Characterization of electrical conductivity of porous metal fiber ...

Materials and Design 37 (2012) 161–165Contents lists available at SciVerse ScienceDirectMaterials and Designjournal homepage: www.elsevier.com/locate/matdesCharacterization of electrical conductivity of porous metal fiber sintered sheetusing four-point probe methodWei Zhou a,b,⇑ , Yong Tang b , Rong Song a , Lelun Jiang a , K.S. Hui c , K.N. Hui da School of Engineering, Sun Yat-sen University, Guangzhou 510006, Chinab School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, Chinac Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kongd Department of Materials Science and Engineering, Pusan National University, Republic of KoreaarticleinfoabstractArticle history:Received 18 October 2011Accepted 29 December 2011Available online 5 January 2012Keywords:B. Fibers and filamentsC. SinteringE. Electrical propertiesNovel porous metal fiber sintered sheets (PMFSSs) with different porosities were fabricated by sinteringcopper fibers. Using four-point probe method, comparative study was conducted to investigate the effectsof probe spacing, porosity, and sintering condition on the electrical conductivity of PMFSS. Our experimentalresults showed that probe spacing plays an important role in determining the electrical conductivity.Uniform probe spacing was adopted in order to reduce the error caused by non-uniformity of probe spacing.The measured electrical conductivity was found to decrease with increasing porosity ranging from70% to 90% for the PMFSS produced under the same sintering condition. Our experimental results werefound to agree well with the theoretical prediction by Liu’s model for the PMFSS with different porosities.The effect of sintering condition on electrical conductivity was also investigated. It was revealed thathigher sintering temperature or longer holding time yields higher electrical conductivity of PMFSS.Ó 2012 Elsevier Ltd. All rights reserved.1. IntroductionPorous metals, as a type of structural and functional materials,have been developing rapidly in recent years [1,2]. Porous metalfiber sintered sheet (PMFSS), a relatively new group of porousmetals have a three-dimensional reticulated structure featuringhigh porosity and large specific surface area. So far, PMFSS hasexhibited many significant engineering applications particularlyin defense and military industry, petrochemical industry, metallurgicalmachinery, automotive industry, and environmental protectionfor its excellent performance in filtration and separation [1],fluid distribution [3], energy absorption [4], biomedical device[5], catalytic reaction [6], and thermal management [7]. Especially,PMFSS has been attracting attentions as a promising electrodematerial for high efficiency batteries [8–10]. Therefore, the electricalconductivity is one of the most important properties need to beconsidered. However, previous research work mainly focused onthe open-celled and close-celled metal foams [11–13]. For PMFSSwith high porosity, limited information has been reported aboutthe relationships between microscopic structures and electricalproperties. Characterizing the electrical conductivity of PMFSS isdemanding especially for its optimal performance in electrodeapplications.⇑ Corresponding author at: School of Engineering, Sun Yat-sen University,Guangzhou 510006, China. Tel./fax: +86 20 39332148.E-mail addresses: zhouw23@mail.sysu.edu.cn, abczhoulin@163.com (W. Zhou).With the development of science and technology as well aseconomy, the demand for porous metals with high porosity andelectrical properties is increasing. Some experimental measurementshave been made for characterizing the electrical propertiesof porous metals. Dharmasena and Wadley [14] measured the electricalconductivity of open-cell aluminum foam using four-pointprobe method. The experimental results of electrical conductivityconfirmed the linear dependence upon density, but the slope wassmaller than that predicted by the unit-cell model. Goodall et al.[15] characterized the electrical conductivity of replicated openporemicrocellular metal over a wide range of relative densityusing four-point probe technique. It was found that the electricalconductivity of metallic foams varied strongly with differentporosities. Liu et al. [16–18] also conducted a series of experimentsto determine the electrical resistivity of nickel foams developed byelectroplating on the polyether sponge sheet using a double circuitbridge. Duan et al. [19] developed a methodology to calculate theapparent resistivity of metallic foam based on the pentagonaldodecahedron model. The calculated evaluations based on thismethodology approximately agree with the experimental resultsof Ni–Cr foams and Ni foams. Recently, Cuevas et al. [20] reviewedthe experimental and theoretical works about the electrical conductivityof metal foams. A new empirical formula was proposedto describe the relationship between porosity and electrical conductivityfor different types of foams.From the above reported work, it is found that the detailedstudy of the relationships relating the porosity and sintering0261-3069/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2011.12.046

