# 2.1.4 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.

$\sigma=|q|\cdot n\cdot \mu\\\underline{j}=\sigma\cdot\color{purple}{\underline{E}}$

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. $\Delta\rho=\alpha_\rho\cdot\rho\cdot\Delta T\approx\frac{0.4\%}{^\text{o}C}$ 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 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! 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 2 μΩcm. ρ(technical semiconductors) around 1 Ω cm. ρ(insulators) > 1 GΩcm.