Hall-effect

The Hall effect occurs when a current-carrying conductor is placed in a magnetic field and is related to the difference between electron conduction and positive-hole conduction. Electron conduction is the dominant factor in the transition metal carbides which, with the exception of WC, all have a negative Hall constant. A discussion of the Hall effect in interstitial carbides is found in Ref 15. 

The Hall effect, an electric field perpendicular to both the impressed current flow and to the applied magnetic field, gives information about the mobility of the charge carriers as well as their sign. The Hall coefficient RH - Ey/JxHe is proportional to the reciprocal of the carrier density. The Hall coefficient is negative for electron charge carriers. 

For Bi-Sr-Ca-Cu-O (a mixture of 2212 and 2223 phases) the Hall coefficient is found (80) to be positive and decreasing from 5 to 3 (x 10 9 ms/C) between 120 to 280 K. In the case of Tl-Ba-Ca-Cu-O (2223 phase) positive RH decreasing from 5 to 3 (xlO-9 ms/C) is measured by the Ong group. There are not yet single crystal measurements in these materials. 

Experimentally obtained numerical data on the Hall coefficient Rh of MSe with M = Sc, Y, La to Nd are missing. Rh 5x 10 cm /C for NdSe was calculated assuming that there is one conduction electron per Nd ion, Reid et al. [11, p. 972]. RH = -2770cm% was reported for SmSe at 300 K by Miller et al. [16]. ErSe has a negative Hall coefficient at room temperature (no value given). Miller, Himes [14]. 

The above equation gives the force exerted on one electron with the elementary charge e, the velocity v moving into a magnetic field of strength H in A.m . Since the force on a charge 

Hence the Hall field varies linearly with the magnetic field H. Introducing the density of electron per unit volume of conductor, n in m it is possible to relate the velocity of the electrons to the current density in A.m along the x-axis as follows  

Therefore, it is possible to write the Hall electric field strength as follows  

By replacing the quantity (1/ne) by the coefficient the relation between the electric current density and the perpendicular applied magnetic induction is given by the following equation  

Since the force on an electron moving through a magnetic field is acted on by the Lorentz force given by F = —e(E + v x B), the equation of motion can be written as 

For a direct current in the x—y plane in the presence of a magnetic field B in the z-direction, the steady-state solution is 

Assume the applied field is in the a -direction causing a current jx to flow. The presence of the field will deflect electrons in the y-direction to the walls of the conductor. Since the current cannot flow out through the walls, a field Ey = B Vx will develop such that Vy = 0. Putting this into the first of the above equations gives 

The Hall coefficient is defined as Ru=Ey/jxBz. Putting jx = o-Ex into Equation 18.24, we find 

We shall see in later chapters that it is possible in semiconductors (and in some metals) for holes in the electrons band structure to act as positively charged carriers. Had the carriers been holes, the signs in the equation of motion would have been reversed resulting in a positive Hall coefficient. (Note This simplified derivation of the Hall effect is only 

Suppose we can make ohmic contacts on a sample. The idea is make a direct measurement of the electric current that crosses the sample when an electric field is applied in a direction x. A uniform magnetic field H is applied in the direction z, which creates a voltage measured in the direction y. The scheme is given by Fig. 13.17. 

Consider the case where we have a cOTicentration n of electrons in the sample. Since they are submitted to the electric field supposed to be in the direction + x, they acquire a drift velocity v in the direction —x. The Lorentz force applied to the 

If there are both electrons and holes, the situation is more complex, but still it is possible to deduce the four parameters n or p, pp. The price to pay to determine 

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Hall effect If a current (I) is passed through a conducting crystal in a direction perpendicular to that of an applied magnetic field (H), the conductor develops a potential (V) between the faces which are mutually perpendicular to both the direction of the current and the magnetic field. This is known as the Hall effect the magnitude of the potential difference is given by... 

The measurement and evaluation methods of chapter 3.1. and 3.2. work with inductive sensors in an absolute circuit. The results on two different formed coils, a pot core coil and a cylinder core coil are selected. For presentation in this paper the third method, described in chapter 3.3., uses a Hall-effect device to detect the information and a coil system in a differential circuit to excite the electromagnetic field. 

