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Simple apparatus for the multipurpose measurements of different thermoelectric parameters
Measurement 45 (2012) 133–139
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Simple apparatus for the multipurpose measurements of different thermoelectric parameters Biplab Paul Materials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India
a r t i c l e
i n f o
Article history: Received 24 March 2011 Received in revised form 31 July 2011 Accepted 10 September 2011 Available online 28 September 2011 Keywords: Thermoelectric measurement Differential method Seebeck coefficient Resistivity Hall coefficient Nernst–Ettingshausen coefficient
a b s t r a c t A simple apparatus for the simultaneous measurement of Seebeck coefficient (a) and electrical resistivity (q) in the temperature range 100–600 K, Hall coefficient (RH) and transverse Nernst–Ettingshausen coefficient (N) in the temperature range 300–600 K of the bar shaped samples has been fabricated. The instrument has been designed so simply that the sample can be easily mounted for the fast measurements of different thermoelectric parameters. The sample holder assembly of the apparatus has been designed so cleverly that any part of that section can be replaced in case of any damage; and so it can be regarded as a modular based system. The apparatus is relatively cheaper in cost and also portable. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Search for a material for thermoelectric application in a wide temperature range must be associated with the ability to measure the Seebeck coefficient of the material in both high and low temperature regimes. In thermoelectric materials, scattering of carriers tunes its thermoelectric properties. So, different scattering mechanisms are intentionally introduced into the materials for the enhancement of their thermoelectric efficiency. Thermoelectric efficiency of a material is defined in terms of a dimensionless parameter, thermoelectric figure of merit ZT = a2T/qk, where T and k are the absolute temperature, and thermal conductivity, respectively. For the measurement of Seebeck coefficient in a bar shaped sample, with dimension typically of the order of 1.3 1.0 10 mm3, a temperature difference (DT) is produced along its length and the corresponding voltage developed between the ends is measured (DV). Seebeck coefficient being the ratio of DDVT , a small error in the measurement of DT will introduce a large error in the value of a. So, the accuracy of the measurements of the temperature E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.09.007
gradient is a major concern for any measuring system. Further, the measurement of temperature dependent electrical resistivity simultaneously with the Seebeck coefficient makes it easy for electrical characterization and causes much reduction in time consumed by the measurement process. Both the integral [1–6] and differential methods [7–17] have been implemented by the researchers to measure the Seebeck coefficient in both high and low temperature regimes. However, the integral method is suitable for very long samples. Usually the samples used by the investigators are generally very small in dimension. So, differential method has become more popular one. However, there are few reports giving details of the instrument, which capable of high temperature transport property measurements [7, 9–11]. Ponnambalam et al. [9] and Burkov et al. [10] developed an apparatus for the measurement of Seebeck coefficient and electrical resistivity at high temperatures. However, their design is somewhat complex and not cost effective. Zhou and Uher [7] developed an instrument for high temperature measurement of Seebeck coefficient and resistivity. However, here the drilling on the sample surface to insert the thermocouple tips and electrical leads do not allow nondestructive characterization of sample. Dasgupta
134
B. Paul / Measurement 45 (2012) 133–139
and Umarji [11] reported the fabrication of an apparatus for the measurement of high temperature value of thermal conductivity and Seebeck coefficient. More recently a review on thermoelectric apparatus was presented by Martin et al. [18]. However, no apparatus can fulfill the purpose of measuring all the four parameters a, q, RH, N alone. In this scenario I have designed and fabricated an apparatus for the nondestructive evaluation of the thermoelectric materials. The instruments are very simple in design, where the sample can be easily mounted to carry out the fast measurements of resistivity and Seebeck coefficient. Sample holder assembly of the instruments has been designed so cleverly that any parts of this section can be easily replaced in case of any damage. Further, the instruments are relatively cheaper in cost and portable. The most advantage of this instrument is that the same apparatus can be used for the simultaneous measurement of Seebeck coefficient and resistivity of any sample in the temperature range 100– 600 K. However, with the present simple design where the accommodation of the cryostat is not straightforward, the measurement of Hall coefficient and Nernst–Ettingshausen coefficient can be done using the same apparatus in the temperature range 300–600 K. 2. Apparatus description Fig. 1 shows the schematic diagram of the instrumental arrangement for the measurement of Seebeck coefficient in
Fig. 1. Schematic representation of the whole instrumental arrangement for the measurement of Seebeck coefficient and electrical resistivity in the temperature range 100–300 K.
the temperature range 100–300 K. Here, to reduce the temperature of sample environment below room temperature the main apparatus is inserted into a liquid nitrogen container. Fig. 2 describes schematically the different parts of the sample holder assembly. In Fig. 2 the copper blocks (1 and 2) in sample holder assembly have diameter slightly less than 6 mm, into which very thin (0.08 mm) type-K thermocouples to sense the temperature and copper wires (3) of diameter 0.06 mm for the measurement of thermoemf are embedded. These copper blocks are heated to raise the temperature from 100 K onwards. The sample (4) is placed between the heating copper blocks. The copper blocks are kept inside the quartz tubes (5 and 6) with inner diameter of 6 mm of thickness 1 mm having a length 11 mm onto which 180 X of kanthal (of diameter 0.1 mm) heaters (7 and 8) are wounded. The heaters are wounded by mica sheets (9 and 10) of width 10 mm, which are pressed-fit inside the other two quartz tubes (11 and 12) of inner diameter 15 mm and outer diameter 17 mm. The quartz tube (5) is suspended by the force of compressive strain developed by the mica sheets. The length of the quartz tubes (11) and (12) are 22 and 10 mm, respectively. Quartz tubes (11) and (12) are placed inside the quartz tube (13) of inner diameter 17 mm and outer diameter 19 mm with length 60 mm. The quartz tube (11) is attached along the inner wall of (13) by the spring action (14). The quartz tube (11) can be easily moved coaxially up and down. Similarly, the copper block (1) can easily pass through the tube (5). This mechanism has been employed so that the sample of different length can be supported between the copper blocks. Two slits of dimension 13 12 mm2 are cut at the diametrically opposite side of the bottom portion of quartz
Fig. 2. Schematic diagram of the sample holder assembly of the apparatus.
