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Magnetic property of ordinary materials
Pyrolytic carbon has one of the largest diamagnetic constants[clarification needed] of any room temperature material. Here a pyrolytic carbon sheet is levitated by its repulsion from the strong magnetic field ofneodymium magnets
Diamagnetism is the property of materials that are repelled by amagnetic field; an applied magnetic field creates aninduced magnetic field in them in the opposite direction, causing a repulsive force. In contrast,paramagnetic andferromagnetic materials are attracted by a magnetic field. Diamagnetism is aquantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force ofmagnetic dipoles in the material. Themagnetic permeability of diamagnetic materials is less than thepermeability of vacuum,μ0. In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but asuperconductor acts as a strong diamagnet because it entirely expels any magnetic field from its interior (theMeissner effect).
Diamagnetism was first discovered whenAnton Brugmans observed in 1778 thatbismuth 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 byWilliam Whewell, Faraday first referred to the phenomenon asdiamagnetic (the prefixdia- meaningthrough oracross), then later changed it todiamagnetism.[2][3]
A simplerule 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.
Diamagnetic material interaction inmagnetic field. On keeping diamagnetic materials in a magnetic field, the electron orbital motion changes in such a way that magnetic dipole moments are induced on the atoms / molecules in the direction opposite to the external magnetic field
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 asferromagnetism orparamagnetism) are so much stronger such that, when different forms of magnetism are present in a material, the diamagnetic contribution is usually negligible. Substances where the diamagnetic behaviour is the strongest effect are termed diamagnetic materials, or diamagnets. Diamagnetic materials are those that some people generally think of asnon-magnetic, and includewater,wood, most organic compounds such as petroleum and some plastics, and many metals includingcopper, particularly the heavy ones with manycore electrons, such asmercury,gold andbismuth. The magnetic susceptibility values of various molecular fragments are calledPascal's constants (named afterPaul Pascal [fr]).
Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore amagnetic susceptibility less than or equal to 0, since susceptibility is defined asχv =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 isχv =−9.05×10−6. The most strongly diamagnetic material isbismuth,χv =−1.66×10−4, althoughpyrolytic carbon may have a susceptibility ofχv =−4.00×10−4 in one plane. Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Becauseχv 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 forgold, which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully withX-ray magnetic circular dichroism, has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution.[5]
Transition from ordinaryconductivity (left) tosuperconductivity (right). At the transition, thesuperconductor expels the magnetic field and then acts as a perfect diamagnet.
If a powerful magnet (such as asupermagnet) is covered with a layer of water (that is thin compared to the diameter of the magnet) then the field of the magnet significantly repels the water. This causes a slight dimple in the water's surface that may be seen by a reflection in its surface.[8][9]
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 ofpyrolytic graphite, which is an unusually strongly diamagnetic material, can be stably floated in a magnetic field, such as that fromrare earth permanent magnets. This can be done with all components at room temperature, making a visually effective and relatively convenient demonstration of diamagnetism.
TheRadboud University Nijmegen, theNetherlands, 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'sJet Propulsion Laboratory (JPL) in Pasadena, California announced it had successfully levitated mice using asuperconducting 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]
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 thePauli exclusion principle, many materials exhibit diamagnetism, but typically respond very little to the applied field.
TheBohr–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.
Paul Langevin's theory of diamagnetism (1905)[17] applies to materials containing atoms with closed shells (seedielectrics). A field with intensityB, applied to anelectron with chargee and massm, gives rise toLarmor precession with frequencyω =eB / 2m. The number of revolutions per unit time is ω / 2π, so the current for an atom withZ electrons is (inSI units)[16]
Themagnetic moment of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with thez axis. The average loop area can be given as, where is the mean square distance of theelectrons perpendicular to thez axis. The magnetic moment is therefore
If the distribution of charge is spherically symmetric, we can suppose that the distribution ofx,y,z coordinates areindependent and identically distributed. Then, where is the mean square distance of the electrons from the nucleus. Therefore,. If is the number of atoms per unit volume, the volumediamagnetic susceptibility in SI units is[18]
The Langevin theory is not the full picture formetals because there are also non-localized electrons. The theory that describes diamagnetism in afree electron gas is calledLandau diamagnetism, named afterLev Landau,[19] and instead considers the weak counteracting field that forms when the electrons' trajectories are curved due to theLorentz force. Landau diamagnetism, however, should be contrasted withPauli paramagnetism, an effect associated with the polarization of delocalized electrons' spins.[20][21] For the bulk case of a 3D system and low magnetic fields, the (volume) diamagnetic susceptibility can be calculated usingLandau quantization, which in SI units is
where is theFermi energy. This is equivalent to, exactly times Pauli paramagnetic susceptibility, where is theBohr magneton and is thedensity of states (number of states per energy per volume). This formula takes into account the spin degeneracy of the carriers (spin-1/2 electrons).
Indoped semiconductors the ratio between Landau and Pauli susceptibilities may change due to theeffective 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 likequantum dots, the description is altered due toquantum 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 theDe Haas–Van Alphen effect, also first described theoretically by Landau.
^"diamagnetic, adj. and n".OED Online. Oxford University Press. June 2017.
^"Magnetic Properties".Chemistry LibreTexts. 2 October 2013.Archived from the original on 17 March 2020. Retrieved21 January 2020.
^Suzuki, Motohiro; Kawamura, Naomi; Miyagawa, hayato; Garitaonandia, Jose S.; Yamamoto, Yoshiyuki; Hori, Hidenobu (24 January 2012). "Measurement of a Pauli and Orbital Paramagnetic State in Bulk Gold Using X-Ray Magnetic Circular Dichroism Spectroscopy".Physical Review Letters.108 (4): 047201.Bibcode:2012PhRvL.108d7201S.doi:10.1103/PhysRevLett.108.047201.PMID22400883.
^Quit007 (2011)."Diamagnetism Gallery".DeviantART.Archived from the original on 16 March 2012. Retrieved26 September 2011.{{cite web}}: CS1 maint: numeric names: authors list (link)
^Drakos, Nikos; Moore, Ross; Young, Peter (2002)."Landau diamagnetism".Electrons in a magnetic field. Archived fromthe original on 27 June 2013. Retrieved27 November 2012.
