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Electronic Properties of Crystals Metallic State SEA OF MOBILE VALENCE ELECTRONS e.g. Li + e-e- Metals are good electric and thermal conductors:- good in comparison with what ? -microscopic description allowing for quantitative predictions ?

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Def. of electrical resistance: current Voltage drop This is not Ohm´s law Ohm´s law: =constant independent from V Material specific quantity: Independent from geometry of the sample Metals follow Ohm´s lawwhy ? Drude model

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The inverse resistivity is called conductivity more generalin the non isotropic case Alternative formulation of Ohms law with the help of I A Current density: L E V Voltage drop V=E L A A

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Resistivity of Selected Materials (~300 K) metalsρ (nΩ·m) nonmetalsρ (Ω·m) aluminum0026.5 aluminum oxide (014 °C)1 x 10 14 brass0064.0 aluminum oxide (300 °C)3 x 10 11 chromium0126.0 aluminum oxide (800 °C)4 x 10 06 copper0017.1 carbon, amorphous0.350 gold0022.1 carbon, diamond2.700 iron0096.1 carbon, graphite650 x 10 -9 lead0208.0 lithium0092.8 germanium0.460 mercury (0 °C)0941.0 manganese1440.0 pyrex 774040,000 nichrome1500.0 quartz75 x 10 16 nickel0069.3 palladium0105.4 silicon640 platinum0105.0 silicon dioxide (0020 °C)1 x 10 13 plutonium1414.0 silicon dioxide (0600 °C)70,000 silver0015.9 silicon dioxide (1300 °C)0.004 solder0150.0 steel, plain0180.0 steel, stainless0720.0 tantalum0131.0 tin (0 °C)0115.0 water, liquid (000 °C)861,900 titanium (0 °C)0390.0 water, liquid (025 °C)181,800 tungsten0052.8 water, liquid (100 °C)012,740 uranium (0 °C)0280.0 zinc0059.0 Covers 25 orders of magnitude

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Drude model First simple classical model for a free electron gas Classical equation of motion: friction due to the scattering processes electric force F=qE accelerating the charge q=-e 0 where v D is the drift velocity superimposed to the random thermal velocity

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Switching off the electric field Relaxation to the thermal velocity within relaxation time Stationary state in an electric field: 0 dQ=q dN dV=Adx where

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consistent with Ohms law preserved in quantized models However, parameters like, e.g., the electron mass become modified effective mass Classical description fails completely in explaining the heat capacity of electrons Classical: N Electrons not observed in experiment

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Warmup: Concept: OHM’s Law. Electrical current is a measure of the rate at which electrical charge moves in a circuit. Electrical current is measured.

Warmup: Concept: OHM’s Law. Electrical current is a measure of the rate at which electrical charge moves in a circuit. Electrical current is measured.

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