December 2012

NASA/TM–2012-217791 

System to Measure Thermal Conductivity and 

Seebeck Coefficient for Thermoelectrics 

Hyun Jung Kim, Jonathan R. Skuza, and Yeonjoon Park 

National Institute of Aerospace, Hampton, Virginia 

Glen C. King and Sang H. Choi 

Langley Research Center, Hampton, Virginia 

Anita Nagavalli 

North Carolina State University, Raleigh, North Carolina 
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December 2012

NASA/TM–2012-217791 

System to Measure Thermal Conductivity and 

Seebeck Coefficient for Thermoelectrics 

Hyun Jung Kim, Jonathan R. Skuza, and Yeonjoon Park 

National Institute of Aerospace, Hampton, Virginia 

Glen C. King and Sang H. Choi 

Langley Research Center, Hampton, Virginia 

Anita Nagavalli 

North Carolina State University, Raleigh, North Carolina 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320

443-757-5802 

	
	


This research was partially supported under the collaborative agreement (IA1–1098) 

between NASA Langley Research Center and the Federal Highway Administration, 

Department of Transportation. The authors appreciate the assistance of Dr. Robert G. 

Bryant, Dr. Catharine C. Fay, and Dr. Stephen J. Hales at the Advanced Materials and 

Processing Branch at NASA Langley Research Center. 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
v

Abstract

The Seebeck coefficient, when combined with thermal and electrical conductivity, is an essential 

property measurement for evaluating the potential performance of novel thermoelectric materials. 

However, there is some question as to which measurement technique(s) provides the most 

accurate determination of the Seebeck coefficient at elevated temperatures. This has led to the 

implementation of nonstandardized practices that have further complicated the confirmation of 

reported high ZT materials. The major objective of the procedure described is for the 

simultaneous measurement of the Seebeck coefficient and thermal diffusivity within a given 

temperature range. These thermoelectric measurements must be precise, accurate, and 

reproducible to ensure meaningful interlaboratory comparison of data. The custom-built thermal 

characterization system described in this NASA-TM is specifically designed to measure the inplane thermal diffusivity, and the Seebeck coefficient for materials in the ranging from 73 K

through 373 K.
vi

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	1

Overview

A thermoelectric (TE) material possesses the ability to convert thermal energy into 

electrical energy through a process known as the Seebeck effect, which is based on electron 

kinetics within differing metallic semiconductors. A thermoelectric module [Figure 1] is a device 

that is specifically used for the conversion of thermal energy to electrical energy. Within a 

thermoelectric module, two semiconductors are present, a p-type and an n-type, which are 

connected thermally in parallel and electrically in series.[1] The p-type and n-type 

semiconductors are doped to have an excess of positive holes or negative electrons, respectively. 

The electrical connection between these semiconductors allows for the transfer of electrons from 

one semiconductor to the other, which enables the flow of current. 

Figure 1 Common thermoelectric module consisting of different semiconductors that are 

connected thermally in parallel and electrically in series.

Figure 2 Electron kinetics within a metal before and after a

temperature gradient is applied.
2

When a temperature gradient is applied to a thermoelectric module (the module is hot on 

one side and cold on the other) the mobility of electrons is affected. The electrons in the 

semiconductors on the hot side of the module have more kinetic energy than the electrons on the 

cold side, due to the presence of thermal energy. Therefore, the cold side of the module obtains 

excess electrons as they diffuse from an area of higher energy (hot side) to one of lower energy

(cold side), leaving an excess of holes at the hot side [Figure 2]. Therefore, when a temperature 

gradient is applied to a thermoelectric module, a charge gradient is also created, resulting in the 

formation of an electric field.[2] This process is reversible, converting electrical energy to 

thermal energy, and is known as the Peltier effect.[3]

Currently, thermoelectric devices still have low conversion efficiencies with ZT = 1.0 –

1.25,[4,5] thereby offering abundant research opportunities that can have a profound impact 

where thermal energy is abundant. Being conscientious about total energy availability requires 

full utilization of resources that are present without damaging and wasting them, as is commonly 

the case. The wasted thermal energy from reactions and processes is no exception. With thermal 

energy being among the highest sources of wasted energy, waste heat can be extremely 

beneficial for the utilization of thermoelectric technology. In a 2008 study conducted by the 

Lawrence Livermore National Laboratory (LLNL), it was found that more energy is wasted than 

is used [Figure 3].[6] This lack of “energy capture” provides ample evidence as to why 

thermoelectric technology must continue to be researched and developed.

