Thermoelectric Performance Study of Cost-Effective Lead Chalcogenides
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2020
Thermoelectric Performance Study of Cost-Effective Lead Chalcogenides
Andrew Manettas
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Thermoelectric Performance Study of Cost-Effective
Lead Chalcogenides
This thesis is presented to fulfil the requirements for the award of the Degree of
Doctor of Philosophy
Institute for Superconducting and Electronic Materials
Faculty of Engineering and Information Sciences University of Wollongong 2020
Andrew Manettas
Supervisor – Alexey V Pan
DECLARATION
This thesis does not contain any material that has been submitted for the award of any degree from this or any other university and, to the best of my knowledge, contains solely original work, not published or written by any other person, except where referenced or acknowledged.
Andrew Manettas
May 2020
ACKNOWLEDGEMENTS
I would like to begin my acknowledgements with the start of my research studies.
My first experience in research was my honours year at UOW, of which Alexey Pan was the honours coordinator. I did not know what I wanted to do after I graduated, but I really enjoyed my honours year and I knew I would have liked to continue doing scientific research. I spoke to Alexey after I finished my honours thesis and he was the one that put me in touch with Sima Aminorroaya-Yamini. So firstly, I need to thank Alexey for helping me begin, and continue my work as a researcher.
Sima was an excellent supervisor; I was starting in a completely new field and I had many questions to ask her. She always left her office door open and encouraged her group members to come and ask questions. I often went in for a quick question and she was always happy to help. Every time I stepped into her office I learned something new, it was always an invaluable experience and I thank her for being so generous with her time.
Working under Sima was the core group of post-grad students, myself, Rafael
Santos, Vaughan Patterson, Jacob Byrnes and Xavi Reales. We had a group chat where we would ask each other questions, and it was mostly a wonderful tool to help each other get through our studies, as well as have some fun discussions.
Then there were the other students who would come for lunch, we would often joke that lunch was the best part of the day! Jonathan Kent, Florian Gebert, Antony Jones, and all the others who I have not mentioned, you guys helped make each day a little bit more exciting. It was a great time to chat with other people about life, our favourite TV shows, and most importantly talk about our scientific work. There were many occasions where, after lunch, we would head back into the lab together to help one another with a problem.
We also had many summer students under Sima’s group come and go throughout my time there and it was always exciting to teach them about our work, show them something new, as well as share and enjoy life experiences and for the international students, hopefully help them enjoy their time in Australia.
I slowly learned that doing a PhD was impossible to do on my own, and that I needed the help of others to ensure I had the correct equipment, and maintain said equipment. The staff of the AIIM workshop, in particular Rob Morgan and Paul
Hammersley, were instrumental in my experimental work. I always felt welcome in the workshop, and you guys were always happy to help me in any way you could.
After Sima left, I had Yusuke Yamauchi as my PhD supervisor. He assisted in writing my papers and set me up with an internship in Japan. This was an invaluable experience for me, I had never been overseas before this, and was never the kind of person to want to go traveling, let alone live in a new country! I was able to work in the labs in Japan and learn a lot of new scientific skills, as well as learn a lot about myself. I could write many pages on my time in Japan, but I will leave that for another time. Thank you for the wonderful experience Yusuke, I would never have had the chance to do that without you and I thank you for it.
On my return from Japan, I had changed supervisors yet again, coming full circle to the start of my research career and now having Alexey Pan as my PhD supervisor.
Alexey was enthusiastic about taking over my project and was able to get me a scholarship extension. This was a huge deal for me, I needed to be able to support myself and Alexey understood that. He let me focus solely on my PhD, finish my work and I was fortunate enough that he was able to assist me. Having Alexey as a supervisor has been a fantastic experience, thank you for helping me finish off my thesis and I hope our paths cross again soon.
Going in to ISEM every day and learning something new was a wonderful experience, and in particular I have to thank one person again. Rafael Santos sat behind me, and was always happy to be annoyed by my silly questions and show me how to be a better scientist. All I had to do was spin my chair around and ask for help, and he would be happy to take the time to assist. I was just beginning my scientific career; I didn’t have much to offer in return so I would always try and repay the favour by helping him wherever possible. If he needed an extra set of hands fixing some equipment, I would try and help, and then you would spend half an hour telling me how to correctly turn something off, showing me how everything worked and explaining the fundamental physics behind it and I loved it. I now have such a deep understanding of the instruments
I used, how they work and what they do, and I have you to thank for it. I continue to have this thirst for knowledge, I want to have a greater understanding of the work I am doing and why, and this follows through to everyday life. I am now more inquisitive, more confident, and overall a better person because of what you taught me. Thank you for teaching me everything from how to use Microsoft Powerpoint to the calibration of a thermoelectric measurement device.
As always, I need to thank my family and friends for being so supportive of my student lifestyle. I am the first in my immediate family to do a post-graduate degree, and without the help of Mum and Dad encouraging me to do continue my studies I could not have done it. I am very lucky that I was able to spend so long at uni, and even luckier that it all worked out so well. I’ll get you back one day, I promise. In my time at UOW I have made lifelong friends that are all still confused by what a PhD is and what I do at work, but you guys help distract me from the academic life, give me the break that I need to get me refreshed for my PhD again on Monday. Thank you for all the social gatherings and movie nights that were an excellent source of stress relief.
My thesis is a combination of all the people that have helped me along the way, thank you again to all those mentioned, and even to those I haven’t (sorry if I didn’t mention you), your help no matter how small has made an impact on my life and I am thankful for it.
ABSTRACT
Global warming and resource management is steadily becoming a more pressing world issue. The use of renewable energy is a solution to many of the world’s problems and if a useful renewable energy source is found, its application would potentially be immediate and widespread across the world. One of the biggest energy sources that could be harnessed is waste heat, which makes up around 70 per cent of the total energy produced by major industry in developed countries like the USA.
Thermoelectric devices directly convert heat into electricity, making thermoelectric materials a promising research area for waste heat recovery. There are many advantages to solid state thermoelectric devices, such as requiring almost no maintenance, being reliable and they can be used in a small scale such as on space missions or on larger applications like industrial blast furnaces. Anywhere that there is waste heat, thermoelectric devices can be used to harness the energy and improve efficiency.
This doctoral work focuses on the study and development of various types of lead chalcogenides, which have been shown to have high thermoelectric performance and have already been utilised in real-world applications. Improving the performance of these materials can lead to thermoelectric devices being used all around the world as a renewable energy source, benefiting all of humanity.
The first set of lead chalcogenides studied is the p-type single-phase quaternary
PbTe-PbSe-PbS system. Here, a large amount of PbS is added to the (PbTe)0.65-x(PbSe)-
0.35(PbS)x composition, in increments of 5% up to 20%, to attempt to increase the power factor and lead to a larger zT, however with compositions containing 15% and 20% PbS the overall zT decreased, with the 0%, 5% and 10% PbS compositions having the highest zT of ~1.4.
The next set of lead chalcogenides studied is the p-type multiphase quaternary
PbTe-PbSe-PbS system. Here, the multiphase composition was investigated as the summation of 2 different single-phase compositions. These single-phase compositions were synthesised and characterised, with their results being combined using the parallel and series models to compare to the multiphase material. The multiphase composition has a maximum zT of ~2 however neither of the models were able to accurately predict this result, with the upper limit of ~1.4 from the parallel model being significantly lower than the expected value of ~2. This large difference can be attributed to the unique band structure of lead chalcogenides that is not considered with these models.
The last set of lead chalcogenides studied is the undoped PbTe-PbSe system, here compositions across the (PbTe)1-x(PbSe)x range were synthesised and characterised, including pure PbTe and PbSe. The x = 0.50 sample had a minimum thermal conductivity of ~0.7 W/m.k, the lowest out of all the other compositions, which makes this a promising composition for future work. By adding a suitable dopant, the high resistivity of
~130 mΩcm would be reduced, which could lead to an increase in the overall zT and improve thermoelectric performance for lead chalcogenides.
