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Levitating pyrolytic carbon

DiamagnetismFrom Wikipedia, the free encyclopedia

Diamagnetic materials create an induced magnetic field in adirection opposite to an externally applied magnetic field, and arerepelled by the applied magnetic field. In contrast, the oppositebehavior is exhibited by paramagnetic materials. Diamagnetism is aquantum mechanical effect that occurs in all materials; when it is theonly contribution to the magnetism the material is called adiamagnet. Unlike a ferromagnet, a diamagnet is not a permanentmagnet. Its magnetic permeability is less than μ0, the permeabilityof vacuum. In most materials diamagnetism is a weak effect, but asuperconductor repels the magnetic field entirely, apart from a thinlayer at the surface.

Diamagnets were first discovered when Sebald Justinus Brugmansobserved in 1778 that bismuth and antimony were repelled bymagnetic fields. In 1845, Michael Faraday demonstrated that it wasa property of matter and concluded that every material responded (ineither a diamagnetic or paramagnetic way) to an applied magneticfield. He adopted the term diamagnetism after it was suggested tohim by William Whewell.[1]

Contents

1 Materials1.1 Superconductors

2 Demonstrations2.1 Curving water surfaces2.2 Levitation

3 Theory3.1 Langevin diamagnetism3.2 In metals

4 See also5 References6 External links

Materials

Diamagnetism, to a greater or lesser degree, is a property of all materials and always makes a weakcontribution to the material's response to a magnetic field. For materials that show some other form ofmagnetism (such as ferromagnetism or paramagnetism), the diamagnetic contribution becomes negligible.Substances that mostly display diamagnetic behaviour are termed diamagnetic materials, or diamagnets.Materials called diamagnetic are those that laymen generally think of as non­magnetic, and include water,

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Notable diamagneticmaterials[2]

Material χv (× 10−5)

Superconductor −105

Pyrolytic carbon −40.9Bismuth −16.6Mercury −2.9Silver −2.6Carbon (diamond) −2.1Lead −1.8Carbon (graphite) −1.6Copper −1.0Water −0.91

Transition from ordinary conductivity(left) to superconductivity (right). Atthe transition, the superconductorexpels the magnetic field and thenacts as a perfect diamagnet.

wood, most organic compounds such as petroleum and some plastics,and many metals including copper, particularly the heavy ones withmany core electrons, such as mercury, gold and bismuth. The magneticsusceptibility values of various molecular fragments are called Pascal'sconstants.

Diamagnetic materials, like water, or water based materials, have arelative magnetic permeability that is less than or equal to 1, andtherefore a magnetic susceptibility less than or equal to 0, sincesusceptibility is defined as χv = μv − 1. This means that diamagneticmaterials are repelled by magnetic fields. However, since diamagnetismis 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 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 ofmagnitude smaller than the magnetism exhibited by paramagnets andferromagnets. Note that because χv is derived from the ratio of theinternal magnetic field to the applied field, it is a dimensionless value.

All conductors exhibit an effective diamagnetism when they experience a changing magnetic field. TheLorentz force on electrons causes them to circulate around forming eddy currents. The eddy currents thenproduce an induced magnetic field opposite the applied field, resisting the conductor's motion.

Superconductors

Superconductors may be considered perfect diamagnets (χv = −1),since they expel all fields (except in a thin surface layer) due to theMeissner effect.[3] However this effect is not due to eddy currents,as in ordinary diamagnetic materials (see the article onsuperconductivity).

Demonstrations

Curving water surfaces

If a powerful magnet (such as a supermagnet) is covered with alayer of water (that is thin compared to the diameter of the magnet)then the field of the magnet significantly repels the water. Thiscauses a slight dimple in the water's surface that may be seen by itsreflection.[4][5]

Levitation

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A live frog levitates inside a 32 mmdiameter vertical bore of a Bittersolenoid in a magnetic field of about16 teslas at the Nijmegen High FieldMagnet Laboratory.[6]

Main article: Magnetic levitation § Diamagnetism

Diamagnets may be levitated in stable equilibrium in a magneticfield, with no power consumption. Earnshaw's theorem seems topreclude the possibility of static magnetic levitation. However,Earnshaw's theorem only applies to objects with positivesusceptibilities, such as ferromagnets (which have a permanentpositive moment) and paramagnets (which induce a positivemoment). These are attracted to field maxima, which do not exist infree space. Diamagnets (which induce a negative moment) areattracted to field minima, and there can be a field minimum in freespace.

A thin slice of pyrolytic graphite, which is an unusually strongdiamagnetic material, can be stably floated in a magnetic field, suchas that from rare earth permanent magnets. This can be done with allcomponents at room temperature, making a visually effectivedemonstration of diamagnetism.

The Radboud University Nijmegen, the Netherlands, has conductedexperiments where water and other substances were successfully levitated. Most spectacularly, a live frog(see figure) was levitated.[7]

In September 2009, NASA's Jet Propulsion Laboratory in Pasadena, California announced they hadsuccessfully levitated mice using a superconducting magnet,[8] an important step forward since mice arecloser biologically to humans than frogs.[9] They hope to perform experiments regarding the effects ofmicrogravity on bone and muscle mass.

