GEOMETRIC FACTOR FOR CONVERSION OF ELECTRICAL RESISTANCE INTO RESISTIVITY Rudolf Podoba1,2, Igor Štubňa1 1

Department of Physics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr.A. Hlinku 1, 949 01 Nitra, Slovakia 2

Department of Physic, Slovak University of Technology in Bratislava, Radlinského 11, 811 07 Bratislava, Slovakia Correspondig author: [email protected]

Abstract The contribution describes an experimental determination of the geometric factor  which transforms measured resistance R into resistivity according to formula   R /  . The factor should be used for a new electrodesample system designed for conductometric thermal analysis of the green ceramic materials. As our experiments showed, the factor is very sensitive for location of the wire electrodes in the sample. For the investigated electrode-sample system   12.88 m-1. Key words: resistivity, resistance, ceramics

1 Introduction Clay-based and kaolin-based ceramics are complex materials of practical and academic interest because of their variety of applications. Thermal behavior of these materials is intensively studied with thermal analyses, mainly DTA, TGA and TDA. Thermal electrical analysis of these materials is used very rare, for example in (Trnovcová et al., 2007; Kozík et al., 1992; Kozík et al., 1988; Chaudhuri et al., 1999a; Sheikh-Zade, 1972a; Sheikh-Zade, 1972b; Chaudhuri et al., 1999b; Demirkiran et al., 2006). Dependencies of electrical properties on different influences (e.g. moisture, porosity, composition and other) are measured much more frequently at room temperature. To measure the electrical conductivity of the ceramic samples, a certain arrangement of the electrodes must be used (Šašek et al., 1981; Oreškin, 1965; Blumenthal, Seitz, 1974). A threeprobe system, which is commonly used, allows measuring the surface conductivity as well as volume conductivity of the sample. The most simple electrode system, so called two-probe system, consists of two electrodes. Its disadvantage is the measuring the sum of the volume and surface currents which can not be separated in this case. But, if the dimensions of the electrodes and the sample are suitable chosen, the surface current is small and can be partially ignored. Of course, such arrangement is only for measurements where high precision is not required. The basic two-probe arrangement represents two parallel plate electrodes with the area S and distance d between them. If the sample has the area S and thickness d, the sample resistance is

R

d , S

(1)

whereis the resistivity of the sample material (Šašek et al., 1981; Blumenthal, Seitz, 1974; Jackson, 1975). Measuring the resistance by a suitable method, the conductivity can be 386

determined. An electrical contact between the sample and electrodes must be reliable during the measurement regardless of changing the sample dimensions as result of drying or heating. Besides that, electrical contacts of high mechanical and chemical quality under a wide range of temperatures must be applied to the sample. The flow of charge carriers can be impeded by barrier layers and/or nonohmic contacts. If high-resistance surface layers exist between the electrode and the sample, the intensity of the applied electric field concentrates at these layers. Therefore, the electric field is distributed inhomogeneously across the sample. These layers can be result of air gaps or foreign material between the electrode and the sample. The problems associated with barrier layers can sometimes be eliminated by applying pressure to the contact area to minimize air gaps or by allowing the electrode material to diffuse a short distance into the interior of the sample. The platinum contacts are usually made using paste which contains some amount of gold. The paste is sprinkled on the surface and Pt wire. This configuration is then heated to 1000 1200 °C. It is obvious, that this method can be used only for hard fired ceramics. Such electrodes were exploited in (Sheikh-Zade, 1972b; Chaudhuri et al., 1999b; Demirkiran et al., 2006). The graphite electrodes can be applied to ceramics in the form of colloidal suspensions called dag. This material can withstand high temperature but must be kept in a reducing atmosphere or vacuum. Graphite electrodes were used for investigation of the green porcelain mixtures in (Trnovcová et al., 2007; Kozík et al., 1992; Kozík et al., 1988). The pressing force, generated by the spring, was also applied. The platinum wire electrodes, infixed directly in the wet plastic kaolin sample, were used in (Sheikh-Zade, 1972a; Sheikh-Zade, 1972b). After drying, ac current was measured during heating up to 1500 °C. As follows from the short description of the contacts, the platinum wire electrodes, which are applied to wet plastic ceramic mass, are most suitable for our goals. We proposed a system consisted of two cylindrical electrodes placed in the sample as visible in Fig. 1. According to our experience, an advantage of this electrode arrangement is 1) free escape of the water vapor from the all surface of the sample, and 2) the electrodes are pressed by the sample material during drying and firing, therefore, the electrical contact is good without external pressing force. Pt wires