TABLE OF CONTENTS
Declaration ...... 2
Acknowledgements ...... 3
Abstract ...... 7
Table of Contents ...... 9
List of Figures ...... 12
List of Tables ...... 15
List of Abbreviations ...... 16
List of Symbols ...... 16
List of Publications ...... 18
CHAPTER 1 – Introduction...... 19
1.1 Motivation and Introduction ...... 20
1.2 Thesis Structure...... 22
CHAPTER 2 – Literature Review ...... 25
2.1 Principles of Thermoelectricity ...... 26
2.1.1 Seebeck effect ...... 26
2.1.2 Peltier effect ...... 27
2.1.3 Electrical resistivity ...... 27
2.1.4 Thermal conductivity ...... 30
2.1.5 Thermoelectric figure-of-merit, zT ...... 31
2.2 Thermoelectric Materials ...... 32 2.2.1 Classification of thermoelectric materials ...... 32
2.2.2 Lead chalcogenides...... 34
2.3 Applications and devices ...... 41
CHAPTER 3 – Experimental Methods and Characterisation Techniques ...... 43
3.1 Overview ...... 44
3.2 Preparation and Synthesis Methods ...... 44
3.2.1 Alloying and doping of lead chalcogenides ...... 44
3.2.2 Spark Plasma Sintering (SPS) ...... 45
3.3 Characterisation Techniques ...... 46
3.3.1 Structural and phase characterisation with X-ray diffraction (XRD) .... 46
3.3.2 Thermoelectric properties characterisation ...... 47
CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe-PbSe-PbS
...... 53
4.1 Motivation ...... 54
4.2 Abstract ...... 54
4.3 Introduction ...... 55
4.4 Method and Experimental Details ...... 57
4.5 Results and discussion ...... 59
4.6 Conclusions ...... 70
CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead
Chalcogenides: Model Compared to Experiment ...... 73 5.1 Motivation ...... 74
5.2 Abstract ...... 74
5.3 Introduction ...... 75
5.4 Methods and Experimental Details ...... 78
5.5 Results and Discussion...... 79
5.6 Conclusions ...... 88
CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series ...... 91
6.1 Motivation ...... 92
6.2 Abstract ...... 92
6.3 Introduction ...... 93
6.4 Method and Experimental Details ...... 94
6.5 Results and Discussion...... 95
6.6 Conclusions ...... 99
CHAPTER 7 – Thesis Conclusions and Future Work ...... 101
7.1 Thesis Conclusions and Future Work ...... 102
CHAPTER 8 - References ...... 104
LIST OF FIGURES
Figure 1.1 - Exhaust gas temperatures across the length of a vehicle, at different operating speeds4...... 21
Figure 2.1 - zT vs carrier concentration, showing the optimal doping concentration for lead chalcogenides1 ...... 29
Figure 2.2 zT for commonly used thermoelectric materials varying across the low- to high-temperature regions. 19...... 34
Figure 2.3 Phase diagram of quaternary system. 1 ...... 40
Figure 3.1 Schematic diagram of the SPS used in this work...... 46
Figure 3.2 Schematic diagram of the laser flash analysis technique for thermal diffusivity measurement...... 49
Figure 3.3 Schematic diagram of the Seebeck coefficient and electrical resistivity apparatus used in this work...... 52
Figure 4.1 (a) XRD patterns of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0,
0.05, 0.10, 0.15, 0.20), showing diffraction peaks from the PbTe matrix. A shift of the peaks towards higher angles is seen when PbSe is added and also as the PbS content increases; (b) Lattice parameter of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0,
0.05, 0.10, 0.15, 0.20) as a function of PbS content...... 60
Figure 4.2 – (a) SEM micrograph of sample 푃푏0.98푁푎0.02푇푒0.65 − 푥푆푒0.35푆푥 (푥
= 0.05). (b) Micrograph representing marked area in solid red line in (a) ...... 61
Figure 4.3 - (a) SEM micrograph of sample 푃푏0.98푁푎0.02푇푒0.65 − 푥푆푒0.35푆푥 (푥
= 0.15). (b) Micrograph representing marked area in solid red line in (a) ...... 62
Figure 4.4 – Electronic transport properties of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x
(x = 0, 0.05, 0.10, 0.15, 0.20) samples: (a) Resistivity; (b) Seebeck coefficient for all samples, the Seebeck coefficient increases across the entire temperature range. The addition of PbS to this system decreases the Seebeck coefficient for the PbTe rich samples.
...... 64
Figure 4.5 Hall coefficient temperature dependence of p-type (PbTe)0.65- x(PbSe)0.35(PbS)x (x = 0, 0.05, 0.10, 0.15, 0.20)...... 65
Figure 4.6 (a) Thermal conductivity of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples
(x = 0, 0.05, 0.10, 0.15, 0.20), with all samples showing a decrease in κ as T increases, as well as an overall decrease as the PbS content increases in the PbTe rich samples; (b)
Lattice thermal conductivity of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0, 0.05,
0.10, 0.15, 0.20), with all samples showing a decrease in κL as T increases, as well as an overall decrease as the PbS content increases in the PbTe rich samples ...... 68
Figure 4.7 Figure of merit (zT) of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x =
0, 0.05, 0.10, 0.15, 0.20), showing a maximum zT for the x = 0, 0.05, and 0.10 samples, and a decrease in thermoelectric performance with additional PbS content...... 70
Figure 5.1 Powder XRD diffraction patterns of the PbTe-rich and PbS-rich samples.
...... 80
Figure 5.2 LSR results for electrical resistivity (a) and Seebeck coefficient (b) of the PbTe-rich, PbS-rich and multiphase samples. The parallel and series model curves are shown by the solid lines. In (b), the model curves coincide...... 84
Figure 5.3 Thermal Conductivity of the PbTe-rich, PbS-rich and multiphase samples. The calculated parallel and series models are shown by the solid curves...... 86
Figure 5.4 Figure of Merit (zT) of the PbTe-rich, PbS-rich and multiphase samples.
The calculated model curves are plotted by the solid lines...... 88 Figure 6.1 (a) Resistivity of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50,
0.70, 0.85, 1); (b) Seebeck Coefficient of (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70,
0.85, 1) ...... 96
Figure 6.2 Thermal Conductivity of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15,
0.35, 0.50, 0.70, 0.85, 1) ...... 98
Figure 6.3 zT of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70, 0.85,
1) ...... 99
LIST OF TABLES
Table 4-1 Carrier concentrations and band gaps of p-type (PbTe)0.65- x(PbSe)0.35(PbS)x (x = 0, 0.05, 0.10, 0.15, 0.20)...... 66
Table 4-2 Room-temperature resistivity and Seebeck coefficient of p-type
(PbTe)0.65-x(PbSe)0.35(PbS)x (x = 0, 0.05, 0.10, 0.15, 0.20)...... 69
Table 6.1 Band Gap of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70,
0.85, 1) ...... 97
LIST OF ABBREVIATIONS
DFT Density Functional Theory
DOS Density of States
EDS Energy Dispersive X-ray Spectroscopy
FCC Face-Centered Cubic
PPMS Physical Properties Measurement System
RTG Radioisotope Thermoelectric Generator
SEM Scanning Electron Microscopy
SPS Spark Plasma Sintering
XRD X-ray Diffraction
LIST OF SYMBOLS
at. % Atomic percentage PF Power Factor
Cp Heat capacity RH Hall coefficient
d Density S Seebeck coefficient
D Thermal diffusivity T Absolute temperature
e Electron charge t Time
λ Wavelength m* Charge carrier effective mass
EF Fermi level wt. % Weight percentage Eg Optical band gap ρ Electrical resistivity
kB Boltzmann constant ΔE Band energy offset
L Lorenz number κtot Total thermal conductivity
κlat Lattice thermal conductivity κe Electronic thermal conductivity
n Charge carrier concentration μ Charge carrier mobility
σ Electrical conductivity zT Thermoelectric figure-of-merit
LIST OF PUBLICATIONS
. Manettas, A., Santos, R., Ferreres, X. R., Aminorroaya Yamini, S., Thermoelectric
Performance of Single-Phase p-type Quaternary (PbTe)0.65-x(PbSe)0.35(PbS)x Alloys.
ACS Applied Energy Materials 2018, 1(5): pp. 1898-1903;
. Aminorroaya Yamini, S., Brewis, M., Byrnes, J., Santos, R., Manettas, A., Pei, Y. Z.,
Fabrication of thermoelectric materials – thermal stability and repeatability of
achieved efficiencies. Journal of Materials Chemistry C 2015, 3(40): pp. 10610-10615;
. Ferreres, X.; Gazder, A.; Manettas, A.; Aminorroaya Yamini, S. Solid-state bonding of
bulk PbTe to Ni electrode for thermoelectric modules. ACS Applied Energy Materials
2018.
. Shaabani, L., Blake, G.R., Manettas, A., Keshavarzi, S., Aminorroaya Yamini, S.,
Thermoelectric Performance of Single-Phase Tellurium-Reduced Quaternary
(PbTe)0.55(PbS)0.1(PbSe)0.35. ACS Omega, 2019. 4(5): p. 9235-9240.
. Manettas, A., Aminorroaya Yamini, S., Pan, A. V., Calculations of Multiphase p-type
PbTe-PbS-PbSe. Submitted.
. Manettas, A., Aminorroaya Yamini, S., Pan, A. V., Characterisation of the Undoped
PbTe-PbSe Series. Finalising submission. CHAPTER 1 – Introduction
CHAPTER 1 – Introduction
CHAPTER 1 – Introduction
1.1 Motivation and Introduction
The need to harness renewable energy and utilise sustainable technologies is increasing as the world is learning the dangers of climate change, as well as fossil fuel resources depleting rapidly. We need to look for alternative methods to generate power and be able to meet the energy demands for humankind.
Thermoelectric devices take heat and convert it to electrical energy, and with this simple principle waste heat could be captured and large amounts of energy become available for other applications with a reusable, safe device1. Currently, thermoelectric devices have low efficiencies that have made them only useful for specific applications2, however if the efficiencies of thermoelectric materials were to improve, thermoelectric devices could become widespread and be a worldwide source of clean energy. Another advantage of solid-state thermoelectric devices is that there are no moving parts, decreasing the need for maintenance, increasing reliability and these materials have the ability to be scaled up, or down in size to fit the required application.
All that is required for a thermoelectric material to generate electricity is an applied heat, creating a temperature difference through the material. In the United States of America, wasted energy from heat makes up ~70%3 of the energy lost in the electrical generation and transportation industries. If thermoelectric devices were able to harness even 10% of this wasted heat, that would be a significant amount of renewable power that could be generated.
One possible application for thermoelectric materials is for use in the automotive industry. The efficiency of motor vehicles would significantly increase and environmental impact decrease with the use of these materials as an additional power source. Looking at Figure 1.1, different sections of a car exhaust can reach almost 800 Celsius at extremely CHAPTER 1 – Introduction high speeds (160 km/hr) however for regular city and highway driving, the exhaust temperature is around 400-700 Celsius. With the correct placement of a thermoelectric generator, a large temperature differential can be applied to a thermoelectric material and large amounts of power can be harnessed from this waste heat.
Figure 1.1 - Exhaust gas temperatures across the length of a vehicle, at different operating speeds4.
The purpose of this thesis is to study the properties high performance, cost- effective lead chalcogenide thermoelectric materials. A large variety of materials are covered in this work including single-phase, multiphase and undoped compositions, and by studying this wide range the effectiveness of lead chalcogenides as thermoelectric materials can be accurately assessed. CHAPTER 1 – Introduction
1.2 Thesis Structure
This thesis consists of seven chapters. Here, a brief description of each chapter is outlined:
Chapter 1 serves as an introduction to the thesis, explains the motivation for the work and contains an outline of the structure.
