Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1937 · 285 citations · 0 references
Natural SciencesMaterials SciencePhysicsCondensed Matter PhysicsMaterials PhysicsMetallic MaterialsConductive MaterialsElectrical ConductivityElectron-phonon InteractionsMetalsConductionConduction ResistanceDebye ModelElectrical ResistivityLattice VibrationsMetallic ConductivityResistivityTemperature-dependent Resistivity
Electrical resistance theory models conduction electrons as independent but interacting with lattice vibrations, with the Grüneisen function G(x) linked to the Debye temperature. Under simplifying assumptions the theory gives a constant‑proportionality formula for resistance, R = const. At low temperatures the theory predicts resistance varies as T⁵.
The theory of electrical resistance developed by Bloch and others reats the conduction electrons as moving independently of one another but interacting with the lattice vibrations. The theory gives for the resistance of a metal, subject to certain simplifying assumptions, the formula R = const. G (ʘ/T) G ( x ) = 5/x 5 ∫ x o ξ 4 dξ/e ξ -1 - 1/e x -1, (1) where ʘ is the Debye characteristic temperature. At low temperatures formula (1) leads to the conclusion that R varies as T 5 . The function G ( x ) was first proposed by Grüneisen.