The National Aeronautics and Space Administration (NASA) has acknowledged the need 

for thermoelectrics and currently utilizes them as spacecraft and satellite power sources.[7] 

These spacecraft and satellites rely on or leverage available sources of energy for power such as

solar and thermoelectric. The temperature gradient created when a spacecraft or satellite has one 

side to the sun and one side to open space is significant. Employing thermoelectric technology in 

space will allow spacecraft and satellites to have an energy source as long as there is a 

temperature gradient present. However, these technologies are not only useful in space. The push 

for more sustainable and renewable energy sources has placed thermoelectrics as one of the most 

promising energy sources for terrestrial applications.[1]
3

Figure 3 The Lawrence Livermore National Laboratory’s finding during their 2008 study 

of energy usage. [6]

A major objective with thermoelectric technology is to maximize efficiency in order to 

take advantage of the abundance of waste heat. With this in mind, the effectiveness and 

performance of a thermoelectric is defined by Equation 1:

 

 

 

 

(1)

where is the Figure of Merit (FoM), is the electrical conductivity, is the Seebeck 

coefficient, and is the thermal conductivity.

The Figure of Merit (FoM) is a measure of the effectiveness of a thermoelectric, where a

higher FoM equates to a higher performance of the thermoelectric (see Table 2 for FoM’s of 

select materials). However, the individual variables that are used in evaluating the FoM must be 

assessed before the FoM can be calculated and analyzed. These variables are: the Seebeck 

coefficient, electrical conductivity, and thermal conductivity. Optimization of these variables 

will lead to a thermoelectric device with a high FoM that efficiently converts thermal to 

electrical energy (or vice versa).

Principle of determining the Seebeck coefficient

Heat moves through a solid material by means of conduction, the transfer of heat energy 

by microscopic diffusion and collisions of particles or quasi-particles within a body due to a 

temperature gradient. The rate of heat transfer per unit area through a material is the heat flux. 

Heat flux is directly proportional to the temperature gradient, and the constant of proportionality 

is the thermal conductivity of the material. There are different mechanisms which can transport 

heat in a material. The first is through vibrations of the internal structure of the material, such as 

vibrations of the crystal lattices or individual atoms. The other mechanism is through electron 

transport. In a material that is electrically conductive, electrons can carry heat from one end to 

another giving rise to the Seebeck effect. A force is needed to stop the drift and maintain 

equilibrium. This force takes the form of a voltage potential that develops to stop the drift of 

electrons, and the magnitude of this effect is quantified by the Seebeck coefficient. Seebeck 

coefficients have units of voltage per unit temperature, usually expressed in microvolts per 

Kelvin, and can be calculated using Equation 2:

 

 

 

(2)

where is the voltage difference between the hot and cold sides of a thermoelectric material 

and is the change in temperature between the sides. Thermocouples are often used to measure 

the temperatures and a voltmeter can be used to measure the voltages . The can have a 

positive or negative value, depending on whether the mobile charges are holes or electrons, thus 

giving the Seebeck coefficient a positive or negative value.[2]
4

Principle of electrical conductivity

Electrical conductivity of a thermoelectric can be measured using several methods, the 

most common being the Hall effect and the four-point probe method. The Hall effect is measured 

by applying magnetic fields perpendicular to the surface of the sample and electrical currents 

along the edges of the sample while measuring the voltage across the sample [Figure 4].[8] The 

electrical conductivity is calculated from Maxwell’s Equations for electrical conductivity, as 

shown with Equation 3:

 (3)

where is current density, is the intensity of the electric field, and is electrical conductivity.

The applied magnetic field and current create a force that pushes mobile charges to one 

side of the material, creating an electric field. This electric field gets stronger until it is equal and 

opposite of the applied magnetic field. 

The Hall effect can be used for other measurements as well, such as bulk concentration 

[/cm3], sheet concentration [/cm2], conductivity [/Ω·cm], and mobility [cm2/V·s] [Figure 4].

Figure 4 A Hall effect experiment (a) experimental set-up of the Hall effect measurement 

and (b) main test page of the system.

Figure 4(a) shows the experimental set-up of the Hall effect measurement using a

compact desktop model with permanent magnets and small circuit system. The Hall effect 

measurement system is a complete system for measuring the resistivity, carrier concentration and 

the electron mobility of semiconductors. The system includes software with I-V curve capability 

for checking the ohmic integrity of the user made sample contacts [Figure 4(b)]. The system can 

be used to characterize various materials including semiconductors and compound 

semiconductors (n-type and p-type), metals, etc., at both 300 K and 77 K (room temperature and 

liquid nitrogen temperature) with a funnel for liquid nitrogen.

Electrical conductivity can also be determined using the four-point probe method [9]. 

This method is conducted by placing four probes (leads) at equidistant intervals in a linear 
5

fashion. Current is supplied through the two outmost probes causing a measurable voltage drop 

between the two inner probes [Figure 5 (a)]. Using Ohm’s law (Equation 4) the resistance R can 

be calculated.

 

 

 

(4)

where is electrical resistance, is voltage and is current.