Chapter 2 explains the fundamental physics behind the thermoelectric effect and thermoelectric materials. A literature review of lead chalcogenide thermoelectric materials is presented, looking at methods to increase thermoelectric performance by studying the properties that contribute to the thermoelectric figure-of-merit, and concluding with the future work and applications of these materials.
Chapter 3 gives an overview of the synthesis methods used in this doctoral work for the fabrication of the thermoelectric materials used, as well as explains the various characterisation techniques used to determine the thermoelectric properties and structural components of a given material. Further details on the materials, synthesis, measurement and analysis will be specified in the relevant chapters.
Chapter 4 reports on the synthesis and performance of the single-phase p-type
PbTe0.65-x-PbSe0.35-PbSx quaternary system. The composition starts with the alloying of
35% PbSe with PbTe, and then replacing PbTe by adding PbS. This enables all samples to remain single-phase even with concentrations of PbS up to 20%. In this work it was shown that this high amount of PbS decreased thermal conductivity, however it also decreased the Seebeck coefficient and so the maximum zT of ~1.4 was lower than compared to the multiphase PbTe-PbSe-PbS system (zT ~2). This chapter is based on the CHAPTER 1 – Introduction work published as: A. Manettas, R. Santos et al., ACS Applied Energy Materials, 2018,
1(5): pp. 1898-1903.
Chapter 5 explores the multiphase PbTe-PbSe-PbS system as 2 separate single- phase components in an attempt to better understand this multiphase system. The two compositions were synthesised and characterised, with their results being compared to the previously measured multiphase system. It was found that by combining the results from both samples and modelling them as a multiphase material, the zT was significantly underestimated. The models’ calculations predicted a maximum zT of ~1.4, which is significantly lower than the multiphase sample’s experimental result of ~2. This is one of the highest zT’s reported and had this been modelled its high performance may have been overlooked.
Chapter 6 looks at the thermoelectric properties of the PbTe-PbSe system, across the entire composition range. Eight compositions across the (PbTe)1-x(PbSe)x range, including pure PbTe and PbSe, were synthesised and their properties measured for this work. PbTe and PbSe have been shown to be promising thermoelectric materials, and there have been many studies on different combinations of PbTe-PbSe alloys, however a complete characterisation of the series has not been done. The results seen in this work give a greater understanding of the properties of the PbTe-PbSe system and how these materials can be utilised in future work, where further alloying or doping may be employed to increase the thermoelectric performance.
Chapter 7 concludes the doctoral thesis with a summary of the experiments performed and looks at future work that is possible for the optimisation of lead chalcogenide thermoelectric materials and their applications.
CHAPTER 2 – Literature Review
CHAPTER 2 – Literature Review
CHAPTER 2 – Literature Review 2.1 Principles of Thermoelectricity
Thermoelectric materials are of interest due to the useful properties of the inherent thermoelectric effects that they have, the Seebeck effect and its inverse, the
Peltier effect. These effects stem from a temperature difference across a thermoelectric material, creating an electrical potential difference.
Almost all materials have thermoelectric properties, however most would have thermoelectric efficiencies that would be almost negligible. There are metals and semiconductors that have appropriate thermoelectric properties that can be used in various applications such as utilising waste heat and generating power from radioisotopes.
Even with better optimised and carefully chosen materials, their overall thermoelectric efficiency is still very poor and as such thermoelectric devices are not widespread. It is challenging to produce useful thermoelectric materials due to the difficulties in the synthesis process as well as simultaneously optimising conflicting thermoelectric properties. These challenges will be discussed later in further detail.
2.1.1 Seebeck effect
The Seebeck effect is a phenomenon whereby a material converts a temperature differential into an electrical potential, giving it the ability to generate electricity5. When a temperature gradient is applied to a material, there is a flow of charge carriers in the direction of the temperature gradient. This movement of charge induces an electric potential across the material, and this can be harnessed as electrical energy. The measure of this effect is given by the Seebeck coefficient (S), which is defined as the ratio of a voltage differential to a temperature differential CHAPTER 2 – Literature Review ∆푉 푆 = (2.1) ∆푇
where ΔV and ΔT are the voltage and temperature differentials in a material, respectively.
The Seebeck coefficient can be calculated from Equation 2.26
2 2 2푘 푇 휋 3 푆 = 퐵 ( ) 푚∗(1 + 푟) (2.2) 3푒ℏ2 3푛
where kB is the Boltzmann constant, T is the temperature, e is the electron charge,
ℏ is the reduced Planck constant, n is the carrier concentration, m* is the charge carrier effective mass, and r is the scattering parameter. This is a general expression for the
Seebeck coefficient and many of these terms are constants, the main variables that are covered in this study are temperature, which changes the relative positions of the electronic bands and therefore the band gap (Eg), carrier concentration, which determines the type and magnitude of the carrier conduction, and density of states (DOS) effective mass, which is mainly a function of the electronic band structure.
2.1.2 Peltier effect
The Peltier effect is the inverse of the Seebeck effect. When an electrical potential is applied to a thermoelectric material, a temperature differential is created. This temperature differential can be used for heating or cooling, depending on the desired application7. Similar to the Seebeck effect, it is also reversible, whereby changing the direction of the applied current swaps the heated and cooled junctions, allowing greater temperature control over a material.
2.1.3 Electrical resistivity
An intrinsic property of thermoelectric materials is electrical resistivity, ρ, or its inverse, electrical conductivity, σ, which is a measure of a material’s ability to conduct CHAPTER 2 – Literature Review electricity. A high electrical resistivity restricts the movement of charge carriers through the material which decreases the possibility for thermoelectric energy conversion.
The Seebeck coefficient and the electrical resistivity both depend on the carrier concentration. Looking at Equation 2.2 a low charge carrier concentration would lead to a high Seebeck coefficient, however this a low charge carrier concentration results in a large electrical resistivity, as seen in Equation 2.38,
1 1 휌 = = (2.3) 휎 푛푒휇
where µ is the charge carrier mobility.
It is important to optimise the carrier concentration in order to maximise the Seebeck coefficient and minimise the electrical resistivity simultaneously. The optimal relation of these two properties is defined as the thermoelectric power factor (PF):
푃퐹 = 푆2⁄휌 (2.4)
It can be seen in Figure 2.1 that the optimal charge carrier concentration for high efficiency thermoelectric materials is ~1019 cm-3 - 1021 cm-3,9 typical of highly degenerate semiconducting materials. CHAPTER 2 – Literature Review
Figure 2.1 - zT vs carrier concentration, showing the optimal doping concentration for lead
chalcogenides1
2.1.3.1 Hall effect
A useful tool to understand how the carriers behave in a thermoelectric material is to perform Hall effect measurements. From these measurements, the carrier mobility and carrier concentration can be determined.5
Hall effect measurements are performed by applying an electric current to a sample, while simultaneously applying a magnetic field perpendicular to the direction of the current and measuring the voltage across the sample. The current causes the charge carriers to experience an electric field and results in a current travelling through the material. The applied magnetic field induces a force called the Lorentz force in the material that acts on the charge carriers, changing their path. Electrons and holes CHAPTER 2 – Literature Review experience the same force in opposite directions, which separates the charges in the material. The voltage potential generated from this charge separation can be measured and is known as Hall voltage (VH). By combining the applied electric current and magnetic field, along with the measured thickness of the sample, it is possible to calculate the Hall coefficient.
퐼푥퐵푧푅퐻 푉퐻푡 1 푉퐻 = ⇔ 푅퐻 = = = 휇휌퐻 (2.5) 푡 퐼푥퐵푧 푛푒
where t is the thickness of the sample, µ the charge carrier mobility and ρH the Hall resistivity.
The measurements described above can be taken at a wide range of temperatures
(~5 – 400 K) and the temperature dependence of the Hall coefficient can be used to determine the type of charge carriers in semiconductors, the existence of subbands within the valence and conduction bands5, and how these affect the electronic properties of the sample.
2.1.4 Thermal conductivity
Thermal conductivity is a measure a material’s ability to transfer heat. In thermoelectric applications where a heat differential is of great importance, a low thermal conductivity is required for efficient operation.
The thermal conductivity in thermoelectric materials can be described by the sum of two contributing effects, the heat transported by electronic charge carriers and the heat transported by lattice vibrations, or phonons. These two sources of heat transfer are known as the electronic thermal conductivity, κe, and the lattice thermal conductivity, κlat, respectively, with the summation of the two giving the total thermal conductivity (κtot). CHAPTER 2 – Literature Review
휅푡표푡 = 휅푒 + 휅푙푎푡 (2.6)
It is not possible to measure κe and κlat separately, however using the Wiedemann-
Franz law, and other measurements to obtain the Seebeck coefficient and electrical resistivity, a calculation can be made for an estimate of the electronic thermal conductivity:
휅푒 = 퐿휎푇 = 푛푒휇퐿푇 (2.7)
where L is the Lorenz number10.
The Lorenz number used is the theoretical limit for degenerate semiconductors of
2.45×10-8 V2K-2,11 as the approximation for non-degenerate semiconductors:
|푆| 퐿 = 1.5 + 푒푥푝 (− ) (2.8) 116
where L is in 10-8 WΩK-2 and S in µV/K.12
The lattice (κlat) thermal conductivity is calculated by subtracting the electronic thermal conductivity (κe) from the total thermal conductivity κtot ( 휅푡표푡 = 휅푙푎푡 + 휅푒) using the Wiedemann-Franz relation, 휅푒 = 퐿0푇/휌 (where L is the Lorenz number and ρ the electrical resistivity).
