Four-probe Conductivity

The hydrogen bis(sulfate) compound exhibits a room-temperature singlecrystal conductivity (four probe) of 2000-2100 ohms-1 cm-1. Thus it can be categorized as a highly conductive species within the tetracyanoplatinate family of compounds. 

The cesium [hydrogen bis(sulfate)] tetracyanoplatinate complex exhibits a room-temperature electrical conductivity (four probe technique) of approximately 113 ohms 1 cm 1, while that of the Rb analog (Pt—Pt - 2.83 A) is 1500-2000 ohms"1 cm 1. 

A simple way to measure the resistivity of soil is a four-pin method in which four probes are drilled into the ground along a straight line at equal distances a and depth b. Then a voltage V is applied to the two inner probes and a current, T, is measured in the two outer probes (Figure 22.16). This test can also be conducted with the help of a ground icster as discussed in Section 22.3, which normally also has a provision for ihis test. 

Accordingly, the ionic conductivity in an electrolyte with negligible electronic conduction (/jon jtolal) may be determined by Ohm s law, provided that unpolarizable electrodes are employed. To overcome this limitation, separate voltage probes in the shape of identical electronic leads connected to the electrolyte at positions separated by a distance L may be employed (four-probe technique [38]). Under these... 

The charge transport and optical properties of the [Si(Pc)0]-(tos)y)n materials as y=0 -+ 0.67 are reminiscent of the [Si(Pc)0]-(BF4)y)n system, but with some noteworthy differences. Again there is an insulator-to-metal transition in the thermoelectric power near y 0.15-0.20. Beyond this doping stoichiometry, the tosylates also show a continuous evolution through a metallic phase with decreasing band-filling. However, the transition seems somewhat smoother than in the BF4 system for y)>0.40, possibly a consequence of a more disordered tosylate crystal structure. Both [Si(Pc)0]-(tos)y)n optical reflectance spectra and four-probe conductivities are also consistent with a transition to a metal at y 0.15-0.20. Repeated electrochemical cycling leads to considerably more decomposition than in the tetrafluoroborate system. 

Si(Pc)0] (S04)o.09)n> i-s limited by the oxidative stability of the sulfate anion. Thermoelectric power, optical reflectivity, magnetic susceptibility, and four-probe electrical conductivity measurements evidence behavior typical of an [Si(PcP+)0]n compound where p 0.20. That is, there is no evidence that the more concentrated counterion charge has induced significant localization of the band structure. 

Fig. 11.2. Scheme of the four-probe method for the measurement of the thermal conductivity. Rc is the contact... 

Fig. 6.7 (a) The variation of electrical conductivity of PVA-EG hybrid with increasing graphene content. Inset shows the dependence of dielectric constant for the hybrid, (b) The variation of conductivity of the polystyrene-graphene hybrid with filler content. Inset shows the four probe setup for in-plane and transverse measurements and the computed distributions of the current density for in-plane condition (reference [8]). 

Hu et al. showed a decrease in electrical resistivity of PVA by four orders of magnitude with a percolation threshold of 6 wt% [68], while biodegradable polylactide-graphene nanocomposites were prepared with a percolation threshold as low as 3 5wt% [46]. For polystyrene-graphene composites, percolation occurred at only 0.1 °/o of graphene filler, a value three times lower than those for other 2D-filler [69]. Figure 6.7(b) shows the variation of conductivity of the polystyrene-graphene composite with filler content. A sharp increase in conductivity occurs at 0.1 % (the percolation threshold) followed by a saturation. The inset shows the four probe set up for in-plane and trans-... 

In agreement with this analysis, single-crystal conductivity measurements using the four-probe technique reveals semiconducting behaviour for /r -(TMTTF)2Re04, as shown in Fig. 6.30. In this case aRj — 0.011 cm and Ea — 0.17 eV. 

