Four-probe method

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

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 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... 

Samples were characterized by X-ray diffraction, magnetic susceptibility and chemical analysis with some results summarized in Table 1. The electrical resistivity measurements were made down to 80 K using a four-probe method. Raman scattering experiments used the excitation line A = 514.5 nm of an Ar+ laser in a quasi-backscattering geometry. The laser power of 5 mW was focused to a 0.1 mm diameter spot on the (010) surface. The averaged laser power density amounts to 6 105 W/m2 which is much less compared to earlier Raman studies in manganites [12-15],... 

The resistance was measured with the standard dc four-probe method with 10pm platinum wire and graphite paste, 10-100pA current and temperatures down to 1.5K. 

We also fabricated Sr2FeMo06 of specimen by SrC03, Fe203, and Mo03, experimentally. Pelletizing is followed by calcinations and sintering at 1273 K for 24 h in the atmosphere of Ar+H2. TE properties are measured by four-probe method up to 800 K. 

Four-Probe Method. If two electrodes are used to probe the resistance of a sample, as shown in Fig. 8.1a, then the resistances of the wires and contacts on both sides are additive and may mask the intrinsic resistance of the sample itself (divorced from the contact resistances). If the sample is long enough, then the four-probe method described in Fig. 8.1c will eliminate the contact resistances A constant current I is passed between electrodes 1 and 4, and the voltage drop V across electrodes 2 and 3 is measured the resistance, after due corrections for geometry effects, is given by Ohm s law. 

Figure 5.11. AC impedance spectra of Nafion 115 membrane at room temperature under fully hydrated conditions, measured with the four-probe method [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.)...

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

In principle, the four-probe method is more accurate than the two-probe, because in the former the interface impedance can be eliminated. However, it was reported that in different frequency ranges the membrane resistance and contact resistance could be easily separated. For example, in the two-probe method, the favourite frequency range is 100 to 500 kHz, while in the four-probe method the range becomes 1 to 100 kHz [11], Thus, both methods can yield reliable results, and the probe distance can affect measurement accuracy. Our experiments using both methods indicated that a large probe distance is required to obtain accurate results. 

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. 

The phase composition of the resulted specimens was identified by X-ray diffraction (XRD). Rod-like pieces (3x3xl5mm) and disk-shaped pieces (2mm thickness and 10mm diameter) were cut out for the electrical conductivity measurement and the thermal conductivity measurement, respectively. Microstmcture and phase distribution were observed by a scanning electron microscopy equipped with EPMA (JEOL JXA-8621MX). Electrical conductivity was measured using a D.C. four-probe method. Thermal conductivity was measured using a laser-flash technique. All the measurements were performed in the temperature range of 300 to 1200 K. 

X-ray residual stress determination was performed on the surface of the samples prepared by HIP sintering. The measured residual stress was compared with the results calculated by the finite element method (FEM). The electrical resistivity was measured by the four probes method on the slices cut from the cylinder samples. In order to inspect the thermal stability, the samples were annealed at 900 °C for 24 hour in vacuum. The microstructure on the section was observed by scanning electron microscope. 

Electrical resistivity measurement adopted conventional four probes method. Seebeck coefficient was measured by the standard DC method. Thermal conductivity k was calculated from density, specific heat, and thermal diffiisivity. Specific heat measurement was carried out by use of a differential scanning calorimeter (DSC model 8230, Rigaku, Japan) compared with a standard material of a -AI2O3. The values of thermal diffiisivity obtained from a differential phase analysis of photo-pyroelectric signal (AL- A 0 analysis) [9]. All measiu ements were done at room temperature. 

The ceramic material obtained by this method (sample C) is compared to those obtained by solid state reactions using either a carbonate (A) or nitrate (B) as the source of barium. Micrographs for the three samples are shown in Figure 1. Note that sample C is homogeneous with a particle size of about 1 micron whereas about 100 and 20 micron particle sizes are observed for samples A and B respectively. Resistivity measurements on the same set of samples, were performed using a standard four-probe method with silver paint contacts in an exchange gas cryostat with a Si-diode thermometer. A Tc of 91K with a transition width of 0.5K is observed for sample C whereas samples B and A exhibit widths of 2 and IK respectively. The Meissner effect was observed to be 35, 65 and 50% for samples A, B and C respectively. 

Electrical Resistivity. The electrical resistivity of these materials was measured from room temperature to 15 K at 5 K intervals on bars, 6-10 mm long and 1 mm square, using a DC four-probe method. The electrical contacts were made with fine platinum wire and silver paste. A constant current of <10 mA was used. The voltage difference was measured to 0.1 fiV. The temperature of the specimen was maintained by a closed-cycle cryogenic system and measured using a calibrated silicon diode. 

Second, channel potential measurements by Kelvin probe force microscopy and the four-probe method, which are described later in this chapter, indicate that the contact resistances and temperature dependences associated with the individual source and drain electrodes are nearly identical. From a thermionic emission... 

Early studies of electrochemically prepared PAn films used cyclic voltammetric techniques for the characterization of their electrochemical properties [16,145], Most of these studies addressed the chemical revesi-bility of the redox chemistry of the PAn films thus prepared and various forms of PAn were proposed to be involved in these redox chemistries [145], Depending on the oxidation state and whether or not it is protonatcd, PAn can be either an insulator or a conductor. The conductivities were measured in the dry state with mostly a four-probe method. Also, the molecular weight of electrochemically prepared PAn was found to be approximately 80000 [145b],... 

The room-temperature conductivities obtained for a number of PPy films appear in Table 12.3. We have applied both the linear four-probe and van der Pauw methods to the measurement of conductivity. The linear four-probe method has certain advantages the samples (narrow strips of film) are easily obtained and any anisotropy of the conductivity (within the film plane) can be investigated. The major source of error in conductivity measurements is the thickness measurement. The latter is conveniently done using a micrometer when the film thickness is greater than about 20 /zm. (Accurate thickness measurements of very thin films require the use of other techniques, such as electron microscopy.) It is advisable to make a number of conductivity measurements using specimens from different regions of a given film. 

The synthesized material consists of mainly multiwalled nanotubes with a nondefect structure and does not contain amorphous carbon. For electrical measurements the powder of MWNTs was pressed in a glass ampoule. The electrical contacts were made by 0.1 mm silver wire. Temperature dependence of the conductivity o(T) was measured by the four-probe method in the temperature range of 4.2 - 300 K. Our previous researches of powder carbon nanostructures carried out by this method [6-8] demonstrated stability and reproducibility of the conductivity measurements. 

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