Arnie Benn, Author at The Quantum Bicycle Society

30. Zinc

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties

Zinc is the 30^th element on the periodic table. It has 30 protons and 35 neutrons for a mass of 65 amu, and 30 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Zinc is the tenth element with electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to the previous d-block transition metals, it is proposed that zinc features p³d⁵-hybridization (just like iron, cobalt, nickel and copper before it). This enables a symmetrical, eight-directional cubic geometry containing 8 di-electrons (see image below).

This pd-hybridization does not need to involve the 3s-orbital electrons, so they can retain their preferred spherical di-electron state. It is also achieved without the need of an electron from the 4s-orbital — as occurs in the case of copper.

The 3^rd shell cubic di-electrons will arrange their double tetrahedra in such a way that minimizes repulsion with the 2^nd shell di-electrons beneath (as depicted in the images below).

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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. (In the view shown above, this cube is tilted to reveal that it is also a double-tetrahedral arrangement — two tetrahedra aligned antiparallel and antiprismatic.)

Each of the eight shell segments 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 ALSO: 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.

As in the case of the previous (transition metal) elements, zinc’s 3^rdshell p³d⁵-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. It is proposed that they are superimposed within it, as a harmonic frequency coincides with its fundamental frequency in a resonance. It is suggested that the 3s² di-electron gives additional stability to the electron configuration within it. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they achieve at least 4-directional symmetry with only their p– and d-orbitals.

Bonding & Ion Formation

(In a few cases, such as chromium (Cr) and copper (Cu), the 4s-orbital outer shell contains only 1 electron, since the other joins the 3rd shell hybridization within in order to help it achieve 8-directional symmetry.)

Magnetic Properties

Like copper, zinc is diamagnetic.

DIAMAGNETISM:
Diamagnetism occurs when a substance is repelled from a magnetic field because it contains di-electrons. These paired electrons are in a state of field cancellation with one another. The presence of an external magnetic field will disrupt the coherence of their di-electron states, raising energy. This causes the atom to repel away from the field in search of a lower energy state. Diamagnetic substances have negative magnetic susceptibility (χ_m) values.

Zinc’s 3^rd shell is full, with a symmetrical arrangement of 8 field-repelling di-electrons, and its 4^th shell has a 4s² di-electron. This gives zinc a lower magnetic susceptibility values than copper, with χ_m = –9.15.

MAGNETIC STRENGTH ANALYSIS:
The following diagram shows the relative paramagnetic and diamagnetic strengths of the transition metals, along with their proposed hybrid orbital geometries. (See Magnetism for more detail.)

CLICK TO ENLARGE: Molar Magnetic Susceptibility values for some of the elements (source)

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

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29. Copper

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties, Electric Properties

Copper is the 29^th element on the periodic table. It has 29 protons and 34 neutrons for a mass of 63.5 amu, and 29 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Copper is the ninth element with electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to the previous d-block transition metals, it is proposed that copper features p³d⁵-hybridization. This enables a symmetrical, eight-directional cubic geometry with 8 di-electrons (see image below).

This pd-hybridization does not need to involve the 3s-orbital electrons, so they can retain their preferred spherical di-electron state. However, it is achieved in the same way as we saw with chromium, where one electron from the 4s-orbital joins the pd-hybridization in order to achieve 8-directional symmetry and lowest energy. (In the views below, this cube configuration is tilted to reveal that it is also a double-tetrahedral arrangement — two tetrahedra aligned antiparallel.)

The 3^rd shell cubic di-electrons will arrange their double tetrahedra in such a way that minimizes repulsion with the 2^nd shell di-electrons beneath (as depicted in the images below).

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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. Each shell segment 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 necessarily zero).

As in the case of the previous (transition metal) elements, copper’s 3^rdshell p³d⁵-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. It is proposed that they are superimposed within it, as a harmonic frequency coincides with its fundamental frequency in a resonance. It is suggested that the 3s² di-electron gives additional stability to the electron configuration within it. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they achieve at least 4-directional symmetry with only their p– and d-orbitals.

Observational evidence may bear out the proposed cubic structure of copper’s 3^rd shell. The following images of copper’s Fermi surface were obtained by Weber (et.al.) using a process known as 2D-ACAR. [Ref]

Fermi surface of copper obtained with 2D-ACAR spectroscopy, compared to proposed electron geometry (far right)

Bonding & Ion Formation

As mentioned above, a 4s¹ electron shell completes the atom. This is because one of the valence electrons drops down into the 3^rdshell hybridization in order to allow it to achieve 8-directional symmetry. (This occurs in a few other cases, for example chromium (Cr) and silver (Ag).)

When forming a metallic crystal, the 4s¹ electron delocalizes to form the metallic bond, and when forming a 1+ ion, it is removed. In both cases, the core electron geometry remains the same.

A second ionization, however, would shift its geometry, perhaps by ionizing one of the hybrid di-electrons. This would retain 8-directional symmetry, but with one of the hybrid orbitals now containing an unpaired electron. It would therefore be expected that the Cu²⁺ ion would be strongly paramagnetic (see below) — due to its single and highly constricted unpaired electron orbital — and the Cu⁺ ion would be diamagnetic. They are. By way of example, CuCl has χ_m = –40 while CuCl₂ has χ_m = +1,080.

Magnetic Properties

Copper is diamagnetic.

Copper’s 3^rd shell is full, with a symmetrical arrangement of 8 field-repelling di-electrons. While it does have one unpaired 4s¹ electron in its valence shell, it is presumed that the diamagnetism of these di-electrons overpowers any paramagnetism due to the 4s¹ electron, giving copper a magnetic susceptibility of χ_m = –5.46.

Zinc, with a full 4s² orbital, has an even lower magnetic susceptibility of χ_m = -9.15. This may imply that the presence of copper’s 4s¹ electron may be disrupting the diamagnetism of its inner symmetrical arrangement of 8 field-repelling di-electrons., decreasing their diamagnetism slightly with respect to an external magnetic field.

The following video shows some of the remarkable effects of copper’s resisting the approach of a strong magnetic field. Watch as a strong magnet is passed quickly over or quickly towards a slab of copper.

Electrical Properties

Copper is the second most electrically conductive metal after silver (Ag), and gold (Au) is third.

Not only are the three in the same group within the d-block, but they also have in common a valence s-orbital that has donated an electron inwards in order to perfect the symmetry of an inner cubic di-electron shell.

We might speculate that such an ‘activated,’ electron-deficient valence conduction band may actually promote the passage of electrical potential. It may simply offer less resistance to it (by having more unoccupied energy states in the band structure that are available to transmit electrons).

However, chromium also has a deficient 4s orbital, but its electrical conductivity is about 10 times smaller than those of the precious metals. We might further speculate that, what separates the three precious-metal good conductors from chromium is the nature of their core electron resonances. In the three precious metal elements, the inner orbitals are all completely filled with di-electrons, which are diamagnetic. We might speculate then that, upon this ‘non-interfering’ foundation, the single-valence-electron conduction band may support the transmission of electrical potential through the metallic crystal quite effectively. In the case of chromium, however, there are five unpaired electrons on the surface of every atomic core in the crystal. Their magnetic field and spin interactions might interfere with the electrons in the conduction band in such a way that diminishes conductivity, due to resistance. It is further conceivable that, given the ratio of electrons involved, it may decrease chromium’s conductivity to merely one tenth of the conductivity of copper and silver.

