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2.1.4 Summary to: Conductors - Definitions and General Properties

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  • 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.


    "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 μcm.
    ρ(technical semiconductors) around 1 cm.
    ρ(insulators) > 1 Gcm.
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