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The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample. Its strength lies in its ability to accurately measure the properties of a sample of any arbitrary shape, as long as the sample is approximately two-dimensional (i.e. it is much thinner than it is wide), solid (no holes), and the electrodes are placed on its perimeter.
Electric circuit with metal and a battery U. The arrows indicate the direction of the electric field E and the electric current density j.. Qualitatively, this relationship is based upon the fact that the heat and electrical transport both involve the free electrons in the metal.
This term, where and correspond to the specific resistivity of the two contacting surfaces, is known as Sharvin resistance. Electrical contacts resulting in ballistic electron conduction are known as Sharvin Contacts. When the radius of a contact spot is larger than the mean free path of electrons, the contact resistance can be treated classically.
The electrical resistance of a uniform conductor is given in terms of resistivity by: [40] = where ℓ is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = πr 2 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current.
The primary model that has historically described Kapitza resistance is the phonon gas model. [4] [5] [6] Within this model are the acoustic mismatch and diffuse mismatch models (AMM and DMM respectively). For both models the interface is assumed to behave exactly as the bulk on either side of the interface (e.g. bulk phonon dispersions ...
As quoted in an online version of: David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition.CRC Press. Boca Raton, Florida, 2003; Section 4, Properties of the Elements and Inorganic Compounds; Physical Properties of the Rare Earth Metals
Solving for and plugging into the above gives the Hall voltage: V H = I x B z n t e {\displaystyle V_{\mathrm {H} }={\frac {I_{x}B_{z}}{nte}}} If the charge build up had been positive (as it appears in some metals and semiconductors), then the V H assigned in the image would have been negative (positive charge would have built up on the left side).