B. Paul / Measurement 45 (2012) 133–139
tube (13) for the purpose of mounting the sample and connecting the sensors and other electrical wires. Quartz tube (13) is squeezed between two ceramic plates (15 and 16) and placed inside a brass frame. The ceramic plates (15 and 16) prevent the direct conduction of heat from the heater to the brass frame. The brass frame consists of two parallel plates (17 and 18) of diameter 37 mm each and of thickness 6 mm. The plates are separated by a distance of 75 mm by four brass pillars (19) of diameter 6 mm each. The brass plate (17) is kept fixed on the brass pillars by the nuts. The four holes of diameter 3 mm drilled and to which fine bored ceramic beads (20) attached and through which all the sensors and electrical wires are passed. In order to establish good thermal contact the sample (4) is squeezed between the copper blocks. For this purpose, pressure is applied on the copper block (1) by a brass screw of diameter 4.5 mm (21), which is supported by the brass frame. To keep the brass screw (21) to be thermally isolated from the copper block (1) the pressure on the copper block is transmitted through a ceramic bead (22), which is attached to the extreme end of the screw through a stainless steel spring (23). Here, the spring action implies a constant force on the sample during the entire experiment. The sensors and all the wires for electrical measurement are Teflon coated and hence electrical insulation and isolation is maintained. The brass frame is attached to the closed end of a brass tube (shown in Fig. 2) of outer diameter 22 mm having an inner thickness of 2 mm. The length of the brass tube is 70 mm, whose open end is fixed to a Teflon rod of diameter 25 mm by the press fitting and screwing method as shown Fig. 1. The Teflon rod is passed through a Teflon frame, which supports a quartz tube of outer diameter 41 mm of thickness 2 mm and length 31 mm by compressive strain. The quartz tube encapsulates the whole sample holder assembly and remains air tight with the inner wall of the Teflon frame by a thin rubber band. A steel pipe of diameter 6 mm is passed through the Teflon frame for evacuating the sample chamber. To measure the electrical resistivity and Seebeck coefficient in the temperature range 300–600 K the main apparatus is kept out of the liquid nitrogen container. Two steel pipes of diameter 3 mm passed through the Teflon rod inside the brass tube as shown in Fig. 1. The water is passed through the steel pipes to avoid the degradation of Teflon rod adjacent to the open end of brass tube during high temperature measurements.
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employed at all the temperatures throughout the measurement runs. 3.1. Seebeck coefficient measurement To measure the Seebeck coefficient either dc or ac method are generally used [19–21]. The dc method is relatively easier method for the transport measurements, which is used here to measure the Seebeck coefficient. In this technique a thermal gradient is established along the sample and both thermoelectric voltage (DV) and temperature difference (DT) across the length of the sample are measured. The Seebeck coefficient is obtained from
a¼
dV DV ¼ dT DT
ð1Þ
The basic principle of measuring the Seebeck coefficient is shown in Fig. 3a. Thermal gradient is generated by producing a temperature difference, across the sample. To produce the thermal gradient the temperature of the heaters raised slowly, typically at a rate of 1.5 °C/min, which allows the steady state condition to be sustained during data collection and negate the error arising from temperature drift. Thermometer attached to the copper block very close to the sample faces indicates the temperature T1 and T2. To measure the temperature Kiethley 2182 nanovoltmeters are used by which thermocouple signal can be converted directly into temperature values with a resolution of 0.001 °C. Due to the temperature difference of DT = T1 T2 a voltage DVS is developed across the sample, which can be either negative or positive depending on the type of the majority carriers (either hole or electron) in the sample. To measure thermo-emf across the sample Keithley 2001 voltmeter is used which can easily measures up to the resolution of 0.01 lV. As already mentioned the Seebeck voltage is measured with the aid of thin copper wires that are embedded in the copper blocks close to the sample faces. So, both the temperature difference (DT) and developed thermoelectric voltage (DVS) are measured between the same two points. However, the voltage detected by the nanovoltmeter across the sample is somewhat different from the value DVS and given by
DV ¼ DV S þ DV 2 þ DV 1
ð2Þ
Here, DV2 is the voltage developed in the copper wire attached to the cold end because of the fact that its one end is at temperature T2 while the other end is at the
3. Measurement procedures Two p-type PbTe bar samples, viz. specimen-I and specimen-II, with room temperature hole concentration of 3.97 1018 and 4.07 1018 cm3, were taken and each was placed between the two heating blocks and sample chambers evacuated to 5 105 Torr to avoid the oxidation during high temperature measurements. To ensure the good thermal contact of the sample faces with the heating blocks sample is squeezed between the blocks by the press screw (21) driven by the steel spring (23) through the ceramic bead (22). The advantage of the spring loading mechanism is that by which a constant force can be
Fig. 3. Schematic representation of the principle of (a) Seebeck coefficient and (b) electrical resistivity measurements.