2.1.5 Thermoelectric figure-of-merit, zT
The thermoelectric properties previously discussed, that is the Seebeck coefficient, electrical resistivity and thermal conductivity can all be combined to calculate the dimensionless thermoelectric figure-of-merit, zT, given by the following equation5:
푆2푇 푧T = 2.9 휌휅푡표푡 CHAPTER 2 – Literature Review Looking at Equation 2.9, it can be seen that the thermoelectric figure-of-merit zT is proportional to the square of the Seebeck coefficient, and inversely proportional to the electrical resistivity and thermal conductivity. These properties depend heavily on the charge carrier concentration, which can be altered by changing the doping level of a material. It is critical to maximise the Seebeck coefficient while minimising the electrical resistivity and thermal conductivity, however this balance can prove challenging when attempting to increase zT. An increase in zT directly corresponds to an increase in efficiency of a thermoelectric generator.8 For a given temperature differential of 100 degrees Celsius across a sample, a material with a zT of 1 would have an efficiency of ~5%.
With the same temperature differential of 100 degrees, a material with a zT of 3 would have an efficiency of ~8%. With a much larger temperature differential of 500 degrees, a material with a zT of 1 would have an efficiency of ~15% whereas a material with a zT of
3 would have an efficiency of ~26%.8 It is clear that a higher temperature differential across a material leads to higher output and better efficiencies, and in addition to that having a higher zT will also improve a device’s efficiency, however the intended use of a thermoelectric material can vary considerably on a case-by-case basis, and so it is important to understand what the application will be for a final product and what efficiencies are needed, as well as any cost considerations and limitations.
2.2 Thermoelectric Materials
2.2.1 Classification of thermoelectric materials
There are many different types of thermoelectric materials for a wide variety of applications, as can be seen from the vast range of materials in Figure 2.2, and a common way of classifying these thermoelectric materials is by the temperature range of operation. Low-temperature thermoelectric materials are considered to operate up to ~
450 K, where bismuth-based alloys are the most commonly used materials. Bismuth CHAPTER 2 – Literature Review telluride has good room-temperature thermoelectric performance, with a zT of ~0.813, however this does not improve with higher temperatures and is restricted by its relatively low melting temperature of ~850 K, limiting its applications and efficiency. Mid-range temperature materials operate up to ~850 K with lead chalcogenides being the most commonly used because of their high performance, which are the focus of this thesis.
Lead-free alternatives are being explored, due to environmental concerns and health issues associated with the use of lead, however their performance is not as high with zT values of ~0.814 and so lead chalcogenides are still a dominant area of research.
Magnesium silicides are another mid-range temperature thermoelectric material that have comparable zT to other materials15, however there is trouble finding an accurate sample fabrication method because there is magnesium loss during synthesis16, and this makes sample preparation challenging and inconsistent. High temperature region materials are considered to operate up to 1300 K, and here silicon-germanium alloys are the most commonly used17, as well as copper sulphides being another high performing high temperature thermoelectric18. CHAPTER 2 – Literature Review
Figure 2.2 zT for commonly used thermoelectric materials varying across the low- to high-temperature regions. 19
2.2.2 Lead chalcogenides
Lead chalcogenides are compounds that are lead-based and alloyed with a Group
16 element, most commonly sulphur, tellurium and selenium. They have a face-centered- cubic (FCC) rock salt structure and are one of the most studied thermoelectric materials suitable in the intermediate temperature range (600− 800 K)20-21, with a wide variety of dopants that have been utilised to improve performance22-23.
These compounds are widely used due to their high zT for both n- and p-type materials24-28. These types of materials were used by NASA to develop radioisotope thermoelectric generators (RTG). RTG’s use the heat generated from the decay of a radioactive material to generate a temperature differential across a thermoelectric material, and this is converted into electricity for use on spacecraft such as the Apollo 12 CHAPTER 2 – Literature Review Viking missions 1 and 2, and are currently being used as a power source for the Curiosity rover on Mars29.
One negative consideration of manufacturing lead chalcogenides is that lead is highly toxic and its toxicity is further enhanced due to its volatility at high temperatures during the sample fabrication process, which can lead to environmental pollution and serious health hazards if exposed to human and animals alike. Legislation will eventually lead to restrictions on the use of hazardous substances, including lead and other heavy metals. While lead-free thermoelectric materials are being investigated, the thermoelectric properties of lead chalcogenides make them the superior choice for thermoelectric generators. Looking at Figure 2.2, the best performing lead-based thermoelectric material has the highest zT of ~2, while the next best lead-free material has a zT of less than 1.5. Lead chalcogenides are an important field of research because of their high zT and will continue to be the highest performing mid-range thermoelectric materials unless major breakthroughs are made in lead-free alternatives.
The extensive studies on PbTe alloys result in a high figure of merit for the single- phase ternary PbTe-PbSe system30 through modification of the band structure to cause band convergence, and the low thermal conductivity achieved due to nanostructuring leads to high thermoelectric performance for ternary PbTe-PbS31 compounds. The pseudoternary system is of importance, in an attempt to increase the power factor and decrease thermal conductivity simultaneously.
Alloying is a proven strategy that leads to high zT’s in materials for high temperature applications, for example, SiGe and TAGS alloys used in the radioisotope thermoelectric generators powering multiple spacecrafts for decades1. Alloying in thermoelectrics provides a wide control of different material properties, including CHAPTER 2 – Literature Review thermal conductivity, band structure, mechanical properties and even carrier density which all contribute to the thermoelectric performance and zT. 32
Lead telluride’s high performance is attained by tuning the electronic structure near the Fermi level, specifically by introducing resonant states, manipulating and utilizing the material’s multiple bands and altering the band gap. The PbTe–PbSe system shows a higher figure of merit than the binary PbTe and PbSe systems in the temperature range of 550–800 K, mainly due to alteration of the electronic band structure33-34. For the
PbTe–PbS system, a high zT is attributed to the reduction in lattice thermal conductivity, which originates from phonon scattering at the interfaces of secondary phases, as PbS shows very limited solubility in the PbTe matrix.26
The Seebeck coefficient and electrical conductivity of degenerately doped semiconductor thermoelectric materials are related through the carrier concentration and the density of states effective mass35. The carrier concentration must be selected to balance the inverse relationship between electrical conductivity and Seebeck coefficient to maximize the power factor and this value can vary among compositions36-37, however as a general rule for lead chalcogenides the optimal doping, as shown in Figure 2.1, is
~1020 carriers/cm3. Increasing the Seebeck coefficient without negatively affecting the electronic conductivity is possible primarily by altering the band structure through increased band degeneracy, and this can be done with a variety of materials as alloys38 in addition to chalcogenides.
By doping with sodium there is enhancement in the electronic transport through promotion of carriers between the heavy and light bands39, producing a high thermoelectric power factor despite reductions in electrical conductivity. CHAPTER 2 – Literature Review In heavily doped p-type PbTe, interaction between the light and heavy hole valence40-41 bands can result in significant increases in the power factor at high temperature42. These methods of band structure engineering can increase the power factor and therefore zT significantly. Alloying PbTe and PbSe alters the convergence temperature of the light and heavy hole valence bands in PbTe43. By increasing the convergence temperature compared to PbTe the power factor is maximized at a higher temperature resulting in a higher zT at around 580° C.
If two bands are present, then the total Seebeck coefficient is a weighted average of the Seebeck coefficients of the individual band, the band with the higher conductivity is more strongly weighted. The Seebeck coefficient usually decreases with the number of carriers n, whereas conductivity increases with n. The total Seebeck coefficient will generally be closer to the smaller value of the two bands. Only when the two band energies are aligned (i.e., they are degenerate), such that the two bands have the same Seebeck coefficient, will the total Seebeck coefficient be maintained while the total conductivity is substantially higher than that of either band alone44. In general, this effect will improve thermoelectric performance when the bands are within 2kBT of each other45, owing to the broadening of the Fermi distribution, making band convergence easier to achieve at higher temperatures.
As the temperature rises, the energy of the light valence band (L band) is gradually reduced and reaches the heavy band (Σ band) edge. The density of states in the Σ band is much higher and it provides a higher Seebeck coefficient than that with the L band alone, given the same carrier density. The convergence of valence bands results in higher thermoelectric efficiency at operating temperatures near 600 K in heavily doped materials where the Σ band contributes to the electronic properties of alloys. At a given carrier concentration, a high Seebeck coefficient can be achieved due to the high density CHAPTER 2 – Literature Review of states (DOS) effective mass. A large total DOS can be due to either a large band degeneracy or a high single-valley density of states effective mass of the degenerate valleys. The density of states effective mass for PbS is shown to be larger than that for
PbTe46. A higher Seebeck coefficient of alloys containing sulphur, frequently in the form of PbS, is expected from the increase in the density of states.
The energies of the two valence bands have been shown to also be adjustable in
PbTe when alloying with PbSe. Alloying PbTe with 10 at% PbSe reduces the band gap at room temperature, however alloying with PbS increases the band gap where a linear relationship between the band gap and the chemical composition is supposed for the
PbTe–PbS alloy35, 46. This predicts that the L-band is shifted to lower energy for samples containing sulphur. The increased band gap slows the degradation of the Seebeck coefficient through the contribution of minority carriers, which are thermally excited across the band gap at high temperatures. Overall the increase in the density of states, combined with the larger band gap, should lead to a higher Seebeck coefficient at high temperature46.
Replacing matrix atoms with solid solution atoms with the largest mass contrast can introduce considerable thermal conductivity reduction into the solid solution alloy10.
Therefore, the large mass contrast between the sulphur atoms and the tellurium matrix atoms is considered to be responsible for the significant reduction in the thermal conductivity of sulphur-containing alloys.
The lattice thermal conductivity of PbS is higher than that of PbTe10 and a large volume fraction of PbS precipitates in multiphase samples with greater than 20% PbS results in an increase in their lattice thermal conductivity and this is detrimental to the overall zT, which is why single-phase samples are of interest. CHAPTER 2 – Literature Review The lattice thermal conductivity is found to decrease significantly after adding a small amount of PbSe into PbS matrix up to the composition of PbSe0.7S0.3 when the carrier mobility remains practically unchanged, indicating the beneficial effect of impurity scattering to increase the thermoelectric performance47. Androulakis et al.24 showed that the PbSe-PbS system can reach a zT of ~1.3 through nanostructuring to decrease the thermal conductivity.
