MM 396: B.Tech. Credit Seminar
HIGH TEMPERATURE SEEBECK COEFFICIENT METROLOGY
Dangi Milind Sudarshan (Roll No. 140110027)
Prof. Titas Dasgupta
Department of Metallurgical Engineering and Materials Science
INDIAN INSTITUTE OF TECHNOLOGY BOMBAY
I hereby declare that the Seminar report titled “HIGH TEMPERATURE SEEBECK COEFFICIENT METROLOGY” submitted to the Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay is a record of work done by me under the guidance of Professor TITAS DASGUPTA towards partial fulfillment for the completion of this course. I have understood the contents of this report and written them in my own words
• History of Seebeck Coefficient
• What is Seebeck Coefficient?
• What are Thermoelectric Materials?
• Applications of Thermoelectric Materials
• Refrigeration (Thermoelectric cooling)
• Power Generation (Thermoelectric generator)
• Space Radioisotope Thermoelectric Generator
• Automotive Thermoelectric Generators
• Methods of Measurement of Seebeck Coefficient
• Integral Method
• Differential Method
• Steady State condition
• Quasi – Steady State condition
• Transient condition
• Problems and Solutions
• Current status in HT Seebeck Measurement (Conclusion)
An overview of the practices and challenges of thermoelectric metrology at high temperatures is presented. Seebeck Coefficient is an essential property measurement for the evaluation of the potential performance of thermoelectric materials. The various applications of thermoelectric materials in refrigeration and power generation including Space radioisotope and Automotive TE generator is summarized along with the properties required for good TE materials. Common sources of voltage and temperature measurement error are described along with the principles to overcome these. The cold – finger effect and the thermocouple – tip – poisoning effect can lead to erroneous results. This report also compares the relevant techniques for measurement of Seebeck coefficient and the apparatus designs that are required for the effective management of uncertainty in high temperature thermoelectric metrology. Measurement uncertainties up to 14% can be observed often in interlaboratory temperature – dependent Seebeck coefficient comparisons. This article will also summarize the current status in high temperature Seebeck Measurement with ----- emerging as a high temperature reference material for Seebeck coefficient measurement due to its good spatial homogeneity along with thermal stability up to 1000K.
CHAPTER – 1
1.1 History of Seebeck Coefficient
Thomas Johann Seebeck, on August 16, 1821, observed magnetic needle deflection by heating one end of a bimetallic loop of bismuth and copper wires. Initially it was termed as “Thermomagnetism”, because disturbing the temperature equilibrium resulted in a deflection of the magnetic needle (magnetism). Thus, a new terminology was proposed namely the Thermoelectric (TE) phenomena, because it was realized that a temperature difference between the junctions induced an electric current, which deflects the magnet following the Ampere’s law. In other words, there occurs a shift in electron energy levels in each of the metals differently and a voltage difference generated creates an electric current which in turn creates a magnetic field around these wires resulting in the magnetic needle deflection.
Thermoelectricity involves the solid – state interconversion of the thermal and electrical energy. The two primary phenomena involved include the Seebeck and Peltier effect. Seebeck effect is the direct conversion of heat into electricity at different wire junctions, whereas, Peltier’s effect is the absorption or liberation of heat at the junction by passage of an electric current through Ohmic interface of dissimilar conductors. A recent surprising discovery the spin – Seebeck effect was observed along permalloy (NiFe) sample length, initiated by a temperature difference and recorded as a spin redistribution measurement.
Fig.1.1 (a) Seebeck’s experimental instrumentation (b) The Seebeck Effect for two dissimilar materials A and B with Interfaces at temperatures T1 and T2, such that T1 < T2 and a proportional voltage is generated. [Ref.1]
1.2 What is Seebeck Coefficient?
The phenomenon of direct conversion of heat into electricity at junctions of different materials is known as the Seebeck effect. It is an essential property for potential performance evaluation of TE materials because of high sensitivity to electronic structure. Thus, Seebeck coefficient is a measure essentially of the per particle transport entropy and proportional to per carrier average energy, relative to the Fermi Energy EF divided by (e) charge per carrier and temperature (T).
S ≈ (1 / eT) '⟨'E−EF'⟩
Seebeck coefficients are typically smaller for metals because the charge carriers that are participating in the electrical transport have energies ≈ kBT, thus smaller energy per carrier. On the other hand, Semiconductors wherein the dopant state carriers within gap band get excited into conduction band have a greater energy per carrier and thus exhibit larger Seebeck coefficients.
