# 2.2.4 Summary to: Conductors - Definitions and General Properties

What counts are the specific quantities:

 Conductivity σ (or the specific resistivity ρ = 1/ σ. current density j. (Electrical) field strength · E. $[\rho]=\Omega\text{m}\\ [\sigma]=(\Omega\text{m})^{-1}=\mathbf{S/m} \text{; S = "Siemens"}$ 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: Reason: Scattering of electrons at defects (including phonons) decreases µ. $\rho=\rho_\text{Lattice}(T)+\rho_\text{defect}(N)$ "ρ(T) rule": about 0,04 % increase in resistivity per K Reason: Scattering of electrons at phonons decreases µ. $\Delta\rho=\alpha_\rho\cdot\rho\cdot\Delta T\approx\frac{0.4\%}{^\circ C}$ 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).

Non-metallic 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: MoSi2 for heating elements in corrosive environments (dishwasher!). Organic conductors (and semiconductors). The future High-Tech key materials?

Numbers to know (order of magnitude accuracy sufficient)

• ρ(decent metals) about μcm.
• ρ(technical semiconductors) around cm.
• ρ(insulators) > 1 Gcm.