Experimental Setup for the Measurement of Low Temperature Seebeck Coefficient of Single Crystal and Bulk Materials

Transcription

1 Journal of Control & Instrumentation IN: (online), IN: (print) Volume 5, Issue Experimental etup for the Measurement of Low Temperature eebeck Coefficient of ingle Crystal and Bulk Materials Naik I. 1 *, Rastogi A. K. 1 Department of Physics, North Orissa University, Baripada , India chool of Physical ciences, Jawaharlal Nehru University, New Delhi , India Abstract A differential thermopower setup is fabricated for both the single crystal and bulk materials in the temperature range of K. One advantage of this apparatus is that the separation can be changed according to the requirement between and 5 mm. In this setup silver paint is used for the improvement of thermal and electrical conductivity between copper (thermocouple) leads and material. eebeck coefficients are measured using a filter circuit at fixed temperature by making different temperature gradients for highly resistive compounds (<100 K) and continuously with a temperature difference of K in case of metallic compounds. This setup is calibrated by using the high purity lead material and used it for the calculation of absolute seebeck coefficient of materials of interest. Our calculated eebeck coefficient of copper from the measurement value of lead differs from the standard value of copper by +1.4 μv/k with a transition around 41 K related to the silver contain. Keywords: o power, differential method, experimental design, computer automation *Author for Correspondence indrajit_naik@yahoo.co.in INTRODUCTION opower gives a lot of information such as nature of charge carriers, number density, etc. for the electrical conductivity. One of the simplest methods to calculate the thermopower of material is eebeck coefficient. The efficiency of the thermopower is calculated from the dimensionless Figure of merit [1], defined by ZT T (1) where is the electrical resistivity, is the total thermal conductivity, and T is the absolute temperature. opower of large efficiency is used for electrical power generation and thermoelectric cooling [ 4]. There are two different methods to obtain the eebeck coefficient: (a) differential method and (b) integrated method. In differential method, a small temperature gradient is created along the length of the material and its thermopower is calculated as ( T) V T, where T is the mean temperature of the material. This apparatus is similar with the reported apparatus up to some extent [5]. Our aim is to make better thermal and electrical contacts between and copper strips/copper leads by using silver paint and reduce the errors (zero offset thermal voltage and noise in high resistive materials) present in thermal voltage at low cost. We have used two thermocouples: (a) Au-Fe (0.07 at % Fe) verses chromel for material temperature measurement and (b) Au- Fe (0.03 at % Fe) verses chromel for measurement of temperature gradient across the material. The materials of bulk and single crystal flakes are mounted easily at room temperature and obtained the thermopower in the temperature range of K. Here alternated heating procedure is adopted by injecting dc current to the heater through diode. The fabrication of holder and simultaneous measurement of resistivity and JoCI (014) 5-30 TM Journals 014. All Rights Reserved Page 5

2 Experimental setup for the measurement Naik and Rastogi thermopower in wide temperature range are reported by others [6 8]. THEORETICAL METHOD When a small temperature gradient is created along the length of the material, eebeck coefficient is defined by V T lim () T 0 T where V and T are differences in thermal voltage and temperature along the length of the material, respectively. The minus sign is introduced in the expression () to satisfy the relation E = T. uppose the induced voltage V is measured by two copper () leads around room temperature T 0 due to the temperature T 1 and T ( T1 T ) at the junctions A and B, respectively, via temperature T1 T1 T1 and T T T at the junction A and B due to the silver paint as shown in Figure 1. Fig. 1: chematic Circuit Diagram for the Measurement of eebeck Coefficient. Then V can be represented as V V V b B dv B B b dv B A a dv A A dv 0 Ag A ( T T) ( TT ) a dv ( T T ) ( T T) ( TT ) ample 1 Ag T T1 Ag T T1 V T T 1 T T1 Ag T T 1 (3) The second term in the right hand side of Eq. (3) arises due to the silver paint. If T1 and T are equals then above expression becomes V T T 1 If T T1 and V Vb Va is positive, then eebeck coefficient of material with respect to copper will be negative. It indicates that electrons are the charge carriers. Equation (3) can be further simplified as follows: V T ample V V T T1 Ag T T1 Ag V Them T (4) Here, V is the voltage measured by Au-Fe (0.03 at % Fe) and chromel differential thermocouple and is the thermopower of the thermocouple. It indicates that the eebeck coefficient of any material calculated with respect to Copper using silver paint as contact contains the contribution of silver to it. Experimental Design Top view of the holder is shown in Figure. Two copper strips, each of the dimensions ~ 10 mm 4.5 mm 0.5 mm are glued over a copper block of the dimension JoCI (014) 5-30 TM Journals 014. All Rights Reserved Page 6