The four-point probe method [Figure 5 (a)] is much more accurate than the similar twopoint probe method because separate current and voltage probes are used.[10] In the two-point 

probe method, the interpretation of the data is more difficult due to the current being passed 

through the same voltage probes making the voltage drop significant. Whereas in the four-point 

probe method, the voltage probes have an extremely low (negligible) voltage drop due to the 

input impedance of the voltmeter, thus giving a more accurate reading.[11] 

The van der Pauw technique, due to its convenience, is widely used in the semiconductor 

industry to determine the resistivity of uniform samples. As originally devised by van der 

Pauw,[12] one uses an arbitrarily shaped, thin-plate sample containing four very small ohmic 

contacts placed on the periphery, preferably in the corners, of the plate. This is why the van der 

Pauw method is usually used, as it is in our case, for Hall effect measurements. A schematic of a 

rectangular van der Pauw configuration is shown in Figure 5 (b). The objective of the resistivity 

measurement is to determine the sheet resistance. Van der Pauw demonstrated that there are 

actually two characteristic resistances RA and RB, associated with the corresponding terminals 

shown in Figure 5 (b). RA and RB are related to the sheet resistance (Rs) through the Van der 

Pauw equation:

 

 

 

 

 

 

 (5)

which can be solved numerically for RS.
6

Figure 5 (a) Set-up of the four-point probe method. This method has a higher accuracy 

than the two-point probe method due to the separate voltage and current probes and (b) 

schematic of a Van der Pauw configuration used in the determination of the two 

characteristic resistances RA and RB.

Principle of thermal conductivity and thermal conductance

Thermal resistance and thermal conductance of the materials are reciprocals of one 

another and can be derived from thermal conductivity and the thickness of the materials. 

Thermal conductivity is the time rate of steady state heat flow through a unit area of a 

homogeneous material induced by a unit temperature gradient in a linear direction perpendicular 

to that unit area, W/m·K. Thermal conductance is the time rate of steady state heat flow through 

a unit area of a material or construction induced by a unit temperature difference between the 

body surfaces, in W/m2·K.

As with the Seebeck coefficient and electrical conductivity, the thermal conductivity of a 

thermoelectric can also be measured using different methods. The direct method of thermal 

conductivity follows Equation 6[13]:

 

 

 

 (6)

where is thermal power, is the cross-sectional area of the thermoelectric sample, is the 

length from one end of the sample to the other end, is the temperature difference from one 

end of the sample to the other, and is thermal conductivity.

The indirect method of calculating thermal conductivity follows Equation 7:

 (7)

where is density, is thermal diffusivity, and is specific heat at the temperature of interest 

.[14]

The Figure of Merit for thermoelectrics can be calculated by determining the Seebeck 

coefficient, electrical conductivity or electrical resistivity, and thermal conductivity. 

Manipulating the material properties associated with these variables can maximize the FoM to 

increase the performance level of the material. For instance, by increasing the electrical 

conductivity while decreasing thermal conductivity would increase the FoM. Typically, thermal 

conductivity increases as electrical conductivity increases. This poses an obstacle for maximizing 

the FoM.[15] Finding a way to minimize thermal conductivity while maximizing electrical 

conductivity, or minimizing electrical resistivity, would produce a thermoelectric of higher 

performance and greater efficiency.

Reported measurement techniques with chart
7

Parameter Publication Characterization System(s) Remark(s)

Seebeck 

coefficient 

(S)

[16]

The sample is placed between two 

copper blocks where ΔT and ΔE are

measured across the two blocks.

● 10 – 300 K ● Through the 

thickness

● Polycrystalline pellets

[17]

The potential difference and change in 

temperature are measured across a heat 

source and heat sink with the sample in 

the middle.

● 150 – 300 K

● Through the thickness

[18]

Thermocouples are used to measure the 

temperature and voltage difference.

● 300 – 1300 K ● Bulk ● In-plane

[19]

The potential difference and change in 

temperature are measured across a heat 

source and heat sink with the sample in 

the middle.

● 296 – 1200 K

● Bulk ● Through the thickness

Electrical 

Conductivity 

(σ)

[20]

Small electron or ion beam deposited 

strips can be connected to larger metallic 

pads for probe readings if they are too 

small. Probing a metallic deposition strip 

on an insulating background gives a 

direct measurement method.

● Temperature not specified

● In-plane

[21]

Two-point probe method with an 

electrometer is used for measurements.

● 300 – 550 K

● Through the thickness

[22]

Van der Pauw Method is used with a

nanovoltmeter to measure conductivity 

and temperature.

● 10 – 300 K ● Through the 

thickness

● Polycrystalline pellets

[23]

Mobility and conductivity are calculated 

from Hall effect measurements.

● 20 – 500 K

● In-plane

[24]

A modified Wheatstone bridge and AC 

current are used.

● 150 – 300 K

● Through the thickness

Thermal 

Conductivity 

(κ)

[25]

Thermal conductivity is measured by the 

transient technique using a line heat 

source.

