26. Iron

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Below: Electron Shell, Bonding & Ions, Magnetic Properties, Temperature, Other Magnetism

Iron is the 26^th element on the periodic table. It has 26 protons and 30 neutrons for a mass of 56 amu, and 26 electrons.

Electron Shell

DISCLAIMER: This is a proposed model, not an experimentally observed map of the iron atom. This electron domain geometry is designed to show the most symmetrical resonance structure for the orbitals, according to the Quicycle model. This is not the only resonance structure possible for this element. (In this series we are also not differentiating between high-spin and low-spin states. These variations should be extrapolated from the geometries shown.)

Iron is the sixth element with electrons in the d–subshell. Building upon the pd-hybridization [ref] we introduced in regard to the previous d-block transition metals, it is proposed that iron has a 3^rd shell containing 4 di-electrons and 4 unpaired electrons in p³d⁵-hybridized, cubic symmetry resonating within a spherical 3s² orbital. The 4 di-electrons and 4 unpaired electrons will arrange themselves in a highly symmetrical, alternating fashion that minimizes repulsion. This structure (shown below) can also be viewed as two intersecting, antiparallel (antiprismatic) tetrahedra, one containing di-electrons, the other single electrons.

In such a configuration, the 4 tetrahedral 2^nd shell di-electrons will align themselves directly beneath the single electrons in the 3^rd shell in order to minimize di-electron repulsion between shells.

NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will form a cubic arrangement that divides the (cuboctahedral) shell into eight equal volumes, with two 4-way symmetries. The entire shell will be filled with electron density. It will be highest at the center of the face of each orbital (as in the traditional hybrid orbital lobe shapes) and will decrease toward the nodal regions between orbitals — as wave structures usually do — where electron density will be lowest (though not zero).

NOTE: Even though it is often useful to talk about these orbitals as separate, they are all — the entire atom is — part of a single, coherent, harmonic, resonant, phase-locked, spherically-symmetrical quantum wave state, and it is all electromagnetic at the root-energy level. Orbitals and their ‘boundaries’ can be seen as nothing more than nodes and antinodes in this harmonic wave structure.

NOTE: The model’s claim is not that an isolated atom always has a definite antinode location in the lab frame. It is that, conditional on one electron being found in a given orbital ‘antinode’ region or direction, the other electrons’ positions must correlated with it in a specific geometric pattern. This conditional-correlation structure is a body-frame feature: it describes the relative positions of electrons within the atom, not their absolute positions in the lab frame. It is the internal frame of reference in which the shell’s wave resonance condition closes and its standing-wave pattern is organized. For a free atom in an unprepared ensemble, all orientations are statistically equivalent so the observed density is typically an orientation average over body-frame orientations, which is observed in the lab frame to be spherically symmetrical.

NOTE: The diagram above should not be read as a static picture of unequal charge fixed at eight corners. For a free atom or a symmetric BCC site, the average electron density must preserve the symmetry of the atom or site. The alternating pattern is therefore best understood as a proposal about how electrons are correlated with one another in a quantum stationary-wave structure.

The diagrams below show iron’s eight 3^rd shell p³d⁵-hybrid orbitals. (The darker blue color represents di-electron orbitals, the lighter blue color represents unpaired electron orbitals.) In reality, the eight volumes will not be exactly equal in size because di-electron orbitals (with charge 2-) will be larger and will repel the unpaired electron orbitals (with charge 1-) more strongly, constricting them. It is therefore proposed that iron’s unpaired core electrons will form a perfect tetrahedral geometry with respect to one another, due to the (tetrahedral) symmetry of the constriction around (and between) them, and that they will become extended, radially outward, as a result of the repulsion from both beside and beneath them.

This double antiparallel tetrahedral symmetry of iron’s 3^rd shell is also known as a dual tetrahedron, in which each point also coincides with a corner of a cubic structure. Two different views of this are offered below.

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Bonding & Ion Formation

When iron atoms bonds with other metal atoms in a solid, they form a crystal structure in which their valence electrons become ‘delocalized’ — shared into a matrix of electron density within which the now-positive atomic cores remain suspended. They are held in their relative positions by a balance between attraction into the electron gas around them and repulsion from the adjacent positive atomic cores. This is the electrostatic nature of metallic bonding. Its electron delocalization is also the reason that metals are such good conductors of both heat and electrical potential.