Recent experiments studying the growth of protein crystals has led to a technique using powerful magnetsto allow growth in ways that counteract Earth's gravity.[10]

A simple homemade device for demonstration can be constructed out of bismuth plates and a fewpermanent magnets that levitate a permanent magnet.[11]

Theory

The electrons in a material generally circulate in orbitals, with effectively zero resistance and act likecurrent loops. Thus it might be imagined that diamagnetism effects in general would be very, very common,since any applied magnetic field would generate currents in these loops that would oppose the change, in asimilar way to superconductors, which are essentially perfect diamagnets. However, since the electrons arerigidly held in orbitals by the charge of the protons and are further constrained by the Pauli exclusionprinciple, 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 apurely classical system. However, the classical theory for Langevin diamagnetism gives the same predictionas the quantum theory.[12] The classical theory is given below.

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Langevin diamagnetism

The Langevin theory of diamagnetism applies to materials containing atoms with closed shells (seedielectrics). A field with intensity B, applied to an electron with charge e and mass m, gives rise to Larmorprecession with frequency ω = eB / 2m. The number of revolutions per unit time is ω / 2π, so the currentfor an atom with Z electrons is (in SI units)[12]

The magnetic moment of a current loop is equal to the current times the area of the loop. Suppose the fieldis aligned with the z axis. The average loop area can be given as , where is the mean squaredistance of the electrons perpendicular to the z axis. The magnetic moment is therefore

If the distribution of charge is spherically symmetric, we can suppose that the distribution of x,y,zcoordinates are independent and identically distributed. Then , where is themean square distance of the electrons from the nucleus. Therefore . If is thenumber of atoms per unit volume, the diamagnetic susceptibility in SI units is

In metals

The Langevin theory does not apply to metals because they have non­localized electrons. The theory for thediamagnetism of a free electron gas is called Landau diamagnetism, and instead considers the weakcounter­acting field that forms when their trajectories are curved due to the Lorentz force. Landaudiamagnetism, however, should be contrasted with Pauli paramagnetism, an effect associated with thepolarization of delocalized electrons' spins.[13][14]

See also

FerromagnetismMagnetochemistryParamagnetismStochastic electrodynamics

References1. Jackson, Roland (21 July 2014). "John Tyndall and the Early History of Diamagnetism". Annals of Science: 4.

doi:10.1080/00033790.2014.929743. Retrieved 28 October 2014.2. Nave, Carl L. "Magnetic Properties of Solids". Hyper Physics. Retrieved 2008­11­09.3. Poole, Jr., Charles P. (2007). Superconductivity (2nd ed.). Amsterdam: Academic Press. p. 23.

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ISBN 9780080550480.4. Beatty, Bill (2005). "Neodymium supermagnets: Some demonstrations—Diamagnetic water". Science Hobbyist.

Retrieved September 2011.5. Quit007 (2011). "Diamagnetism Gallery". DeviantART. Retrieved September 2011.6. "The Frog That Learned to Fly". High Field Laboratory. Radboud University Nijmegen. 2011. Retrieved

September 2011.7. "The Real Levitation". High Field Laboratory. Radboud University Nijmegen. 2011. Retrieved September 2011.8. Liu, Yuanming; Zhu, Da­Ming; Strayer, Donald M.; Israelsson, Ulf E. (2010). "Magnetic levitation of large

water droplets and mice". Advances in Space Research 45 (1): 208–213. Bibcode:2010AdSpR..45..208L.doi:10.1016/j.asr.2009.08.033.

9. Choi, Charles Q. (2009­09­09). "Mice levitated in lab". Live Science. Retrieved September 2011.10. Kleiner, Kurt (08­10­2007). "Magnetic gravity trick grows perfect crystals". New Scientist. Retrieved September

2011. Check date values in: |date= (help)11. "Fun with diamagnetic levitation". ForceField. 02­12­2008. Retrieved September 2011. Check date values in:

|date= (help)12. Kittel, Charles (1986). Introduction to Solid State Physics (6th ed.). John Wiley & Sons. pp. 299–302. ISBN 0­

471­87474­4.13. Chang, M. C. "Diamagnetism and paramagnetism" (PDF). NTNU lecture notes. Retrieved 2011­02­24.14. Drakos, Nikos; Moore, Ross; Young, Peter (2002). "Landau diamagnetism". Electrons in a magnetic field.

Retrieved 27 November 2012.

External links

Video of a museum­style magnetic elevation train model that uses diamagnetism(http://www.youtube.com/watch?v=8tFsrGRwOOM)Videos of frogs and other diamagnets levitated in a strong magnetic field(http://www.ru.nl/hfml/research/levitation/diamagnetic/)Diamagnetic Levitation (YouTube) (http://www.youtube.com/watch?v=ezXYE5iFM_o)Large Pyrolytic Carbon Square Floating (YouTube) (https://www.youtube.com/watch?v=OiEVrhmThts)Video of a piece of neodymium magnet levitating between blocks of bismuth.(http://netti.nic.fi/~054028/images/LevitorMK1.0­1.mpg)

Website about this device, with images (in Finnish). (http://netti.nic.fi/~054028/)

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Categories: Electric and magnetic fields in matter Magnetic levitation Magnetism

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