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Engineering LibreTexts

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.