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Conduction zone

From EverybodyWiki Bios & Wiki


Conduction zone refers to the network of electron paths between molecules in a conductor where electrons can flow along the paths at the same energy level, resulting in currents. An electron, with an energy level below the conduction zone, remains confined within its orbital[1] inside the individual molecule and it cannot produce any current. To create currents in a conductor, electrons must be at a sufficient energy level to move in the conduction zone.[2] So, the space in a conductor is divided into two different types of regions: the network of conduction zone and isolated cells around individual molecules, somewhat like cement and pebbles in a piece of concrete. A conduction zone does not always appear in all materials. It is necessary for conductors, but absent in insulators. A superconductor[3] is a special conductor with valence orbitals intersecting the conduction zone. Therefore, the valence electrons move naturally in the conduction zone without the need for energy to elevate them to the conduction zone. It is important to note that the term conduction band refers to a different concept defined in band theory.[4]

The term conduction zone was introduced in the "Unified Theory of Low and High-Temperature Superconductivity."[2] It establishes a unified theoretical framework for both low and high-temperature superconductivity[5] and provides a cohesive approach to understanding the differences among insulators, conductors, and superconductors. Insulating, conducting and superconducting can be different electrical states of the same matter. Transitions between these states are typically associated with the conduction zone's response to changes in pressure and temperature conditions. Furthermore, the concept of the conduction zone provides a comprehensive explanation for various phenomena observed in superconductivity and offers practical guidelines for the search and development of superconductors that operate under standard conditions on Earth.

Attraction Coefficient

Outer shells of the electron cloud of atoms in a molecule are typically distributed unevenly, resulting in various intermolecular forces.[6] Intermolecular attractions, or bonds, hold molecules at a close distance, which is crucial to the development of conduction zones, enabling electrons to flow between molecules. It is important to note that molecular bonds, such as covalent bonds[7] allow electrons to move between atoms within individual molecules but do not facilitate electron movement between different molecules necessary for the current generation.

To learn the influence of bonding intensity on conduction zones and to identify the boundary between the conduction zone and molecule cells in a conductor, the concept of attraction coefficient is introduced, denoted by the symbol c.[2] This coefficient models the intensity of the attraction on an electron by an adjacent molecule, such as that due to a metallic bond.[8] Assume that an electron is attracted by its nucleus with an equivalent charge Q, taking into account other electrons in the same molecule, the attraction to the electron by an adjacent molecule in the crystal lattice can be modeled as it is from a charge of cQ. The value of c is typically between 0 and 1. An adjacent molecule with an electron hole has the equivalent influence on the electron to that from the original molecule, i.e., c = 1. When c = 0, it indicates the adjacent molecule has no influence on the electron. Hence, the force exerted on the electron by both molecules can be determined, even when considering all the molecules in the crystal. Consequently, the energy level of the electron and the potential fields between molecules can be calculated at any given location within the lattice structure.

For instance, the Coulomb force[9] exerted on an electron on the centerline between two molecules can be determined by

F=KQe[1r2−c(2R−r)2]

where K represents the Coulomb constant,[10] e is the charge of the electron, r is the orbital radius of the electron, and R is the half distance between the centers of the two molecules, representing the distance to the border between the molecules. Different values of c model various attraction intensities due to different bonds between molecules. This model may be extended to include the influences of all the molecules in the crystal lattice of a conductor. However, the effects of other molecules decrease rapidly with increasing distance from the original molecules, making their contributions less significant in the overall interaction.

Using this model, the energy level of an electron is calculated along the centerline between two single-atom molecules with c = 1.[2] It increases from a negative value near the nucleus of its atom, reaches zero at an orbital radius or a distance from its nucleus that is 0.382 of the half nuclei distance between the two atoms, and becomes positive further toward the border between the atoms. The positive energy level indicates the electron is no longer confined by its nucleus and is capable of moving between different molecules. Therefore, the region with positive energy defines the conduction zone. The zero energy point identifies the intersection of the centerline with the boundary between the molecule cell and the conduction zone.

When c = ⅓, the energy level becomes positive at an orbital radius that is 0.785 of the distance to the border, resulting in a smaller or narrower conduction zone. With c = 0, the energy level remains entirely negative, indicating the absence of a conduction zone, which corresponds to the insulating state of matter. In general, the width of the conduction zone decreases with decreasing c and disappears at a value of around 0.225. This demonstrates the relationship between the attraction coefficient, representing bonding intensity between molecules, and the extent of the conduction zone, relating to the electrical state of matter.