162 W. Zhou et al. / Materials and Design 37 (2012) 161–165condition with the electrical conductivity of PMFSS is lacking incurrent literature. In the present study, the PMFSS with a threedimensionalreticulated structure was fabricated through thesolid-state sintering of copper fibers. Four-point probe methodwas used to investigate the dependences of electrical conductivityof PMFSS on the probe spacing, porosity, sintering condition.2. Experimental procedures2.1. Manufacturing process of PMFSSAs reported previously [21], the processing procedure of PMFSSwas divided into five steps including fiber chipping, mold-pressing,sintering, cooling, and testing. First of all, the continuous copperfibers were fabricated by cutting method with a multi-tooth tool.These copper fibers were then cut into segments with length rangingfrom 10 to 20 mm. Next, the copper fibers were randomly distributedinto the packing chamber of the mold pressing equipment.Then pressure was applied by screwing the bolt apparatus. In doingso, a semi-finished PMFSS with the same shape of the packingchamber was obtained. Sintering was then carried out in hydrogengas atmosphere with constant pressure of 0.3 MPa. Different sinteringtemperatures ranging from 700 °C to 1000 °C were taken.Stage heating method was used to optimize the heating rate, whichwas kept at 300 °C/h when the temperature was below 800 °C,while reduced to 200 °C/h as the temperature was above 800 °C.The holding time was set as either 30 min or 60 min. When the sinteringwas completed, the sample was removed from the furnaceand cooled to room temperature in air. Finally, the mold pressingequipment was disassembled and the PMFSS was ready for electricalcharacterization. The appearance of PMFSS produced by abovemanufacturing procedure was shown in Fig. 1.Since the obtained PMFSS has a regular geometric shape, we cancalculate the average porosity using the quality–volume methodformulated byhð%Þ ¼ 1MqV 100where V is the volume of PMFSS (cm 3 ), M, is the mass of PMFSS (g),and q is the density of red copper (g/cm 3 ).2.2. Electrical conductivity measurementsScanning electron microscopy (JSM-6380LA, Japan) wasadopted to observe the microscopic structure of PMFSS. Themeasurements of electrical conductivity were performed by fourpointprobe method in which four sharp probes are mechanicallyð1Þpressed on the testing sample surface, as shown in Fig. 2. An inlinefour-point probe was placed on the surface of the testing sample[14]. A constant current was applied through the outer currentprobes using constant current electric power (Xia Men MingweiElectricity CO., ITD, China, D-50D). The voltage drop across thetwo inner voltage probes was measured with a digital voltmeter(Agilent, USA, HP34401A). The electrical resistivity r is given by[14].2p V Ir ¼ h i ð2Þ1X 1þ 1 1 1X 3 X 1 þX 2 X 2 þX 3where X 1 , X 2 , and X 3 are the probe spacings shown in Fig. 2. Theelectrical conductivity r (in units of S/m) is expressed asr ¼ 1 rIn order to reduce the cell size effects and characterize the overallelectrical behavior, the dimension of samples was taken as70 40 4 mm which was several times larger than the pore size[12]. In order to eliminate the polarization effect and potential offset,voltage drop was measured under forward and reverse currentdirections and the average of the measured absolute values wascalculated [15,22]. For the specific porosity and sintering condition,ten specimens were prepared. Their mean value was taken as theelectrical conductivity of PMFSS with such porosity and sinteringcondition. All measurements were performed in ambient conditionwith temperature approximately 25 °C.3. Results and discussion3.1. Microscopic observations of PMFSSBefore sintering, the copper fibers were distributed randomly inthe pressing mold. The compression was then conducted to makecontact regions among fibers.During sintering process, sintering joints were formed amongfibers as a result of material migration at elevated temperature.Fiber’s metallurgy unification occurred, resulting in PMFSS with athree-dimensional reticulated structure [21]. Fig 3a shows the typicalthree-dimensional reticulated structure of PMFSS sintered at800 °C for 30 min. Such structure has been used as catalyst carrieras well as heat transfer medium in the last 3 years [23,24]. FromFig. 3b, we found that there were two types of sintering jointspresented in PMFSS including fiber-to-fiber surface contact andcrossing fiber meshing [21,25]. It was also noted that PMFSS couldhave a wide porosity range from 60% to 98%, large pore size, andinterconnected pores. Moreover, it is easily to find that copperfibers have a large number of surface microstructures afterð3ÞE=70% E=80% E=90%IICurrent probe Voltage probes Current probeEquipotential surfacePMFSS SampleCurrent flow lineFig. 1. Appearance of PMFSS with different porosities produced by the solid-statesintering of copper fibers.Fig. 2. Schematic diagram of four-point probe method for measuring the electricalconductivity of PMFSS.