Fig.1.2 (a) Ideal energy band diagrams representing electronic conduction for metal; n-type, p-type semiconductors [Ref1] (b) Ideal Seebeck coefficient measurement geometry, with small point contact thermocouples [Ref.2]
Also known as thermopower, Seebeck coefficient is sensitive to defects, phase transformations and impurities in the materials. It is proportionality constant of the voltage (∆V) developed by applying a temperature gradient (∆T) across the junctions of different materials. Seebeck measurements at high temperatures are often challenging, as it is difficult to reproduce and maintain consistency in the results of thermal and voltage measurements. This calls for improved measurement techniques and apparatus for better and accurate results.
S = (∆V/∆T)
CHAPTER – 2
2.1 What are Thermoelectric Materials?
Thermoelectricity involves direct heat to electrical energy or electrical energy to heat energy solid – state interconversion involving Seebeck and Peltier effect phenomena. Though the TE devices have low conversion efficiency they still find application in NASA’s radioisotope TE generator for space power generation, electronic refrigeration, temperature measurement. TE devices require minimal maintenance, offer compact and quiet operation and are environment friendly. TE materials with higher efficiency at higher temperatures are desirable for efficient temperature measurements. Also, higher efficiencies enable practical thermal and electrical energy conversion. The thermoelectric figure of merit ZT governs the efficiency of conversion of waste heat to electrical energy.
ZT = (σ S2T / k)
Thus a good thermoelectric material should have large Seebeck coefficient S, high electrical conductivity with thermal conductivity k low. Absolute temperature is T. The Seebeck coefficient, thermal conductivity and electrical conductivity are strongly interdependent. Thus, repeated measurement of these quantities will help in optimization and identification of thermoelectric materials. The value of S and σ usually increases with the high charge carrier concentration. A custom – designed system can provide flexibility in the simultaneous routine measurement and data analysis with the applicability of the apparatus applicable even at high temperatures above 1000K. Power factor is an important factor being a criterion for the selection of materials in thermoelectric devices. High power factor materials generate more energy while in a space – constrained application.
Power factor = σS2
The aim of this study is to analyze the various methods of measurement of Seebeck coefficient at high temperature including the steady state, quasi steady state and transient state conditions, and, finding the solutions to these measurement techniques’ problems and improving the efficiency and precision of measurements at high temperatures. Presently there is an error of approximately 5 to 10%. Acceptable efficiencies occurs with ZT>1 with the recent progress states that using the nanoscale enhancement higher efficiencies (ZT>2) can be achieved.
Fig.2.1 (a) The Variation of Seebeck coefficient (S), thermal conductivity (k), figure of merit (ZT) and
electrical conductivity σ with the temperature for thermoelectric materials [Ref.3]
Fig.2.1 (b) Temperature-dependence figure of merit (ZT) for PbTe:Na, PbTe:Tl, Pb0.97Mg0.03Te:Na and Pb1xMnxTe:Na, all calculated using the heat capacity of Blachnik. Much like Pb1-xMnxTe:Na, the Pb1-xMnxTe:Na alloy has ~30% greater average ZT (inset) in the temperature range studied. [Ref.3]
2.2 Applications of TE materials
2.2.1 Refrigeration (Thermoelectric cooling)
‘Thermoelectric coolers’ or ‘Peltier coolers’ are thermoelectric materials, which are used as refrigerators with their operation based on the Peltier effect. Vapor – Compression refrigeration is a more common a technology used than Peltier cooling. Advantage of using a Peltier cooler is its flexible shape, small size and lack of refrigerant, with the main disadvantage being its low efficiency. Peltier coolers are used in niche applications today, where efficiency is not important.
Fig 2.2.1 Thermoelectric Cooler [Ref.4] Fig.2.2.2 Thermoelectric Generator [Ref.4]
2.2.2 Power Generation (Thermoelectric generator)
The power generation mode uses the concept of Seebeck effect. Since, ZT – the figure of merit has no upper limit and with ZT approaching infinity, efficiency approaches Carnot limit for thermoelectrics. These are lightweight, reliable and of small size and these generators serve the niches application where less importance is of efficiency and cost than the reliability. The internal combustion engines capture 20-25% of energy that is being released during fuel combustion. Increased mileage and more comforts levels along with more electricity generation can be achieved by an increase in the conversion rate. Cogeneration plants generally use the heat that is produced during the generation of electricity for various alternative purposes. Also, Solar thermal energy generation involves the power generation mode using the Seebeck effect.