Work has been done on single-phase sodium doped PbTe, alloyed with PbS up to its solubility limit which is extended to larger concentrations than in the ternary system of PbTe–PbS due to the presence of PbSe48. A zT of ~1.6 was achieved which is higher than ternary PbTe–PbSe and PbTe–PbS at similar carrier concentrations than the binary PbTe,
PbSe and PbS alloys49-51.
The quaternary system shows a larger Seebeck coefficient than the ternary PbTe–
PbSe alloy46, suggesting that there is a wider band gap, valence band energy offset and heavier carriers effective mass. Also, the existence of PbS in the alloy further reduces the lattice thermal conductivity originated from phonon scattering on solute atoms with high contrast atomic mass.
The ternary PbTe–PbSe and PbSe–PbS systems have unlimited solubility over the entire composition range and as such are always solid solutions. However, the components of the PbTe–PbS system show very limited solubility with respect to each other and phase separation of PbS precipitates in the PbTe matrix at the PbTe-rich side of the phase diagram occurs via nucleation and growth. This behaviour is also seen in the
PbTe–PbSe–PbS quaternary system, where the addition of PbSe shifts the upper curve of the miscibility gap to lower temperatures, as seen in Figure 2.3 by the red line for 10 at%
PbSe. CHAPTER 2 – Literature Review
Figure 2.3 Phase diagram of quaternary system. 1
Among all the lead chalcogenides, the pseudobinary systems PbTe-PbS, PbTe-PbSe and PbSe-PbS have been studied and developed to relatively high performance32. PbTe-
PbS exhibits well-defined nanostructuring50 both on the PbTe-rich side of the composition where PbTe is the matrix and PbS is the second phase and on the PbS-rich side where the inverse occurs. The compounds selected in Chapter 4 of this study are single-phase with a PbTe rich matrix, and the solubility limit of PbS is increased in the matrix due to the addition of PbSe.
The high thermoelectric performance of solid solution quaternary PbTe–PbSe–PbS alloys is a relatively new research direction for lead chalcogenides, based on adjusting the band gap and the energy separation between the upper and the lower valence bands to enhance the Seebeck coefficient while simultaneously achieving low thermal conductivity due to scattering of long wavelength phonons at point defects52-53. This quaternary system also benefits whereby the tellurium in the base composition in replaced by either selenium or sulphur. Tellurium costs ~$5000/kg, selenium around ~$700/kg and with CHAPTER 2 – Literature Review sulphur costing ~$1600/kg this substitution of tellurium with other elements greatly decreases the cost of manufacturing lead chalcogenides and on an industrial scale, this makes synthesising and implementing lead chalcogenides a much more cost-effective option.
2.3 Applications and devices
A thermoelectric pair is the physical component that forms the make-up of a thermoelectric device. Thermoelectric pairs consist of p- and n-type semiconducting materials, that are connected electrically in series and thermally in parallel; so that current can flow through the device and that the temperature differential is maintained across the thermoelectric material. When in use, these devices undergo frequent thermal cycling and are subjected to high temperature gradients which lead to issues of mechanical stress for the materials. These effects of high temperature fluctuations on the properties of these materials are critical to understand, especially because two unique (p- and n-type) semiconducting materials are being used. This can be mitigated by using materials that behave similarly under large temperature changes. Fortunately lead chalcogenides can be both n- and p-type semiconductors54-56, and work has been done on solid state bonding of both these n- and p-type compounds to an electrode,57-58 inferring that by combining both of these electrodes a thermoelectric device can be created solely with high performance lead chalcogenides.
Thermoelectric materials are already being used around the world, as well as outside the world on many different space missions. Radioisotope thermoelectric generators (RTG) have been shown to be an invaluable asset for any space mission, increasing efficiency of a trip with a simple solid-state thermoelectric device59. CHAPTER 2 – Literature Review Another useful application is for thermoelectric materials to be implemented into solar cells60 and cars, and work has already begun on improving efficiency by using them61. CHAPTER 3 – Experimental Methods and Characterisation Techniques
CHAPTER 3 – Experimental Methods and
Characterisation Techniques
CHAPTER 3 – Experimental Methods and Characterisation Techniques
3.1 Overview
This chapter explains the synthesis and characterisation techniques used on all samples produced for this thesis. There are various fabrication techniques to obtain reproducible, high performance materials that vary depending on the composition required and desired use of the material.
The general method for the preparation of all samples is outlined in this chapter, and any further details will be explained in the relevant chapters.
3.2 Preparation and Synthesis Methods
3.2.1 Alloying and doping of lead chalcogenides
The high purity chemicals used in this thesis were purchased as individual elements, and the desired compositions alloyed by mixing a stoichiometric ratio of the required elements in a quartz ampoule. The handling of these chemicals was performed in a glovebox with an argon atmosphere and < 0.1 ppm O2 and < 0.1 ppm
H2O to reduce the risk of oxidisation or contamination of the materials, and to ensure that they would maintain their high purity. Where sulphur is used in a composition, lead and sulphur are first combined to make PbS with a slower heating rate and melted at 1100° C, followed by furnace cooling, to ensure that all the sulphur fully reacts with the lead. This PbS is then alloyed with the remaining elements to synthesise the total compositions.
In Chapters 4 and 5 lead is alloyed with selenium and PbS, and sodium is used as a dopant to make the required p-type materials. In this particular case of p-type doping it is critical to ensure that there is no loss of sodium before melting due to its CHAPTER 3 – Experimental Methods and Characterisation Techniques
highly reactive nature, and so these samples are combined in a carbon-coated quartz ampoule.
These ampoules are sealed and evacuated before heating to 1100° C and held at that temperature for 6 hours to homogenise the melt, followed by cooling. The samples in Chapters 4 and 5 were cooled by water quenching and then annealed at
550° C for 72 hours. This process is to ensure the homogenous distribution of sodium throughout the sample and to stabilise the performance of the material. After the material has been melted and appropriately cooled in the quartz ampoule, the resulting ingot is then hand ground into a fine powder and sintered using Spark
Plasma Sintering.
3.2.2 Spark Plasma Sintering (SPS)
The fabrication of samples for their thermoelectric properties to be measured was done by the high temperature and high pressure sintering of powders using spark plasma sintering (SPS). The SPS equipment used in this thesis is a Spark
Plasma Sintering system from Thermal Technology using 12 mm diameter, high density graphite dies and punches.
The powders are put under high uniaxial compressive pressure and high temperature simultaneously, while the chamber is constantly being evacuated by a vacuum pump. Spark plasma sintering controls the temperature by applying a high current to the graphite die and powder set, sending current through the die, and therefore through the powder particles. Due to the small size of the powder particles, small contact points are exposed to the current and this causes high current densities, which decreases the time the sample is at high temperature compared to CHAPTER 3 – Experimental Methods and Characterisation Techniques
hot pressing, decreases the temperature needed for sintering which in turn reduces oxidation and lessens grain growth.62
Figure 3.1 Schematic diagram of the SPS used in this work.
3.3 Characterisation Techniques
3.3.1 Structural and phase characterisation with X-ray diffraction (XRD)
The structural and phase characterisation of all thermoelectric materials in this thesis were performed with X-ray diffraction. X-ray diffraction shows the phases present in the powders and further analysis can be performed to investigate the structural characteristics of samples. The XRD instrument used was a GBC MMA diffractometer. CHAPTER 3 – Experimental Methods and Characterisation Techniques
XRD characterisation is done by rotating a detector around a sample that has a beam of X-rays incident on it and measuring the intensity of radiation at each angle.
A spectrum is then produced showing where the X-rays are diffracted by the sample.
By comparing with a database of known materials, the crystal structure of the sample can be identified and the distances between atomic planes can be calculated.
The GBC MMA diffractometer uses a source of X-rays (Cu target, wavelength 휆 =
1.5418 Å) incident on the sample, and the measurement shows a spectrum where there are peaks in intensity when the conditions satisfy Bragg’s law, 푛휆 = 2푑푠푖푛휃, where 푛 is an integer of the order of reflection, 휆 is the wavelength of the X-ray radiation, 푑 the distance between the atomic layers of the crystal, and 휃 the angle between the incident rays and the sample.
3.3.2 Thermoelectric properties characterisation
To determine a composition’s effectiveness as a thermoelectric material several measurements need to be taken of its thermal and electronic properties, which can be used to calculate the thermoelectric figure-of-merit, zT. These measurements are to get the thermal conductivity, Seebeck coefficient and electrical resistivity across a temperature range. These data are used in conjunction with the previous characterisation information to obtain a complete picture of the thermoelectric properties of a material and an understanding of what characteristics determine those properties.
It is important to consider many factors when investigating a thermoelectric material, the composition of the material as well as the fabrication process can have a major impact on its properties. Looking at all the information that can be obtained CHAPTER 3 – Experimental Methods and Characterisation Techniques
about a given material, one can begin to understand the fundamental behaviour of its properties and potentially optimise them to increase its zT.
3.3.2.1 Thermal conductivity
In order to acquire a material’s thermal conductivity, first the thermal diffusivity must be measured, and then using other measured values the thermal conductivity can be calculated. In this work, the thermal diffusivity was measured using a Linseis LFA-1000, which uses the laser flash method63.
Thermal diffusivity is a measure of the rate of transfer of heat in a material.
