Temperature Dependence of Resistivity

For temperatures above 20% of the Debye temperature, the resistivity increases linearly with temperature as suggested by Matthiessen s rule. The slope a is pretty much the same for a given metal, regardless of the defects and impurities. The first-order dependence of resistivity on T can be understood from a simple model. The collision cross section between an electron and the core ions in a metal is proportional to the square of the amplitude of its vibration. The square of the amplitude of an oscillator is proportional to its thermal energy kT (assuming T d, so all of the modes are active). The collision time t is directly proportional to the mean free path A, which is inversely proportional to the collision cross section. Therefore, conductivity is inversely proportional to T. 

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Fig. 1. (a) Comparison of normalised electrical conductivity of individual MWCNTs (Langer 96 [17], Ebbesen [18]) and bundles of MWCNTs (Langer 94 [19], Song [20]). (b) Temperature dependence of resistivity of different forms (ropes and mats) of SWCNTs [21], and chemically doped conducting polymers, PAc (FeClj-doped polyacetylene [22]) and PAni (camphor sulfonic acid-doped polyaniline [2. ]) [24]. 

Fig. 6.4. The temperature dependencies of resistivity of the sensor. / - in vacuum 2 - in the vial with antimony.

These postulated mechanisms3 are consistent with the observed temperature dependence of the insulator dielectric properties. Arrhenius relations characterizing activated processes often govern the temperature dependence of resistivity. This behavior is clearly distinct from that of conductors, whose resistivity increases with temperature. In short, polymer response to an external field comprises both dipolar and ionic contributions. Table 18.2 gives values of dielectric strength for selected materials. Polymers are considered to possess... 

High conductivity for transition metal complexes of TTF-dithiolate ligands have long been known, due to the mixing of n-d orbitals resulting in a small HOMO-LUMO gap [80]. At present, 17 is the most reliable metal in this category (ctrt = 4 X 10 S cmT, metallic down to 0.6 K) based on its purity, temperature dependencies of resistivity and magnetic susceptibility, and de Haas-van Alphen (dHvA) oscillations [48, 75]. 

Figure 4 Temperature dependence of resistance of a single crystal Tl-Ba-Ca-Cu-O normalized by the value at 130 K at various magnetic fields for (a) H perpendicular to c-axis and (b) H parallel to c-axis. Ref. 13.

Figure 6.21 Temperature dependence of resistivity for some typical oxide ceramics. From W. D. Kingery, H. K. Bowen, and D. R. Uhknann, Introduction to Ceramics. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Figure 6.46 Temperature dependence of resistivity for a V2O3-PMMA composite of various volume fractions V2O3 at 1 kHz. Reprinted, by permission, from D. M. Moffatt, J. Runt, W. Huebner, S. Yoshikawa, and R. Nenham, in Composite Applications, T. L. Vigo and B. J. Kinzig, eds., p. 56. Copyright 1992 by VCH Publishers, Inc.

Fig. 5. Energy above the valence band of levels reported in the literature for GaP. Arrangement and notations are the same as in Fig. 4. Abbreviations for experimental methods not defined in Fig. 4. are temperature dependence of resistivity (RT), temperature dependence of minority-carrier lifetime (LT), Hall effect (H), and photostimulated electron paramagnetic resonance (PEPR).

Fig. 49. The temperature dependence of resistivity in the a-b plane of YbNi2B2C. The inset shows the low temperature data plotted as a function of T2. Note that the resistivity axis is offset from zero (Yatskar et al. 1996).

Special attention is paid to transport properties (resistance and Hall effect) because they are very sensitive to external parameters being the base for working mechanisms in many types of sensors and devices. The magnetic field and temperature dependences of resistance and Hall effect are considered in the framework of the percolation theory. Various types of magnetoresistances such as giant and anisotropic ones as well as their mechanisms are under discussion. 

Consideration of a system with widespread granule sizes shows that in the case when the temperature dependence of resistance of a nanocomposite is described by the —1/2 law, the characteristic temperature To oc X 3/2. The temperature dependence of the Hall resistance is described by the same law (see Eq. (18)) ... 

Figure 19(a) shows the temperature dependence of resistance R(T) for bismuth nanowire arrays (dw = 7 - 200 nm) synthesized by vapor deposition and measured by Heremans et al. (2000). Hong et al. (1999) reported similar resistance measurements on bismuth wires of larger diameters (200 nm to 2, uni) prepared by electrochemical deposition (Fig. 19(b)). These two studies... 

Fig. 19. (a) Measured temperature dependence of resistance for bismuth nanowire arrays of various wire diameters dw (Heremans et al, 2000). (b) R(T)/R(290 K) for bismuth wires of larger dw measured by Hong et al. (1999). (c) Calculated R(T)/R(300 K) of 36-nm and 70-nm bismuth nanowires (Lin et al, 2000b). The dashed curve refers to a 70-nm poly crystalline wire with increased boundary scattering. 

So the character of the temperature dependence of resistance is determined by the character of the temperature dependences of the concentrations of electrons (n), holes (p) and their mobilities (pn and pp) respectively. 

This increase of electrical resistivity in GaN Mg crystals is related to a drastic decrease in free electron concentration. The temperature dependence of resistivity for these samples is typical for hopping conductivity [24] which suggests that the Fermi level lies within the gap. The optical absorption data... 

According to the experimental results obtained on untwinned YBCO single crystals [1, 2, 3], temperature dependence of resistivity in the planes is linear, i.e. ppiane = d + 0-2T, where a and <22 are constants. On the other hand, temperature dependence of the chain resistivity in YBCO was found to follow approximately a quadratic dependence, i.e. Pchain = b +, where bi and 62 are constants [3]. T2 dependence... 

Proton 1/Ti of heavily doped polyacetylene films with different dopants such as FSO3H, FICIO4, iodine, bromine and potassium was measured by Shimizu et al.113 and the behaviour expected for a quasi-ID metal was not found. Some of them showed a time dependence of 1/Ti. They have deduced the temperature dependence of resistivity from the 1/Ti and 1/Ti versus temperature shows T1 5 behaviour above 40 K and deviates from such behaviour below 40 K. Mizoguchi and Kuroda107 have given a comprehensive review of many investigations of NMR relaxation of both 1FI and 13C in undoped polyacetylene. 

Benoit et al. 2001 (41) SWCNT Arc Discharge As-synthesized Casting CNT Loading levels 0.1 to 8 wt% Film Electrical conductivity increases with CNT content by 9 orders of magnitude from 0.1 to 8% mass fraction with percolation threshold 0.33 wt%. Temperature dependence of resistivity for 0.2 to 8 wt% SWCNT composite films showed that percolating network is affected at low temperature, enhancing the relative resistivity ... 

Fig. 8.18 Typical temperature dependence of resistivity in a carbon-black composite exhibiting switching behaviour.

A comparable temperature dependence of resistivity was obtained for a mixed phase sample of Cel2. The formation of apparently metallic phases for only the iodides of five lanthanide and actinide elements is considered in terms of the stoichiometry, the electronic structure of the cation, the possible nature of the band, and the role of the anion. In contrast, the intermediate Lai2.1,2 phase exhibits semiconduction. Its magnetic data between 80° and 300° K. can be best accounted for if the reduced component is considered to be La ", [Xe]5d with a ground term, a spin-orbit coupling constant A — 050 cm. and only small covalency and asymmetry parameters. 

FIGURE 7-19 Temperature Dependence of Resistivity in Semiconductors, Metals, and Superconductors. 

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