● 6 – 20 oC

● Through the thickness

[26]

Thermal conductivity is calculated using 

known heat flows, equations, and

assumptions about the heat flow.

● 278 – 293 K

● Through the thickness
8

[27]

The Laser Flash method involves heating 

a homogenous material with a laser 

while measuring the temperature versus 

time.

● 77 and 300 K

● Through the thickness

[28]

A current is sent through a metallic strip 

at a certain frequency to heat the sample 

and the thermal conductivity is evaluated 

by measuring the frequency dependence 

of the temperature oscillations.

● 35 – 500 oC

● Through the thickness

[29]

An alternating heat pulse is applied at 

one end of a metal rod while leaving the 

other end at room temperature. The 

thermal conductivity can be measured 

using the temperature at two points on 

the metal rod that are measured as a 

function of time.

● Temperature not specified

● In-plane

The following are the previously reported best methods for measuring the Seebeck 

coefficient and thermal conductivity, which are measured by our TE characterization system.

Electrical conductivity is not discussed from here because our TE system does not measure this 

parameter. Therefore, in order to calculate the ZT factor, it must be measured using the Hall 

effect system (see Figure 4).

Reported Seebeck coefficient system

The Seebeck coefficient of a thermoelectric material can be measured by placing the 

material in between two conducting metal blocks, such as copper. One end of the sample is 

heated while the other acts as a heat sink, dispersing the heat, thus cooling that side. 

Thermocouples are then placed on the thermoelectric material, between the metal blocks. This 

set up for the measurement of the Seebeck coefficient is one of the simplest and most widely 

used. When one side of the module is heated up the thermocouples register the temperature 

difference in the material. This change in temperature produces a detectable voltage drop, which 

is measured with the thermocouples as well. The measurements are made for different ambient 

temperatures that relate to the operating range of the thermoelectric.

Reported thermal conductivity system

Currently, there are two primary methods for determining the thermal conductivity of a

material. One is the Flash method, which uses a high energy pulse to deliver a short burst of 

energy to the sample while measuring the temperature on the opposite side. The other method is 

called the Three Omega method and is an adaptation of Angstrom’s method. Both the Three 

Omega and Angstrom’s methods use a periodic heat source to generate a heat wave in the 

sample. The methods then measure the amplitude decay and the phase shift of the heat wave as it 

travels through the sample. The Flash method is a very fast test that measures the thermal 

conductivity through the thickness of a sample. This works for a bulk material, but a thin ceramic 

or metallic film depends strongly on the orientation so it should be tested along its crystal axes. 

The noticeable disadvantage of the Flash method is that it does not allow for testing of the 
11

Seebeck coefficient because the test occurs so quickly that the temperature differences are too 

small to gather meaningful data for the Seebeck coefficient. Angstrom’s method held some 

promise, but commercially available systems altered the sample, possibly changing its thermal 

characteristics.

Motivation of TE characterization system setup

The Seebeck coefficient, when combined with thermal and electrical conductivity, is an 

essential property measurement for evaluating the potential performance of novel thermoelectric 

materials. However, there is some question as to which measurement technique(s) provides the 

most accurate determination of the Seebeck coefficient at elevated temperatures. This has led to 

the implementation of nonstandardized methods that have further complicated the confirmation 

of reported high materials. A major consideration for the procedure described is for the 

simultaneous measurement of the Seebeck coefficient and thermal diffusivity within a 

temperature range. These thermoelectric measurements must be reliable, accurate, and consistent

to ensure meaningful interlaboratory comparison of data.

Practical design criteria and performing calculation

Chamber, temperature control, and sample holder

Thermal conductivity is a function of temperature, so data must be gathered across a 

range of temperatures. The standard range is from about 73 K (-200 oC) to 373 K (100 oC). Two 

systems are needed to gather data for this entire range: one to go from cryogenic to room 

temperature and another to go from room temperature up to 373 K. The two systems should be 

similar in design so that the method is consistent throughout the range. The cryogenic chamber is 

a highly confined space, so all components of the system are required to be small and perform in 

a vacuum. The system must operate in a vacuum because at cryogenic temperatures any air or 

moisture in the chamber will condense on the sample. The contact probes must be made of a 

material that minimizes heat conduction, i.e. has a low thermal conductivity. Accurate 

measurements must be taken quickly, and be corrected for any offsets that may occur such as the 

Seebeck effect of the probes in the voltage measurements. The selected system closely resembles 

other systems that use Angstrom’s method. The sample is mounted vertically with a heater 

attached to an arm and resting on the cold plate. The probes are mounted in a spring assembly 

and can be moved in and out to achieve the desired pressure. Temperature is measured using Ttype thermocouples and voltage is measured using a lead from each thermocouple. The heater is 

a three watt 1000 Ω resistor attached to the specimen clamp. Data are gathered using three multichannel Keithley nanovoltmeters and the raw data is processed via a computer program [see 

Figure 6].
12

Figure 6 (a) Thermal characterization system and (b) an exploded view of (a).