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atmospheric temperature (Tatm). Similarly, due to a temperature difference T1 Tatm across the copper wire attached to the hot end a voltage DV1 is developed. If aCu is the Seebeck coefficient of copper wire then the above equation can be written as
DV ¼ DVS þ aCu ðT 2 T 1 Þ
ð3Þ
where DV2 + DV1 is replaced by aCu (T2 T1). So, the Seebeck coefficient can be written as
a¼
DV S DV aCu ¼ T2 T1 DT
ð4Þ
To reduce the error in the measurement of Seebeck coefficient, it is taken as the slope of the linear plot of thermoelectric voltage against the temperature difference across the samples. However, it is to be ensured that the temperature difference DT across the sample must be small (3–8 K) so that the Seebeck coefficient falls in the linear range. This practice of measuring Seebeck coefficient eliminates the error introduced by the offset voltages arising from the inhomogeneities in thermocouple and nonequilibrium contact interfaces [7,9]. It also avoids the assumption that the curves must pass through the point (DV = 0, DT = 0). The obtained Seebeck coefficient is not the absolute one but it is the Seebeck coefficient relative to copper. To obtain the absolute Seebeck coefficient of the sample the contribution arising from the copper has been corrected. The accuracy of the Seebeck coefficient depends on the accuracy in the measurement of temperature gradient and voltage difference. It is estimated that the uncertainty in the measurement in temperature gradient of 3–8 K to be within ±0.4%. The accuracy in the voltage gradient measurement is found to be within ±0.6%, which is mainly originated from the noise in voltage developed across the sample. The total error in the measurement of Seebeck coefficient is estimated to be within ±1%. Fig. 4a and b show the temperature dependent Seebeck coefficient in the temperature range 100–600 K of the specimen-I and specimen-II. The Seebeck coefficient measurement of the sample was performed several times both in heating and cooling mode and the discrepancy between the individual data points was found not to exceed ±1%. The obtained values of Seebeck coefficient of the PbTe specimens are well matched with the values obtained from Pisarenko plot [22] for similar carrier concentration. 3.2. Electrical resistivity measurement The basic principle of electrical resistivity measurement is shown in Fig. 3b. Here, a constant current I is passed through the sample by the copper wires attached to the copper block. Two more ends of the copper wires are attached at the middle of the sample using silver paint, which are used to measure the potential drop V1 where V1 = VIR + VTE, VIR being the resistive voltage due to current I1 and VTE is the contribution from the thermo-emf. To nullify the thermo-emf VTE the current (I2) is suddenly reversed in direction (negative) to measure the voltage V2 where V2 = VIR + VTE. The sample resistance can be obtained from the relation
R¼
V 1 V 2 ðV IR þ V TE Þ ðV IR þ V TE Þ V IR ¼ ¼ I1 I 2 2Iav Iav
ð5Þ
where Iav=(I1 I2)/2. However, for the accuracy of the electrical resistivity measured by this method care should be taken that VIR must be greater than or comparable to VTE. In the present study for the determination of electrical resistivity a current of I = 10 mA is passed through the sample. The sample resistivity is calculated by using the equation
q¼
RA LV
ð6Þ
where A is the cross sectional area of the sample and LV is the distance between the center of the voltage contacts. However, the electrical resistivity obtained by this method can be somewhat different from the actual resistivity of the sample. This is because when a current is passed through the metal/semiconductor interfaces of the sample, due to Peltier effect, heat is liberated at one current contact and is absorbed at the other, which results in a thermal gradient and consequent thermoelectric voltage across the sample. Unfortunately voltage developed due to Peltier effect cannot be nullified by averaging the readings for forward and reverse current direction. This is because the reversal of current reverses the direction of both the temperature gradient and its corresponding thermoelectric voltage. However, the fast switching of current polarity and reduction in measurement time can negate the Peltier effect as the thermal gradient requires finite time to propagate. In the present study the switching of sample current and data collection time are faster than the propagation time of thermal gradient and thus the voltage arising from the Peltier effect is very much reduced. In time duration of data collection a fluctuation of only ±0.01 °C in the value of DT is observed, which is attributed to the Peltier effect, giving rise to an error of ±0.3% in the measurement of voltages. Other source of error in estimation of electrical resistivity is the uncertainty in the measurement of sample dimension. The uncertainty in the measurement of Lv (measured under the microscope) is within ±0.4%. The uncertainty in estimation of sample cross-section is ±0.5%. The total error in the measurement of resistivity is estimated to be within ±1.2%. However, if the sample is not uniform then the error in the measurement of electrical resistivity may exceed ±1.2%. Electrical resistivity measurement was performed several times on the same sample both in heating and cooling mode and discrepancy between the individual data points was not found to exceed ±1.2%. Fig. 4c and d show the temperature dependent electrical resistivity of the specimen-I and specimen-II in the temperature range 100–600 K. 3.3. Hall coefficient measurement By the above described instrument the Hall coefficient of the sample in the temperature range 300–600 K can easily be measured. For the measurement of Hall coefficient of the specimens the sample holder assembly is placed vertically between two magnetic pole pieces. When a current I is passed through the sample along the x-direction and a
B. Paul / Measurement 45 (2012) 133–139
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Fig. 4. Temperature dependent Seebeck coefficient of (a) specimen-I and (b) specimen-II and electrical resistivity of (c) specimen-I and (d) specimen-II in the temperature range 100–600 K.
magnetic field BZ is applied along the z-direction an electromotive force (EH) is generated along the y-direction, which is schematically shown in Fig. 5a. The Hall coefficient (RH) is defined by the equation
EH ¼ RH J x Bz
ð7Þ
where Jx is the current density along the x-direction. For the measurement of Hall voltage, two electrical leads of copper is attached at the mid of the opposite faces perpendicular to the y-direction. To avoid the error in the measurements, introduced by the theromagnetic effect, sufficient care should be taken to ensure that there arise no thermal gradients across the length of the sample at the high temperatures, i.e. the temperature at the upper end of the sample (T1) must be equal to the temperature (T2) at its lower end. However, it is difficult to maintain the isothermal condition while measuring the Hall voltages. Because of Peltier effect a thermal gradient is developed along the length of the sample, which through Nernst–Ettingshausen effect gives rise to a voltage, often called the Nernst voltage, perpendicular to both current and magnetic field direction. In the present study measurement is performed quickly that the thermal gradient does not get sufficient time to propagate and hence reducing the magnitude of Nernst voltage developed across the sample. It is found in time duration of Hall data collection only a temperature difference of ±0.01 °C to develop along the length of the sample, which contributes an error of ±1.7% in the measurement of Hall coefficient. The Hall coefficient was taken as the slope at zero magnetic field of the transverse Hall resistivity with respect to the field. This method is significant to nullify
Fig. 5. Schematic representation of the principle of (a) Hall coefficient and (b) Nernst coefficient measurements.