2.2.3 Space Radioisotope Thermoelectric Generator
Space Radioisotope TE generator used by NASA for deep space power generation is based on power generation using thermocouples (electronic device with different conductors forming junctions at different temperatures generating temperature dependent voltages) in an array for the conversion of the heat, which is released by radioactive material’s decay into electrical energy by Seebeck effect. Also, GPHS – RTG has no moving parts.
Fig 2.2.3 Space Radioisotope Thermoelectric Generator [Ref.4]
2.2.4 Automotive Thermoelectric Generators (ATEG)
Waste heat from an internal combustion engine (IC) gets converted into electricity in an ATEG by the Seebeck effect. It consists of four elements mainly cold side heat generator, hot side heat generator, compression assembly system and thermoelectric materials. The waste heat generated by the engine’s exhaust or coolant is converted by ATEGs into electricity thus decreasing fuel consumption but extra fuel is consumed due to its weight.
Fig 2.2.4 Automotive Thermoelectric Generator [Ref.4]
CHAPTER – 3
3. Methods for Measurement of Seebeck Coefficient
For a good Seebeck coefficient measurement the primary requirements include: (a) Spatially synchronous Voltage and temperature measurements i.e. measurement of voltage and temperature at the same location and time; (b) good electrical and thermal contact of the probes with the specimen; (c) Minimal extraneous contributions during low voltages (microvoltages) acquisition. Two primary techniques are used for measuring the Seebeck Coefficient: the integral method and the differential method.
Fig.3 Graphical illustrations of the integral and differential Seebeck coefficient measurement methods [Ref 1]
3.1 Integral method
In this method (or large ∆T), fixed temperature T1 is maintained at one end, T2 = T1 + ∆T at the opposite end. Differentiating the entire data set Vab (T1, T2) with respect to T2 an analysis gives
Sab (T2) = Sb (T2) - Sa (T2) = ∂ ⁄ ∂T2 (Vab (T1, T2))
Absolute Seebeck coefficient of sample being measured is Sa (T), while Sb (T) being the already known Seebeck coefficient of reference leads. ‘a’ and ‘b’ are the materials and the electric potential dependent on temperature is given by Vab (T1, T2). The fitting method should comprise minimal oscillation data set due to amplification of small random biased errors in the derivative. The integral method is effective in approximating the TE operating conditions and the minimization of the influence of offsets of voltage, due to the application of large thermal gradients resulting in even larger signals of voltage. But, maintaining isothermal T1 temperature at high temperatures is very difficult and requires corrections and fits. Thus, it is useful for semidegenerate semiconductors, loner samples, wires, semimetals and metallic ribbons.
3.2 Differential method
The majority of Seebeck coefficient characterization at high temperatures is comprised by the differential method (or small ∆T). Across the specimen, small thermal gradient is applied at the mean temperature T0 = (T1 + T2)/2, i.e. T1=T0 - ∆T/2 and T2 = T0 +∆T/2. Here, the measurement of Seebeck coefficient is exclusively given by the ratio of electrical potential to the temperature difference, the condition being that ∆T/ T0 «1 and also ∆S/ Tab «1 and neglect latter term below. Assuming observation time scales, Differential methods are categorized into three conditions.
3.2.1 The Steady state condition
Observation time is instrumentation dependent and can be defined as interval for acquiring one voltage measurement (with the assumption that T1, T2 and Vab are simultaneously measured). This method was first used for simultaneous measurement of Seebeck coefficient, Hall effect and Nernst effect in tellurium by Wold in 1916. Platinum – rhodium thermocouples were used for measurement of temperature differences (2 to 10 °C). (Fig.3.2.1 (b)) Germanium rods Seebeck coefficient was measured by Bidwell 2.4cm long and between the temperatures -191 and 675 °C. The thermal gradient varied between the temperatures 5 to 60 °C due to the distance adjustments within the vertical chromel wire furnaces’ heating profile.
