To find the origin of the T 2 difference between the BlochGrüneisen law and the Debye law, a resistivity statistical model for ideal metals is presented. In the model, the system is regarded as a phonon system in which all phonons have the same momentum value, i.e., the mean momentum. The principal point of the simplified model is that the electrons located at the Fermi surface are scattered by these mean-momentum phonons. It is found that the electrical resistivity of an ideal metal is directly proportional to the phonon concentration and the square of the phonon mean momentum, which first related the electrical resistivity to the phonon parameters. The theoretical results from the model are consistent with experimental observations that the electrical resistivity is directly proportional to temperature T at high temperatures, and to T 5 at very low temperatures, naturally, this is consistent with the BlochGrüneisen law. It is found by theoretical analyses that the heat capacity of a solid at very low temperatures is only proportional to the phonon concentration. Therefore, the contribution of the square of phonon mean momentum to the electrical resistivity brings about the T 2 difference between the BlochGrüneisen law and the Debye law. PACS Nos.: 72.10.Di, 65.40.Ba
The effects of Pr on the microstructure and nonlinear electrical properties of the (Co,Ta)-doped SnO2 varistors were investigated. It was found by characterizing the samples sintered at 1350 oC that the breakdown voltage increases significantly from 500v/mm to 1200v/mm, and the relative permittivity decreased rapidly from 2525 to 1199 with increasing Pr6O11 concentration from 0 to 1.20 mol%. The analysis of samples’ microscopic structure showed that the grain size of SnO2 rapidly decreases from 5.1 to 3.7 µm with increasing Pr6O11 concentration from 0 to 1.20mol% .The significant decrease of SnO2 grain size is the main reason for raising breakdown voltage and reducing permittivity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.