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What counts are the specific quantities:
- Conductivity s (or the specific resistivity r
= 1/ s.
- current density j.
- (Electrical) field strength · E.
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[ r] = Wm
[ s] = ( Wm)–1 = S/m; S = "Siemens"
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The basic equation for s is:
n = concentration of carriers,
µ = mobility of carriers. |
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Ohm's law states:
It is valid for metals, but not for all materials. |
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s (of conductors / metals) obeys (more
or less) several rules; all understandable by looking at n and particularly µ. |
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Matthiesen rule:
Reason: Scattering of electrons at defects (including phonons) decreases
µ. | |
| r = rLattice(T)
+ rdefect(N) |
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"r(T) rule":
about 0,04 %
increase in resistivity per K
Reason: Scattering of electrons at phonons decreases µ. |
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| Dr |
= |
ar · r ·
DT |
» | 0,4%
oC |
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Nordheim's rule:
Reason: Scattering of electrons at B atoms decreases µ. |
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Major consequence: You can't beat the conductivity of pure Ag by "tricks"
like alloying or by using other materials
(Not considering superconductors). |
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Non-metallic conductors are extremely important. |
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Transparent conductors (TCO's)
("ITO", typically oxides). |
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No flat panels displays = no notebooks etc. without ITO!
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Batteries, fuel cells, sensors, ...
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| Example: MoSi2 for heating elements in corrosive environments (dishwasher!). |
| The future High-Tech key materials? |
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Ionic conductors (liquid and solid). |
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Conductors for high temperature applications; corrosive environments, ..
(Graphite, Silicides,
Nitrides, ...). | |
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Organic conductors (and semiconductors). |
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Numbers to know (order of magnitude accuracy sufficient) |
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r(decent metals) about 2 mWcm.
r(technical semiconductors) around 1 Wcm.
r(insulators) > 1 GWcm. |
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© H. Föll (Advanced Materials B, part 1 - script)