the spurious voltages developed in the circuit. Other source of error is the uncertainty in the measurement of sample dimension, which contributes an error of ±0.9% in estimation of Hall coefficient. The total error in the measurement of Hall coefficient is estimated to be within ±2.6%. Hall measurements was performed several times both in heating and cooling mode and the discrepancy between individual data points was not found to exceed ±2.6%. Hole concentration, p, was determined by p = 1/eRH, where e is
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Fig. 6. Temperature dependent hole concentration of (a) specimen-I and (b) specimen-II and hole mobility of (c) specimen-I and (d) specimen-II in the temperature range 300–600 K.
Fig. 7. Temperature dependent Nernst coefficient of specimen-I and specimen-II in the temperature range 300–500 K.
the electronic charge. Fig. 6a and b show the temperature dependent hole concentration of specimen-I and specimen-II in the temperature range 300–600 K. The temperature dependent mobility of hole l of specimen-I and specimen-II, calculated from the equation 1/q = pel, where e is the electronic charge, is shown in Fig. 6c and d. The mobility of hole has been found to vary as l/Tm with m = 2.43 and 2.48 for specimen-I and specimen-II, respectively, which is in consistent with the results as reported
elsewhere [23] confirming the accuracy of the Hall measurements. 3.4. Nernst–Ettingshausen coefficient measurement When a thermal gradient dT/dx exists in a conductor along the x-direction and a magnetic field Bz is applied along the z-direction, an electromotive force (ENE) is developed in the conductor in y-direction, which is schematically
B. Paul / Measurement 45 (2012) 133–139
described in Fig. 5b. The field ENE is called the Nernst field and expressed as
ENE ¼ NBz
dT dX
ð8Þ
where N is the Nernst–Ettingshausen coefficient and often abbreviated as Nernst coefficient. The above-described apparatus can be used easily to measure the value of N in the temperature range 300–600 K. For the measurement of N, sample holder assembly is placed vertically between the two magnetic pole pieces. Nernst voltages were measured at the low-field condition (lB 1, where l is the electron mobility) by reversing the sign of the magnetic field quickly and taking the differences in transverse voltages. Nernst coefficient was obtained from the slope of the linear plot of Nernst voltage against the magnetic field. During the measurement of Nernst coefficients a temperature gradient is developed along the direction of Nernst field and so the value measured here is called the adiabatic Nernst coefficient. Nernst coefficient measurement was performed several times both in heating and cooling mode and the discrepancy between the individual data points was found not to exceed ±3%. Fig. 7 shows the temperature dependent Nernst coefficient of specimen-I and specimenII in the temperature range 300–500 K. 4. Summary An apparatus has been designed so that it can be used for the multipurpose measurements of different thermoelectric parameters. It is noted that the accuracy of the measurements of the temperature gradient is a major concern for such measurements. So, care has been taken to implement this design aspect relating to measurement of temperature gradient. Further, the measurement of temperature dependent electrical resistivity simultaneously with the Seebeck coefficient with this equipment makes it easy for electrical characterization and causes much reduction in time consumed by the measurement process, particularly due to quick mounting of the samples in the holder. Acknowledgments The authors acknowledge technical support from Mr. Ratanlal Mukherjee and Mr. Pijush Chakroborty. References [1] C. Wood, A. Chmielewski, D. Zoltan, Measurement of Seebeck coefficient using large thermal gradient, Rev. Sci. Instrum. 59 (1988) 951–954.
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[2] M. Muhibbullah, M.O. Hakim, M.G.M. Choudhury, Studies on Seebeck effect in spray deposited CuO thin film on glass substrate, Thin Solid Film 423 (2003) 100–107. [3] V.D. Das, J.C. Mohanty, Size and temperature effects on thermoelectric power of b-tin thin films, J. Appl. Phys. 54 (1983) 977–981. [4] S.R.S. Kumar, S. Kasiviswanathan, A hot probe setup for the measurement of Seebeck coefficient of thin wires and thin films using integral method, Rev. Sci. Instrum. 79 (2008) 024302. [5] F.G. Wick, Some electrical properties of silicon, Phys. Rev. 25 (1907) 382–390. [6] R.J. Gripshover, J.B. VanZytveld, J. Bass, Thermopower of pure aluminum, Phys. Rev. 163 (1967) 598–603. [7] Z. Zhou, C. Uher, Apparatus for Seebeck coefficient and electrical resistivity measurements of bulk thermoelectric materials at high temperature, Rev. Sci. Instrum. 76 (2005) 023901. [8] O. Boffoue, A. Jacquot, A. Dauscher, B. Lenoir, Experimental set up for the measurement of the electrical resistivity and thermopower of thin films and bulk materials, Rev. Sci. Instrum. 76 (2005) 053907. [9] V. Ponnambalam, S. Lindsey, N.S. Hickman, T.M. Tritt, Sample probe to measure resistivity and thermopower in the temperature range of 300–1000 K, Rev. Sci. Instrum. 77 (2006) 073904. [10] A.T. Burkov, A. Heinrich, P.P. Konstantinov, T. Nakama, K. Yagasaki, Experimental set-up for thermopower and resistivity measurements at 100–1300 K, Meas. Sci. Technol. 12 (2001) 264–272. [11] T. Dasgupta, A.M. Umarji, Apparatus to measure high-temperature thermal conductivity and thermoelectric power of small specimens, Rev. Sci. Instrum. 76 (2005) 094901. [12] A.L. Pope, R.T. Littleton IV, T.M. Tritt, Apparatus for the rapid measurement of electrical transport properties for both ‘‘needlelike’’ and bulk materials, Rev. Sci. Instrum. 72 (2001) 3129–3131. [13] W.H. Kettler, R. Wernhardt, M. Rosenberg, Differential ac method of thermopower measurement, Rev. Sci. Instrum. 57 (1986) 3054– 3058. [14] J. Chaussy, A. Guessous, J. Mazue, Simultaneous measurements of thermopower, thermal conductivity, and electrical resistivity between 1.2 and 350 K, Rev. Sci. Instrum. 52 (1981) 1721–1727. [15] P.I. Wold, The hall effect and allied phenomena in tellurium, Phys. Rev. 7 (1916) 169–193. [16] C.C. Bidwell, Resistance and thermo-electric power of metallic germanium, Phys. Rev. 19 (1922) 447–455. [17] A.E. Middleton, W.W. Scanlon, Measurement of the thermoelectric power of germanium at temperatures above 78 K, Phys. Rev. 92 (1953) 219–226. [18] J. Martin, T. Tritt, C. Uher, High temperature Seebeck coefficient metrology, J. Appl. phys. 108 (2010) 121101. [19] F. Chen, J.C. Cooley, W.L. Hults, J.L. Smith, Low-frequency ac measurement of the Seebeck coefficient, Rev. Sci. Instrum. 