Iron usually makes the Fe²⁺ or the Fe³⁺ ion, the formal oxidation states Fe(II) and Fe(III), but oxidation state is formal bookkeeping rather than a complete electron-density description. For formal Fe(II) d⁶, the domain bookkeeping permits 4 Di-electrons and 4 Unpaired electrons (4D+4U, 8 occupied directions; maximum local S=2), 5D+2U (7 occupied directions; maximum local S=1), and 6D+0U (6 occupied directions; S=0). For formal Fe(III) d⁵, it permits 3D+5U, 4D+3U, and 5D+1U, corresponding under parallel metal-local coupling to S=5/2, 3/2, and 1/2. These are occupancy partitions, not assigned geometries or energies. Ligand field, coordination geometry, covalency, redox-active ligands, and exchange coupling select the physically relevant states.

TECHNICAL COUNTING NOTE:
If D proposed domains contain electron pairs and U contain single electrons, then N=2D+U and occupied directions, k=D+U, so U=2k−N. This only counts unpaired electrons within the chosen model space. It does not determine which arrangement has the lowest energy or how those spins couple to produce the total spin.

The isolated Fe⁺ ion is different. Its measured ground state is 3d⁶4s¹ ⁶D₉/₂ while 3d⁷ ⁴F₉/₂ begins 1872.567 cm⁻¹ higher. Formal Fe(I) in coordination chemistry is conventionally d⁷ and need not retain a spectator 4s electron.

Bare-ion configurations and formal oxidation states must not be conflated. Iron compounds of the same formal oxidation state can be diamagnetic, paramagnetic, or exchange-coupled; magnetic response must be assigned to a specified compound

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Magnetic Properties

Iron (Fe), cobalt (Co), and nickel (Ni) are ferromagnetic (see below), but iron is significantly more ferromagnetic that the other two. (See Magnetism for more detail.)

UNPAIRED ‘CORE’ VALENCE ELECTRONS:
While iron’s 3d electrons are technically still valence electrons, which contribute electron density to the crystal electronic band structure in the conduction electron matrix — the 3D electron gas — of the solid metal crystal, some of the 3d electron density remains concentrated around the atomic cores.

PARAMAGNETISM:
Unpaired ‘core’ valence electrons are still free to respond to and orient themselves with an external magnetic field. In doing so, they cancel magnetic field with that external field (through destructive interference), which lowers energy and attracts them towards the field. The paramagnetic atom as a whole is then attracted, along with these electrons, towards the magnetic field — attracted equally to the ‘north’ as to the ‘south’ polarity. This is called paramagnetism, and it is an expected property of metals with unpaired electrons.

When the external field is removed, the electron spins within adjacent paramagnetic atoms return to their previous, random distribution. (See paramagnetic strength trend analysis for more details.)

FERROMAGNETISM:
Ferromagnetism, however, occurs when the electrons in a substance are able to retain their internal crystalline magnetic field alignment after the external field that aligned them is removed. The solid can then act as a permanent magnet. This property therefore depends directly upon how well the unpaired electrons on adjacent atoms can link their spins and magnetic fields, thereby holding one another in alignment.

It is here suggested that there may be two criteria required in order for the atoms of a metal crystal to achieve ferromagnetic spin bonding, and thus, a crystal-wide ferromagnetic spin resonance:

1. CRYSTAL GEOMETRY: For optimal spin bonding, unpaired core electrons should have an electron domain geometry that matches the crystal unit cell geometry. We propose that the 8-directional symmetries that arise as a result of pd-hybridization may provide these.
2. SUFFICIENT ORBITAL EXTENSION: Unpaired ‘core’ valence electrons require constriction and radial extension in order to interact significantly (via spin bonding) with similarly extended core electrons on adjacent atomic cores in a crystal. We propose that this is achieved as a result of sufficient di-electron (electron pair) repulsion within the atomic shell, along with added repulsion from the di-electrons in the 2^nd shell that lie directly beneath the unpaired core electron orbitals. This criterion is therefore intimately related to the electron geometry (from criterion #1 above), as well as to the number of same-shell di-electrons constricting the unpaired electron orbitals.

NOTE: This geometry matching and radial extension are Quicycle hypotheses, not established necessary-and-sufficient criteria for ferromagnetism. Ferromagnetism is a collective band-and-exchange phenomenon. The Quicycle model attempts to account for why this band-and-exchange state is achieved in only such specific cases. This hypothesis has yet to quantitatively reproduce magnetic moments, exchange interactions, temperature dependence, and phase behavior.

In this model it is suggested that only with both of these criteria fulfilled (see below), will a transition metal be ferromagnetic. If only one is present, or if constriction and extension are not sufficient, the element will be paramagnetic.