The sensor of the third method is a Hall-effect device situated in a magnetic field of two differential arranged exiting coils. Fig. 3 shows the construction of the sensor probe. 

Due to the symmetrical construction the resulting magnetic field between the two coils is zero in y-direction, if a conductive structure is symmetrically situated in the area a (see fig. 3) in the near of the probe. A resulting field is detectable by the Hall-effect device, if there are unsym-metrics in the structure in area a. The value of the Hall voltage is proportional to the detected magnetic field. 

All measured signals include errors described in chapter 4.2.1.. Especially the data of the Hall-effect device, curve... 

Examples of even processes include heat conduction, electrical conduction, diflfiision and chemical reactions [4], Examples of odd processes include the Hall effect [12] and rotating frames of reference [4], Examples of the general setting that lacks even or odd synnnetry include hydrodynamics [14] and the Boltzmaim equation [15]. 

It is a white crystalline, brittle metal with a pinkish tinge. It occurs native. Bismuth is the most diamagnetic of all metals, and the thermal conductivity is lower than any metal, except mercury. It has a high electrical resistance, and has the highest Hall effect of any metal (i.e., greatest increase in electrical resistance when placed in a magnetic field). 

Hallcomid HallcomidM18-OL Hall current Hall defects Hall effect... 

The first term on the right represents scalar conduction and the second term the Hall effect. This is generally expressed in terms of the Hall parameter l3 = so that... 

The main cause of anode wear is electrochemical oxidation or sulfur attack of anodic surfaces. As copper is not sufficiently resistant to this type of attack, thin caps of oxidation and sulfur-resistant material, such as platinum, are bra2ed to the surface, as shown in Eigure 15a. The thick platinum reinforcement at the upstream corner protects against excessive erosion where Hall effect-induced current concentrations occur, and the interelectrode cap protects the upstream edge from anodic corrosion caused by interelectrode current leakage. The tungsten undedayment protects the copper substrate in case the platinum cladding fails. 

Temperature dependent Hall effect measurements have also been carried out in the temperature range 30 to 260 K on a K3C60 thin film [116]. For three... 

Song et al. [16] reported results relative to a four-point resistivity measurement on a large bundle of carbon nanotubes (60 um diameter and 350 tm in length between the two potential contacts). They explained their resistivity, magnetoresistance, and Hall effect results in terms of a conductor that could be modeled as a semimetal. Figures 4 (a) and (b) show the magnetic field dependence they observed on the high- and low-temperature MR, respectively. 

Kennedy and Benedick [67K02, 68K03] were successful in carrying out difficult Hall effect measurements in germanium samples explosively loaded at the upper end of the elastic range. Nevertheless, the measurements did not provide sufficient information to develop a physical interpretation. 

The main use of elemental As is in alloys with Pb and to a lesser extent Cu. Addition of small concentrations of As improves die properties of Pb/Sb for storage batteries (see below ), up to 0.75% improves the hardness and castabilily of type metal, and 0 5-2.0% improves the sphericity of Pb ammunition. Automotive body solder is Pb (92%),, Sb (5 0%), Sn (2.5%) and As (0.5%). Intcrnxitallic compounds with Al, Ga and In give the 111-V semiconductors (p 255) of which GaAs and InAs are of particular value for light-emitting diodes (LEDs), tunnel diodes, infrared emitters, laser windows and Hall-effect devices (p. 258). 

As widi arsenic, semiconductor grade Sb is prepared by chemical reduction of highly purified compounds AlSb, GaSb and InSb have applications in infrared devices, diodes and Hall-effect devices. ZnSb has gootl themioelectric properties. Applications of various conipounjs of Sb will be mentioned when die compounds tbemselves are discussed. 

K. von Klitzing (Stuttgart) discovery of the quantized Hall effect. 

At very high frequencies, the current is measured by assessing one of the effects that it produces. Several techniques are possible, e.g. (1) measuring the temperature rise when the current flows through a known resistance or (2) using a Hall-effect probe to measure the electromagnetic field created by the current. 

Figure 10. (a) Two-mode cavity and (b) microwave circuit for Faraday rotation (microwave Hall effect) experiments. 

Figure 43. Microwave transmission in a two-mode resonator as a function of the magnetic field strength for measurement of the microwave Hall effect in FeS2 (two measurements with an offset difference).16...

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