Credence for this conjecture might come from the fact that, even though chromium has a much lower electrical conductivity than copper, it nevertheless has a much higher conductivity than its immediate neighbors in the 3d-block — vanadium (V) and manganese (Mn) — which each have full valence 4s²-orbitals. (Though this fact is not conclusive on its own.)

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

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28. Nickel

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties

Nickel is the 28^th element on the periodic table. It has 28 protons and 31 neutrons for a mass of 59 amu, and 28 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Nickel is the eighth element with electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to the previous d-block transition metals, it is proposed that nickel has a 3^rd shell containing 6 di-electrons and 2 unpaired electrons in p³d⁵-hybridized, cubic symmetry. The 2 unpaired electrons will occupy two opposite corners in the cubic configuration. This structure (shown below from two perspectives) can also be viewed as two intersecting, antiparallel (and antiprismatic) tetrahedra with one electron in each occupying the two opposite ‘axial’ positions.

In such a case, one of the 4 tetrahedral 2^nd shell di-electrons will align itself opposite one of the single electrons in the 3^rd shell, allowing all other 2^nd and 3^rd shell di-electrons to orient their directions roughly between one another in order to minimize repulsion between shells.

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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 a 6-way and a 2-way symmetry. 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).

The diagram below shows only nickel’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 nickel’s unpaired electron orbitals will form a linear (axial) geometry with respect to one another, due to the symmetry of the constriction around (and between) them, and that they will become extended, radially outward, as a result of its magnitude, as well as the repulsion from the 2^nd shell beneath them.

*Fig. 2: Nickel’s 3^rd shell cubic 2-electron and 6-di-electron configuration. Oblique view (left) and top view (right).*

Although nickel’s electron geometry is effectively linear, the double antiparallel tetrahedral symmetry of its 3rd 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.

Fig. 3: ‘Cubic’ view of a nickel atom’s eight 3^rd shell p³d⁵-hybrid orbitals around the atomic core (black), along with a dual tetrahedron formed from two ‘antiparallel’ (antiprismatic) intersecting tetrahedra.

Bonding & Ion Formation

When nickel 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.

When nickel interacts ionically, it usually makes the Ni²⁺ ion, though there are other possibilities (such as the Ni³⁺ or Ni⁴⁺ ions). The Ni²⁺ ion forms when the atom loses its 4s² valence electrons. The Ni³⁺ ion forms when the Ni²⁺ ion loses another electron. It is here proposed that the 3^rd electron will be lost from one of the 3^rd shell di-electrons, since this is the only way to retain 8-directional symmetry. The Ni³⁺ ion will therefore achieve the same (hexagonal bipyramidal) electron configuration we saw in cobalt (Co) and manganese (Mn), though without any 4s-electron density. The Ni⁴⁺ ion will therefore achieve the same (cubic) electron configuration we saw in iron (Fe).

In ionic crystals — without delocalized electron density — nickel ions no longer conduct electricity. They will, however, still be magnetically active because they still hold unpaired electrons. While metallic nickel is ferromagnetic (see below), nickel ions will be strongly paramagnetic.

Magnetic Properties

Iron (Fe), cobalt (Co), and nickel (Ni) are ferromagnetic, though nickel is the least ferromagnetic of the three. (See Magnetism for more detail.)

*Fig. 4: Ferromagnetic strength trend in the metals of the 3d-block.*

UNPAIRED CORE ELECTRONS:
The presence of unpaired core electrons determines an element’s magnetic properties. While these electrons may technically be called core electrons, for the purposes of this discussion, we recognize that in a metal, if we exclude the valence “conduction” electrons, the pd-hybrid orbital electrons do become ‘valence electrons’ in a sense. Not in the sense that they can participate in chemical reactions, but in the sense that they are now in the outermost shell of the atomic cores, which are suspended in the conduction electron matrix — the 3D electron gas — of the solid metal crystal.

Unpaired core electrons are protected from reacting with other atoms. They are held in their geometry by atomic orbital constraints, they are kept from pairing up with each other by the spin and field exclusion of degeneracy, and it is proposed that they are stabilized by the presence of the 3s² orbital ‘fundamental’ [ref].

PARAMAGNETISM:
Protected unpaired core electrons are, however, 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 core 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:
As we discussed regarding iron (Fe) and cobalt (Co), however, ferromagnetism 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 proposed that there are two criteria that are required in order for the atoms of a metal crystal to achieve ferromagnetic spin bonding, and thus, a crystal-wide ferromagnetic spin resonance.

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.
SUFFICIENT ORBITAL EXTENSION: Unpaired core electrons require constriction and radial extension in order to interact (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.

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.

CRITERION #1: NICKEL’S CRYSTAL GEOMETRY:
Nickel is ferromagnetic below its Curie Temperature (of 354°C), and has a face-centered cubic (FCC) crystal structure. When heated past its Curie Temperature, it loses its ferromagnetism in favor of paramagnetism.

*Fig. 5a: Diagrams of iron’s BCC body-centered cubic (left) and nickel’s FCC face-centered cubic (right) crystal structures.*

In a FCC crystal (above, right), each atom has 12 nearest neighbors. These nearest neighbors lie on the diagonals of the faces of the FCC unit cell (top right, above). As such, the tetrahedral crystal geometry proposed for iron (Fe) would not align in this “45º” paradigm. It would, however, allow for atoms with linear spin interactions to align.

*Fig. 5b: Diagrams of iron’s tetrahedral BCC nearest neighbor relationship (left) and nickel’s linear FCC nearest neighbor relationship (right)*

Since it is proposed that nickel has a linear geometry of unpaired electron orbitals, an FCC crystal structure (above, right) may allow for an effective spin bonding resonance to align within a nickel crystal.

A clear shortcoming of this electron structure is that, while it may facilitate the correct geometric alignment for ferromagnetic spin bonding in nickel, there are only two unpaired electrons spin bonding per atom, as opposed to four in the case of iron. As such, it makes sense that the ferromagnetism of nickel would be far weaker than that of iron, resulting in a more easily-disrupted ferromagnetic spin resonance and a lower Curie Temperature.

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

In addition to nickel’s 2 linear unpaired electrons, its 3^rd shell also contains 6 di-electrons. (These are depicted by large black dots in fig. 6 below, and by the “6” in its center). Furthermore, 1 of the 4 di-electrons in the 2^nd shell is aligned directly beneath one of the unpaired electrons of the 3^rd shell.

*Fig. 6: Nickel’s extended core unpaired electron orbitals*

Di-electron orbitals are larger than unpaired electron orbitals, and they have double the charge. They therefore repel unpaired electron orbitals more strongly. It has been proposed that 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 nickel, the unpaired electron orbitals are experiencing this form of constriction from 7 di-electrons — 6 from beside/around them in the same shell, and 1 from beneath them in the 2^nd shell.