The Nature of Resistivity and Superconductivity

Due to Coulomb's force, an electron, carrying a negative charge, is always influenced by nearby nuclei and electrons.[10] Its movement is governed by the fields, not randomly within a conductor. Each electron travels in an orbital path corresponding to its energy level. At low energy levels, an electron is limited to its atomic orbitals.[1] It may move between atoms within the same molecule, such as shared electrons in a covalent bond.[7] However, these movements do not produce electrical currents. As a result, low-energy electrons are confined in their molecule cells before being excited into high levels by external energy.

At higher energy levels, an electron can travel between molecules along the conduction zone, generating a current in a conductor.[2] The conduction zone can be perceived somewhat as a shared orbital at a high energy level among multiple molecules and serves as an isoenergy pathway for electrons to flow between molecules in a conductor. It is important to note that a conduction zone is not a free space between molecules where electrons can move randomly. A conduction zone is filled with electrical fields created by charges of surrounding molecules where only electrons with sufficient energy can travel in it. Hence, instead of random movement, the flow of electrons in a conductor is completely governed by the electrical fields between molecules.

To create currents in a conductor, valence electrons must be elevated to the conduction zone. The energy required to raise electrons is the cause of electrical resistance.[11] The excited electrons tend to retreat to lower orbitals where there are electron holes, dissipating their energy as heat in the form of photons.[12] Therefore, the resistivity of a conductor relates directly to the energy gap between the conduction zone and valence orbitals, and specifically, a smaller gap corresponds to lower resistivity.[2] In the case of a superconductor, some valence orbitals intersect the conduction zone, effectively eliminating the energy gap. Hence, the valence electrons reside naturally in the conduction zone without the need to lift to the zone for creating currents, resulting in zero resistance.

Explaining the Properties of Superconductivity

In an external magnetic field, moving electrons in the conduction zone of a superconductor are deflected by the Lorentz force.[13] Consequently, the electrons circulate in a direction to generate a magnetic field that compensates for the external field inside the superconductor and superimposes the field outside,[2] resulting in the Meissner effect.[14] The number of moving electrons in the conduction zone limits the maximum current density in the superconductor, known as the critical current density of the superconductor.[15] As the external magnetic field increases to an intensity where the movement of all electrons in the conduction zone cannot completely cancel the applied field, the remaining external field deflects the orbital electron movement, primarily the valence electrons. The electron clouds are compressed along the direction of the external field. To a certain extent, the valence electrons are pulled below the conduction zone, resulting in the destruction of superconductivity.[2] The maximum survival field is known as the critical field of the superconductor.[16] This explains the correlation between the critical magnetic field and the critical current density of a superconductor.


A type-II superconductor[17] is typically composed of alloys or compounds. The bonding strengths and width of the conduction zones vary between different molecules. As a result, its superconductivity in different regions survives in different external magnetic fields. The two critical fields of a type-II superconductor are the minimum and maximum survival fields. Due to the asymmetric crystal structure, the superconductivity of the same region may be destroyed at different field intensities from different directions. Thus, the critical fields of a type-II superconductor are sensitive to and vary in the direction of the applied fields. In the mixed state, the regions where superconductivity is destroyed become normal conductors and form vortices,[18] allowing the external magnetic fields to pass through. As the applied field increases, more and more regions with higher critical fields are destroyed, increasing the density of vortices.

The flux quantum is the minimum value of magnetic flux, which is created by the movement of a single electron.[19] It can be determined by the Schrödinger equation to be h/2e, where h represents the Planck constant and e is the charge of an electron. This prediction can be verified using a superconductor in a donut shape. For an electron to move between molecules, it must start with an electron orbital transition which also results in an electron hole. Thus, the flow of an electron must be accompanied by a drift of the electron hole, therefore creating two flows of charges simultaneously. The minimum flux in a donut-shaped superconductor is a result of the two flows in opposite directions around the donut, equivalent to two electrons moving in the same direction. This predicts the minimum flux in a superconductor to be twice the flux quantum, which has been confirmed in experiments by B. S. Deaver and W. M. Fairbank,[20] and independently by R. Doll and M. Näbauer.[21]

Electrical Resistance State of Matter

Solid and fluid are different sheering resistance states of matter at various pressures and temperatures.[22] Similarly, a substance can also display different electrical resistance states (insulating, conducting, and superconducting) and transitions from one state to another at different pressures and temperatures.[2]