72 (2001) 4201–4206. [20] M. Atibin, H. Ghamlouch, P. Fournier, Measurement of the Seebeck coefficient by an ac technique: application to high-temperature superconductors, Rev. Sci. Instrum. 64 (1993) 2938–2941. [21] M.A. Howson, M.B. Salamon, T.A. Friedmann, Anomalous peak in the thermopower of YBa2Cu3O7-d single crystals: a possible fluctuation effect, Phys. Rev. B 41 (1990) 300–306. [22] S.J. Thaigarajan, V. Jovovic, J.P. Heremans, On the enhancement of the figure of merit in bulk nanocomposites, Phys. Status Solidi (RRL) 1 (2007) 256–258. [23] R.S. Allgaier, W.W. Scanlon, Mobility of electrons and holes in PbS, PbSe, and PbTe between room temperature and 4.2 K, Phys. Rev. 11 (1958) 1029–1037.
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Simple apparatus for the multipurpose measurements of different thermoelectric parameters Biplab Paul Materials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India
a r t i c l e
i n f o
Article history: Received 24 March 2011 Received in revised form 31 July 2011 Accepted 10 September 2011 Available online 28 September 2011 Keywords: Thermoelectric measurement Differential method Seebeck coefficient Resistivity Hall coefficient Nernst–Ettingshausen coefficient
a b s t r a c t A simple apparatus for the simultaneous measurement of Seebeck coefficient (a) and electrical resistivity (q) in the temperature range 100–600 K, Hall coefficient (RH) and transverse Nernst–Ettingshausen coefficient (N) in the temperature range 300–600 K of the bar shaped samples has been fabricated. The instrument has been designed so simply that the sample can be easily mounted for the fast measurements of different thermoelectric parameters. The sample holder assembly of the apparatus has been designed so cleverly that any part of that section can be replaced in case of any damage; and so it can be regarded as a modular based system. The apparatus is relatively cheaper in cost and also portable. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Search for a material for thermoelectric application in a wide temperature range must be associated with the ability to measure the Seebeck coefficient of the material in both high and low temperature regimes. In thermoelectric materials, scattering of carriers tunes its thermoelectric properties. So, different scattering mechanisms are intentionally introduced into the materials for the enhancement of their thermoelectric efficiency. Thermoelectric efficiency of a material is defined in terms of a dimensionless parameter, thermoelectric figure of merit ZT = a2T/qk, where T and k are the absolute temperature, and thermal conductivity, respectively. For the measurement of Seebeck coefficient in a bar shaped sample, with dimension typically of the order of 1.3 1.0 10 mm3, a temperature difference (DT) is produced along its length and the corresponding voltage developed between the ends is measured (DV). Seebeck coefficient being the ratio of DDVT , a small error in the measurement of DT will introduce a large error in the value of a. So, the accuracy of the measurements of the temperature E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.09.007
gradient is a major concern for any measuring system. Further, the measurement of temperature dependent electrical resistivity simultaneously with the Seebeck coefficient makes it easy for electrical characterization and causes much reduction in time consumed by the measurement process. Both the integral [1–6] and differential methods [7–17] have been implemented by the researchers to measure the Seebeck coefficient in both high and low temperature regimes. However, the integral method is suitable for very long samples. Usually the samples used by the investigators are generally very small in dimension. So, differential method has become more popular one. However, there are few reports giving details of the instrument, which capable of high temperature transport property measurements [7, 9–11]. Ponnambalam et al. [9] and Burkov et al. [10] developed an apparatus for the measurement of Seebeck coefficient and electrical resistivity at high temperatures. However, their design is somewhat complex and not cost effective. Zhou and Uher [7] developed an instrument for high temperature measurement of Seebeck coefficient and resistivity. However, here the drilling on the sample surface to insert the thermocouple tips and electrical leads do not allow nondestructive characterization of sample. Dasgupta
134
B. Paul / Measurement 45 (2012) 133–139
and Umarji [11] reported the fabrication of an apparatus for the measurement of high temperature value of thermal conductivity and Seebeck coefficient. More recently a review on thermoelectric apparatus was presented by Martin et al. [18]. However, no apparatus can fulfill the purpose of measuring all the four parameters a, q, RH, N alone. In this scenario I have designed and fabricated an apparatus for the nondestructive evaluation of the thermoelectric materials. The instruments are very simple in design, where the sample can be easily mounted to carry out the fast measurements of resistivity and Seebeck coefficient. Sample holder assembly of the instruments has been designed so cleverly that any parts of this section can be easily replaced in case of any damage. Further, the instruments are relatively cheaper in cost and portable. The most advantage of this instrument is that the same apparatus can be used for the simultaneous measurement of Seebeck coefficient and resistivity of any sample in the temperature range 100– 600 K. However, with the present simple design where the accommodation of the cryostat is not straightforward, the measurement of Hall coefficient and Nernst–Ettingshausen coefficient can be done using the same apparatus in the temperature range 300–600 K. 2. Apparatus description Fig. 1 shows the schematic diagram of the instrumental arrangement for the measurement of Seebeck coefficient in
Fig. 1. Schematic representation of the whole instrumental arrangement for the measurement of Seebeck coefficient and electrical resistivity in the temperature range 100–300 K.