sample

Fig. 1A fundamental electrode arrangement

Assuming the sample dimensions are much larger than diameters of electrodes and the distance between them, the resistance between the electrodes is (Jackson, 1975; Podoba, Podolinčiaková, 2011). 387

R

 1  a a2  , ln   1   t  2r 4r 2 

(2)

wherer is the radius of the electrodes, a is distance between them and t is the thickness of the sample, and a  2r . This formula (originally derived for infinite sample) can be also used for finite sample if its square area (see Fig. 1) is larger than 3030 mm and diameter of the electrodes are 0.5 mm and the distance between them is 6 mm (Podoba, Podolinčiaková, 2011). Unfortunately, the sample of such big size can not be placed into small laboratory furnace. That is a reason why we designed a new form of the electrode-sample system. The goal of this contribution is description of the electrode-sample system and to show how to calculate conductivity of the sample material using the new system. 2 Experimental Volt-ampere method with two-probe arrangement was used for determination of the resistance of the sample according to Fig. 2. A sample

V

PS

Fig. 2 Scheme of the volt-ampere method. A – ac microammeter, V – ac voltmeter, PS – ac powersupply 9.6 V/50 Hz The ac voltage was chosen to avoid electrolysis on the electrodes. Multimeter Metex M4640A and multimeter Hameg HM 8012 were used as the voltmeter and ammeter, respectively. Samples were made from a mixture of Sedlec kaolin (75 wt.%) and the water (25 wt.%). Two types of the samples were prepared: 1. Thin discs of the thickness 3.13 mm. Their diameter varied from 13.6 mm to 41.8 mm. These samples were between two brass cylindrical electrodes (diameter 6.8 mm) as depicted in Fig. 3.

1

2 Fig. 3 Disc sample (1) between cylindrical electrodes (2)

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Resistance of the sample was calculated using Eq. (1), where d is the thickness of the sample and S is an area of the electrode (144 mm2). 2. The second type of the samples is shown in Fig. 4. The samples were of the prismatic shape 20×10×10 mm with two kanthal electrodes (diameter 0.4 mm), which were placed into the sample as shown in Fig. 4. The initial distance between the electrodes was 3,3 mm. Preparation of the samples is described in detail in (Podoba, 2011). sample Pt wire

Pt wire

251659264 Fig. 4 Prismatic sample with wire electrodes ci ostane The contact between the sample and the wires is reliable due to contraction of the ceramic material during drying [9] as well as during sintering. 3 Results and discussion The electrical resistance was measured for 2 h at the temperature of 20,5 °C and air humidity of 27 %. Under these conditions, the sample lost the water from 23.75 wt.% to 19.27 wt.% which lead to increase in the resistance of the sample. The relationship between the resistance and the wetness of the sample was also measured under the same conditions. This relationship, showed in Fig. 5, served for a correction of the results. These results were calculated by the percentage increase in resistance, depending on the decrease in moisture samples. This allowed us to calculate what would be the resistance of the sample, if its moisture changed.