As pressure increases, while the distance between molecules is reduced, the resistivity of a conductor decreases with the reduction in the gap between the conduction zone and valence orbitals. This explains the observations of negative correspondence between pressure and resistivity.[23][24][25] At certain high pressures, this gap can eventually be reduced to zero, eliminating electrical resistance and resulting in superconductivity. This is why more and more superconductors are obtained at high pressures and some ceramics, expected insulators, transition to superconductors at high pressures.[26][27][28][29]

At low temperatures, electrons tend to retreat to lower orbitals, decreasing the repulsion between molecules. As a result, the surrounding pressure on Earth becomes more significant, reducing molecular distance and creating a compression effect equivalent to a pressure increase. This explains the positive correlation between temperature and resistivity in conductors, as well as why conventional superconductors are typically observed at low temperatures.[30][31]

Attractions, or bonds, develop at short distances between molecules. Some of them, such as compression bonds,[32] are induced primarily due to interaction between molecules at high pressures. Hence, the attraction coefficient typically increases with pressure, which also reinforces the negative relationship between pressure and resistivity.

In general, increasing pressure reduces the gap between the conduction zone and valence orbitals, therefore, decreasing the resistivity of conductors.[2] Pressure increases the attraction coefficient, leading to wider conduction zones and also reducing the resistivity of conductors. Thus, as pressure increases, a conduction zone may develop in an insulator, which transitions the insulator into a conductor. As pressure increases further, the conduction zone becomes wider and the gap between the conduction zone and valence orbitals decreases, reducing the resistivity of the conductor. At even higher pressures, the gap can be completely closed, eliminating the resistance in the conductor and resulting in a superconductor. As mentioned earlier, the decrease in temperature at a constant surrounding pressure creates an equivalent compression effect, resulting in a positive correlation between temperature and resistivity. Therefore, pressure and temperature play crucial roles in determining the electrical states of matter.

The critical point of a superconductor refers to the specific transition temperature observed at a particular pressure. For a conventional superconductor, this critical point is measured under normal Earth pressure. A superconductor may exhibit multiple critical temperatures at different pressures.[2] All these critical points collectively depict the superconducting transition boundary in a state diagram.

From a different perspective, the resistivity of a conductor can be conceptualized as a function of pressure and temperature. This relationship can be visualized as a surface, where each point on the surface represents the resistivity at a specific pressure and temperature. The superconductivity transition boundary is the curve where the surface intersects with the pressure-temperature plane at zero resistivity.

At the microscopic level, the conducting-superconducting transition boundary signifies the pressures and temperatures under which the conduction zone starts to overlap with valence orbitals. The conducting-insulating transition boundary indicates the pressures and temperatures at which the width of the conduction zone reduces to zero, which corresponds to an attraction coefficient of approximately 0.225 predicted in the model mentioned earlier.

Search for Room-Temperature Superconductors

With the understanding of the microscopic nature of superconductivity, the pursuit of room-temperature superconductors is no longer a random endeavor but becomes a deliberate engineering task. While the conduction zone theory predicts superconducting to be an ordinary state of matter,[2] the vast majority of substances exhibit superconductivity only under extremely high pressures and/or low temperatures. For practical applications, it is necessary to develop superconductors that can operate under normal conditions on Earth. To achieve this goal, the engineering task needs to leverage intermolecular attractions to overcome the repulsions. By arranging molecules in close proximity, it becomes possible to create expansive conduction zones that overlap with valence orbitals.

Electronegativity[33][34] plays a crucial role in the selection of elements for engineering superconductors. It is important to avoid elements with excessively high electronegativity, as they tend to tightly hold onto electrons, hindering the flow of current between molecules. Conversely, elements with insufficient electronegativity are unable to establish the necessary intermolecular attractions needed to develop wider conduction zones.

To prevent certain atoms from excessively retaining electrons, it is advantageous to choose elements with a narrow range of electronegativities. By maintaining a close range of electronegativities among the selected elements, it becomes possible to strike a balance that promotes the formation of interconnected conduction zones and facilitates optimal electron flow between different molecules.

The molecular structure of compounds and alloys that incorporate a combination of large and small atoms gives rise to irregular intermolecular fields and forces, thereby increasing the likelihood of fostering intermolecular attractions. However, it is essential to steer clear of excessively complex, large compound molecules as they can disrupt the connectivity of conduction zones, similar to the situation observed in most insulators.

