### 4.2.3 Summary to: Dia- and Paramagnetism

| Dia- and Paramagentic propertis of materials are of no consequence whatsoever for products of electrical engineering (or anything else!) |  |
Normal diamagnetic materials: cdia » – (10–5 - 10–7) Superconductors (= ideal diamagnets): cSC = – 1 Paramagnetic materials: cpara » +10–3
|  | Only their common denominator of being essentially "non-magnetic" is of interest (for a submarine, e.g., you want a non-magnetic steel) |
|  | For research tools, however, these forms of magnitc behavious can be highly interesting ("paramagentic resonance") |
| Diamagnetism can be understood in a semiclassical (Bohr) model of the atoms as the response of the current ascribed to "circling" electrons to a changing magnetic field via classical induction (µ dH/dt). |  |
|  | The net effect is a precession of the circling electron, i.e. the normal vector of its orbit plane circles around on the green cone. Þ |
|  | The "Lenz rule" ascertains that inductive effects oppose their source; diamagnetism thus weakens the magnetic field, cdia < 0 must apply. |
| Running through the equations gives a result that predicts a very small effect. Þ A proper quantum mechanical treatment does not change this very much. |  |
cdia = – | e2 · z · <r> 2 6 m*e | · ratom | » – (10–5 - 10–7)
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| The formal treatment of paramagnetic materuials is mathematically completely identical to the case of orientation polarization |  |
W(j) = – µ0 · m · H = – µ0 · m · H · cos j
Energy of magetic dipole in magnetic field
N[W(j)] = c · exp –(W/kT) = c · exp |  | m · µ0 · H · cos j kT | = N(j)
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(Boltzmann) Distribution of dipoles on energy states
M | = | N · m · L(b)
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b | = | µ0 · m · H kT |  |  |
Resulting Magnetization with Langevin function L(b) and argument b
|  | The range of realistc b values (given by largest H technically possible) is even smaller than in the case of orientation polarization. This allows tp approximate L(b) by b/3; we obtain: |
cpara | = | N · m2 · m0 3kT
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|  | Insertig numbers we find that cpara is indeed a number just slightly larger than 0. |

© H. Föll (Advanced Materials B, part 1 - script)