the temperature range 100–300 K. Here, to reduce the temperature of sample environment below room temperature the main apparatus is inserted into a liquid nitrogen container. Fig. 2 describes schematically the different parts of the sample holder assembly. In Fig. 2 the copper blocks (1 and 2) in sample holder assembly have diameter slightly less than 6 mm, into which very thin (0.08 mm) type-K thermocouples to sense the temperature and copper wires (3) of diameter 0.06 mm for the measurement of thermoemf are embedded. These copper blocks are heated to raise the temperature from 100 K onwards. The sample (4) is placed between the heating copper blocks. The copper blocks are kept inside the quartz tubes (5 and 6) with inner diameter of 6 mm of thickness 1 mm having a length 11 mm onto which 180 X of kanthal (of diameter 0.1 mm) heaters (7 and 8) are wounded. The heaters are wounded by mica sheets (9 and 10) of width 10 mm, which are pressed-fit inside the other two quartz tubes (11 and 12) of inner diameter 15 mm and outer diameter 17 mm. The quartz tube (5) is suspended by the force of compressive strain developed by the mica sheets. The length of the quartz tubes (11) and (12) are 22 and 10 mm, respectively. Quartz tubes (11) and (12) are placed inside the quartz tube (13) of inner diameter 17 mm and outer diameter 19 mm with length 60 mm. The quartz tube (11) is attached along the inner wall of (13) by the spring action (14). The quartz tube (11) can be easily moved coaxially up and down. Similarly, the copper block (1) can easily pass through the tube (5). This mechanism has been employed so that the sample of different length can be supported between the copper blocks. Two slits of dimension 13 12 mm2 are cut at the diametrically opposite side of the bottom portion of quartz
Fig. 2. Schematic diagram of the sample holder assembly of the apparatus.
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tube (13) for the purpose of mounting the sample and connecting the sensors and other electrical wires. Quartz tube (13) is squeezed between two ceramic plates (15 and 16) and placed inside a brass frame. The ceramic plates (15 and 16) prevent the direct conduction of heat from the heater to the brass frame. The brass frame consists of two parallel plates (17 and 18) of diameter 37 mm each and of thickness 6 mm. The plates are separated by a distance of 75 mm by four brass pillars (19) of diameter 6 mm each. The brass plate (17) is kept fixed on the brass pillars by the nuts. The four holes of diameter 3 mm drilled and to which fine bored ceramic beads (20) attached and through which all the sensors and electrical wires are passed. In order to establish good thermal contact the sample (4) is squeezed between the copper blocks. For this purpose, pressure is applied on the copper block (1) by a brass screw of diameter 4.5 mm (21), which is supported by the brass frame. To keep the brass screw (21) to be thermally isolated from the copper block (1) the pressure on the copper block is transmitted through a ceramic bead (22), which is attached to the extreme end of the screw through a stainless steel spring (23). Here, the spring action implies a constant force on the sample during the entire experiment. The sensors and all the wires for electrical measurement are Teflon coated and hence electrical insulation and isolation is maintained. The brass frame is attached to the closed end of a brass tube (shown in Fig. 2) of outer diameter 22 mm having an inner thickness of 2 mm. The length of the brass tube is 70 mm, whose open end is fixed to a Teflon rod of diameter 25 mm by the press fitting and screwing method as shown Fig. 1. The Teflon rod is passed through a Teflon frame, which supports a quartz tube of outer diameter 41 mm of thickness 2 mm and length 31 mm by compressive strain. The quartz tube encapsulates the whole sample holder assembly and remains air tight with the inner wall of the Teflon frame by a thin rubber band. A steel pipe of diameter 6 mm is passed through the Teflon frame for evacuating the sample chamber. To measure the electrical resistivity and Seebeck coefficient in the temperature range 300–600 K the main apparatus is kept out of the liquid nitrogen container. Two steel pipes of diameter 3 mm passed through the Teflon rod inside the brass tube as shown in Fig. 1. The water is passed through the steel pipes to avoid the degradation of Teflon rod adjacent to the open end of brass tube during high temperature measurements.