3 Journal of Control & Instrumentation Volume 5, Issue IN: (online), IN: (print) ~5 mm 0 mm and 4 mm thickness. The copper block was attached directly with the head of the cold finger of CCR (Close Cycle Refrigerator) by four screws at four corners for good stability of temperature related to accurate calculation of eebeck coefficient. A thin mica sheet is used between copper block and two copper strips to make the electrical isolation between the body of the CCR and material. The separation between the strips is about 3 mm and it can be changed according to the requirement. Each strip is glued with a heater made out of thick film resistor of 33 for heating purpose by GE varnish. For the measurement of temperature gradient across the material, the junctions of the differential thermocouple Au-Fe (0.03 at % Fe) versus chromel are embedded in the groves of the copper strips by silver paint. This silver paint makes thermocouple junctions permanent and good thermal and electrical conductivity between thermocouple and copper strips. Then the copper leads are placed close to the thermocouple junction to minimize the errors in measurements. One copper lead is fixed with the thermocouple junction whereas the other one is electrically isolated from the copper strip and thermocouple junction by a cigarette paper. All the leads including thermocouples, Au-Fe (0.03 at %Fe) versus chromel are taken out of the vaccum chamber and connected with the measurement devices after thermally sunk at the mean temperature in between the copper block and head of the cold finger. Two Keithley Nano voltmeter of 181 and 18 model are used for recording the voltages. To make the temperature difference along the material, current is applied from the Keithley 44 current source. One copper lead from each heater is connected with the neutral point of the current source whereas other two leads (one lead from each heater) are connected with the positive terminal of the current source through diode of opposite polarity. This helps to easily interchange the heating procedure by changing the sign of dc current. The material temperature is measured by a temperature controller (scientific instrument model 5500) using calibrated Au-Fe (0.07 at % Fe) versus chromel thermocouple whose tip is attached in between the head of the cold finger of CCR and holder. Good thermal conductivity of this thermocouple with material via holder is verified through finding the transition points at nearly same temperature in resistivity (material is attached directly with the thermocouple via mica sheet) and thermopower (material is attached with the thermocouple via holder using this set up) for different compounds. All the instruments are controlled by a personal computer through the Q-basic program. The collection of data through Q-basic program in a computer is found correct after checking it manually by implementing different amounts of current to the heater. Fig. : Top View of the Probe with Mounted ample. Measurement Procedure When the is mounted over the two copper strips using silver paint spreads on the contact area of material with copper strip. To create a real thermal e.m.f. along the material, a minimum of 10 ma current is applied. This amount of current can make a temperature difference of about K. Then measured thermal e.m.f. of the material in our set up contains the series combination e.m.f. of Ag, material and Ag. This e.m.f. exhibits the fluctuation of zero offset thermal voltage of nanovolt order due to the fluctuation of mean JoCI (014) 5-30 TM Journals 014. All Rights Reserved Page 7

4 Experimental setup for the measurement Naik and Rastogi material temperature. To avoid these fluctuations, following points are considered: (a) the material temperature was raised in a controlled manner at the rate of ~0.5 K/min from 16 to 300 K and (b) each reading was taken at particular material temperature. ometimes spurious voltages from the measurement circuit are added to it. To obtain the correct value of seebeck coefficient, zero offset thermal voltage and spurious voltages have to be eliminated through using formula 5(a) and 5(b) by heating both ends of the material. After a predetermined time of heating corresponding thermal voltages are recorded by the computer. If VTH1, VT 1 and VTH, VT are the voltages measured by copper leads and thermocouple, Au-Fe (0.03 at % Fe) verses chromel, respectively, for two heaters. Then V V are the mean voltages and V V V TH1 TH (5a) VT1 VT V (5b) The time for making a stable temperature difference is not same for all compounds. In metallic compound, it creates within a small time period of 1 min. But in case of high resistive compounds of semiconductors, it takes more time to maintain a fixed temperature difference. Another problem is also noticed in semiconductors that the thermal e.m.f. is not stable. To overcome these problems, we have adopted the following procedure as explained below. Metallic Compounds al voltage is small and sometimes spurious voltages are comparable to the actual thermal voltage across the material. To recover the actual value of thermal voltage from the recorded value at one particular material temperature, we have used the formula given in Eqs. 5(a) and 5(b). To obtain the eebeck coefficient at particular temperature, the value V V is multiplied with the of out. standard thermopower value of the thermocouple, Au-Fe (0.03 at % Fe) verses chromel. Insulating Compounds al voltage is noisy. To reduce the noise a filter circuit made up of ferrite inductors and capacitor is added to the thermal voltage leads. This filter circuit is kept inside the CCR quite near to the material. One terminal from each capacitor is grounded to the common earth of the power supply through the body of the CCR. This arrangement was able to reduce noise considerably, permitting an accuracy of about 5% in thermopower of materials with resistance up to about 100 K. In this case V out V. is calculated from the graph plotted between V vs V with different supply current at particular material temperature. Then the eebeck coefficient is calculated by multiplying V out V. and standard thermopower value of the thermocouple, Au- Fe (0.03 at % Fe) verses chromel. Absolute opower In this setup, eebeck coefficient of the material is measured with respect to the copper leads (see expression 3 and 4). In order to find (T ), we have measured the thermopower on high purity lead sheet with the same set up. Using Eq. (4) for lead, we have calculated (T ) by substituting the standard tabulated absolute eebeck coefficient of [9] as given below. Pb Pb V V T T 1 Ag V Them (6) This expression contains the contribution of silver to seebeck coefficient. The obtained value of (T ) is now substituted in Eq. (4) to find the absolute value of thermopower for measured material. V V (7) ample Pb V V ample Pb JoCI (014) 5-30 TM Journals 014. All Rights Reserved Page 8