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CRITERION #1: IRON’S CRYSTAL GEOMETRY:
Iron is ferromagnetic below its Curie Temperature (of 770°C), and has a body-centered cubic (BCC) crystal structure. When heated at ambient pressure, iron remains BCC α-Fe as it passes through its Curie Temperature near 1,043–1,044K (770°C). It then becomes paramagnetic. Near 1,185K (912°C), BCC α-Fe transforms into FCC γ-Fe. This clarifies that, according to this model, the Curie transition is a loss of collective magnetic coherence due to thermal disruption, even if the lattice structure does not change.

In a BCC crystal, the nearest neighbors to the blue body-centered atom in the center of the unit cell (above, left) will be the 8 white atoms arranged in a cube diagonally around it at the corners of the unit cell. This means that, in atoms with tetrahedral or double-tetrahedral  (cubic) electron configurations — like that proposed here for the iron atom — the electron orbitals should align geometrically when in a BCC crystal structure. Such an alignment should, in turn, help to facilitate the proposed spin bonding (that will be discussed below).

When a BCC crystal is rotated through 54.75° — half a tetrahedral angle — it can more easily be seen as two superimposed, antiparallel (and antiprismatic) tetrahedral structures that pass through every crystal vertex. Each iron atom can therefore be seen as representing the center of a dual tetrahedron. (See also fig. 3 & fig. 4 above.) The points of one tetrahedron represent the positions of the 3^rd shell di-electron orbitals (the black dots in the images below), and the other tetrahedron represents the positions of the 3^rd shell unpaired electron orbitals (the pink dots).

Through any particular iron atom, a perfect, almost diamond-like tetrahedral crystal structure of unpaired electrons runs one way, and a superimposed tetrahedral crystal structure of di-electrons runs antiparallel (and antiprismatic) to it. (Through each adjacent iron atom, the situation is reversed.) This links all of the iron atoms throughout the crystal into a single, continuous, harmonic, crystal-wide resonance of spin-bonding connection.

This dual crystal structure — a network of spin-bonding unpaired electrons nested through a non-bonding, diamagnetic di-electron network — not only creates a very stable and coherent harmonic quantum state that pervades the crystal, but the intersecting di-electron network also serves to constrict the channels of that resonance further. This should serve to enhance the coherence of its connections into what we might imagine as channels of higher-density magnetic (or spin) flux. It is a harmonic resonance of both where spin is and where it is not.

It is proposed that this highly structured tetrahedral spin-bonding crystal resonance is what gives iron its powerful ferromagnetism.

CRITERION #2: SUFFICIENT ORBITAL EXTENSION:
As was proposed above, though, the alignment of spin and field may not be enough to effect a ferromagnetic resonance on its own. Since these are interactions between ‘core’ valence electrons, it is proposed that their influence (and connections) may need to be enhanced and extended outward from the atomic cores in order to be felt by adjacent atoms in the crystal significantly enough to facilitate ferromagnetic spin bonding.

According to this model, in addition to iron’s 4 tetrahedral unpaired electrons, its 3^rd shell also contains 4 di-electrons. (These are depicted by large black dots in fig. 11, below right, and by the “4” in its center). Furthermore, it is proposed that the 4 di-electrons in the 2^nd shell are aligned directly beneath the unpaired electrons of the 3^rd shell.

Di-electron orbitals have double the charge, and they must therefore repel unpaired electron orbitals more strongly than the reverse. It has been hypothesized that, with enough di-electrons around and beneath them, this can not only constrict the unpaired electron orbitals but also cause them to become extended radially outward from the atomic core. In the case of iron, the unpaired electron orbitals are experiencing this form of constriction from eight di-electrons — 4 from beside/around them in the same shell, and 4 from beneath them in the 2^nd shell.

It is proposed in this model that the combination of all this di-electron repulsion forces the influence of the unpaired electron orbitals to be extended further outward. This extends the influence of these electrons’ spins and magnetic fields into the electron gas around the atomic cores (as shown in fig. 11, below left), and it is suggested that this is what makes electron spin interactions between adjacent crystalline iron atoms possible. [Ref]

(We also proposed that this concept of spin bonding explains the underlying physical mechanisms behind Pauli’s Exclusion Principle and Hund’s 2^nd Rule.)

NOTE: Quicycle proposes that pair-rich and single-rich conditional-density regions can have different radial and angular moments. Pair count alone does not determine radius, Fe–ligand bond length, or exchange. Antibonding occupation, covalency, screening, and occupied-direction count also contribute. The claim that pair-rich domains laterally constrict and radially extend single-rich domains must still be calculated.