Under the condition of steady state, Seebeck coefficient calculation using differential methods is done by the linear fit of the electric potential/temperature difference multiple data points rather than one. This helps in avoiding the assumption of curve intersection with the ordinate (i.e. Vab =0, ∆T = 0). This eliminates the offset voltages, which arise from inhomogeneities of thermocouple and their nonequilibrium contact surface. Acutely incrementing temperature gradients are selected so as to satisfy the linearity assumption in Sab (T). To eliminate offset voltages, the multiple gradient method was used. InAs sample is clamped between the rods of graphite by using the Nickel/Chromium thermocouples, which then measure the gradients of temperature between 5 and 20 °C between the room temperature and 1000 °C. Now, the resulting slope of each of the lines can be used for calculating the Seebeck coefficient with an accurate estimation within 5 V/C.
Fig.3.2.1 (a) Seebeck coefficient apparatus described by Burkov. Copyright 2001 by the Institute of Physics [Ref.2] (b) Early Seebeck coefficient apparatus described by Bidwell. Copyright 1922 by American Physical Society [Ref.2] (c) Seebeck coefficient apparatus described by Zhou - Uher. Copyright 2005, American Institute of Physics [Ref.2]
3.2.2 The quasi – steady state condition
The time burden for proper stabilization of each ∆T increment might be inefficient and impractical incase of steady – state condition. Thus, the condition of quasi – steady state was used for enabling rapid measurements of Seebeck coefficient. In this method we measure multiple electric potential/temperature difference data points simultaneously along with employing a continuous increasing heat flux and not the multiple static and steady state ∆T’s. But for the proper implementation of the dynamic techniques multiple and high impedance nanovoltmeters are required. There might be enough thermal drift distorting the correspondence of temperature and voltage during the finite required time for switching and measuring the next voltage that can smear the Seebeck coefficient. This error in the measurement of the Seebeck coefficient is proportion to the voltage and temperature drift occurring between each channel acquisition’s time intervals which are compounded usually over the three measurements of voltage per data point.
To minimize distortions, temperature gradient’s time dependence can be fitted and interpolated to obtain the corresponding values of the electric potential. Modern embodiment of quasi steady state condition for differential method was proposed by Wood wherein Seebeck coefficients up to 1900 K can be measured by the apparatus by a sample’s compression between two of the fused – quartz light pipes. W – Nb thermocouples are used and inserted near each pipe’s end into the drilled holes (Fig 3.2.2 (a)). The light pipes are illuminated using tungsten filaments of 600 W at each end for generating a dynamic temperature impulse (=5K). These are then toggled inversely so as to maintain the average sample temperature constant.
Ponnambalam and Tritt had developed an apparatus for measuring the Seebeck coefficient and resistivity in axial flow arrangement between 300 and 1000 K. Silver blocks spring are used for compressing the samples and to maintain consistency loaded externally to the furnace (Fig.3.2.2 (b)). The gradient sweep (3 to 5 °C) is measured by the type K thermocouples with silver epoxied to blocks of silver, while the electrical potential being measured by the platinum wires. There is a steady rate increase in the furnace’s base temperature rather than stabilizing it at the each of the temperature of interest.
Fig.3.2.2 (a) Seebeck coefficient apparatus described by Wood , Copyright 1985, American Institute of Physics [Ref.1] (b) Seebeck coefficient apparatus described by Ponnambalam and Tritt, Copyright 2006, American Institute of Physics [Ref.1]
3.2.3. The transient (or ac) condition
The transient condition was introduced way back in 1970s for eliminating the steady state condition’s rigorous thermal stability demand. Characterization of transient condition can be done by a sinusoidal temperature difference ∆T Sin (ωt), with ∆T between 10 to 500mK and ω/2π between 0.1 to 60 Hz. Lock – in amplifiers does the continuous extraction of the corresponding temperature and voltage amplitudes for obtaining the Seebeck coefficient. Extraneous voltages are eliminated rapidly by the modulation of the temperature difference. Also, much smaller ∆T values are used as compared to the steady – state condition. The transient condition is the most commonly used one as this involves continuous measurements of both the voltage and temperature and gives less erroneous results as compared to the other two conditions.
Sensitivity of non – steady state conditions is more to heat capacity, thermal diffusibility, geometry and the mass of the measured materials. Thus requiring position adjustments of thermocouples, adjustment of the sinusoidal frequency and the thickness of the sample. Position adjustments can ensure attenuation of ∆T properly towards the cold end, while the thermal diffusibilty can help scaling the frequency. At lower frequencies, greatest magnitude of ∆T occurs leading to a more accurate Seebeck coefficient measurement based on the signal–to–noise – ratio.