Seebeck coefficient

The program records the temperature and voltage differences versus time, then uses these 

values to compute the thermal diffusivity and the Seebeck coefficient. The Seebeck coefficient is 

calculated in one of two ways depending on the method that the data were gathered. If the entire 

loop was gathered (both the heating and cooling sides of the curve) then linear fits for the heating

and cooling sides of the curve are computed and averaged to find the best possible fit. If only one 

side of the curve is gathered, then a linear fit for the voltage versus temperature data is calculated

where the slope of the fit is the Seebeck coefficient. Theoretically, the voltage difference should 

vary linearly with the temperature difference on both the heating and cooling phases, but this is 

not always so because the sample is changing temperature as the test progresses. Hence the 

Seebeck coefficient changes resulting in a hysteresis loop instead of a linear plot.

Thermal diffusivity

The thermal diffusivity is calculated using the temperature differences versus time 

measured by the thermocouples, specifically the maximum temperature reached by both the cold 

and hot sides and Equations 8 and 9:

 

 

 

 

 

(8)

 (9)
13

where is the thermal diffusivity, is the length between the thermocouples, is the specimen 

geometric dimension coefficient that depends upon the nature of the setup and sample shape, 

is the time difference between the maximum hot side temperature and the maximum cold side 

temperature, is the amplitude of the temperature wave on the hot side and is the amplitude 

of the temperature wave on the cold side [Figure 7]. Equation 8 comes from Angstrom’s method

and requires the user to input both (by measuring the actual distance between the probes) and 

(by testing a known sample). Calibration of the system requires selection of a value for that is 

the actual distance between the hot and cold probes, then testing a known sample and adjusting 

so that the measurement is correct. The values for and should be checked against another 

known sample with a different thermal conductivity. is the maximum change in the hot 

temperature, and is the maximum change in cold temperature. The time between the two 

maximums is . The formula for the thermal conductivity works well as long as there is a welldefined peak in the temperature graphs. 

Figure 7 Physical definitions of the variables within the equation of thermal diffusivity; 

(a) typical data plot for thermal conductivity measurement and (b) setup for thermal 

diffusivity measurement.

The thermoelectric characterization system setup with fixture design

The thermal characterization system in this NASA-TM is designed to measure the inplane thermal diffusivity and the Seebeck coefficient for materials in the range of temperatures 

from 73 K through 373 K. As shown, the system consists of a resistance heater mounted on an 

adjustable sample clamp arm which is attached to the base plate (cold block). This resistance 

heater gives a thermal pulse to the specimen that exceeds the ambient temperature. The geometry 

of the sample should be square-shaped, approximately 1 cm × 1 cm, with all opposite faces 

parallel, to mount vertically with a heater attached to an arm and resting on the cold plate. If the 

sample is a thin film on a substrate, the substrate should have a thermal conductivity a few orders 

of magnitude lower than the sample to prevent the substrate effect. A probe assembly, mounted 

to the base plate, simultaneously measures the hot and cold temperatures and the Seebeck 

voltage from a heat pulse traveling from the resistance heater to the colder base plate.
14

The system developed here uses three Keithley 2182A nanovoltmeters for simultaneous 

measurements of the thermal diffusivity and Seebeck coefficient. A Keithley 6221 DC and AC 

current source is used to apply power to a high power resistor. The nanovoltmeters and the 

current source are connected to a computer with GPIB interface. A schematic diagram of the 

system is shown in Figure 12. When a thermal pulse is created within a sample by a DC/AC 

current source, the thermal pulse is transported by both energetic electrons and phonons through 

the sample to the colder base plate. Two thermocouples that are placed on a sample with a 

certain gap distance measure temperatures instantaneously to identify the thermal pulse that 

passes through the specimen. The temperature difference between the probes and the time 

interval on which it occurs will indicate the thermal diffusivity of the sample material. The 

thermal conductivity can then be calculated from the thermal diffusivity data if the density and 

specific heat are known. As shown in Figure 8, two voltage probes are almost collocated with 

two thermocouples in proximity to measure the Seebeck coefficient which is an intrinsic 

property of a material. The voltage difference between two locations (or two temperatures at two 

locations) indicates the electrostatic potential associated with temperature and is called the 

Seebeck coefficient.

Figure 8 Thermal characterization system schematic diagram.

These two important parameters, the thermal conductivity and Seebeck coefficient, are 

the key factors to determining the FoM of thermoelectric materials. The system itself is 

configured for the measurements of these two parameters from cryogenic to high temperatures. 

There are no such systems available to cover an entire temperature range. The unique nature of 

this system is to measure the thermal conductivity and Seebeck coefficient simultaneously. 