For more on the relative trend in ferromagnetic strength, see Magnetism & Magnetic Trends.

The following image is designed to evoke the idea of the extended, spin-bonding orbitals using a different analogy. While no analogy is ever a complete representation, it may be somewhat fitting in this case. Electron orbitals in the atomic quantum state have components that we might be able to think of as a type of ‘sub-quantum plasma flow state.’ The image below, of plasma tufts around an electrode, may evoke the idea of an arrangement of such extended ferromagnetic orbitals from the surface of the atomic core.

We might imagine a crystal of iron atomic cores, each like the electrode shown above, suspended in its 3-dimensional electron gas, perhaps like the violet electrode glow.  In the case of iron, each positive atomic core would have 4 tufts, arranged tetrahedrally, each occupied by one of the 4 unpaired 3^rd shell electrons. The remaining 4 positions of its 3^rd shell cubic arrangement would be occupied by non-interacting di-electrons — also arranged tetrahedrally, though not extended, and with the di-electron orbitals separating the unpaired electron orbital tufts from one another. (The right-most image in fig. 11, above — — might portray this idea nicely, though in a slightly exaggerated manner.)

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Curie Temperature & Structural Transition

On cooling at ambient pressure, FCC γ-Fe transforms to BCC α-Fe near 912°C while still paramagnetic. Ferromagnetic order appears only on further cooling through about 770°C, without another crystallographic transition. We might interpret this to mean that, only when thermal energy is reduced to below a certain threshold is the coherence of spin bonding strong enough to hold the crystal in a spin-optimized arrangement.

FCC is cubic close packing with ABC stacking; HCP uses AB stacking. They have the same ideal coordination number but are distinct structures. The BCC→FCC transformation and loss of ferromagnetic order occur at different temperatures.

RELATIVE STRENGTH & CURIE TEMPERATURE:
Iron is by far the most strongly ferromagnetic of the three metals, yet cobalt has a higher Curie Temperature. This means that, even though iron is more strongly magnetic, cobalt (Co) can hang on to its magnetization to a much higher temperature. That must mean its ferromagnetic spin resonance is stronger than iron’s. How might we explain this?

According to the present proposed model, we might speculate that the reason for this is as follows. Cobalt contains three instances of ferromagnetic spin bonding (FSB) per atom, and the resonance is essentially two-dimensional, in the hexagonal crystal layers. Iron contains four instances of FSB per atom, and the resonance is three-dimensional and perfectly tetrahedral throughout the lattice. This causes iron to have a far more significant ferromagnetic spin resonance throughout its crystal, making it more strongly ferromagnetic than cobalt.

However, each of cobalt’s three instance of FSB involves 3 electrons holding each other in spin resonance. Each of iron’s four instances involve only 2-electron resonances. As such, cobalt’s spin bonding resonances are stronger and will therefore be able to withstand higher temperatures without thermalization disrupting them out of resonance. It is therefore proposed that this is what gives cobalt a higher Curie Temperature than iron, in spite of its weaker ferromagnetic strength.

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Other Types Of Magnetism

ANTIFERROMAGNETISM:
Antiferromagnetism is a state in which the unpaired electron spins on adjacent atoms in the metallic crystal are anti-parallel to one another. This creates a net spin-zero state for the crystal as a whole, and it will therefore not exert an external magnetic force.

It is proposed that antiferromagnetism is not a form of ferromagnetism, but rather a ‘local’ resonance resulting from an electron-gas coupling.

For more information, see chromium (Cr) or Magnetism & Magnetic Trends.

OTHER TYPES OF MAGNETISM:
There are also other types of magnetism, for example ferrimagnetism, altermagnetism, and an effect known as ‘spin glass‘ involving neodymium (Nd), but these will not be investigated here.

For more information, see Magnetism & Magnetic Trends.

References:
See DeMystifySci Podcast: The Strange Behavior Of Humans And Magnets for a brief video discussion of this concept.
A. Benn, J.G. Williamson, ‘pd-Hybridization And The Electron Geometry Of Fluorine, Neon And Iron’, Quicycle Journal (2024)
 J.G. Williamson, A. Benn, M. Rudolph, ‘Quantum Spin Coherence In 4 Derived 3-Spaces’, Quicycle Journal (2022)

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PARAMAGNETIC 3d METALS: Scandium, Titanium, Vanadium, Chromium (also antiferromagnetic), Manganese
OTHER FERROMAGNETIC 3d METALS: Iron, Cobalt, Nickel
DIAMAGNETIC 3d METALS: Copper, Zinc

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