It is proposed that the combination of all this di-electron repulsion forces the influence of nickel’s unpaired electron orbitals to be extended significantly further outward (just as a spinning cylinder, forced to become thinner, that responds by becoming longer). This extends the influence of these electrons’ spins and magnetic fields into the electron gas around the atomic cores (as shown in fig. 6, above), and it is suggested that this is what makes electron spin interactions between adjacent crystalline nickel atoms possible. [Ref]

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

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

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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27. Cobalt

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties, Temperature

Cobalt is the 27^th element on the periodic table. It has 27 protons and 32 neutrons for a mass of 59 amu, and 27 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Cobalt is the seventh element with electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to the previous d-block transition metals, it is proposed that cobalt has a 3^rd shell containing 5 di-electrons and 3 unpaired electrons in p³d⁵-hybridized, hexagonal bipyramidal symmetry. The 5 di-electrons occupy three symmetrically distant equatorial positions and the two axial positions, in order to minimize repulsion. The 3 unpaired electrons occupy the remaining equatorial positions in between. (This is a similar electron structure to manganese, which has 3 di-electrons and 5 single electrons in this same configuration.)

In such a case, the 4 tetrahedral 2^nd shell di-electrons will align themselves with one di-electron opposite one of the single electrons in the 3^rd shell, allowing all other 2^nd and 3^rd shell di-electrons to orient their directions roughly between one another in order to minimize repulsion between shells.

Fig. 1: Electron orbital structure of cobalt.

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NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical hexagonal bipyramidal structure that divides the shell into eight roughly equal volumes, with a 5-way and a 3-way symmetry. 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).

The diagram below shows only cobalt’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 repel the unpaired electron orbitals (with charge 1-) more strongly, constricting them. It is therefore proposed that cobalt’s unpaired electron orbitals will form an equatorial, trigonal planar geometry with respect to one another, and that they will become somewhat extended, radially outward, as a result of this constriction. (The axial and equatorial di-electron orbitals will also differ somewhat in size due to their different 2-way versus 3-way geometric constraints.)

*Fig. 2: Cobalt’s 3-electron and 5-di-electron symmetrical configuration. Oblique view (left) and top view (right).*

Bonding & Ion Formation

When cobalt 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 electrical potential.

When cobalt interacts ionically, it usually makes the Co²⁺ or the Co³⁺ ion (though there are other possibilities). The Co²⁺ ion forms when the atom loses its 4s² valence electrons. The Co³⁺ ion forms when the Co²⁺ ion loses another electron. It is here proposed that the 3^rd electron will be lost from one of the di-electrons, since this is the only way to retain 8-directional symmetry. The Co³⁺ ion will therefore achieve the same cubic (double-tetrahedral) electron configuration we saw in iron (Fe), though without any 4s-electron density.

*Fig. 3: The orbitals of cobalt (left), the Co²⁺ ion (center), and the Co³⁺ ion (right)*

In ionic crystals — without delocalized electron density — cobalt atoms no longer conduct electricity. They will, however, still be magnetically active because they still hold unpaired electrons. While metallic cobalt is ferromagnetic (see below), cobalt ions will be strongly paramagnetic.

Magnetic Properties

Iron (Fe), cobalt (Co), and nickel (Ni) are ferromagnetic. Cobalt is much less ferromagnetic than iron, but more so than nickel. (See Magnetism for more detail.)

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:
As we discussed regarding iron (Fe), however, ferromagnetism 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.

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.
SUFFICIENT ORBITAL EXTENSION: Unpaired core electrons require constriction and radial extension in order to interact (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.

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

CRITERION #1: COBALT’S CRYSTAL GEOMETRY:
Cobalt is ferromagnetic below its Curie Temperature (of 1,115°C) — which is much higher than iron’s Curie Temperature. It has a hexagonal close-packed (HCP) crystal structure below about 450ºC, and a face-centered (FCC) crystal structure above 450ºC. When heated past its Curie Temperature, cobalt loses its ferromagnetism in favor of paramagnetism.

Fig. 5: Diagrams of cobalt’s low-temperature hexagonal close-packed (HCP) structure (left) and its face-centered cubic (FCC) crystal structures (right).

In a normal hexagonal close-packed (HCP) structure (above, left), hexagonal planar layers stack on top of one another, with the atoms of one layer nestling in between the atoms of the adjacent layer for maximum packing density. There are two possible ways to offset the second layer, so there are two variations on an A-layer’s position — called a B- or a C-layer. In HCP, the layers alternate between the A and B alignments only, resulting in a crystal in which the atoms of every other layer are vertically aligned in an A-B-A-B-etc pattern. (As we see in the top view in figure 5, above, this leaves some thin columnar gaps through the crystal.)

In a face-centered cubic (FCC) crystal (fig. 5 above, on the right), the layers cycle through both offset positions, creating an A-B-C-A-etc pattern. The difference between the B- and C-layers is a rotation through 30º of the hexagonal layer. In figure 6 (below, right), that would be the equivalent of having the three purple spheres nestled in the other three of the six positions between the yellow spheres. This structure is also known as cubic close-packing (CCP).

As we see in the ‘cubic’ view (in fig. 5, above, far right), unlike HCP, the FCC structure leaves no columnar gaps through the crystal. (This can be more clearly seen in figure 7 below.) In both close-packing structures, HCP and FCC, each atom has 12 nearest neighbors.

Fig. 6: Side view (left) and top view (right) of cobalt atoms forming a hexagonal close-packed (HCP) crystal structure in ABA form. The black dots represent 3^rd shell di-electrons. The pink dots represent 3^rd shell unpaired electrons — *CLICK HERE* *to interact with this object.*

Fig. 7: Alternative views of hexagonal close-packing (HCP) on the left — CLICK HERE to interact with this object; and face-centered cubic (FCC) on the right — CLICK HERE to interact with this object.

According to cobalt’s proposed electron domain geometry, its 3 unpaired electron orbitals, in an equatorial trigonal planar arrangement, would align perfectly within the hexagonal layers of both HCP and FCC crystal geometry. Every other corner of each ‘hexagon’ would then find three extended unpaired electron orbitals, one from each of three adjacent atoms, attracted into a coherent ‘tri-electron’ Parallel Spin Bonding (PSB) state in the electron gas ‘gaps’ between the atoms in the crystal. (These are the groups of 3 pink dots in fig. 6 above).

The other three gaps will therefore find three di-electrons approaching each other, one from each atom. (These are the groups of 3 black dots in fig. 6). As in the case of iron, these di-electron orbitals repel each other. Since they are neither constricted nor extended, they will not be as close to one another, as will the spin bonding unpaired electrons (and they may perhaps behave almost like ‘diamagnetic bumpers,’ adding stability to the coherence of the crystal state.)

