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2.2.4 Summary to: Conductors - Definitions and General Properties

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    2762
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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.
    \[[\rho]=\Omega\text{m}\\ [\sigma]=(\Omega\text{m})^{-1}=\mathbf{S/m} \text{; S = "Siemens"}\]
    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.