The laser flash method consists of heating one side of a cylindrical sample with a laser, and then measuring the time that the heat in the sample takes to travel through the sample. This heat travels in the form of phonons and is radiated out from the sample as infrared radiation which is collected by an infrared detector, seen in
Figure 3.2. The detector takes voltage measurements before and after the laser is pulsed to measure how long it takes for the heat to travel through the sample, and this data is used to calculate at what time the voltage signal is at half of its maximum amplitude. Using these values, the thermal diffusivity (D)can be calculated:
2 퐷 = 0.1388 퐿 /푡1⁄2 (3.1)
where L is the sample thickness and t1/2 is the time taken to reach half of the maximum amplitude of the temperature signal. CHAPTER 3 – Experimental Methods and Characterisation Techniques
Figure 3.2 Schematic diagram of the laser flash analysis technique for thermal diffusivity
measurement.
The heat capacity (퐶푝) for lead chalcogenides can be estimated numerically, and the density (d) of the sample is obtained by measuring its mass and dimensions.
By multiplying these values together with the measured thermal diffusivity, the thermal conductivity (κtot) can be calculated.
휅푡표푡 = 푑 × 퐷 × 퐶푝 (3.2) CHAPTER 3 – Experimental Methods and Characterisation Techniques
3.3.2.2 Seebeck coefficient and electrical resistivity
The Seebeck effect is an instrumental phenomenon to understand in the study of thermoelectric materials, and hence it is significant to measure the Seebeck coefficient accurately. A temperature difference is required to measure the Seebeck coefficient; therefore, two different temperature controls are needed to obtain the information. The overall temperature of the sample and the sample chamber need to be independently measured and precisely controlled. Another source of heat needs to be applied to the sample to generate a temperature differential between the two ends of the thermoelectric material. The sample temperature and applied temperature differential need to be precisely measured, as does the voltage that is generated from this temperature differential. Both the temperature and voltage differentials have to be measured at well-defined temperatures within the sample, which leads to issues in measurement such as sample and probe thermal expansion, and heat transfer through the thermocouples that are used for temperature and voltage measurement. The electrical resistance is measured using the same thermocouples by passing a given electrical current through the sample and measuring the voltage differential generated. By measuring the sample dimensions and distance between the probes the resistivity can be calculated. Using these principles, the Seebeck coefficient and electrical resistivity are measured simultaneously. In this thesis, a Linseis LSR-3 Seebeck Coefficient and Electrical
Resistivity system was used in which the Seebeck coefficient was measured using the slope method for each temperature point in a quasi-steady-state mode.
CHAPTER 3 – Experimental Methods and Characterisation Techniques
3.3.2.2.1 Experimental details for Seebeck coefficient and electrical resistivity measurements
The Seebeck coefficient and electrical resistivity measurements were performed on a Linseis LSR-3, using a parallelepiped-shaped sample, with the sample chamber having a helium atmosphere of ~ 0.5 bar. The chamber is evacuated and flushed with helium 3 times to ensure the environment is clear of any contaminants. The reduced pressure helium atmosphere is used to avoid a large pressure increase inside the sample chamber at high temperatures, as well as facilitating good heat conduction throughout the chamber to ensure accurate measurements. The thermoelectric material being characterised is placed between two platinum electrodes to hold them in place that allow current to pass through for the electrical resistivity measurements. The electrical resistance measurements are performed by passing a constant current of 100 mA through the sample and using two thermocouples to measure the voltage drop across the sample. The electrical resistivity is then calculated using the measured resistance from the machine, the dimensions of the sample and the thermocouple probe distance. The temperature gradient needed to measure the Seebeck coefficient is created by an additional heat source in the lower platinum electrode. The temperature gradients used in this work was 1-10 K across the sample. The two thermocouples, that are Pt/Pt + 10% Rh; S- type, were placed in contact with the sample to measure the temperature and voltage variation in the sample, seen in Figure 3.3. Pressure from a spring holds the thermocouples in place, to ensure good contact during thermal expansion at high temperature. The sample area, comprising of the sample, thermocouple probes, platinum electrodes and gradient heater, is housed inside a metallic radiation shield, CHAPTER 3 – Experimental Methods and Characterisation Techniques
and the temperature of the whole sample chamber is controlled by heating elements programmed by the user.
Figure 3.3 Schematic diagram of the Seebeck coefficient and electrical resistivity apparatus used in this work.
CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
CHAPTER 4 – Thermoelectric Performance of p-
type Single-phase PbTe-PbSe-PbS
CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
4.1 Motivation
The quaternary system PbTe-PbSe-PbS has been shown to be a useful, high zT thermoelectric material. Due to the low solubility of PbS in PbTe a secondary phase appears with a relatively low percentage of PbS. The addition of PbS can increase the Seebeck coefficient and decrease thermal conductivity, however having a secondary phase can negatively impact on properties such as resistivity and thermal conductivity at higher temperatures, therefore, a study on single-phase
PbTe-PbSe-PbS could prove to increase the zT on the already valuable quaternary system.
This is also beneficial financially as the sulphur is replacing tellurium in the sample, and tellurium is around 5 times more scarce than platinum,64 hence making these samples a more cost-effective thermoelectric material compared to ordinary
PbTe.
4.2 Abstract
The quaternary system comprising of lead chalcogenides PbTe, PbSe and PbS has been an important area of research as they have high performance, reproducible results and can be utilised as both an n- and p-type system.
Adding PbS to PbTe has been shown to increase the Seebeck coefficient and decrease thermal conductivity however a secondary phase appears with low concentrations of PbS. This secondary phase can prove challenging for obtaining consistent results as the material’s behaviour changes on heating and cooling of the sample, as well as limiting the thermoelectric properties. Single-phase samples have CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS consistent behaviour across the whole temperature range on both heating and cooling and have achieved high zT.
Replacing PbTe with PbSe increases the solubility of PbS in the PbTe matrix and should allow for samples with high concentrations of PbS to remain single- phase.
It was found that all samples did remain single-phase with the increased solubility from PbTe-PbSe alloying, however there was no significant improvement in performance with increasing concentrations of PbS. The thermal conductivity decreased linearly with added PbS however the Seebeck coefficient also decreased, leading to a maximum zT of ~ 1.4 for the x = 0.10 sample.
4.3 Introduction
Solid-state thermoelectric generators, which convert heat to electricity, have been identified as candidates for waste heat recovery7. The conversion efficiency is defined by the dimensionless thermoelectric figure-of-merit 푧푇 = 푆2휎푇/휅, where T is the operating temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity, consisting of the lattice and electronic components of the thermal conductivity, κL and κe, respectively. Alloying thermoelectric materials provides wide control of different material properties, including the thermal conductivity, structural properties, band gap, and carrier density which all contribute to the thermoelectric performance25, 32. Among the thermoelectric materials, lead chalcogenides have been shown to have high conversion efficiencies in the mid-range temperature region (~ 300 – 600 °C)65. The high performance of PbTe is achieved by tuning the electronic structure near the CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Fermi level, manipulating and utilising the material’s multiple bands, and altering the band gap1, 5.
Several studies on PbTe alloys report a high figure-of-merit for the single-phase ternary PbTe-PbSe system30, 33. Alloying PbTe with PbSe alters the convergence temperature of the light and heavy hole valence bands43. By having a higher convergence temperature than that of pure PbTe, the power factor is maximized at a higher temperature, resulting in a greater zT at ~ 580 °C. In the PbTe-PbS system, low thermal conductivity due to alloying, as well as nanostructuring, leads to high thermoelectric performance66. The reduction in thermal conductivity comes from phonon scattering at the interfaces of the secondary phases, as PbS shows very limited solubility in the PbTe matrix26.
The PbSe-PbS system has been researched10 and has shown to decrease lattice thermal conductivity compared to the PbSe and PbS binary systems due to impurity scattering, however in extrinsic PbSe-PbS32 this improvement does not lead to a higher zT than the PbTe-PbSe system due to a reduced power factor from a lower carrier mobility.
The ternary PbTe–PbSe and PbSe–PbS systems have unlimited solubility over the entire composition range and as such, are always solid solutions10, 67-68.
Nevertheless, the components of the PbTe–PbS system show very limited solubility with respect to each other, and phase separation of PbS precipitates in the PbTe matrix on the PbTe-rich side of the phase diagram occurs via nucleation and growth.
This behaviour is also observed in the quaternary system PbTe–PbSe–PbS, where the addition of PbS causes a secondary phase to appear69. A large amount of PbSe increases the solubility of PbS in PbTe70, allowing (PbTe)0.65-x(PbSe)0.35(PbS)x CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS samples to still behave as solid solutions with a large concentration of PbS in the
PbTe matrix. Single-phase samples can maintain lower thermal conductivity, as PbS has a higher lattice thermal conductivity than PbTe, and a large volume fraction of
PbS precipitates in multiphase samples results in an increase in the lattice thermal conductivity5.
Sodium is a commonly used p-type dopant for lead chalcogenides,66, 69 and in heavily doped multiphase PbTe-PbS samples a large percentage of sodium will partition to the secondary PbS phase. This sodium segregation is detrimental to performance65, therefore, single-phase sodium doped PbTe is of interest in order to maximize the power factor.
Synthesis of the quaternary PbTe-PbSe-PbS system with sodium doping enables a greater power factor, similar to that in the PbTe-PbSe system, although a decrease in the Seebeck coefficient is seen due to the increased concentration of PbS, decreasing the power factor overall. In addition to the power factor modification, a simultaneous decrease in lattice thermal conductivity, similar to that in the PbTe-
PbS system, leads to a larger zT.
4.4 Method and Experimental Details
Sample Fabrication
Pure PbS was fabricated by mixing a stoichiometric ratio of Pb (99.999%) and S
(99.999%) and reacting at high temperature in an evacuated quartz ampoule, which is followed by furnace cooling. The Pb0.98Na0.02Te0.65-xSe0.35Sx (x = 0, 0.05, 0.10, 0.15,
0.20) samples were fabricated by mixing a stoichiometric ratio of high purity Pb
(99.999%), Se (99.999%), PbS, Te (99.9%), and Na (99.9%) in an evacuated carbon- CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS coated quartz ampoule and heating to 1100° C. Samples were held at that temperature for 10 hours to homogenise the melt, followed by water quenching.