Within each layer in the crystal, the spin-bonding and diamagnetic relationships between the atoms will be the same, whether it is in HCP or FCC form. While this seems to be essentially a planar resonance through the crystal, as we will see, it is proposed that the relative rotation of the layers — HCP versus FCC — can also allow or prevent an additional crystalline spin resonance between layers.

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

In addition to cobalt’s 3 trigonal planar unpaired electrons, its 3^rd shell also contains 5 di-electrons. (These are depicted by large black dots in the image below, and by the “5” in its center). Furthermore, 2 of the 4 di-electrons in the 2^nd shell are aligned almost directly beneath two of the unpaired electrons of the 3^rd shell. This should serve to constrict and extend the unpaired electron orbitals in a similar way to that proposed for iron. (While there may be less di-electron repulsion from the 2^nd shell than in iron, there is more same-shell di-electron repulsion than in iron.)

Fig. 8: Cobalt’s extended core unpaired electron orbitals. CLICK HERE to interact with this object.

Di-electron orbitals are larger than unpaired electron orbitals, and they have double the charge. They therefore repel unpaired electron orbitals more strongly. It has been proposed that 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 cobalt, the unpaired electron orbitals are experiencing this form of constriction from 7 di-electrons — 5 from beside/around them in the same shell, and 2 from beneath them in the 2^nd shell.

It is proposed that the combination of all this di-electron repulsion forces the influence of cobalt’s unpaired electron orbitals to be extended significantly further outward (just as a spinning cylinder, forced to become thinner, that responds by becoming longer). This extends the influence of these electrons’ spins and magnetic fields into the electron gas around the atomic cores, and it is suggested that this is what makes electron spin interactions between adjacent crystalline cobalt atoms possible. [Ref]

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

Curie Temperature & Structural Shift

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.

THE STRUCTURAL TEMPERATURE SHIFT:
In terms of cobalt shifting from HCP to FCC when passing 450ºC, we might speculate that this is due to an additional (and weaker) spin resonance that can arise between layers.

As we mentioned above, HCP has columnar gaps that line up vertically (axially) through the crystal (as shown in figure 7 above). This could conceivably allow for the tri-electron spin-bonding resonances at three of the hexagonal corners to achieve an additional vertical (axial) element to their resonance. Since this resonance would occur between planes, across a larger crystal distance (than the tri-electron spin-bonding at the planar corners), it would be a weaker resonance. It might therefore only be able to attract the crystal into this structure at lower temperatures, when the disruption of thermalization is lower. In fact, the additional resonance may even be necessary in order to overcome greater di-electron repulsion, which may equally result from the presence of columnar inter-layer di-electron interactions.

We might further speculate that, when transitioning into FCC form, since the columnar gaps are no longer present, it is mainly the planar (equatorial trigonal) resonance that remains. The lack of columnar gaps should result in weaker (or shorter sets of) vertical electron interactions between layers, and this may therefore represent a state of lower di-electron repulsion. If so, it may cause the crystal to prefer this structure at higher temperatures in order to compensate for the instability due to thermalization.

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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26. Iron

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

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

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Iron is the sixth element with electrons in the d–orbital. 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.

Fig. 1: Iron’s electron configuration.CLICK HERE to interact with this object

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).

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.

*Fig. 2: Iron’s cubic 4-electron and 4-di-electron configuration. Oblique view (left) and top view (right).*

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.

Fig. 3: ‘Cubic’ and ‘tetrahedral’ views of an iron atom’s eight 3^rd shell p³d⁵-hybrid orbitals around the atomic core (black), along with a dual tetrahedron formed from two ‘antiparallel’ (antiprismatic) intersecting tetrahedra.

Fig. 4: ‘Cubic’ view of an iron atom’s eight 3^rd shell p³d⁵-hybrid orbitals around the atomic core (black), along with a dual tetrahedron formed from two ‘antiparallel’ (antiprismatic) intersecting tetrahedra.

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.

When iron interacts ionically, it usually makes the Fe²⁺ or the Fe³⁺ ion (though there are other possibilities). The Fe²⁺ ion forms when the atom loses its 4s² valence electrons. The Fe³⁺ ion forms when the Fe²⁺ ion loses another electron. It is here proposed that the 3^rd electron will be lost from one of the 3^rd shell di-electrons, since this is the only way to retain 8-directional symmetry. The Fe³⁺ ion will therefore achieve the same (hexagonal bipyramidal) electron configuration we saw in chromium (Cr) and manganese (Mn), though without any 4s-electron density.

*Fig. 5: Neutral Fe atom (left), Fe²⁺ ion (center), and Fe³⁺ ion (right)*

In ionic crystals — without delocalized electron density — iron ions no longer conduct electricity. They will, however, still be magnetically active because they still hold unpaired electrons. While metallic iron is ferromagnetic (see below), iron ions will be strongly paramagnetic.

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.)

*Fig. 6: Ferromagnetic strength trend in the metals of the 3d-block.*

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.

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.
SUFFICIENT ORBITAL EXTENSION: Unpaired core electrons require constriction and radial extension in order to interact (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.

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 past its Curie Temperature, it shifts to a face-centered cubic (FCC) crystal structure, and it also loses its ferromagnetism in favor of paramagnetism.

*Fig. 7: Diagrams of iron’s BCC body-centered cubic (left) and FCC face-centered cubic (right) crystal structures.*

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).

Fig. 8: Three views at different angles of a body-centered cubic crystal of iron atoms with double-tetrahedral electron orbital structure. The black dots represent the relative positions of the 3^rd shell di-electrons and the pink dots, the 3^rd shell unpaired electrons. *CLICK HERE* *to interact with this object*.

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.

Fig. 9: *Three views of the double tetrahedral electron spin-bonding geometry through a single iron atom. The pink dots represent spin-bonding 3^rd shell unpaired electrons*. *The black dots represent non-interacting 3^rd shell di-electrons.* CLICK HERE *to interact with this object*.

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.

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, the 4 di-electrons in the 2^nd shell are aligned directly beneath the unpaired electrons of the 3^rd shell.

Di-electron orbitals are larger than unpaired electron orbitals, and they have double the charge. They therefore repel unpaired electron orbitals more strongly. It has been proposed that 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 that the combination of all this di-electron repulsion forces the influence of the unpaired electron orbitals to be extended significantly further outward (just as a spinning cylinder, forced to become thinner, that responds by becoming longer). 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]

*Fig. 11: Iron’s extended core unpaired electron orbitals.CLICK HERE to interact with the object (in the center).*

(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.)

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.

*Fig. 12: Spherical electrode plasma tufts recorded by the SAFIRE Project, along with an imagined extrapolation (inset).*

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.)

Curie Temperatures & Annealing

The symmetry and homogeneity of iron’s crystalline alignment is enhanced when it is annealed while being magnetized. The process of slowly cooling the iron to below its Curie Temperature (770°C), in the presence of an external magnetic field, allows the iron atoms to align with each other more perfectly and symmetrically as the metal slowly transitions from its (paramagnetic) FCC crystal form into its ferromagnetic BCC form. 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 less dense but spin-optimized arrangement. Thus, as a result of its perfect geometric optimization, annealed iron has stronger ferromagnetism than regular iron.