The probe assembly [Figure 9] houses the hot and cold side voltage probes ( and ) 

for measuring Seebeck voltages and the thermocouples ( and ) for measuring temperature 

difference and thermal diffusivity (see Figure 7). All probes are fabricated with stainless steel 
15

tubing and collars with pressure applied to the sample with tungsten wire springs. The 

dimensions and material type may be altered without affecting the assembly function. The probe 

spacing can also be varied in the vertical direction for compatibility with the sample material and 

heat source, although the horizontal spacing should be as small as possible. The voltage probes 

are fiberglass-wrapped copper wire bonded in place with a ceramic compound, such as Cotronics 

Resbond 919. This compound has a low thermal conductivity. The thermocouple probes are 

similarly made using T-type thermocouples, although other types may be used depending on the 

temperature range of interest.

Figure 9 Probe assembly; (a) schematic diagram for probe housing and (b) copper 

probe housing.

The sample clamp arm assembly consists of a copper support post, two piece stainless 

steel support arm, and a resistor heater. The support post [Figure 10] is made of copper for 

dissipating the heat generated from the resistor heater after the heat pulse is applied to the 

sample, (see Figure 7). A bolt threaded in the side secures the support arm and allows different 

lengths of samples to be tested. For samples with a greater distance between the hot and cold 

temperature measurements, it will be necessary to extend the support arm height for the longer 

sample.

Figure 10 Sample clamp arm; (a) schematic diagram, (b) top view, (c) bottom view, and (d) 

support post with back plate.
16

The support arm [Figure 11] is made of stainless steel for directing the energy of the 

initial heat pulse through the sample and for dissipating the residual heat through the support 

post. The two pieces clamp the sample heater assembly (see Figure 6).

Figure 11 Sample clamp arm with support arm; (a) schematic diagram and (b) 

assembled, side view.

The heater assembly, shown in Figure 12, consists of a resistor heater attached to a 

sapphire sheet with thermally conducting, electrically insulating ceramic compound (see Figure 

6). The sapphire conducts the residual heat through the support arm after the heat pulse is applied 

to the test sample. The source of the applied heat pulse can be a resistor, coil heater, laser diode, 

or similar device. It should apply heat evenly along the entire width of the sample. Lead wires 

for supplying current should be able to withstand the ambient temperature of the sample during 

testing in addition to the heat generated from the heater. Sample measurements are taken at 

several increments within the ambient temperature range of approximately 73 K through 373 K. 

For slow ambient temperature ramp times, the measurements may be taken in a continuous mode 

while the ambient temperature is changing as long as the ambient temperature change is 

accounted for in the calculations. Alternatively, the ambient temperature for each measurement 

increment can be allowed to stabilize before taking the measurement. The second method will 

also allow more than one measurement to be taken and averaged at each ambient temperature 

increment.

Figure 12 Heater assembly; (a) side view and (b) back view with resistance heater in 

ceramic.
17

The entire thermal characterization test fixture can be used in both a cryogenic chamber 

and a vacuum furnace. The probe assembly is removable to allow a different thermocouple type 

to be used for the temperature range of interest and to allow a different vertical probe spacing to 

permit samples in a wide range of thermal diffusivities to be tested.

The base plate, Figure 13, (see also Figure 6) functions as a heat sink (cold block) in the 

measurement system. A shallow groove in the plate holds the sample against the probes. The 

groove must be coated with electrical insulating compound. Electrical isolation of the entire 

sample is required to isolate the probe measurements.

Figure 13 Base plate; (a) top view without support post and (b) back view with support 

post.

The characterization system was custom-built to accommodate specific design details. A 

picture of the TE characterization system is shown in Figure 14 that is comprised of a vacuum 

system, temperature controlled oven, and a semi-automatic data acquisition system. Thermal 

measurement control and output is accomplished through computer software. A LabVIEW®

software program can be used to apply the heater current for a user-designated pulse time and to 

record the thermal diffusivity and the Seebeck coefficient. 

Figure 14 The low temperature TE characterization system.
18

Program logic to measure thermal conductivity and Seebeck coefficient

Custom-designed software was written to allow for semi-automatic data acquisition and 

analysis [Figure 15].

Figure 15 LabVIEW®graphical user interface

Description of Front Panel controls and their use in the program

A) LabVIEW® Run – “Click” to depress this button and begin the LabVIEW®program. A 

message will be displayed and the program will not run if an error is encountered.

B) Clear Data & Continue – This button clears the data in memory, initializes parameters, and 

then continues to take measurements.

C) Save Data & Continue – This button allows the data in memory to be saved before clearing it

(data are never automatically saved). Measurements continue after the data are saved and 

cleared.