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employed at all the temperatures throughout the measurement runs. 3.1. Seebeck coefficient measurement To measure the Seebeck coefficient either dc or ac method are generally used [19–21]. The dc method is relatively easier method for the transport measurements, which is used here to measure the Seebeck coefficient. In this technique a thermal gradient is established along the sample and both thermoelectric voltage (DV) and temperature difference (DT) across the length of the sample are measured. The Seebeck coefficient is obtained from
a¼
dV DV ¼ dT DT
ð1Þ
The basic principle of measuring the Seebeck coefficient is shown in Fig. 3a. Thermal gradient is generated by producing a temperature difference, across the sample. To produce the thermal gradient the temperature of the heaters raised slowly, typically at a rate of 1.5 °C/min, which allows the steady state condition to be sustained during data collection and negate the error arising from temperature drift. Thermometer attached to the copper block very close to the sample faces indicates the temperature T1 and T2. To measure the temperature Kiethley 2182 nanovoltmeters are used by which thermocouple signal can be converted directly into temperature values with a resolution of 0.001 °C. Due to the temperature difference of DT = T1 T2 a voltage DVS is developed across the sample, which can be either negative or positive depending on the type of the majority carriers (either hole or electron) in the sample. To measure thermo-emf across the sample Keithley 2001 voltmeter is used which can easily measures up to the resolution of 0.01 lV. As already mentioned the Seebeck voltage is measured with the aid of thin copper wires that are embedded in the copper blocks close to the sample faces. So, both the temperature difference (DT) and developed thermoelectric voltage (DVS) are measured between the same two points. However, the voltage detected by the nanovoltmeter across the sample is somewhat different from the value DVS and given by
DV ¼ DV S þ DV 2 þ DV 1
ð2Þ
Here, DV2 is the voltage developed in the copper wire attached to the cold end because of the fact that its one end is at temperature T2 while the other end is at the
3. Measurement procedures Two p-type PbTe bar samples, viz. specimen-I and specimen-II, with room temperature hole concentration of 3.97 1018 and 4.07 1018 cm3, were taken and each was placed between the two heating blocks and sample chambers evacuated to 5 105 Torr to avoid the oxidation during high temperature measurements. To ensure the good thermal contact of the sample faces with the heating blocks sample is squeezed between the blocks by the press screw (21) driven by the steel spring (23) through the ceramic bead (22). The advantage of the spring loading mechanism is that by which a constant force can be
Fig. 3. Schematic representation of the principle of (a) Seebeck coefficient and (b) electrical resistivity measurements.
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atmospheric temperature (Tatm). Similarly, due to a temperature difference T1 Tatm across the copper wire attached to the hot end a voltage DV1 is developed. If aCu is the Seebeck coefficient of copper wire then the above equation can be written as
DV ¼ DVS þ aCu ðT 2 T 1 Þ
ð3Þ
where DV2 + DV1 is replaced by aCu (T2 T1). So, the Seebeck coefficient can be written as
a¼
DV S DV aCu ¼ T2 T1 DT
ð4Þ
To reduce the error in the measurement of Seebeck coefficient, it is taken as the slope of the linear plot of thermoelectric voltage against the temperature difference across the samples. However, it is to be ensured that the temperature difference DT across the sample must be small (3–8 K) so that the Seebeck coefficient falls in the linear range. This practice of measuring Seebeck coefficient eliminates the error introduced by the offset voltages arising from the inhomogeneities in thermocouple and nonequilibrium contact interfaces [7,9]. It also avoids the assumption that the curves must pass through the point (DV = 0, DT = 0). The obtained Seebeck coefficient is not the absolute one but it is the Seebeck coefficient relative to copper. To obtain the absolute Seebeck coefficient of the sample the contribution arising from the copper has been corrected. The accuracy of the Seebeck coefficient depends on the accuracy in the measurement of temperature gradient and voltage difference. It is estimated that the uncertainty in the measurement in temperature gradient of 3–8 K to be within ±0.4%. The accuracy in the voltage gradient measurement is found to be within ±0.6%, which is mainly originated from the noise in voltage developed across the sample. The total error in the measurement of Seebeck coefficient is estimated to be within ±1%. Fig. 4a and b show the temperature dependent Seebeck coefficient in the temperature range 100–600 K of the specimen-I and specimen-II. The Seebeck coefficient measurement of the sample was performed several times both in heating and cooling mode and the discrepancy between the individual data points was found not to exceed ±1%. The obtained values of Seebeck coefficient of the PbTe specimens are well matched with the values obtained from Pisarenko plot [22] for similar carrier concentration. 3.2. Electrical resistivity measurement The basic principle of electrical resistivity measurement is shown in Fig. 3b. Here, a constant current I is passed through the sample by the copper wires attached to the copper block. Two more ends of the copper wires are attached at the middle of the sample using silver paint, which are used to measure the potential drop V1 where V1 = VIR + VTE, VIR being the resistive voltage due to current I1 and VTE is the contribution from the thermo-emf. To nullify the thermo-emf VTE the current (I2) is suddenly reversed in direction (negative) to measure the voltage V2 where V2 = VIR + VTE. The sample resistance can be obtained from the relation
R¼
V 1 V 2 ðV IR þ V TE Þ ðV IR þ V TE Þ V IR ¼ ¼ I1 I 2 2Iav Iav
ð5Þ
where Iav=(I1 I2)/2. However, for the accuracy of the electrical resistivity measured by this method care should be taken that VIR must be greater than or comparable to VTE. In the present study for the determination of electrical resistivity a current of I = 10 mA is passed through the sample. The sample resistivity is calculated by using the equation
q¼
RA LV
ð6Þ
where A is the cross sectional area of the sample and LV is the distance between the center of the voltage contacts. However, the electrical resistivity obtained by this method can be somewhat different from the actual resistivity of the sample. This is because when a current is passed through the metal/semiconductor interfaces of the sample, due to Peltier effect, heat is liberated at one current contact and is absorbed at the other, which results in a thermal gradient and consequent thermoelectric voltage across the sample. Unfortunately voltage developed due to Peltier effect cannot be nullified by averaging the readings for forward and reverse current direction. This is because the reversal of current reverses the direction of both the temperature gradient and its corresponding thermoelectric voltage. However, the fast switching of current polarity and reduction in measurement time can negate the Peltier effect as the thermal gradient requires finite time to propagate. In the present study the switching of sample current and data collection time are faster than the propagation time of thermal gradient and thus the voltage arising from the Peltier effect is very much reduced. In time duration of data collection a fluctuation of only ±0.01 °C in the value of DT is observed, which is attributed to the Peltier effect, giving rise to an error of ±0.3% in the measurement of voltages. Other source of error in estimation of electrical resistivity is the uncertainty in the measurement of sample dimension. The uncertainty in the measurement of Lv (measured under the microscope) is within ±0.4%. The uncertainty in estimation of sample cross-section is ±0.5%. The total error in the measurement of resistivity is estimated to be within ±1.2%. However, if the sample is not uniform then the error in the measurement of electrical resistivity may exceed ±1.2%. Electrical resistivity measurement was performed several times on the same sample both in heating and cooling mode and discrepancy between the individual data points was not found to exceed ±1.2%. Fig. 4c and d show the temperature dependent electrical resistivity of the specimen-I and specimen-II in the temperature range 100–600 K. 3.3. Hall coefficient measurement By the above described instrument the Hall coefficient of the sample in the temperature range 300–600 K can easily be measured. For the measurement of Hall coefficient of the specimens the sample holder assembly is placed vertically between two magnetic pole pieces. When a current I is passed through the sample along the x-direction and a
B. Paul / Measurement 45 (2012) 133–139
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Fig. 4. Temperature dependent Seebeck coefficient of (a) specimen-I and (b) specimen-II and electrical resistivity of (c) specimen-I and (d) specimen-II in the temperature range 100–600 K.