When heated back above its Curie Temperature, iron reverts back to the denser face-centered cubic (FCC) structure, which is equivalent to hexagonal close-packing (in ‘ABC’ form). There are now no longer 8 but 12 nearest neighbors for each atom in the crystal packing, andthe optimal geometry is no longer tetrahedral but linear (as shown by the grey lines through the BCC and FCC units in fig. 10 below).

*Fig. 10: Diagrams of iron’s tetrahedral BCC nearest neighbor relationship (left) and nickel’s linear FCC nearest neighbor relationship (right)*

It is at this point that the iron loses its ferromagnetism. (It will, however, still remain strongly paramagnetic!)

It is proposed that this loss of ferromagnetism occurs because the change in packing and density causes the tetrahedral hybrid orbitals to no longer align perfectly with those of their crystalline neighbors. This should disrupt the crystal-wide spin-bonding coherence. The iron will remain paramagnetic because the ‘mis-aligned’ unpaired electron orbitals will still respond eagerly to the field cancellation offered by an external magnetic field.

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?

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.

Fig. 13: Electron spin alignments for ferromagnetism (left), antiferromagnetism (center), and ferrimagnetism (right)

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.

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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25. Manganese

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties

Manganese is the 25^th element on the periodic table. It has 25 protons and 30 neutrons for a mass of 55 amu, and 25 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Manganese is the fifth element with electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to the previous d-block transition metals, it is proposed that manganese, like chromium (Cr), has a 3^rd shell containing 3 di-electrons and 5 unpaired electrons in p³d⁵-hybridized, hexagonal bipyramidal symmetry. The three p-orbital di-electrons occupy three symmetrically distant equatorial positions to minimize repulsion. The 5 unpaired electrons occupy the remaining equatorial and axial positions. An electron from the 4s-orbital is therefore not needed (as it is in the case of chromium) in order to achieve 8-directional symmetry. (See image below.)

This pd-hybridization does not need to involve the 3s-orbital electrons, so they can retain their preferred spherical di-electron state, within which (or upon which) the hybrid orbitals will resonate like harmonics upon a fundamental.

In such a configuration, the 4 tetrahedral 2^nd shell di-electrons will align themselves with one di-electron opposite one of the single electrons in the 3^rd shell, allowing all other di-electrons to orient their directions roughly between one another in order to minimize repulsion between shells.

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NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical hexagonal bipyramidal structure that divides the 3^rd shell into eight roughly equal volumes, with 5-way and 3-way symmetries. Each shell segment 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).

The diagram below only shows manganese’s eight 3^rd shell p³d⁵-hybrid orbitals. (The darker color represents di-electrons, the lighter color represents unpaired electrons. The sharp edges should not be taken too literally!)

Manganese’s eight 3^rd shell *p³d⁵*-hybrid orbitals (left) and top view (right)

It is also proposed that the stronger repulsion and larger charge density of the three di-electrons will cause them to take up slightly more space and will therefore constrict the five unpaired degenerate electron orbitals slightly. It is expected that this would increase the magnetic signatures of these electrons. (See Magnetic Properties below.)

As in the case of scandium, titanium, vanadium, and chromium, manganese’s 3^rdshell p³d⁵-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. It is proposed that they are superimposed within it, as a harmonic frequency coincides with its fundamental frequency in a resonance. It is suggested that the 3s² di-electron gives additional stability to the electron configuration within it, even though it contains 5 unpaired electrons. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they achieve at least 4-directional symmetry with only their p– and d-orbitals.

Bonding & Ion Formation

The 4s²-orbital di-electron shell completes the atom. When forming a metallic crystal, the 4s² electrons delocalize to form the metallic bond, and when forming a 2+ ion, they are removed. In both cases, the core electron geometry remains the same. (A third ionization, however, would shift its geometry by moving the 2 remaining di-electrons into the axial positions. This assumes that one of the di-electrons will be ionized, rather than an unpaired electron, in order to retain 8-directional symmetry.)

Magnetic Properties

Manganese has a total of five unpaired electrons. In all elements prior to the d-block, unpaired electrons have occurred in the outer (valence) shell of the atom. Those are the electrons involved in chemical reactions. Manganese is the fifth case of an atom with unpaired core electrons. They are protected from reacting (at least, until manganese becomes a Mn²⁺ ion), and they are stabilized by the 3s di-electron ‘fundamental.’ We propose that it is this protection and stabilization of unpaired core electrons that allows them to interact magnetically, and that consequently determines an element’s magnetic properties.

UNPAIRED CORE ELECTRONS:
While these electrons may technically be called core electrons, for the purposes of this discussion, we recognize that in a metal, if we exclude the valence “conduction” electrons, the pd-hybrid orbital electrons do become ‘valence electrons’ in a sense. Not in the sense that they can participate in chemical reactions, but in the sense that they are now in the outermost shell of the atomic cores, which are suspended in the conduction electron matrix — the 3D electron gas — of the solid metal crystal.

PARAMAGNETISM:
In the presence of an external magnetic field, an unpaired core electron will orient its spin to align with the magnetic field. This will cause the atom to be drawn into and toward that field — via magnetic field cancellation — giving it a positive magnetic susceptibility (χ_m) value. This attractive force is called paramagnetism, and its effects only last as long as the external magnetic field is present. We might therefore presume that, the stronger the paramagnetism, the more ‘unpaired electron character’ is present. Surprisingly, this does not seem to go according the number of unpaired electrons present, as the diagram below illustrates. There must therefore be other contributing factors, which we will investigate below.

Manganese is the most paramagnetic metal of the 3d row (excluding the ferromagnetic iron, cobalt, and nickel) even though it has fewer unpaired electrons than chromium and more than iron, cobalt, and nickel. (As to the reason that manganese is not ferromagnetic, click HERE .)

Magnetic susceptibility strength trend in the metals of the 3d-block, compared to the numbers of unpaired electrons present.

Manganese’s five unpaired electrons are arranged in a hexagonal bipyramidal structure. The images below are intended to represent the orientation of these 5 electrons in an external (or adjacent atom’s) magnetic field (whose north pole is pointing upwards). (The arrows inside the atom represent the unpaired electrons and the black dots represent the relative positions of the di-electrons.)

Manganese has five unpaired electrons, and it therefore makes sense that it should have the highest magnetic susceptibility value (χ_m = +511) of the (non-ferromagnetic) 3d transition metals. It is here proposed that this is due to the spin bonding and field cancellation that occurs between its five unpaired electrons, given their proximity, degeneracy, and slight orbital constriction.

If we consider scandium’s single unpaired electron to have an EME ≈ 1e^– (with χ_m = +295), and titanium’s 2 linear spin bonding electrons to have an EME ≈ 0.51e^– (with χ_m = +151), along with vanadium’s 3 parallel spin bonding electrons to have an EME ≈ 0.97e^– (with χ_m = +285), and chromium’s 5 linear and parallel spin bonding electrons to have a disrupted EME ≈ 0.57e^– (with χ_m = +167), then manganese’s 5 linear and parallel spin bonding electrons appear to have an EME ≈ 1.73e^–. That equates to about 0.35e^– of electron signature contributed per electron.

