm{Fe}(\mathrm{CO}{)}_4{]}^{2-}$, with the first iron sandwiched between the two open ${\eta }^5$ faces and the second carrying four carbonyls. It is not the symmetric arrangement with one cage on each iron, which would contradict the specified single cage-interacting metal site.

The donor fragment $[\mathrm{F}{\mathrm{e}}^{\mathrm{II}}{L}_2{]}^{2-}$ has $d^6+2(6)=18$ electrons; the external neutral $\mathrm{Fe}(\mathrm{CO}{)}_4$ fragment has $8+4(2)=16$. Metal-to-metal donation therefore provides a natural 18-electron acceptor adduct. In covalent-single-bond oxidation-state bookkeeping, the analogous assignments Fe(III)/Fe(−I) give $d^5+12+1=18$ and $d^9+8+1=18$. In either account the whole species has two negative charges. The outside iron can have an approximately trigonal-bipyramidal five-coordinate arrangement when the Fe–Fe direction and its four CO ligands are counted.

The important structural distinction is a bis(dicarbollide) iron donor joined to an exo tetracarbonyl iron acceptor. Formula and electron counting alone do not uniquely fix all carbonyl angles or prove a particular crystalline conformation.

An individual bipyramid is chiral. Matching helicities at the two iron centres give the homochiral $\Delta \Delta$ and $\Lambda \Lambda$ enantiomers, with the three spanning connections winding in opposite senses in the two structures. The idealized molecular framework has a threefold axis but no mirror plane, inversion centre or improper rotation that converts it into itself. Achiral synthesis can give a racemic mixture of these chiral cages; racemic bulk composition does not make each cage achiral. The corresponding experimentally characterized methyl-substituted Fe–Pd bipyramid contains both homochiral enantiomers in its crystal.^[ref]

The idealized cage is chiral, with point group $O$, rather than $O_h$. The eight iron tris-chelate units have the same helicity within one cage; the two enantiomers are all-$\Delta$ and all-$\Lambda$. The fourfold axes pass through opposite Pd face centres, and the threefold axes pass through opposite Fe corners. There are also proper twofold rotations through opposite cube-edge midpoints. These proper rotations preserve the local handedness. Mirror planes, inversion and improper rotations would reverse each Fe propeller and are absent from an individual homochiral cage. The proper cubic group has 24 operations: $E$, $8C_3$, $6C_4$, $3C_2$ along the face axes and $6C_2$ along edge axes. Real conformations and crystal packing can lower this idealized molecular symmetry.

The six diphosphines bind the six Pd centres, occupying two adjacent sites on each and displacing two pyridines per Pd. Reassembly therefore favours the two-connected Pd nodes of the bipyramid instead of the cube's four-connected nodes. The balanced transformation isThus two cages of type 4 and four free metalloligands of type 3 form per cage 5. iron, palladium, ligand and charge balances all close. Strong phosphine chelation drives the donor replacement, while the release of additional discrete species can favour entropy. The analogous conversion is observed experimentally in the cited heterobimetallic system.^[ref]

A material with paramagnetism develops a magnetization parallel to a weak applied magnetic field intensity, with positive magnetic susceptibility and no spontaneous magnetization in its paramagnetic phase. Molecular oxygen is an example; it has unpaired electron spins.

A material with diamagnetism develops an induced magnetization opposing the applied magnetic field, with negative magnetic susceptibility. A closed-shell atom such as helium is an example; its orbital response is diamagnetic.

A ferromagnet has a spontaneously ordered magnetization below its Curie temperature, even in the limit of vanishing applied magnetic field. Iron below its Curie temperature is an example. Different magnetic domains can cancel the net moment of an unmagnetized bulk sample, despite nonzero local spontaneous magnetization.

Using the supplied iron parameters givesAn internal Weiss molecular field depends on temperature through $M(T)$. Its low-temperature saturation estimate uses $M_s=ng{\mu }_{B}J\simeq 1.58\times 10^6\mathrm{A}{\mathrm{m}}^{-1}$:At and above $T_C$ the zero-applied-field magnetization vanishes in this model, so this is a saturation estimate, not the field at $T_C$.

Use the paper's stipulated face-centered cubic lattice, which has twelve nearest neighbours. The saturated one-ion alignment scale isDividing the effective field among twelve equivalent neighbours gives the per-bond exchange interaction scaleTo specify the convention, write the Heisenberg model as $\mathcal{H}=-\mathcal{J}{\sum }_{⟨ij⟩}{\mathbf{J}}_i\cdot {\mathbf{J}}_j$, with dimensionless angular-momentum operators and each bond counted once. Then $g{\mu }_B{B}_e=12\mathcal{J}⟨J_z⟩$, so $\mathcal{J}=3k_B{T}_C/[12J(J+1)]\simeq 11.2\mathrm{meV}$ here. A convention with $-2{\mathcal{J}}^{\prime }$ instead has ${\mathcal{J}}^{\prime }=5.62\mathrm{meV}$. The total saturated interaction energy per ion is $-12\mathcal{J}{J}^2/2\simeq -67.4\mathrm{meV}$; the factor of one half avoids counting each bond twice.

Take ${\lambda }_{\mathrm{Fe}}\simeq 0.1937\mathrm{nm}$ for the unresolved iron $K_{\alpha }$ doublet. The underlying tabulated $K_{\alpha 1}$ and $K_{\alpha 2}$ wavelengths are approximately $0.193604$ and $0.193998\mathrm{nm}$.^[ref]

Using the inferred $a\simeq 0.348\mathrm{nm}$, Bragg's law gives the following approximate cone angles:The exact angles inherit the lattice-parameter uncertainty. Five reflection families are kinematically possible with this longer wavelength: $h^2+k^2+l^2\le (2a/{\lambda }_{\mathrm{Fe}}{)}^2\simeq 12.9$. The next FCC family, 400, cannot satisfy Bragg's law.

A cylindrical Debye-Scherrer camera records paired curved lines where each diffraction cone intersects the film. Both forward and backward cones can be intercepted. The last three families are back reflections here, unlike the rings recorded on the original forward flat plate. Film position is proportional to camera angle along the equatorial circumference, rather than to $L\tan 2\theta$; the incident and transmitted beam holes must also be distinguished from reflections. A sufficiently resolved exposure may separate the characteristic doublet, but the schematic does not claim to predict line intensities.

The printed numerical ratios are about $35$, not about $10$:The qualitative contrast is nevertheless meaningful. FCC aluminium has close-packed glide planes and relatively mobile dislocations. Magnesium also has easy close-packed basal glide, although it lacks enough equivalently easy slip systems for arbitrary room-temperature polycrystal deformation.

BCC iron has no close-packed plane. Its screw-dislocation cores and lattice-friction barrier give much stronger resistance to glide; thermally activated kink motion makes the critical stress particularly temperature- and rate-sensitive. This is the relevant Peierls-stress explanation. A high polycrystal constraint factor cannot explain the supplied contrast, because the data are already critical resolved shear stresses. Neither the precise factor35 nor a universal BCC/FCC ratio follows from crystal packing alone: purity, dislocation structure, temperature and testing conditions also matter.