D) Save Data & Stop – This button allows the data in memory to be saved before stopping the 

program.
19

E) GPIB Addresses – Variable inputs for GPIB addresses of the hot side thermocouple (Hot 

TC1), cold side thermocouple (Cold TC2), voltage difference between the thermocouples 

(Voltage V3), cold junction resistance temperature detector (Res. V4), chamber thermocouple 

(Chamber TC), and the heater (Heater).

F) Setpoint – Selection of the temperature setpoint for the chamber.

G) PID Tuning Parameters – Sets the tuning parameters (proportional, integral, derivative) for 

the heater’s temperature controller.

H) Heater Range – This controls the maximum heater output.

I) Update – This button executes the values entered for the Setpoint, PID tuning parameters, and 

the Heater range.

J) Density – The user may enter the sample density for calculation of the thermal conductivity.

K) Specific Heat – The user may enter the specific heat for calculation of the thermal 

conductivity.

L) Calculate – This button will calculate the thermal diffusivity (and possibly thermal 

conductivity) from the acquired data.

Indicators and what user is measuring

M) Data Points – Displays the total number of data points saved in memory.

N) Timers – The absolute computer clock time, which is used to assign the relative time at 

which data are taken. Measurements begin at time equal to zero.

O) Real-time Measurement Parameters – These display the real-time values of the hot (V1) and 

cold (V2) thermocouple voltages, the hot (TC1) and cold (TC2) thermocouple temperatures, the 

hot and cold thermocouple temperature difference (TC1 – TC2), the voltage difference between 

the hot and cold thermocouples (V3), the cold junction resistance (R4), the cold junction 

temperature (T4), the chamber thermocouple voltage (V5), and the chamber thermocouple 

temperature (TC5). 

P) Voltage Difference Plot – The measured voltage difference between the hot (TC1) and cold 

(TC2) thermocouples is plotted versus relative time.

Q) Temperature Difference Plot – The measured temperature difference between the hot (TC1) 

and cold (TC2) thermocouples is plotted versus relative time.

R) Seebeck Coefficient Plot – The instantaneous (green curve) and average (last five 

measurements, red curve) Seebeck coefficients are plotted versus relative time.

S) Differential Fitting of Seebeck Coefficient Plot – The difference in voltage versus the 

difference in temperature of the hot and cold thermocouples is plotted (green data). A linear fit to 

these data is displayed and the Seebeck coefficient using differential fitting is calculated (red 

curve) and displayed numerically.
20

T) Absolute Temperature Plot – The absolute temperature of the hot (TC1) and cold (TC2) 

thermocouples versus relative time is plotted.

U) Delta Temperature Plot – The change in temperature from the initial temperature of both the 

hot (red curve) and cold (blue curve) thermocouples versus relative time is plotted.

V) Chamber Temperature Plot – The temperature of the chamber thermocouple versus relative 

time is plotted and displayed numerically.

W) Thermal Diffusivity Parameters – Numerical displays for the initial temperatures of the hot 

(TC1) and cold (TC2) thermocouples, their maximum temperatures and the time at which they 

occurred, and the temperature difference between the maximum and initial values.

X) Length – The distance between the hot (TC1) and cold (TC2) thermocouples.

Y) Time Gap – The time elapsed from the maximum temperature of the hot (TC1) thermocouple 

to the maximum temperature of the cold (TC2) thermocouple.

Z) Thermal Diffusivity – This value is the calculated thermal diffusivity.

AA) Thermal Conductivity – The thermal conductivity is calculated if the sample density and 

specific heat are known.

Calibrating the system

In our design, the distance between the probes is always the same, so the length can be 

measured to within a few tenths of a millimeter with a micrometer and then any small 

adjustments that need to be made can be accomplished by adjusting the constant to fit the 

known samples (see Equation 8). The known samples should be from the expected range of use. 

Since the primary use of the system is testing thermoelectric materials, and these materials tend 

to have low thermal diffusivities, an insulator like glass makes a good calibration sample. At the 

other end of the spectrum, graphite is a good choice because it is available as a calibration 

sample, and it has high thermal conductivity so it is at the very edge of the system’s range.

DATA comparison (with our system and NETZSCH LFA 457 MicroFlash®

Table 1 Calculated and tested thermal diffusivity with graphite, quartz glass, silicon wafer, 

and 2948 glass slide with NASA Langley Method at room temperature.
21

(a) Reference [30]

(b) κ = αρc (equation 9), where is the thermal conductivity, is the thermal diffusivity, is the 

density, and is the specific heat of the sample.

(c) Data from NASA Langley’s Instrumentation 

Table 2 Tested data comparison of quartz and micro-scale Bi2Te3 grains covered with 0.5

wt% and 0.05 wt% Au samples with ASTM E1461 Flash Method [31] and NASA 

Langley’s Instrumentation
22

Appendix (Manual): Work instructions for Thermal Characterization

[1] Preparing the sample

- The geometry of both bulk and thin film samples should be square-shaped, approximately 10

mm × 10 mm. Although, samples between 5 mm and 20 mm and up to 3 mm in thickness are 

acceptable.