This value of 0.35e^– is very similar to vanadium’s 0.32e^–, and when we compare the two geometries, there is an interesting similarity. The three hybrid unpaired-electron orbitals in vanadium are at 90° to one another, and in a planar arrangement through the atom. In the orbital structure of manganese (and chromium), this same planar, 90° relationship exists — except that there are three iterations of it (if we consider three axial sections). In all three cases, there are also 3 di-electrons in the shell, similarly constricting the unpaired electron orbitals. Each of these iterations should manifest a similar amount of electron energy reduction due to spin bonding, given the geometric similarity.

We might therefore expect the ‘per electron’ numbers to be comparable, and they should also shed light on what chromium’s numbers might have been without the single-valence-electron issue. Manganese’s χ_m value is obviously larger than vanadium’s, though, because it has two more electrons (of roughly the same EME) contributing to its signature.

PARAMAGNETIC STRENGTH ANALYSIS:
The following diagram shows the relative paramagnetic strengths of the transition metals, along with their proposed hybrid orbital geometries. (See paramagnetic strength trend analysis for more detail.)

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

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24. Chromium

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties, Electric Properties

Chromium is the 24^th element on the periodic table. It has 24 protons and 28 neutrons for a mass of 52 amu, and 24 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Chromium is the fourth element to feature electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to scandium (Sc), titanium (Ti), and vanadium (V), it is proposed that chromium has a 3^rd shell containing 3 di-electrons and 5 unpaired electrons in p³d⁵-hybridized, hexagonal bipyramidal symmetry. The three p-orbital di-electrons occupy three symmetrically distant equatorial positions to minimize repulsion. The 5 unpaired electrons occupy the remaining equatorial and axial positions. (See image below.)

This pd-hybridization does not need to involve the 3s-orbital electrons, which can remain in their preferred spherical di-electron state, within which (or upon which) the hybrid orbitals will resonate like harmonics upon a fundamental. However, one electron from the 4s-orbital must join the 3^rd shell hybridization in order to achieve symmetry in eight directions, and to avoid the asymmetry of seven directions.

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NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical hexagonal bipyramidal structure that divides the 3^rd shell into eight roughly equal volumes, with 5-way and 3-way symmetries. Each shell segment 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).

The diagram below only shows chromium’s eight 3^rd shell p³d⁵-hybrid orbitals. (The darker color represents di-electrons, the lighter color represents unpaired electrons. The sharp edges should not be taken too literally!)

Chromium’s eight 3^rd shell *p³d⁵*-hybrid orbitals (left) and top view (right)

As in the case of scandium, titanium, and vanadium’, chromiums 3^rdshell p³d⁵-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. They are superimposed within it as a harmonic frequency coincides with its fundamental frequency in a resonance. It is proposed that the 3s² di-electron gives additional stability to the electron configuration within it, even though it contains 5 unpaired electrons. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they achieve at least 4-directional symmetry with only their p– and d-orbitals.

Bonding & Ion Formation

In chromium, a 4s¹-orbital valence shell completes the atom. This is because one of the valence electrons drops down into the 3^rdshell hybridization in order to allow it to achieve 8-directional symmetry. (This occurs in a few other cases, for example copper (Cu) and silver (Ag).)

When forming a metallic crystal, the 4s¹ electron delocalizes to form the metallic bond, and when forming a 1+ ion, it is removed. In both cases, the core electron geometry remains the same. (A second ionization, however, would shift its geometry by moving the 2 remaining di-electrons into the axial positions. This assumes that one of the di-electrons will be ionized, rather than an unpaired electron, once again in order to retain 8-directional symmetry.)

Magnetic Properties

Chromium is the only metal that is naturally antiferromagnetic at room temperature (see below), though it loses this antiferromagnetism in favor of paramagnetism at a rather low Curie Temperature of 38ºC. Let us first consider its paramagnetic strength, when compared to the paramagnetic strength of the other 3d transition metals.

Chromium has a total of six unpaired electrons, though one of these is a valence electron. In all elements prior to the d-block, unpaired electrons have occurred only in the outer (valence) shell of the atom. Those are the electrons involved in chemical reactions. Chromium is the fourth case of an atom with unpaired core electrons, and it has five of them, in addition to its single unpaired valence electron. The core electrons are protected from reacting (at least, until chromium becomes a Cr⁺ ion), and they are stabilized by the 3s di-electron ‘fundamental.’ We propose that it is this protection and stabilization of unpaired core electrons that allows them to interact magnetically, and that consequently determines an element’s magnetic properties.

When chromium is above its Curie Temperature of 38ºC, it is the third most paramagnetic metal of the 3d row — excluding the ferromagnetic iron, cobalt, and nickel — even though it has the most unpaired core electrons, with five.

As described above, it is proposed that chromium has five unpaired 3^rd shell electrons arranged in a hexagonal bipyramidal electron structure. Due to orbital constriction by the 3 di-electron orbitals in the same shell, the 5 unpaired electron orbitals should be slightly compressed (and concentrated).

The images below are intended to represent the orientation of these electrons in an external (or adjacent atom’s) magnetic field (whose north pole is pointing upwards). (The purple arrows inside the atom represent the 5 unpaired electrons and the black dots represent the relative positions of the 3 di-electrons.)

The colorless wireframe here represents the presence of a single s-electron. CLICK HERE to interact with this object

If we exclude the 4s¹ electron, chromium has five times as many unpaired core electrons as scandium (with χ_m = +295), yet chromium has a lower magnetic susceptibility value of only χ_m = +167. It is also a lower value than manganese (Mn), which also has five unpaired core electrons but with both of its 4s² electrons. It is here proposed that this is due to the parallel spin bonding and field cancellation that occurs between its three unpaired electrons, given their proximity, degeneracy, and orbital constriction.

It is also proposed that the case of manganese (Mn) is a better approximation of the strength of this electron geometry (with χ_m = +511) than chromium. As in the case of vanadium, the effective magnetic electron count (EME) of both chromium and manganese’s five 3^rd shell unpaired electrons will be reduced due to spin bonding and field cancellation within its equatorial and axial symmetries. Given the presence of two more equatorial electrons than in vanadium, this electron geometry becomes paramagnetic enough for manganese to have a higher χ_m value than scandium.

In the case of chromium, however, the presence of the electron deficient 4s¹ orbital — or indeed, of the electron-deficient electron gas — may disrupt the electron coherence, even if only with respect to the external field. If so, this would weaken these electrons’ response to an external field. In this case, it results in the atom having a weaker χ_m value, overall, than scandium with its single unpaired electron.