See also

References

  1. ↑ 1.0 1.1 Orchin, Milton; Macomber, Roger S.; Pinhas, Allan; Wilson, R. Marshall (2005). "1. Atomic Orbital Theory" (PDF). The Vocabulary and Concepts of Organic Chemistry (2nd ed.). Wiley. Archived from the original (PDF) on 9 October 2022. Unknown parameter |url-status= ignored (help) Search this book on
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 Liu, Jerry Z. (2019). "Unified Theory of Low and High-Temperature Superconductivity". Stanford University. Archived from the original on 9 February 2023. Retrieved 8 September 2022. Unknown parameter |url-status= ignored (help)
  3. ↑ Combescot, Roland (2022). Superconductivity. Cambridge University Press. pp. 1–2. ISBN 9781108428415. Search this book on
  4. ↑ Ashcroft, N. W.; Mermin, N. D. (1976). Solid State Physics. Brooks/Cole. ISBN 978-0-03-083993-1. Search this book on
  5. ↑ Grant, Paul Michael (2011). "The Great Quantum Conundrum". Nature. Nature Publishing Group. 476 (7358): 37–39. doi:10.1038/476037a. PMID 21814269. Unknown parameter |s2cid= ignored (help)
  6. ↑ Margenau H, Kestner NR (1969). Theory of Intermolecular Forces. International Series of Monographs in Natural Philosophy. 18 (1st ed.). Oxford: Pergamon Press. ISBN 978-0-08-016502-8. Search this book on
  7. ↑ 7.0 7.1 Whitten, Kenneth W.; Gailey, Kenneth D.; Davis, Raymond E. (1992). "7-3 Formation of Covalent Bonds". General Chemistry (4th ed.). Saunders College Publishing. p. 264. ISBN 0-03-072373-6. Search this book on
  8. ↑ Brown, Theodore L.; LeMay, H. Eugene Jr.; Bursten, Bruce E.; Murphy, Catherine; Woodward, Patrick (2017). Chemistry: The Central Science (14th ed.). Pearson. ISBN 978-0-13-441423-2. Search this book on
  9. ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2013). Fundamentals of Physics. John Wiley & Sons. pp. 609, 611. ISBN 9781118230718. Search this book on
  10. ↑ 10.0 10.1 Huray, Paul G. (2010). Maxwell's Equations. Hoboken, New Jersey: Wiley. pp. 8, 57. ISBN 978-0-470-54991-9. OCLC 739118459. Search this book on
  11. ↑ Gleick, James (1986-10-21). "PHYSICISTS FINALLY GET TO SEE QUANTUM JUMP WITH OWN EYES". The New York Times. ISSN 0362-4331. Retrieved 2021-12-06.
  12. ↑ Itano, W.M.; Bergquist, J.C.; Wineland, D. J. (2015). "Early observations of macroscopic quantum jumps in single atoms" (PDF). International Journal of Mass Spectrometry. 377: 403. Bibcode:2015IJMSp.377..403I. doi:10.1016/j.ijms.2014.07.005.
  13. ↑ Griffiths, David J. (2017). Introduction to Electrodynamics (4th ed.). Cambridge University Press. p. 218. ISBN 978-1-107-01402-2. Search this book on
  14. ↑ Meissner, W.; Ochsenfeld, R. (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". Naturwissenschaften. 21 (44): 787–788. Bibcode:1933NW.....21..787M. doi:10.1007/BF01504252. Unknown parameter |s2cid= ignored (help)
  15. ↑ Blatter, G.; Feigel'man, M. V.; Geshkenbein, V. B.; Larkin, A. I.; Vinokur, V. M. (1994). "Critical Current Density and Flux Pinning in High-Temperature Superconductors". Reviews of Modern Physics. 66 (4): 1125–1388. doi:10.1103/RevModPhys.66.1125.
  16. ↑ De Gennes, P. G. (1964). "Magnetic Field Effects in Type-II Superconductors". Reviews of Modern Physics. 36 (2): 225–237. doi:10.1103/RevModPhys.36.225.
  17. ↑ Rjabinin, J. N.; Shubnikow, L. W. (1935). "Magnetic Properties and Critical Currents of Supra-conducting Alloys". Nature. 135 (3415): 581. Bibcode:1935Natur.135..581R. doi:10.1038/135581a0. Unknown parameter |s2cid= ignored (help)