[2] Mounting the Sample

- The bottom of the sample rests in a groove in the cold plate.

- The top of the sample is held in place by the heater arm.

- Secure the heater arm using the screw in the upright section of the arm assembly. Pliers should 

be used as the head of the screw cannot be reached.

- After securing the sample bring the probe assembly into contact with the sample and apply 

pressure so that all the probes contact the surface. The probes are on springs so make sure that 

each probe is in contact with the sample.

- Secure the probe assembly using the two hex screws at its base.

[3] Evacuating the chamber

- Place the chamber cover on the chamber and secure it with four hex screws with washers.

- Ensure that the vent valve is closed.

- Open the valve at the end to connect the chamber to the vacuum pump.

- Turn on the vacuum pump.

- Let the chamber reach a vacuum of at least 5 mTorr.

[4] Running the Test

- Open the program “Combined Seebeck Diffusivity” in the Shared Documents folder.

- At the opening screen, set the following values:

o GPIB Addresses (default values should be correct)

o Setpoint Temperature of Chamber (room temperature)

o PID Tuning Parameters

o Heater Range (off).

- Press Run – Starts the program.

- Once measurements are stabilized, press Clear & Continue to dump the previous data and begin 

measurements. 

- To end a test, press Calculate, and then press Save & Continue to save the data in an array.
23

- To exit the program, make sure that the heater is off, and press the Save & Stop or the Stop 

button.

[5] Internal Program Operation

- Program initiation:

Various instruments are initialized when the program first starts. These include the 

nanovoltmeters for thermocouples (chamber, hot, cold) and the potential difference between the 

hot and cold thermocouples, the cold reference junction resistance temperature detector, and the 

heater. The beginning time is also initialized.

- Loop:

After initiation, the program enters a while loop, which is the main loop for the program. 

It will repeat until the stop button is clicked. Inside the loop, data are acquired from the various 

instruments, displayed numerically, plotted in graphs, and used to calculate certain parameters.

These data, graphs, and numerical displays are described under the section on front panel 

controls. User supplied inputs while the loop is running can be altered; these include clearing or 

saving data, changing the chamber temperature, changing the heating parameters, and calculating 

thermal parameters. These raw and computed data are saved in a two-dimensional array that 

grows as the loop iterates and can be saved by the user to a specified filename.

The block diagram of the LabVIEW®program is shown below in full, along with 

magnified sections of the code. 


lock diagram below is enlarged and sectioned on the next four pages. 
 25

Initialization of the instruments for data 

acquisition and the computer’s clock 

occur outside the loop structure. 
 26

Sending and receiving data from instruments. 

Conversion of voltages to temperatures. 

Saved data array. 

Calculating Seebeck coefficients 

and plotting data. 
27

Sending and receiving data from instruments. 

Conversion of voltages to temperatures. 

Calculation of maximum 

temperatures and times for thermal 

diffusivity measurements. 

Calculation of thermal diffusivity 

and conductivity (if applicable). 
 28

Heater control. 

Plotting temperature data for 

diffusivity measurements. 


	


	

	












	






	

	









	

	
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212?1=02<;2*22REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

System to Measure Thermal Conductivity and Seebeck Coefficient for 

Thermoelectrics 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Kim, Hyun-Jung; Skuza, Jonathan R.; Yeonjoon, Park; King, Glen C.; 

Choi, Sang, H.; Nagavalli, Anita

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-20213

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 31

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

The Seebeck coefficient, when combined with thermal and electrical conductivity, is an essential property measurement for 

evaluating the potential performance of novel thermoelectric materials. However, there is some question as to which 

measurement technique(s) provides the most accurate determination of the Seebeck coefficient at elevated temperatures. This 

has led to the implementation of nonstandardized practices that have further complicated the confirmation of reported high ZT 

materials. The major objective of the procedure described is for the simultaneous measurement of the Seebeck coefficient and 

thermal diffusivity within a given temperature range. These thermoelectric measurements must be precise, accurate, and 

reproducible to ensure meaningful interlaboratory comparison of data. The custom-built thermal characterization system 

described in this report is specifically designed to measure the in-plane thermal diffusivity, and the Seebeck coefficient for 

materials in the ranging from 73 K through 373 K. 

15. SUBJECT TERMS

Seebeck coefficient; Thermal conductivity; Thermoelectric characterization system; Thermoelectric materials

18. NUMBER

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 PAGES

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(443) 757-5802

a. REPORT

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c. THIS PAGE

U

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Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

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5f. WORK UNIT NUMBER

392259.02.07.9923.11

11. SPONSOR/MONITOR'S REPORT

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NASA/TM-2012-217791

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1. REPORT DATE (DD-MM-YYYY)

01- 12 - 2012