If we consider scandium’s single unpaired electron to have an EME ≈ 1e^– (with χ_m = +295), and titanium’s 2 linear spin bonding electrons to have an EME ≈ 0.51e^– (with χ_m = +151), along with vanadium’s 3 parallel spin bonding electrons to have an EME ≈ 0.97e^– (with χ_m = +285), then chromium’s 5 linear and parallel spin bonding electrons appear to have an EME ≈ 0.57e^–. That equates to about only 0.11e^– of electron signature contributed per electron. As stated, we propose that this is due to the 4s¹ electron disruption.

ANTIFERROMAGNETISM:
As mentioned above, chromium is the only metal that is naturally antiferromagnetic at room temperature, though it loses this antiferromagnetism in favor of paramagnetism at a rather low Curie Temperature of 38ºC.

This means that there is something about chromium’s electron structure that, when it is in crystalline metallic form at room temperature, its lowest energy state occurs when the electrons on adjacent atoms in the crystal are oriented with a magnetically antiparallel arrangement.

(NOTE: In the case of electrons, magnetically antiparallel does not mean the same as opposite spins. The former is a magnetic alignment distinction; the latter is a spin component phase relationship. Electrons of opposite spin can be either magnetically parallel or antiparallel. In the case of Hund’s 2^nd Rule, adjacent degenerate electrons will both align magnetically parallel and will have the same spins, in order to create the lowest energy composite state. [ref])

The precise mechanism behind chromium’s antiferromagnetic state remains a matter under investigation, though it is believed to relate to the Fermi surface geometry within the crystal (rather than the crystal periodicity itself). [Ashcroft, Ch. 33]

If we were to speculate, based upon the present sub-quantum mechanical model, it seems plausible that the driving force behind causing the electrons on adjacent atoms to align their magnetic moments antiparallel and their spins opposite might be the pairing up of the 4s¹ electrons, from adjacent atoms, in the electron gas. This might then cause the degenerate, unpaired pd-hybrid electrons to orient their spins to match the spin of their valence electron, in order to resonate mutually at the lowest energy. (Their coherence might explain why and how they both determine the Fermi surface in a crystal.)

If this conjecture is correct, it would account for why none of the other 3d transition metals are naturally antiferromagnetic. Each of the other 3d metal atoms contributes 2 valence electrons to the electron gas. They therefore do not require a valence electron of opposite spin from an adjacent atom in order to find the stability of an electron coupling (or, at least, a spin-zero average), and this form of coupling is therefore not present to anti-align the core unpaired electron orbitals of adjacent atoms. (Copper is an exception, since it also donates a valence electron into its core… although it contains no unpaired core electrons, which is why it is diamagnetic.)

According to this conjecture, it would seem that chromium’s antiferromagnetism does not arise from a crystal-wide spin-bonding resonance, as it does in the case of ferromagnetism. (It would therefore not be a form of ferromagnetism. It is proposed that chromium’s unpaired electron orbitals do not experience sufficient orbital extension to be ferromagnetic, due to constriction from only 3 same-shell di-electrons.) Consequently, the crystal structure of chromium — which is body-centered cubic (BCC) — should have no meaningful bearing on the mechanism behind its antiferromagnetism (as it would have in the case of a ferromagnetic crystal).

It is therefore proposed that the antiferromagnetism of chromium arises from an electron coupling resonance within the (valence) electron gas that binds the crystal. (This region is where the above-mentioned Fermi surface, as well as the valence and conduction bands are located.) Thus, even though the unpaired core electrons are not significantly extended, it is proposed that they do not need to be in order to resonate in degeneracy — to couple — with their own valence electron. (Perhaps we might even think of it as a kind of ‘local paramagnetism.’)

Since the coupling valence electron from each adjacent nearest-neighbor atom will have opposite spin, the (magnetic) core electrons of these adjacent atoms will therefore have opposite spins.

When the temperature increases enough to reach the Curie temperature, however, there is enough thermalization present to disrupt this weak electron gas coupling resonance, to the point where an external magnetic field will overwhelm it in favor of a crystal-wide paramagnetic alignment with the now-dominant external field. If this field is removed, the crystal will remain paramagnetic — with random magnetic alignments of the core electrons — until it cools below its Curie Temperature, at which time the electron gas coupling resonance can gain enough ‘traction’ over thermalization to re-enable antiferromagnetism.

Electrical Properties

It is interesting to note that the three best electrical conductors — silver (Ag), copper (Cu), and gold (Au) — all share a feature with chromium: a single valence s-orbital electron. However, chromium is a much weaker electrical conductor.

What separates the three precious-metal good conductors from chromium is the nature of their core electron resonances. In the three precious metal elements, the inner orbitals are all completely filled with di-electrons, which are diamagnetic. We might speculate then that, upon this ‘non-interfering’ foundation, the single-valence-electron conduction band may support the transmission of electrical potential through the metallic crystal quite effectively. In the case of chromium, however, there are five unpaired electrons on the surface of every atomic core in the crystal. Their magnetic field and spin interactions might interfere with the electrons in the conduction band in such a way that diminishes conductivity, due to resistance. It is further conceivable that, given the ratio of electrons involved, it may decrease chromium’s conductivity to merely one tenth of the conductivity of copper and silver.

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

23. Vanadium

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties

Vanadium is the 23^rd element on the periodic table. It has 23 protons and 28 neutrons for a mass of 51 amu, and 23 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Vanadium is the third element to feature electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to scandium (Sc) and titanium (Ti), it is proposed that vanadium has a 3^rd shell containing 3 di-electrons and 3 unpaired electrons in a p³d³-hybridized, octahedral symmetry (see image below). The 3 di-electron and the 3 unpaired electron sets are each planar arrangements, and they lie orthogonal (90⁰) to one another in making up the octahedral electron geometry.

This pd-hybridization does not need to involve the 3s-orbital electrons, and they can return to their preferred spherical di-electron state, within which (or upon which) the hybrid orbitals will resonate like harmonics upon a fundamental.

In such a configuration, the 4 tetrahedral di-electrons in the 2^nd shell will align themselves with two di-electrons roughly opposite two of the unpaired electrons in the 3^rd shell, allowing the other di-electrons to orient their directions roughly between one another, in order to minimize repulsion between shells.

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NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical octahedral structure that divides the 3^rd shell into six roughly equal volumes, with two 3-way symmetries, one of di-electrons and the other of unpaired electrons. Each shell segment 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).

It is also proposed that the stronger repulsion and larger charge density of the three di-electrons will constrict the three unpaired electron orbitals, bringing these three degenerate electrons into closer proximity. It is conceivable that this might even increase the coherence of the parallel spin bonding between them. (See Magnetic Properties below.)

As in the case of scandium and titanium, vanadium’s 3^rdshell p³d³-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. They are superimposed within it as a harmonic frequency coincides with its fundamental frequency in a resonance. It is proposed that the 3s² di-electron gives additional stability to the electron configuration within it, even though it contains 3 unpaired electrons. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they also achieve at least 4-directional symmetry with only their p– and d-orbitals.