These samples were then annealed at 550 °C for 72 hours. The resulting ingot was then hand ground into a fine powder and sintered using spark plasma sintering (SPS) under vacuum at an axial pressure of 40 MPa, 520 °C for 30 minutes.
Transport property measurements
The thermal diffusivity (휆) was measured using a Linseis LFA 1000 instrument with the laser flash method, and the thermal conductivity (휅) was calculated by 휅 =
퐶푝 × 휆 × 푑. The density (푑) was calculated using the measured weight and dimensions of the sample, and the specific heat capacity (퐶푝) was estimated using:
푇 퐶 (푘 푝푒푟 푎푡표푚) = (3.07 + 4.7 × 10−4 × ( − 300))33 푝 퐵 퐾
The resistivity (ρ) and Seebeck coefficient (S) were measured in a Linseis LSR-3.
The combined uncertainty for all measurements involved in zT determination is
~20%.
Hall measurements:
The low temperature (5 – 400 K) Hall coefficient was measured using a Quantum
Design Physical Properties Measurement System (PPMS-14T) up to 2T. The carrier concentration (n) is calculated from: n = 1/eRH, where e is the electronic charge and
RH is the Hall coefficient.
Materials characterisation
X-ray diffraction
The crystallographic structure and composition were determined using X-ray diffraction (XRD) with a GBCeMMA X-ray diffractometer with Cu Kα radiation (λ = CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
1.544 Å, 40 kV, 25 mA). The lattice parameters were calculated using Rietveld analysis of X-ray diffraction patterns.
Electron microscopy analyses
To study the microstructures of compositions 푥 = 0.05 and x = 0.15 the samples were hot mounted in Struers Polyfast conductive resin. Samples were first mechanically polished down to a 1 µm surface roughness followed by fine polishing using cross-sectional ion milling on a Leica TIC -020 operating at 2 kV for 20 minutes.
Scanning electron microscopy (SEM) on the samples was conducted in a JEOL JSM
7001F microscope equipped with Energy Dispersive X-ray Spectroscopy (EDS). The conditions for analysis were set at 15 kV, ~5.1 nA probe current, and 10 mm working distance fitted with an Oxford Instruments Nordlys-II camera interfacing with the
Aztec software suite.
4.5 Results and discussion
The X-ray diffraction patterns of all the samples are shown in Figure 4.1(a), which can be indexed to the NaCl type face-centred cubic (FCC) crystal structure, with no evidence of a secondary phase. As there is further alloying with PbS, the diffraction peaks are shifted to higher angles, as PbS has a smaller lattice parameter
(5.36 Å) than both PbTe (6.46 Å) and PbSe (6.12 Å). Rietveld refinement was utilised to accurately determine the lattice parameters of the matrix by extrapolating from high angle diffraction peaks. The lattice parameter as a function of the PbS concentration is shown in Figure 4.1(b). The lattice parameter decreases linearly with increasing PbS, following Vegard’s law for solid solutions. CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Figure 4.1 (a) XRD patterns of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0, 0.05, 0.10, 0.15,
0.20), showing diffraction peaks from the PbTe matrix. A shift of the peaks towards higher angles is
seen when PbSe is added and also as the PbS content increases; (b) Lattice parameter of p-type
(PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0, 0.05, 0.10, 0.15, 0.20) as a function of PbS content. CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
The microstructures of samples x = 0.05 and 0.15 were studied via scanning electron microscopy (SEM) equipped with electron dispersive X-ray spectroscopy
(EDS).
Micrographs in Figure 4.2 are representative of microstructures found in sample x = 0.05 and shows large variation in grain size comprising grains larger than 50 µm down to just a few microns. However, to the extent that SEM analysis permits no precipitates were found in the matrix. Figure 4.2(a) shows a magnified view of fewer grains, where grain boundaries are defined clearly without the apparent formation of precipitates. Moreover, a qualitative investigation of chemical composition was undertaken by point and area EDS analysis. These reported results of similar compositions across the grains suggesting that no secondary phases were formed and that the difference seen in grain’s contrast is due to their different crystallographic orientation.
Figure 4.2 – (a) SEM micrograph of sample 푷풃ퟎ.ퟗퟖ푵풂ퟎ.ퟎퟐ푻풆ퟎ.ퟔퟓ−풙푺풆ퟎ.ퟑퟓ푺풙 (풙 = 0.05). (b)
Micrograph representing marked area in solid red line in (a) CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Figure 4.3 micrographs correspond to sample x = 0.15, these are considered characteristic of the sample, showing homogeneous porosity within the grains and grain boundaries as seen in Figure 4.2(a). However, qualitative chemical analysis was conducted using EDS point and area analysis revealing no signs of secondary phases or precipitates. Figure 4.3(b) highlights delineated grain boundaries and grain contract is due to different crystallographic orientation.
Figure 4.3 - (a) SEM micrograph of sample 푷풃ퟎ.ퟗퟖ푵풂ퟎ.ퟎퟐ푻풆ퟎ.ퟔퟓ−풙푺풆ퟎ.ퟑퟓ푺풙 (풙 = 0.15). (b)
Micrograph representing marked area in solid red line in (a)
The resistivity and Seebeck coefficient of all the (PbTe)0.65-x(PbSe)0.35(PbS)x samples as a function of temperature are shown in Figure 4.4(a) and Figure 4.4(b), respectively. The addition of PbS does not have a significant effect on the resistivity, with the x = 0.05, 0.10, and 0.20 samples having a similarly high maximum resistivity of ~3.2 mΩ∙cm at 850 K, and the x = 0 and 0.15 samples have slightly lower ones at
~3 and ~2.8 mΩ∙cm, respectively. Figure 4.4(b) shows the Seebeck coefficients of all the samples as a function of temperature. An increase in the PbS content causes a systematic decrease in the Seebeck coefficient value at 850 K from ~ 250 µV/K for x = 0 to ~ 200 µV/K for x = 0.20. This decrease in the Seebeck coefficient can be CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS attributed to the expected larger energy band offset between the light and heavy hole bands obtained through alloying with PbSe and PbS44.
The energy of the light valence band (L) in PbTe is reduced with an increasing temperature until it reaches the heavy valence band (Σ)35, 46. The density of states
(DOS) in the Σ band is higher than the L band71 and it allows for a larger Seebeck coefficient than the L band alone, for a given carrier density. In heavily doped materials when these two valence bands converge at higher temperatures the Σ band is able to contribute to the electronic properties of the alloy, causing a maximum in power factor.
The band gap and the energy offset between the two valence bands in PbTe have been shown to be adjustable by alloying with PbSe and PbS35, 46. Electronic band structure calculations show that the Σ-band exists at a lower energy level than PbTe in both PbSe and PbS71, so it is expected that the heavy valence band would move to lower energy levels with PbSe and PbS alloying. This larger band offset decreases the effective mass (m*) and consequently lowers the Seebeck coefficient. The band gap of the (PbTe)0.65-x(PbSe)0.35(PbS)x system increases with added PbS70, and this causes a decrease in the contribution to electrical conduction by minority carriers72, which are thermally excited across the band gap, delaying the maximum Seebeck coefficient value to a higher temperature.
Figure 4.4(a) demonstrates that the resistivity value changes almost linearly with the temperature, and Figure 4.4(b) shows that the Seebeck coefficient reaches the plateau region at temperatures higher than 750 K, indicating that alloying with PbSe and PbS has increased the energy band offset, with the convergence of bands occurring at much higher temperatures. CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Figure 4.4 – Electronic transport properties of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x (x = 0, 0.05,
0.10, 0.15, 0.20) samples: (a) Resistivity; (b) Seebeck coefficient for all samples, the Seebeck
coefficient increases across the entire temperature range. The addition of PbS to this system
decreases the Seebeck coefficient for the PbTe rich samples. CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
The temperature dependence curves of the Hall coefficient (RH) of the (PbTe)0.65- x(PbSe)0.35(PbS)x samples (x = 0, 0.05, 0.10, 0.15, 0.20) exhibit extremely low RH values (Figure 4.5), in line with the high concentration of dopant, which resulted in a charge carrier concentration, n, of approximately 1 × 1020 - 3.5 × 1020 cm-3. The temperature dependence of the Hall coefficient for all the samples shows typical two-band behavior5: at low temperatures, RH is roughly constant, as the majority of the holes are located in the higher-energy-level L valence band44, 46; at temperatures above ~100 K, a significant upturn in RH is observed, due to an increased contribution to the electronic conduction by the Σ band, as, above this temperature, holes are able to populate both valence subbands.
Figure 4.5 Hall coefficient temperature dependence of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x (x = 0,
0.05, 0.10, 0.15, 0.20). CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Table 4.1 shows that the addition of PbS (band gap, Eg = 0.37 eV) to PbSe (Eg =
0.27 eV) and PbTe (Eg = 0.29 eV) increases the band gap of the alloy70. An increase in band gap delays the maximum Seebeck value to a higher temperature72, and in the
PbTe-PbSe system, allows the compound to reach a higher maximum Seebeck value due to the altered band structure30, although in the current set of samples, where the ternary system of (PbTe)0.65(PbSe)0.35 compound is alloyed with PbS, the Seebeck coefficient values are decreased by alloying at a constant Na dopant concentration
(1 at.% Na). This follows from the results seen previously in Figure 4.4(b), where an increased band offset decreases the effective mass and leads to the decrease in the
Seebeck coefficient.
Table 4-1 Carrier concentrations and band gaps of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x (x = 0, 0.05,
0.10, 0.15, 0.20).