To avoid Seebeck coefficient’s frequency dependence, thickness of the sample must be smaller than the length of thermal diffusion λ = (D/πƒ)1/2, where thermal diffusibility of the material is given by D and ƒ is the frequency satisfying the relation (d/λ)«1. Thus, promoting a one dimensional homogeneous temperature distribution. The thickness required of 0.1 to 0.2 mm might be considered impractical for many brittle thermoelectric materials.
Using the technique of a tungsten lamp chopped at 21 Hz, low temperature differences of about 0.03 K can be achieved. A laser modulated ac technique can also be used. The technique of square wave pulses, which are in opposite phase with respect to each other, can be used for a bipolar or toggled heating. Due to the differences in the heat capacity and thermal conductivity of the sample, each heater must produce identical ∆T than power. Thus, transient condition or the ac condition for differential method of Seebeck coefficient measurement is much more reliable and widely used as compared to the steady – state or quasi – steady state condition. As it allows for the simultaneous measurement of temperature and voltage to a large extent with an error of about 5 to 10 %. We discuss the solutions to such problems in the next chapter.
CHAPTER – 4
4. Problems and Solutions
While the Seebeck coefficient does not depend on geometry (of isotropic materials), the result might be affected by the spatial arrangement of the probes. The early thermal conductivity measurements led to the development of the two primary arrangements (Fig.4 (i)), due to the requirement of ∆T measurement under axial heat flux for quantities S and k. Thus, Seebeck coefficient is measured using the emergent electric potential. The temperature difference and electric potential measurement in the axial – flow technique (two – probe) are done on the probes. These probes are in direct contact with the specimen’s end. This arrangement provides better electrical and thermal contact. On the other hand, the potentiometric arrangement (four – probe) measures the voltage difference and the temperature difference at the two equidistant points from the cold and hot ends on a sample (or inserted in the sample) and on the axis that is parallel to the thermal gradient. For accuracy, each temperature/voltage probe’s diameter must be very small as compared to their in-between effective diameter. This will ensure that the measured temperature and the actual temperature are equal to a very large extent with little or no error.
Fig.4 (i) Diagram comparing potentiometric four-probe and axial-flow two-probe arrangements, where T1<T2 [Ref.1]. (ii) Three general geometries for measurement of the Seebeck coefficient, shown in cross-sectional view. (a) 2-point geometry where thermocouples are embedded in heater blocks [Ref.2] (b) off-axis 4-point method where thermocouples contact the side of the sample [Ref.2] (c) our proposed uniaxial 4-point method. The upper and lower green blocks represent heaters and/or heat sinks, the center yellow block the bulk sample, and blue narrow rods the thermocouples. [Ref.2]
For a good Seebeck coefficient measurement the primary requirements include: (a) Spatially synchronous Voltage and temperature measurements i.e. measurement of voltage and temperature at the same location and time; (b) good electrical and thermal contact of the probes with the specimen; (c) Minimal extraneous contributions during low voltages (microvoltages) acquisition. The two – point geometry thus avoids the chemical reactions occurring between the sample and the embedded thermocouple (Fig.4 (ii)(a)). But it does have the contact resistance leading to temperature measurement offsets. The 4 – point geometry eliminates the contact resistances between the heat source/sink and the sample (Fig.4 (ii)(b)).
But at high temperatures, thermocouples generally tend to draw away the heat from the sample. This effect is known as the ‘cold finger effect’, which leads to temperature difference across the beads of the thermocouple. Thus, leading to the measurement of voltage and temperature at different locations having different temperatures (Fig.4 (iii)(a)). At high temperatures, in soft samples, plastic deformation can occur leading to poor contact. ‘We now propose a uniaxial four – point method (Fig.4 (ii)(c)). This will eliminate the ‘thermocouple tip poisoning effect’. In this design, the ceramic tube of the thermocouple is heat sunk to heaters, thus reducing the cold – finger effect. Main advantages include: (a) direct contact between the thermocouple and the sample surface, (b) isothermal temperature surface contacted by the thermocouple junctions. The proposed arrangement allows a range of sample sizes and shapes to be measured, (c) uniaxial design is advantageous as it allows the thermocouples to exert, on the sample surface, larger forces that contribute to minimize the contact resistances.