Metallic behavior down to low temperatures was reported on a compacted pellet of TI2PC [46] with very high conductivity of ctrt 10" S cm (four-probe method using indium lead wires). A specific three-dimensional crystal architecture of TI2PC is anticipated to form a three-dimensional semimetallic band. However, the... 

The electrical conductivity of several of these compounds has been reported.88 Compressed pellet four-probe measurements at room temperature are usually in the range 10 2-5 fl I cm-1 although a value of 150-500 has been reported for orientated polycrystals. Most of the compounds show semiconductor behaviour with activation energies of about 35 meV. Ko.6o[Ir(CO)2Cl2]-0.5H20 shows evidence of a transition to more metal-like behaviour near room temperature,88 It seems very likely that if good quality single crystals of these compounds could be obtained then they would exhibit conduction properties similar to those of the cation-deficient tetracyanoplatinates or bis(oxalato)platinates. 

In an attempt to maximize interactions between the metal dithiolene anions, Underhill and Ahmad studied the lithium salt of the [Pt S2C2(CN)2 2] cation.121,122 Slow aerial oxidation of a 50% aqueous acetone solution of H2[Pt S2C2(CN)2 2] and LiCl yielded a black microcrystalline product of small shining black needles and black platelets. Four-probe DC conduction studies on the needle-shaped crystals showed the room temperature conductivity along the needle axis to be 100 Q i cm-1. 

Ir(CO)3Br is isostructural with the chloro complex but with a slightly longer intrachain separation (2.854 A). The four-probe DC conductivity in the iridium atom chain direction is, however, only 3 x 10-4 Dr1 cm-1 and this, together with the variation of conductivity and thermopower with temperature, indicates that the bromo complex is a semiconductor.161 The structure of Ir(CO)3I shows more disorder and could not be refined accurately, but the Ir—Ir separation is 2.858 A. 

The dc four-probe method was used to determine the conductivity at 25 =S T =S 900°C and 5 X 10 5 =S pQ =S 1 atm. Gold wire contacts were made to a rectangular bar with dimensions 9.02 X 2.54 X 1.91 mm. The electrical conductivity and oxygen nonstoichiometry (8) as a function of p0 were determined by using gas-tight electrochemical cells. The details of the method can be found elsewhere but are briefly summarized here.12,13... 

Figure 3. The four-probe dc conductivity of I, a0 2Sr0 8I, co. i I io.4 f from Po2 = 1 to 10 4 atm. Closed symbols correspond to the measurements from high to low temperature and open marks correspond from low to high.

Fig. 1.14. Electrode pattern for a four-probe set up. The corresponding voltage profile along the conducting channel is shown in the bottom part of the figure.

One possible electrode arrangement for the four-probe conductivity measurements, used often in solid-state electrochemistry... 

Figure 5.8. a Schematic diagram of a two-probe conductivity cell [9], (Reproduced by permission of ECS—The Electrochemical Society, from Xie Z, Song C, Andreaus B, Navessin T, Shi Z, Zhang J, Eloldcroft S. Discrepancies in the measurement of ionic conductivity of PEMs using two- and four-probe AC impedance spectroscopy) b Equivalent circuit of the two-probe method. 

Table 5.1. Conductivity data for Nafion l 15 obtained from the two-probe and four-probe methods [9]...

The Rb based on the sample cannot be calculated correctly, since the electric charge transfer resistance and the electric double layer in an electrode interface are also detected as a resistance, even if bias voltage is impressed to the measurement cell in order to measure the ionic conductivity. For the ionic conductivity measurement, a dc four-probe method, or the complex-impedance method, is used to separate sample bulk and electrode interface [4]. In particular, the complex-impedance method has the advantage that it can be performed with both nonblocking electrodes (the same element for carrier ion and metal M) and blocking electrodes (usually platinum and stainless steel were used where charge cannot be transferred between the electrode and carrier ions). The two-probe cell, where the sample is sandwiched between two pohshed and washed parallel flat electrodes, is used in the ionic conductivity measurement by complex-impedance method as shown in Figure 6.1. 

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