magnetic field BZ is applied along the z-direction an electromotive force (EH) is generated along the y-direction, which is schematically shown in Fig. 5a. The Hall coefficient (RH) is defined by the equation
EH ¼ RH J x Bz
ð7Þ
where Jx is the current density along the x-direction. For the measurement of Hall voltage, two electrical leads of copper is attached at the mid of the opposite faces perpendicular to the y-direction. To avoid the error in the measurements, introduced by the theromagnetic effect, sufficient care should be taken to ensure that there arise no thermal gradients across the length of the sample at the high temperatures, i.e. the temperature at the upper end of the sample (T1) must be equal to the temperature (T2) at its lower end. However, it is difficult to maintain the isothermal condition while measuring the Hall voltages. Because of Peltier effect a thermal gradient is developed along the length of the sample, which through Nernst–Ettingshausen effect gives rise to a voltage, often called the Nernst voltage, perpendicular to both current and magnetic field direction. In the present study measurement is performed quickly that the thermal gradient does not get sufficient time to propagate and hence reducing the magnitude of Nernst voltage developed across the sample. It is found in time duration of Hall data collection only a temperature difference of ±0.01 °C to develop along the length of the sample, which contributes an error of ±1.7% in the measurement of Hall coefficient. The Hall coefficient was taken as the slope at zero magnetic field of the transverse Hall resistivity with respect to the field. This method is significant to nullify
Fig. 5. Schematic representation of the principle of (a) Hall coefficient and (b) Nernst coefficient measurements.
the spurious voltages developed in the circuit. Other source of error is the uncertainty in the measurement of sample dimension, which contributes an error of ±0.9% in estimation of Hall coefficient. The total error in the measurement of Hall coefficient is estimated to be within ±2.6%. Hall measurements was performed several times both in heating and cooling mode and the discrepancy between individual data points was not found to exceed ±2.6%. Hole concentration, p, was determined by p = 1/eRH, where e is
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Fig. 6. Temperature dependent hole concentration of (a) specimen-I and (b) specimen-II and hole mobility of (c) specimen-I and (d) specimen-II in the temperature range 300–600 K.
Fig. 7. Temperature dependent Nernst coefficient of specimen-I and specimen-II in the temperature range 300–500 K.
the electronic charge. Fig. 6a and b show the temperature dependent hole concentration of specimen-I and specimen-II in the temperature range 300–600 K. The temperature dependent mobility of hole l of specimen-I and specimen-II, calculated from the equation 1/q = pel, where e is the electronic charge, is shown in Fig. 6c and d. The mobility of hole has been found to vary as l/Tm with m = 2.43 and 2.48 for specimen-I and specimen-II, respectively, which is in consistent with the results as reported
elsewhere [23] confirming the accuracy of the Hall measurements. 3.4. Nernst–Ettingshausen coefficient measurement When a thermal gradient dT/dx exists in a conductor along the x-direction and a magnetic field Bz is applied along the z-direction, an electromotive force (ENE) is developed in the conductor in y-direction, which is schematically
B. Paul / Measurement 45 (2012) 133–139
described in Fig. 5b. The field ENE is called the Nernst field and expressed as
ENE ¼ NBz
dT dX
ð8Þ
where N is the Nernst–Ettingshausen coefficient and often abbreviated as Nernst coefficient. The above-described apparatus can be used easily to measure the value of N in the temperature range 300–600 K. For the measurement of N, sample holder assembly is placed vertically between the two magnetic pole pieces. Nernst voltages were measured at the low-field condition (lB 1, where l is the electron mobility) by reversing the sign of the magnetic field quickly and taking the differences in transverse voltages. Nernst coefficient was obtained from the slope of the linear plot of Nernst voltage against the magnetic field. During the measurement of Nernst coefficients a temperature gradient is developed along the direction of Nernst field and so the value measured here is called the adiabatic Nernst coefficient. Nernst coefficient measurement was performed several times both in heating and cooling mode and the discrepancy between the individual data points was found not to exceed ±3%. Fig. 7 shows the temperature dependent Nernst coefficient of specimen-I and specimenII in the temperature range 300–500 K. 4. Summary An apparatus has been designed so that it can be used for the multipurpose measurements of different thermoelectric parameters. It is noted that the accuracy of the measurements of the temperature gradient is a major concern for such measurements. So, care has been taken to implement this design aspect relating to measurement of temperature gradient. Further, the measurement of temperature dependent electrical resistivity simultaneously with the Seebeck coefficient with this equipment makes it easy for electrical characterization and causes much reduction in time consumed by the measurement process, particularly due to quick mounting of the samples in the holder. Acknowledgments The authors acknowledge technical support from Mr. Ratanlal Mukherjee and Mr. Pijush Chakroborty. References [1] C. Wood, A. Chmielewski, D. Zoltan, Measurement of Seebeck coefficient using large thermal gradient, Rev. Sci. Instrum. 59 (1988) 951–954.
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