New thermocouple material combinations development at a rapid rate can be achieved by using the cross geometry (Fig.4 (iii)(b)). There exists mechanical contact between the wires. Thus, the high thermal conductivity will ensure accurate temperature measurements. We also need to ensure that voltage and temperature measurements occur simultaneously, for which we can employ zig – zag data collection technique wherein first the voltage is measured, then T1, T2 and then T1 again and then voltage measurement. Thus, average of these two voltage readings and temperature T1 reading can be a good approximation to such measurements. Also, for the transient condition of the differential method for Seebeck coefficient measurement data needs to be collected at the same time. Various Sheathed thermocouples employed are shown in Fig.4 (iv) with an overview of the junction connection’s advantages and disadvantages under TABLE 1.
Fig.4 (iii) (a) Two probes made from thermocouple with the beads. This spatial arrangement can lead to erroneous results when thermal gradients are present across thermocouple with beads and across the sample’s area of contact. [Ref.2] (b) Crossed – wire geometry on a isothermal sample surface. Mechanical force used to ensure good thermal and electrical contact. [Ref.2] (iv) Options for Thermocouple Sheathing [Source: Bibl.3]
TABLE 1: Overview of Thermocouple Junction Configurations [Source: Bibl.2]
Junction Configuration Advantages Disadvantages
Exposed Fastest response (0.1 to 2 s) Ground loop and noise potential,
Most prone to physical damage,
No chemical protection
Exposed Bead Fast response (15s) Ground loop and noise potential,
Prone to physical damage,
No chemical protection
Sealed and Grounded Physical and chemical protection Ground loop and noise potential,
Slow response (~40 s)
Sealed and isolated Electrical protection (avoids ground loops and noise),
Physical and chemical protection Slowest response (~75 s)
CHAPTER – 5
5. Current Status in High Temperature Seebeck Measurement (Conclusion)
Precise Seebeck coefficient determination provides a reliable performance analysis basis in materials development in the thermoelectrics field. Measurement uncertainties of up to 14% can be often observed in temperature – dependent Seebeck coefficient interlaboratory comparisons or currently employed instruments’ error analyses. For traceable Seebeck coefficient measurement at high temperature, Iron Disilicide can be used as a reference material between 300K to about 1000K. The application temperature is limited to 800K due to the chemical reaction of Au and iron silicide, where Au is used as a sensor material in the device used for measurement.
Round – Robin test was carried out for obtaining a realistic survey on deviations in the measurements between t renowned laboratories in the bulk thermoelectric characterization field. Temperature dependent electrical conductivity and Seebeck coefficient determination was carried out with measurements under integral conditions. The results are shown in Fig.5 (a) and Fig.5 (b). Standard deviations of Seebeck coefficient and electrical conductivity for the Iron Disilicide samples were found to be close to 3 to 5 % and approximately 4% respectively. β – FeSi2 shows good spatial homogeneity over large sample size, mechanical stability, nontoxicity, low price and thermal stability for Seebeck coefficient, making this material as a good future reference material choice. Further processing and contacting development of iron silicide can qualify the stable thermoelectric generators as the high-temperature standard for calibration for the properties necessary for the high temperature thermoelectric metrology.
A suitable standard is still lacking for the thermoelectric figure of merit zT, although a major improvement is represented by development of Seebeck coefficient standard (β – FeSi2). For high temperature power conversion application, continued development of newer TE materials requires accurate and reliable characterization of the thermal and electrical properties with Seebeck coefficient being an essential property. While it might be uncertain experimentally to determine the most accurate arrangement or method or condition for high temperature determination of Seebeck coefficient, primary requirements always remain the same. The temperature and voltage measurements must be at the same time and location with probes having great electrical and thermal contact with specimens. A facile and flexible design maximizes the accuracy of measurement and provides rapid reproducible data collection.
Fig.5 (a) Comparison of international Robin – Round test results on temperature dependent Seebeck coefficient measurement of samples of Iron Disilicide. The standard deviation of Seebeck coefficient data was determined to lie between 3% and 5% within the application temperature range [Ref.5] (b) Comparison of international Robin – Round test results on temperature dependent electrical conductivity measurement of samples of Iron Disilicide. When omitting lowest results data in the laboratory or above 800K, the standard deviation was approximately 4% for electrical conductivity [Ref.5]
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