Diamagnetism
Condensed matter physics |
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Diamagnetism is the property of materials that are repelled by a
Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was repelled by magnetic fields.[1] In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by William Whewell, Faraday first referred to the phenomenon as diamagnetic (the prefix dia- meaning through or across), then later changed it to diamagnetism.[2][3]
A simple rule of thumb is used in chemistry to determine whether a particle (atom, ion, or molecule) is paramagnetic or diamagnetic:[4] If all electrons in the particle are paired, then the substance made of this particle is diamagnetic; If it has unpaired electrons, then the substance is paramagnetic.
Materials
Diamagnetism is a property of all materials, and always makes a weak contribution to the material's response to a magnetic field. However, other forms of magnetism (such as
Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore a magnetic susceptibility less than or equal to 0, since susceptibility is defined as χv = μv − 1. This means that diamagnetic materials are repelled by magnetic fields. However, since diamagnetism is such a weak property, its effects are not observable in everyday life. For example, the magnetic susceptibility of diamagnets such as water is χv = −9.05×10−6. The most strongly diamagnetic material is bismuth, χv = −1.66×10−4, although pyrolytic carbon may have a susceptibility of χv = −4.00×10−4 in one plane. Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Because χv is derived from the ratio of the internal magnetic field to the applied field, it is a dimensionless value.
In rare cases, the diamagnetic contribution can be stronger than paramagnetic contribution. This is the case for gold, which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with X-ray magnetic circular dichroism, has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution.[5]
Material | χv [× 10−5 (SI units)] |
---|---|
Superconductor | −105 |
Pyrolytic carbon | −40.9 |
Bismuth | −16.6 |
Neon | −6.74 |
Mercury | −2.9 |
Silver | −2.6 |
Carbon (diamond) | −2.1 |
Lead | −1.8 |
Carbon (graphite) | −1.6 |
Copper | −1.0 |
Water | −0.91 |
Superconductors
Superconductors may be considered perfect diamagnets (χv = −1), because they expel all magnetic fields (except in a thin surface layer) due to the Meissner effect.[7]
Demonstrations
Curving water surfaces
If a powerful magnet (such as a
Levitation
Diamagnets may be levitated in stable equilibrium in a magnetic field, with no power consumption. Earnshaw's theorem seems to preclude the possibility of static magnetic levitation. However, Earnshaw's theorem applies only to objects with positive susceptibilities, such as ferromagnets (which have a permanent positive moment) and paramagnets (which induce a positive moment). These are attracted to field maxima, which do not exist in free space. Diamagnets (which induce a negative moment) are attracted to field minima, and there can be a field minimum in free space.
A thin slice of
The Radboud University Nijmegen, the Netherlands, has conducted experiments where water and other substances were successfully levitated. Most spectacularly, a live frog (see figure) was levitated.[11]
In September 2009, NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California announced it had successfully levitated mice using a superconducting magnet,[12] an important step forward since mice are closer biologically to humans than frogs.[13] JPL said it hopes to perform experiments regarding the effects of microgravity on bone and muscle mass.
Recent experiments studying the growth of protein crystals have led to a technique using powerful magnets to allow growth in ways that counteract Earth's gravity.[14]
A simple homemade device for demonstration can be constructed out of bismuth plates and a few permanent magnets that levitate a permanent magnet.[15]
Theory
The electrons in a material generally settle in orbitals, with effectively zero resistance and act like current loops. Thus it might be imagined that diamagnetism effects in general would be common, since any applied magnetic field would generate currents in these loops that would oppose the change, in a similar way to superconductors, which are essentially perfect diamagnets. However, since the electrons are rigidly held in orbitals by the charge of the protons and are further constrained by the Pauli exclusion principle, many materials exhibit diamagnetism, but typically respond very little to the applied field.
The Bohr–Van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. However, the classical theory of Langevin for diamagnetism gives the same prediction as the quantum theory.[16] The classical theory is given below.
