2.2.4 Summary to: Conductors  Definitions and General Properties
 Page ID
 2762
What counts are the specific quantities:

\[[\rho]=\Omega\text{m}\\ [\sigma]=(\Omega\text{m})^{1}=\mathbf{S/m} \text{; S = "Siemens"}\] 
The basic equation for σ is: n = concentration of carriers, µ = mobility of carriers. 
\[\sigma=q\cdot n\cdot \mu\] 
Ohm's law states: It is valid for metals, but not for all materials. 
\[\underline{j}=\sigma\cdot\color{purple}{\underline{E}}\] 
σ (of conductors / metals) obeys (more or less) several rules; all understandable by looking at n and particularly µ.
Matthiesen rule: 
\[\rho=\rho_\text{Lattice}(T)+\rho_\text{defect}(N)\] 
"ρ(T) rule": 
\[\Delta\rho=\alpha_\rho\cdot\rho\cdot\Delta T\approx\frac{0.4\%}{^\circ C}\] 
Nordheim's rule: Reason: Scattering of electrons at B atoms decreases µ. 
\[\rho\approx\rho_\text{A}+\text{const.}\cdot [B]\] 
Major consequence: You can't beat the conductivity of pure Agby "tricks" like alloying or by using other materials
(Not considering superconductors).
Nonmetallic conductors are extremely important.
Transparent conductors (TCO's) ("ITO", typically oxides). 
No flat panels displays = no notebooks etc. without ITO! 
Ionic conductors (liquid and solid).  Batteries, fuel cells, sensors, ... 
Conductors for high temperature applications; corrosive environments, .. (Graphite, Silicides, Nitrides, ...). 
Example: MoSi_{2} for heating elements in corrosive environments (dishwasher!). 
Organic conductors (and semiconductors).  The future HighTech key materials? 
Numbers to know (order of magnitude accuracy sufficient)
 ρ(decent metals) about 2 μΩcm.
 ρ(technical semiconductors) around 1 Ωcm.
 ρ(insulators) > 1 GΩcm.