Temperature coefficient of the resistivity

Fig. 7.10 Temperature coefficient of the resistivity of amorphous Mg-Bi. From Ferrier...

Suppose a current I flows through a sample of resistance Rq. Rq is defined as the resistance of the sample at zero current. Because of the Joule effect, the resistance will increase by AR = Rof3AT, where (3 is the temperature coefficient of the resistance. As above, one can write AT rsj RqP, and this approximation therefore gives AR Rol)", The voltage V across the sample is therefore given by... 

Fig. 5.4.8 Temperature coefficient of the resistance of Nfoo-xCr,. alloys as a function of the Cr content x. The data are taken from [3]...

To obtain a sufficiently high sheet resistance for strain gauges, the thickness of the NiCr layers have to be in the range of 50-100 nm. If the thickness is significantly below 100 nm, surface effects become important for the electrical behavior. In consequence, the electrical properties deviate from the bulk properties [31]. Typically, the resistivity increases with decreasing thickness while the temperature coefficient of the resistance decreases. Another consequence is that the surface... 

High temperature coefficient of the resistivity (TCR), close to the bulk value of 3850 ppm K-1. 

Fig. 12 Temperature coefficient of the resistivity of synthesized metal(metal oxide)-polymer nanocomposites vs. metal content...

The temperature dependence of the resistance shows negative temperature coefficient of the resistance (dR/dT<0) in the whole investigated temperature... 

CPs have rarely been produced in a form ordered enough to exhibit a small positive temperature coefficient of resistivity. This so-called metallic behavior is normally not seen in the transport properties of as-grown CPs, like PPys, PThs, or PANIs, where the negative temperature coefficient of the resistivity is generally attributed to hopping. 

The atomic disorder associated with the amorphous state leads to completely different transport properties from those encountered in the crystalline state. Experimental results of the electrical resistivity, the Hall effect, magnetoresistance, thermoelectric power and the occurrence of. superconductivity are discussed in section 8. The main emphasis is placed on the electrical resistivity. The occurrence of negative temperature coefficients of the resistivity is related to models based on the extended Ziman theory. In the low temperature regime the resistivity often shows a In T... 

The (Sni-j Luj )Lu4Fe6Sni8 and (Sni jTmj )Tm4Fe6Sn g phases have a high resistivity as well (fig. 36). The substitution of a part of Sn atoms by Lu atoms [i.e. the composition (Sno.6Luo4)Lu4Fe6Sni8] leads to a negative temperature coefficient of the resistivity (Skolozdra 1993). 

In spite of the clear signatures of the metallic state, however, the heavily doped conjugated polymers do not exhibit traditional metallic behavior in transport [173] and optical properties [1155]. Instead, they show a negative temperature coefficient of the resistivity dp/dT < 0) the dc conductivity is activated with temperature, so that the dc conductivity decreases by several orders of magnitude as the temperature is lowered. Furthermore, the optical spectra do not show the Drude-like behavior expected for a typical metal in the infrared. Rather, an electronic pseudo-gap of about 0.1-0.2 eV has been observed, below which the optical conductivity is suppressed [1155]. These nonmetallic behaviors arise from the disorder of the sample, originating from a combination of molecular-scale disorder and mesoscale inhomogeneity. 

Semiconductors thus have over a wide temperature range the opposite dependence of resistance on temperature to that of metals. Typically, one may have as many at 10 charge carriers per cubic centimeter at room temperature, and specific resistances may vary from 10 to 10ncm. Mathematically Eq. (3) expresses the change of resistance with temperature. Three constants, Roo, B, and 0, are characteristic for a particular semiconductor. The temperature coefficient of the resistivity may be ten times that of a typical metal resistance thermometer. 

For the international practical temperature scale the platinum thermometers serve as standard (interpolation) instruments with characteristics values such the reduced resistance, the temperature coefficient of the resistance and the platinum temperature. Interpolation polynomials of the third to fifth degrees, using as the principal reference points 0, 100 and 419.58 °C (fusion of Zn) are used most frequently (as a standard accessory of commercial products). Another form of resistance thermometers are films or otherwise deposited layers (0.01 to 0.1 pm thick). They can be suitably covered to protect against corrosive media and platinum deposited on ceramics can withstand temperatures up to 1850 K. Non-metals and semiconductor elements can be found useful at low temperatures. 

Although resistivities as low as 10 /7cm have been reported for iodine-doped oriented polyacetylene parallel to the draw direction (chain axis), a positive temperature coefficient of the resistivity, typical of a metal, has not been observed. This indicates that defects or transport perpendicular to the chain axis limit the conductivity. We conclude, therefore, that the 500 A mean free path is not limited by phonon scattering. This implies that significantly higher room temperature conductivities will be achieved as the quality of the material is improved. The absence of any positive temperature coefficient implies that values at least an order of magnitude higher are to be expected i.e., the intrinsic conductivity at room temperature is greater than 10 S/cm. 

The temperature dependences of the conductivity at 8 kbar, parallel and perpendicular to the chain axis, are shown in Fig. 2.20 [125,126]. Although the room temperature conductivity decreases above 4 kbar, the temperature dependence at 8 kbar is substantially reduced. The values of pr at ambient pressure and at 8 kbar, parallel to the chain axis, are 3 and 2.2 respectively, and those perpendicular to the axis are 3 and 2.8, respectively, demonstrating substantial enhancement of the interchain transport at high pressure. Nevertheless, a positive temperature coefficient of the resistivity has not been observed. Thus, even at high pressure, the combination of weak interchain transport and disorder limit the three-dimensional mean free path in this metallic quasi-one-dimensional conducting polymer. 

The PTCR effect refers to anomalies observable in some semiconductors or ionic conductors, in that the resistivity increases significantly with the temperature (PTCR = positive temperature coefficient of the resistance). Trivial but powerful PTCR effects rely on composites of insulating... 

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