Langevin diamagnetism
The magnetic moment of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the z axis. The average loop area can be given as , where is the mean square distance of the
If the distribution of charge is spherically symmetric, we can suppose that the distribution of x,y,z coordinates are
In atoms, Langevin susceptibility is of the same order of magnitude as Van Vleck paramagnetic susceptibility.
In metals
The Langevin theory is not the full picture for
where is the Fermi energy. This is equivalent to , exactly times Pauli paramagnetic susceptibility, where is the Bohr magneton and is the density of states (number of states per energy per volume). This formula takes into account the spin degeneracy of the carriers (spin ½ electrons).
In doped semiconductors the ratio between Landau and Pauli susceptibilities may change due to the effective mass of the charge carriers differing from the electron mass in vacuum, increasing the diamagnetic contribution. The formula presented here only applies for the bulk; in confined systems like quantum dots, the description is altered due to quantum confinement.[22][23] Additionally, for strong magnetic fields, the susceptibility of delocalized electrons oscillates as a function of the field strength, a phenomenon known as the De Haas–Van Alphen effect, also first described theoretically by Landau.
See also
- Antiferromagnetism
- Magnetochemistry
- Moses effect
- Diamagnetic inequality – Mathematical inequality relating the derivative of a function to its covariant derivative
References
- ^ Gerald Küstler (2007). "Diamagnetic Levitation – Historical Milestones". Rev. Roum. Sci. Techn. Électrotechn. Et Énerg. 52, 3: 265–282.
- PMID 26221835.
- ^ "diamagnetic, adj. and n". OED Online. Oxford University Press. June 2017.
- ^ "Magnetic Properties". Chemistry LibreTexts. 2 October 2013. Retrieved 21 January 2020.
- PMID 22400883.)
{{cite journal}}
: CS1 maint: multiple names: authors list (link - ^ Nave, Carl L. "Magnetic Properties of Solids". Hyper Physics. Retrieved 9 November 2008.
- ISBN 9780080550480.
- ^ Beatty, Bill (2005). "Neodymium supermagnets: Some demonstrations—Diamagnetic water". Science Hobbyist. Retrieved 26 September 2011.
- ^ Quit007 (2011). "Diamagnetism Gallery". DeviantART. Retrieved 26 September 2011.
{{cite web}}
: CS1 maint: numeric names: authors list (link) - ^ "Diamagnetic Levitation". High Field Laboratory. Radboud University Nijmegen. 2011. Retrieved 26 September 2020.
- ^ "The Real Levitation". High Field Laboratory. Radboud University Nijmegen. 2011. Retrieved 26 September 2011.
- .
- ^ Choi, Charles Q. (9 September 2009). "Mice levitated in lab". Live Science. Retrieved 26 September 2011.
- ^ Kleiner, Kurt (10 August 2007). "Magnetic gravity trick grows perfect crystals". New Scientist. Retrieved 26 September 2011.
- ^ "Fun with diamagnetic levitation". ForceField. 2 December 2008. Archived from the original on 12 February 2008. Retrieved 26 September 2011.
- ^ ISBN 978-0-471-87474-4.
- ISSN 0368-3893.
- ISBN 978-0471415268.
- ^ Landau, L. D. "Diamagnetismus der metalle." Zeitschrift für Physik A Hadrons and Nuclei 64.9 (1930): 629-637.
- ^ Chang, M. C. "Diamagnetism and paramagnetism" (PDF). NTNU lecture notes. Archived (PDF) from the original on 4 May 2006. Retrieved 24 February 2011.
- ^ Drakos, Nikos; Moore, Ross; Young, Peter (2002). "Landau diamagnetism". Electrons in a magnetic field. Retrieved 27 November 2012.
- .
- S2CID 119330207.
External links
- Media related to Diamagnetism at Wikimedia Commons
- The Feynman Lectures on Physics Vol. II Ch. 34: The Magnetism of Matter