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Dia- and Paramagentic propertis of
materials are of no consequence whatsoever for products of electrical
engineering (or anything else!) |
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Normal diamagnetic materials: cdia » –
(10–5 - 10–7)
Superconductors (= ideal diamagnets): cSC = – 1
Paramagnetic materials: cpara
» +10–3 |
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Only their common denominator of
being essentially "non-magnetic" is of interest (for a submarine,
e.g., you want a non-magnetic steel) |
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For research tools, however, these forms of
magnitc behavious can be highly interesting ("paramagentic
resonance") |
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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). |
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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 |
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The "Lenz rule" ascertains that
inductive effects oppose their source; diamagnetism thus weakens the magnetic
field, cdia < 0 must
apply. |
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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. |
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| 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 |
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| W(j) = –
µ0 · m · H
= – µ0 · m · H ·
cos j |
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| Energy of magetic dipole in magnetic field |
| N[W(j)] =
c · exp –(W/kT) = c
· exp |
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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 |
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| Resulitn Magnetization with Langevin function L(b) and argument b |
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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: |
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Insertig numbers we find that cpara is indeed a number just slightly
larger than 0. |
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© H. Föll (Advanced Materials B, part 1 - script)
