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## Electronic Properties of Crystals

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**e.g.**Li+ Electronic Properties of Crystals Metallic State e- SEA OF MOBILE VALENCE ELECTRONS ? Metals are good electric and thermal conductors: - good in comparison with what -microscopic description allowing for quantitative predictions ?**Def. of electrical resistance:**Independent from geometry of the sample current Voltage drop This is not Ohm´s law Ohm´s law: =constant independent from V ? Metals follow Ohm´s law why Drude model Material specific quantity:**Alternative formulation of Ohm’s law with the help of**V E L The inverse resistivity is called conductivity more general in the non isotropic case A Voltage drop V=E L Current density: I A A**Drude model**First simple classical model for a free electron gas friction due to the scattering processes Classical equation of motion: electric force F=qE accelerating the charge q=-e0 where vD is the drift velocity superimposed to the random thermal velocity**relaxation time**dQ=q dN where Switching off the electric field Relaxation to the thermal velocity within Stationary state in an electric field: 0 dV=Adx**consistent with Ohm’s law**preserved in quantized models effective mass However, parameters like, e.g., the electron mass become modified Classical description fails completely in explaining the heat capacity of electrons Classical: N Electrons not observed in experiment