Presentation on theme: "Electronic Properties of Crystals Metallic State SEA OF MOBILE VALENCE ELECTRONS e.g. Li + e-e- Metals are good electric and thermal conductors:- good."— Presentation transcript:
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 ?
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
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
Resistivity of Selected Materials (~300 K) metalsρ (nΩ·m) nonmetalsρ (Ω·m) aluminum aluminum oxide (014 °C)1 x brass aluminum oxide (300 °C)3 x chromium aluminum oxide (800 °C)4 x copper carbon, amorphous0.350 gold carbon, diamond2.700 iron carbon, graphite650 x lead lithium germanium0.460 mercury (0 °C) manganese pyrex ,000 nichrome quartz75 x nickel palladium silicon640 platinum silicon dioxide (0020 °C)1 x plutonium silicon dioxide (0600 °C)70,000 silver silicon dioxide (1300 °C)0.004 solder steel, plain steel, stainless tantalum tin (0 °C) water, liquid (000 °C)861,900 titanium (0 °C) water, liquid (025 °C)181,800 tungsten water, liquid (100 °C)012,740 uranium (0 °C) zinc Covers 25 orders of magnitude
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
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
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