Fig. 5 Relationship between resistivity and moisture. Experiments with different sample diameter according to Fig. 3 did not show any dependence of the resistivity on the diameter. The value of the resistivity calculated from Eq. (1) was  = 428 m. Simultaneously with this measurement, a measurement of the resistance of the sample depicted in Fig. 4 was carried out. Since the same material was measured in 389

both experiments, the same resistivity must be determined from them. As follows from Eq. (1) and Eq. (2), the resistance can be written as R    f ( x1 , x2 ,...) ,

(3)

wheref is a function of geometrical parameters xi which characterize shape and size of the sample and electrodes. These geometrical parameters are known, i.e. we can calculate numerical value of the function   f ( x1 , x2 ,...) . Then we can rewrite Eq. (3) as R    or R 

1



.

(4)

We have  = 428 m from Eq. (1) which must be equal   R2 /  determined from the arrangement depicted in Fig. 4. Since R2 is measured, we obtain a numerical value of the geometrical parameter  = 12.88 m-1. We also found a significant influence of the location of the wires in Fig. 3 on the resistance R2, therefore, the wires must be located in the same position in every experiment. Then we can calculate the resistivity using the arrangement in Fig. 3 as 

R . 12.88

(5)

4 Conclusion A new sample-electrode system for measurement of the green ceramic material resisitvity was investigated. Geometrical parameter , which transforms the measured resistance of the sample into resistivity of the sample material according to formula   R /  , was determined. Acknowledgements This work was supported by the grant VEGA 1/0464/12 and UGA VI/20/2012. 5 References Trnovcová, V. – Furár, I. – Hanic, F.: Influence of technological texture on electrical properties of industrial ceramics. J. Physics and Chemistry of Solids, 68 (2007), 1135-1139 Kozík, T. – Trnovcová, V. – Mariani, E. – Štubňa, I. – Roháč, J.: The temperature dependence of the electric conductivity of unfired porcelain mixture. Ceramics-Silikáty, 36 (1992), 6972 Kozík, T. – Trnovcová, V. – Mariani, E. - Štubňa, I.: Relaxation of electrical properties of electroporcelain compacts over the temperature rangeof 20-250 °C. Silikáty (1988), 233240 Chaudhuri, S.P. – Patra, S.K. – Chakraborty, A.K.: Electrical resisitvity of transition metal ion doped mullite. J. European Ceramic Society, 19, 1999a, 2491-2950 Sheikh-Zade, R.M.: Issledovanija spekanija kaolina metodom elektroprovodnosti. Ogneupory, 1972a, N1, 21-23 (in Russian) Sheikh-Zade, R.M.: Study of kaolin sintering by an electric conductivity method. Refractories and Industrial Ceramics, 13, 1972b, N1, 22-23 Chaudhuri, S.P. – Sarkar, P. – Chakraborty, A.K.: Electrical resistivity of porcelain in relation to constitution. Ceramics International, 25, 1999b, 91-99 Demirkiran, A.S. – Artir, R. – Avci, E.: Electrical resistivity of porcelain bodies with natural zeolite addition. Ceramics International, 36, 2006, 917-921 390

Šašek, L. et al.: Laboratorní metody v oboru silikátů. SNTL/ALFA, Bratislava, 1981 (in Czech) Oreškin, P.T.: Elektroprovodnosť ogneuporov. Izd. Metallurgija, Moskva 1965 (in Russian) Blumenthal, R.N. – Seitz, M.A.: Experimental techniques. In: Electrical conductivity in ceramics and glass, part A. Edited by N.M. Tallan, Marcel Dekker Inc., New York 1974, 35-178 Jackson, J. D.: Classical Electrodynamics. Wiley nad Sons, New York 1975, p. 80 Podoba, R., Podolinčiaková, J.: Needle electrodes for the measurementof DC and AC conductivity of ceramics, In: Didmattech XXIV 2011 : Problems in teachers education. Konferencja, Krakow, 15.09.2011. - Kraków : Instytut Techniki UP, 2011, 31-34. Podoba, R.: Apparatus for measuring the temperature dependence of DC electrical conductivity of ceramics. In: Young Researchers 2011: PhD Students, Young Scientists and Pedagogues Conference Proceedings, CPU Nitra 2011, 553 – 556

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