5 Journal of Control & Instrumentation Volume 5, Issue IN: (online), IN: (print) This expression is free from the silver contribution to seebeck coefficient. This is same as the subtraction of seebeck coefficient of lead from the seebeck coefficient of material measured w.r.t.. We have used this setup and found absolute seebeck coefficient on Nbe and V 4 free from the anomaly present at 41 K [10, 11]. REULT AND DICUION The temperature dependence thermopower of leads is shown in Figure 3. The eebeck coefficient of lead measured w.r.t. gave an anomaly at 41 K. This is also present in our calculated (T ) (Figure 4), obtained after subtracting the absolute eebeck coefficient of pure lead from the measured thermopower of lead with respect to [9]. Pb This ensures that the contribution of Ag to Pb and makes this transition in all the compounds measured in this setup as we found in Eqs. (4) and (6), respectively. To neglect the contributions of Ag in for a particular material, we have to add the obtained value of in as given in Eq. (7), which will provide the absolute eebeck coefficient of the material. Fig. 3: Temperature Dependence eebeck Coefficient of LEAD. olid Circles are Measured Value w.r.t. Copper using the Probe Described in This Article and tars are Reported abs. Value of Lead by Blatt et al. [9]. In the other hand the value of is less than 1 μv/k over entire range of our measurements, therefore correction has little qualitative effects on. The inset of Figure 4 shows the difference, approximately about +1.4 μv/k, between calculated and reported thermopower of copper [9, 1]. They are very close to each other below 50 K whereas above 50 K it shows deviation when we added +1.4 μv/k in our calculated thermopower of copper as shown in Figure 4. We hope, the major factors in the discrepancy of and Pb above 50 K in our results are due to the contributions of Ag and purity of the copper wire that we have used is unknown as in Eq. (6). The purity of the material also affects the absolute value of as reported for Pb [9]. Fig. 4: Temperature dependence eebeck Coefficient of Copper. (a) Abs. opower Data Reported by Blatt et al. [9] and (b) Calculated opower Data Contain Ag using the Probe Described in This Article. CONCLUION In our present work, we have made a differential seebeck coefficient setup in a simple way as discussed above for laboratory use at low cost. Here, silver paint is used at the JoCI (014) 5-30 TM Journals 014. All Rights Reserved Page 9

6 Experimental setup for the measurement Naik and Rastogi junctions for the improvement of thermal conductivity provides anomaly around 41 K in all the materials and can be removed by subtracting the measured data of standard material (here we have taken Lead). The anomaly temperatures of the material related to their electronic structure are found in good agreement with reported values of resistivity, magnetization, etc. ACKNOWLEDGEMENT One of the authors (I. Naik) acknowledge to C..I.R., India for the financial support to develop this set up at chool of Physical ciences, J.N.U., New Delhi REFERENCE 1. Disalvo FJ. Theroelectric cooling and power generation. cience. 1999; 85:703 4p.. Goldsmid HJ. oelectric Refrigeration. New York: Plenum Press; Tritt TM. oelectric run hot and cold. cience. 1996; 7: 176 8p. 4. Tritt TM. oelectric materials: Holey and unholy semiconductors. cience. 1999; 83(5403):804 1p. 5. Pope AL, Littleton IV RT, Tritt TM. Apparatus for the rapid measurement of electrical transport properties for both needle-like and bulk materials. Rev ci Instrum. 001; 7(7):319 33p. 6. Nakama T, Burkov AT, Heinrich A, et al. Experimental setup for thermopower and resistivity measurement at K. 17 th International Conference on oelectrics; p. 7. Boffoue O, Jacquot A, Dauscher A, et al. Experimental setup for the measurement of the electrical resistivity and thermopower of thin films and bulk materials. Rev ci Instrum. 001; 76(5): p. 8. Ponnambalam V, Lindsey, Hickman N, et al. ample probe to measure resistivity and thermopower in the temperature range of K. Rev ci Instrum. 001; 77(7): p. 9. Blatt FJ, chroeder PA, Foiles CL, et al. oelectric Power of Metals. 7 West 17 th treet, New York: Plenum Press; Naik I, Ratogi AK. Transport properties of H-Nbe : Effect of Ga-intercalation. Physica B 010; 405:955-63p. 11. Naik I, Yadav C, Rastogi AK. A crossover from incoherent-metal to fermiliquid behavior in V 4 : Transport and magnetic properties upon substituting Zn for. Phys Rev B. 007; 75(11): p. 1. Dugdale J. The Electrical Properties of Metals and Alloys. 5 Hill treet, London: Edward London; JoCI (014) 5-30 TM Journals 014. All Rights Reserved Page 30