### 2.2.4 Summary to: Conductors - Definitions and General Properties

| What counts are the specific quantities: Conductivity s (or the specific resistivity r = 1/ s. current density j. (Electrical) field strength · E. |  |
[ r] = Wm [ s] = ( Wm)–1 = S/m; S = "Siemens"
|  | The basic equation for s is: n = concentration of carriers, µ = mobility of carriers. |  |
s = |q| · n · µ
|  | Ohm's law states: It is valid for metals, but not for all materials. |  |
j = s · E
| s (of conductors / metals) obeys (more or less) several rules; all understandable by looking at n and particularly µ. |  |
|  | Matthiesen rule: Reason: Scattering of electrons at defects (including phonons) decreases µ. |  |
r = rLattice(T) + rdefect(N)
|  | "r(T) rule": about 0,04 % increase in resistivity per K Reason: Scattering of electrons at phonons decreases µ. |  |
D r | = | ar · r · D T | » | 0,4% oC
--- | --- | --- | --- | ---
|  | Nordheim's rule: Reason: Scattering of electrons at B atoms decreases µ. |  |
r » rA + const. · [B]
| Major consequence: You can't beat the conductivity of pure Ag by "tricks" like alloying or by using other materials (Not considering superconductors). |  |
| Non-metallic conductors are extremely important. |  |
|  | Transparent conductors (TCO's) ("ITO", typically oxides). |  |
No flat panels displays = no notebooks etc. without ITO!
Batteries, fuel cells, sensors, ...
Example: MoSi2 for heating elements in corrosive environments (dishwasher!).
The future High-Tech key materials?
|  | Ionic conductors (liquid and solid). |
|  | Conductors for high temperature applications; corrosive environments, .. (Graphite, Silicides, Nitrides, ...). |
|  | Organic conductors (and semiconductors). |
| Numbers to know (order of magnitude accuracy sufficient) |  |
r(decent metals) about 2 m Wcm. r(technical semiconductors) around 1 Wcm. r(insulators) > 1 GWcm.
Questionaire
All Multiple Choice questions to 2.1

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