  18. ↑ Orthacker, Angelina. "Superconductivity" (PDF). Technical University of Graz.
  19. ↑ London, Fritz (1950). Superfluids: Macroscopic Theory of Superconductivity. John Wiley & Sons. p. 152. Search this book on
  20. ↑ Deaver, Bascom; Fairbank, William (1961). "Experimental Evidence for Quantized Flux in Superconducting Cylinders". Physical Review Letters. 7 (2): 43–46. Bibcode:1961PhRvL...7...43D. doi:10.1103/PhysRevLett.7.43.
  21. ↑ Doll, R.; Näbauer, M. (1961). "Experimental Proof of Magnetic Flux Quantization in a Superconducting Ring". Physical Review Letters. 7 (2): 51–52. Bibcode:1961PhRvL...7...51D. doi:10.1103/PhysRevLett.7.51.
  22. ↑ M.A. Wahab (2005). Solid State Physics: Structure and Properties of Materials. Alpha Science. pp. 1–3. ISBN 978-1-84265-218-3. Search this book on
  23. ↑ Machado, A.J.S.; Renosto, S.T.; Santos, C.A.M. dos; Alves, L.M.S.; Fisk, Z. (2012). Defect Structure Versus Superconductivity in MeB2 Compounds (Me = Refractory Metals) and One-Dimensional Superconductors. doi:10.5772/48625. ISBN 978-953-51-0794-1. Unknown parameter |s2cid= ignored (help) Search this book on
  24. ↑ Vaidya, R.; Bhatt, N.; Patel, S.G.; Jani, A.R.; Garg, A.; Vijayakumar, V.; Godwal, B. (2003). "Effect of pressure on electrical resistance of WSe2 single crystal". Pramana -- Journal of Physics. 61 (1): 183–186. Bibcode:2003Prama..61..183V. doi:10.1007/BF02704523. Unknown parameter |s2cid= ignored (help)
  25. ↑ Souza, E.L. de; Gomes, J.E.; Araújo, F.G.S.; Oliveira, C.P. de (2006). "Improvement of metallic joint electrical conductivity using a novel conductive paste produced from recycled residues". Rev. Esc. Minas. 59 (2): 213–216. doi:10.1590/S0370-44672006000200011.
  26. ↑ J. G. Bednorz; K. A. Müller (1986). "Possible high Tc superconductivity in the Ba−La−Cu−O system". Z. Phys. B. 64 (1): 189–193. Bibcode:1986ZPhyB..64..189B. doi:10.1007/BF01303701. Unknown parameter |name-list-style= ignored (help); Unknown parameter |s2cid= ignored (help)
  27. ↑ "1987: J. Georg Bednorz, K. Alex Müller". Nobelprize.org. The Nobel Prize in Physics. Archived from the original on September 19, 2008. Retrieved April 19, 2012.
  28. ↑ Choi, Charles Q. "A New Iron Age: New class of superconductor may help pin down mysterious physics". Scientific American. Retrieved October 25, 2019.
  29. ↑ Ren, Zhi-An; Che, Guang-Can; Dong, Xiao-Li; Yang, Jie; Lu, Wei; Yi, Wei; et al. (2008). "Superconductivity and phase diagram in iron-based arsenic-oxides ReFeAsO1−δ (Re=rare-earth metal) without fluorine doping". EPL. 83 (1): 17002. arXiv:0804.2582. Bibcode:2008EL.....8317002R. doi:10.1209/0295-5075/83/17002. Unknown parameter |s2cid= ignored (help)
  30. ↑ Combescot, Roland (2022). Superconductivity. Cambridge University Press. pp. 1–2. ISBN 9781108428415. Search this book on
  31. ↑ Fossheim, Kristian; Sudboe, Asle (2005). Superconductivity: Physics and Applications. John Wiley and Sons. p. 7. ISBN 9780470026434. Search this book on
  32. ↑ Liu, Jerry Z. (2021). "Superfluids Are Not Fluids". Stanford University. Archived from the original on 8 April 2023. Retrieved 10 July 2022. Unknown parameter |url-status= ignored (help)
  33. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Electronegativity". doi:10.1351/goldbook.E01990
  34. ↑ Jensen, W.B. (1996). "Electronegativity from Avogadro to Pauling: Part 1: Origins of the Electronegativity Concept". Journal of Chemical Education. 73 (1): 11–20. Bibcode:1996JChEd..73...11J. doi:10.1021/ed073p11.


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