Bonding & Ion Formation

The 4s²-orbital di-electron shell completes the atom. When forming a metallic crystal, the 4s² electrons delocalize to form the metallic bond, and when forming a 2+ ion, they are removed. In both cases, the core electron geometry remains the same. (A third ionization, would either leave the 2 remaining di-electrons in linearly opposite positions — if one of the di-electrons is ionized — or if it loses an unpaired electron, it will change it to the geometry of the previous element, titanium.)

Magnetic Properties

Vanadium has three unpaired electrons. In all elements prior to the d-block, unpaired electrons have occurred in the outer (valence) shell of the atom. Those are the electrons involved in chemical reactions. Vanadium is the third case of an atom with unpaired core electrons. They are protected from reacting (at least, until vanadium becomes a V²⁺ ion), and they are stabilized by the 3s di-electron ‘fundamental.’ We propose that it is this protection and stabilization of unpaired core electrons that allows them to interact magnetically, and that consequently determines an element’s magnetic properties.

Vanadium is the second least paramagnetic metal of the 3d row — excluding the diamagnetic copper and zinc — even though it has three times as many unpaired electrons as scandium, the second most paramagnetic.

As described above, it is proposed that vanadium has three unpaired electrons arranged in a planar arrangement within an octahedral electron structure. Due to the orbital constriction by the 3 di-electron orbitals in the same shell, the 3 unpaired electron orbitals should be compressed (and concentrated) into a slightly narrower wedge-like section of the spherical system.

The images below are intended to represent the orientation of these 3 electrons in an external (or adjacent atom’s) magnetic field (whose north pole is pointing upwards). (The purple arrows inside the atom represent the unpaired electrons and the black dots represent the relative positions of the di-electrons.)

While vanadium has three unpaired electrons — three times as many as scandium — it has a slightly lower magnetic susceptibility value of χ_m = +285, though still higher than titanium (with χ_m = +151). It is here proposed that this is due to the parallel spin bonding and field cancellation that occurs between its three unpaired electrons, given their proximity, degeneracy, and orbital constriction.

When unpaired electrons align linearly, as in the case of titanium (Ti), it was proposed that field cancellation occurs between them due to destructive interference, and that in ‘spin-space,’ the linear spin bonding reduces the magnetic signature of the electrons — their effective magnetic electron count (EME). In the case of vanadium, there are three electrons spin bonding together, but this time they are parallel spin bonding adjacent to one another. We might expect that this would increase the coherence of the spin bonding and decrease EME. On the other hand, the unpaired electrons are also being compressed together by the repulsion of 3 di-electron orbitals in the same shell, which should increase their EME. As such, it makes sense that each of vanadium’s electrons might contribute a diminished EME, though not quite as diminished as in the case of titanium.

If we consider scandium’s single unpaired electron to have an EME ≈ 1e^– (with χ_m = +295), and titanium’s 2 linear spin bonding electrons to have an EME ≈ 0.51e^– (with χ_m = +151), then vanadium’s 3 spin bonding electrons would have an EME ≈ 0.97e^–. That equates to about 0.32e^– of electron signature contributed per electron.

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

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22. Titanium

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties

Titanium is the 22^nd element on the periodic table. It has 22 protons and 26 neutrons for a mass of 48 amu, and 22 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Titanium is the second element to feature electrons in the d–orbital. Building upon the pd-hybridization we introduced in regard to scandium (Sc), it is proposed that titanium has a 3^rd shell containing 3 di-electrons and 2 unpaired electrons in p³d²-hybridized, trigonal bipyramidal symmetry. [Ref] The three p-orbital di-electrons will occupy the equatorial positions for maximum distance, since di-electrons repel more strongly than single electrons, forcing the 2 unpaired electrons into the two axial positions. This pd-hybridization does not need to involve the 3s-orbital electrons, and they can return to their preferred spherical di-electron state, within which (or upon which) the hybrid orbitals will resonate like harmonics upon a fundamental.

In such a configuration, the 4 tetrahedral 2^nd shell di-electrons will align themselves with one di-electron opposite one of the single axial electrons in the 3^rd shell, allowing the remaining 2^nd and 3^rd shell di-electrons to orient their directions roughly between one another, in order to minimize repulsion between shells.

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NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical trigonal bipyramidal structure that divides the shell into five roughly equal volumes, with 2-way and 3-way symmetries. Each shell segment 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).

As in the case of scandium, titanium’s 3^rdshell p³d²-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. They are superimposed within it as a harmonic frequency coincides with its fundamental frequency in a resonance. It is proposed that the 3s² di-electron gives additional stability to the electron configuration within it, even though it contains 2 unpaired electrons. The remaining elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they also achieve at least 4-directional symmetry with only their p– and d-orbitals.

Bonding & Ion Formation

The 4s²-orbital di-electron shell completes the atom. When forming a metallic crystal, the 4s² electrons delocalize to form the metallic bond, and when forming a 2+ ion, they are removed. In both cases, the core electron geometry remains the same. (A third ionization, however, would either shift the 2 remaining di-electrons into the axial positions — if one of the di-electrons is ionized — or if it loses an unpaired electron, it will change to the geometry of the previous element, scandium.)

Magnetic Properties

Titanium has two unpaired electrons. In all elements prior to the d-block, unpaired electrons have occurred in the outer (valence) shell of the atom. Those are the electrons involved in chemical reactions. Titanium is the second case of an atom with unpaired core electrons. They are protected from reacting (at least, until titanium becomes a Ti²⁺ ion), and they are stabilized by the 3s di-electron ‘fundamental.’ We propose that it is this protection and stabilization of unpaired core electrons that allows them to interact magnetically, and that consequently determines an element’s magnetic properties.

Titanium is the least paramagnetic metal of the 3d row — excluding the diamagnetic copper and zinc — even though it has twice as many unpaired electrons as scandium, which is the second most paramagnetic.

As described above, it is proposed that titanium has two unpaired electrons arranged linearly and axially in its trigonal bipyramidal electron structure. The images below are intended to represent the orientation of these 2 electrons in an external (or adjacent atom’s) magnetic field (whose north pole is pointing upwards). (The purple arrows inside the atom represent the unpaired electrons and the black dots represent the relative positions of the 3 di-electrons in that shell.)

While titanium has two unpaired electrons — twice as many as scandium — it has a much lower magnetic susceptibility value of only χ_m = +151, about half of scandium’s value (of χ_m = +295). It is here proposed that this is due to the linear spin bonding and magnetic field cancellation that occurs between the two unpaired core electrons, as a result of their linear geometry.

When two unpaired, same-spin electrons align linearly, their magnetic fields are aligned in such a way that allows field cancellation to occur between them through destructive interference. In ‘spin-space,’ overall spin is reduced through ‘linear spin bonding‘ (LSB). It is proposed that this reduces what we refer to as the effective magnetic electron (EME) signature with respect to an external magnetic field, and thus, will manifest as a weaker magnetic susceptibility for the atom.

If we consider scandium’s single unpaired electron to have an EME ≈ 1e^– (with χ_m = +295), then titanium’s 2 linear spin bonding electrons (with χ_m = +151) would have an EME ≈ 0.51e^–. That equates to about 0.25e^– of electron signature contributed per electron.

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

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