W. Zhou et al. / Materials and Design 37 (2012) 161–165 163(a)(b)(c)Fig. 3. SEM images of PMFSS produced by the solid-state sintering of copper fibers: (a) three-dimensional reticulated structure of PMFSS sintered at 800 °C for 30 min, (b)SEM image of bonding types among fibers in the PMFSS, and (c) surface microstructures of single copper fiber after sintering at 800 °C for 30 min.sintering at 800 °C for 30 min, as shown in Fig. 3c. When the sinteringtemperature was increased, a majority of the surface microstructuresdisappeared, giving rise to the smooth surface of thefibers [21]. Therefore, the microscopic structures of PMFSSdepended on the sintering condition.3.2. Effect of probe spacing on the electrical conductivity of PMFSSTo analyze the effect of probe spacing on electrical conductivity,different probe spacings were adopted to measure the electricalconductivity of PMFSS with porosity of 90% sintered at 800 °C for30 min. In this study, four sets of probe spacing were selectedincluding set A (X 1 = X 2 = X 3 = 70/3 mm), set B (X 1 = X 3 = 20 mm,X 2 = 30 mm), set C (X 1 = 15 mm, X 2 = 25 mm, X 3 = 30 mm), and setD(X 1 = X 2 = X 3 = 15 mm). The measured electrical conductivity ofPMFSS using different probe spacings is shown in Fig. 4. It wasobserved that set A and set D exhibited similar electrical conductivityplots. However, set B and C showed the increase of electricalconductivity. Thus, uniform probe spacing was adopted to measurethe electrical conductivity of PMFSS. Moreover, the electrical conductivityof PMFSS was found to decrease with increasing inputvoltage. This can be attributed to the increase of temperaturecaused by higher input voltage [26]. Besides, the average valuesof the measurements with different probe spacings are shown inFig. 5. It was found that the average values of electrical conductivitywere little lower than that of the metal foam with same porosity of6S/mElectrical conductivity0.120.110.100.090.080.070.060.05Probe spacing AProbe spacing BProbe spacing CProbe spacing D0.0 0.2 0.4 0.6 0.8 1.0Voltage (mV)Fig. 4. Measured electrical conductivity of PMFSS using different probe spacings.6 S/mAverage electrical conductivity0.120.100.080.060.040.020.055A0.0850.063BCProbe spacings0.056Fig. 5. Average measured electrical conductivity of PMFSS using different probespacings.90% [11,14]. Also, the approximate average values of electricalconductivity were found when the uniform probe spacing was selected.In the following section, uniform probe spacing of set Awas taken to measure the electrical conductivity of PMFSS.3.3. Effect of porosity on the electrical conductivity of PMFSSPorosity is the most characteristic feature of porous materials.So far, several models have been proposed to bridge the relationshipbetween electrical conductivity and porosity for porous metals,which can help to improve the design of the materials. Forinstance, after measuring the electrical conductivity of Ni foamproduced by metal deposition techniques, Langlois and Coeuret[27] firstly proposed a half-empirical formula relating the electricalconductivity and the porosity for porous material with high porosityranging from 97% to 97.8% as follows:r ¼ 1 h4 r 0 ð4Þwhere r and r 0 are the electrical conductivity of the porous andcompact metals, respectively, and h stands for the porosity.Eq. (4) is obtained from only a few experiments based on thenickel foams. Taking the differences of the specific manufacturingprocesses into account, the formula was revised to be [16].D