Carrier concentration (cm-3) Composition Band Gap (eV) 70 Below 100K Room temperature
x = 0 1.7×1020 1.0×1020 0.305
x = 0.05 1.7×1020 1.0×1020 0.310
x = 0.10 2.7×1020 1.7×1020 0.318
x = 0.15 2.4×1020 2.0×1020 0.325
x = 0.20 2.5×1020 4.3×1020 0.335
CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Figure 4.6(a) shows the total thermal conductivity as a function of temperature for all (PbTe)0.65-x(PbSe)0.35(PbS)x samples. All samples show behaviour that is typical of heavily doped semiconductors, where the thermal conductivity decreases with increasing temperature. In a solid solution alloy, the lattice thermal conductivity can be decreased by replacing matrix atoms with larger mass-contrast atoms17. Here, the large mass contrast between the sulphur atoms and the tellurium matrix atoms causes a greater reduction in the lattice thermal conductivity with increasing Suplhur content, which originates from phonon scattering on solute atoms of sulphur-containing alloys35, 46. This explains the systematic decrease in thermal conductivity with PbS alloying of (PbTe)0.65(PbSe)0.35 (Figure 4.6(a)). The lattice thermal conductivity (κL) is shown in Figure 4.6(b) and is calculated by κL = κ
– ([1.5+e(-S/116)×10-3]×T/ρ) 12 CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
Figure 4.6 (a) Thermal conductivity of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0, 0.05,
0.10, 0.15, 0.20), with all samples showing a decrease in κ as T increases, as well as an overall
decrease as the PbS content increases in the PbTe rich samples; (b) Lattice thermal conductivity of
p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0, 0.05, 0.10, 0.15, 0.20), with all samples showing a decrease in κL as T increases, as well as an overall decrease as the PbS content increases in the PbTe
rich samples CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS
The room temperature Seebeck coefficient and resistivity were measured using home-built devices. The resistivity apparatus uses the van der Pauw method. The results in Table 4.2 show that the Seebeck coefficient decreases from ~50 µV/K to
~38 µV/K with added PbS and that there in an increase in the resistivity with additional PbS content at higher concentrations (x = 0.15, x = 0.20.) There is good agreement with the results from both the room temperature data obtained from the home-built devices (Table 4.2) and results obtained from the Linseis LSR (Figure
4.4).
Table 4-2 Room-temperature resistivity and Seebeck coefficient of p-type (PbTe)0.65- x(PbSe)0.35(PbS)x (x = 0, 0.05, 0.10, 0.15, 0.20).
Composition Resistivity (mΩ∙cm) Seebeck coefficient (µV/K)
x = 0 0.59 48.34
x = 0.05 0.61 50.39
x = 0.10 0.60 38.81
x = 0.15 0.76 39.56
x = 0.20 0.75 38.31
The calculated values for zT, from the measured results, of all the samples up to
850 K are shown in Figure 4.7. The thermal conductivity is improved with increasing
PbS content, although a simultaneous decrease in the Seebeck coefficient and increase in the resistivity occur with no overall benefit to zT. The x = 0, 0.05, and 0.10 CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS compounds have the highest zT of ~1.4 at 850 K. Comparing these 35% PbSe samples to the similarly doped 10% PbSe system26, which has a maximum zT of ~1.5 for 5% PbS, shows that there is no significant improvement in zT by alloying the
PbTe-PbSe system with a larger percentage of PbS.
Figure 4.7 Figure of merit (zT) of p-type (PbTe)0.65-x(PbSe)0.35(PbS)x samples (x = 0, 0.05, 0.10,
0.15, 0.20), showing a maximum zT for the x = 0, 0.05, and 0.10 samples, and a decrease in
thermoelectric performance with additional PbS content.
4.6 Conclusions
The maximum zT value for all the (PbTe)0.65-x(PbSe)0.35(PbS)x (x = 0, 0.05, 0.10,
0.15, 0.20) samples is ~1.4 at 850 K for three different samples (x = 0, 0.05, and 0.10).
This is slightly lower than for similarly alloyed systems with 10% PbSe26, although this is advantageous, as tellurium is a rare element and, as such, is increasing in CHAPTER 4 – Thermoelectric Performance of p-type Single-phase PbTe- PbSe-PbS value, so replacing it with sulphur without any significant detriment to the overall performance represents progress towards lower tellurium concentrations in thermoelectric materials.
CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
CHAPTER 5 –Thermoelectric Properties of
Quaternary Multiphase p-type Lead
Chalcogenides: Model Compared to Experiment
CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
5.1 Motivation
The quaternary multiphase PbTe-PbS-PbSe system has been shown to have a high zT of ~2, with the use of appropriate alloying and doping in order to optimise its thermoelectric properties. Further optimisation could lead to an increase in zT even higher than 2, and so a detailed understanding of the mechanisms that increase the thermoelectric properties of these multiphase samples is necessary in order to achieve such an improvement.
Single-phase lead chalcogenide alloys have beneficial properties such as reproducible behaviour on heating and cooling and low thermal conductivity without nanostructuring which makes them desirable to work with, however they have still not achieved the high zT that their multiphase counterparts have. By looking at the multiphase system as two single-phase compositions and learning which of the fundamental thermoelectric properties drive this high performance, it may be possible to take the best properties of these single-phase systems and combine them with the multiphase systems to increase their zT.
5.2 Abstract
The multiphase (PbTe)0.65(PbS)0.25(PbSe)0.1 sample shows an experimental value for the figure of merit zT of ~ 2, which is one of the highest ever reported. To understand such remarkable functionality, the constituents of its microstructure, consisting of the dominant matrix phase and secondary phase of precipitates, was previously analysed individually and as a combined composition both experimentally and with the help of the mixture model for two-phase materials. To accomplish this property analysis and compare it to the results for the high- CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment performing multiphase sample, the composition of the matrix and precipitate phases were established by three-dimensional atom probe tomography and found to respectively be Pb0.985Na0.015Te0.83Se0.09S0.08 and Pb0.94Na0.06Te0.06Se0.14S0.80. In this work these compositions have been individually synthesised and their properties measured. It is found that neither measured individual phase, nor the model is able to account for the high zT value obtained for the multiphase sample. Some moderate success is attained for the description of its thermal conductivity over the entire temperature range measured, as well as for the resistivity and Seebeck coefficient only up to ~600 K. However, at higher temperatures the resistivity of the multiphase sample exhibits significant change in its behaviour, ultimately leading to the high zT, which is not compensated by the reduction of the Seebeck coefficient. These changes are attributed to the behaviour of the energy band structure, which is not taken into account in the simplistic model, likely leading to the abrupt changes in the Hall coefficient indicating detrimental changes of charge carrier concentration.
5.3 Introduction
Solid-state thermoelectric generators, which convert heat to electricity if a heat gradient is applied, have been identified as candidates for waste heat recovery into usable energy7. The conversion efficiency is defined by the dimensionless figure of merit 5,
풛퐓 = 푺ퟐ흈푻/휿 (5.1)
where T is the operating temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity consisting of the lattice and electronic components of the thermal conductivity κL and κE, respectively. Recent CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment advances such as carrier optimisation and nanostructuring have increased the zT values from 1 to ~2 47, 73-74.
Amongst thermoelectric materials, lead chalcogenides have been shown high figure of merit values in the mid-range temperature region (600–900 K) 35. The ternary PbTe-PbSe and PbS-PbSe systems have been shown to have high zT due to suitable band structure engineering 43 increasing the power factor and decreasing the lattice thermal conductivity 10. The fabrication of a quaternary PbTe-PbSe-PbS system consisting of all 3 compounds with both n- and p-type doping has been shown to combine the benefits 35. The multiphase quaternary system has shown to decrease thermal conductivity and have a higher Seebeck coefficient with increased PbS content 25, 69. A secondary PbS phase in the PbTe system is reported to have a substantial impact on the resistivity in the PbTe-PbSe-PbS system 65. Changes in temperature lead to a variation in the chemical composition, which in turn leads to different resistivity behaviour on heating and cooling. Single-phase lead chalcogenides do not have such a variation 26, 44. Therefore, considering these differences upon optimising the thermoelectric transport properties of lead chalcogenides should lead to substantial enhancement of their properties by nanoengineering and/or simplification of their fabrication with designed properties.
A sodium doped (PbTe)0.65(PbS)0.25(PbSe)0.1 sample, hereafter referred to as the multiphase sample, was shown in a previous study to have two distinct phases consisting of a PbTe matrix and PbS precipitates by using transmission electron microscopy (TEM) 73, and three-dimensional atom probe tomography 75 identified the matrix and precipitates to possess compositions of Pb0.985Na0.015Te0.83Se0.09S0.08 and Pb0.94Na0.06Te0.06Se0.14S0.80, respectively. In this work, these exact two CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment compositions, hereafter referred to as the PbTe-rich and PbS-rich samples, respectively, were fabricated and measured separately and then their results combined and modelled using the series and parallel models 76, in a similar fashion as it also was done for two-phase magnetic materials 77.
The parallel and series models 76 are analytical models that have been used 78-80 to estimate a range of properties, such as electrical and thermal conductivities, of various two-phase materials, by considering the microstructure of a multiphase material as the summation of two separate individual phases or materials. These models calculate an upper and lower limit for each property. These extremes indicate the range of properties achievable in two-phase materials for nanoengineering, while single-phase compounds may exhibit only limited functionality.
The parallel model calculates the upper limits of the system and is given by the rule of mixtures76:
휏푃 = 휏1푓1 + 휏2(1 − 푓1) (5.2)
where 푓1 is the volume fraction of one phase, τ can be the thermal conductivity κ or electrical conductivity σ, and the series model to calculate the lower limit is given by76:
휏푆 = 휏1휏2/(휏1(1 − 푓1) + 휏2푓1) (5.3)
In the same manner, the Seebeck coefficient can be calculated with the parallel model by:
푆푃 = [푆1휎1푓1 + 푆2휎2(1 − 푓1)]/[휎1푓1 + 휎2(1 − 푓1)] (5.4)
Similarly, for the series model, we obtain:
푆푆 = [푆1휅2푓1 + 푆2휅1(1 − 푓1)]/[휅2푓1 + 휅1(1 − 푓1)] (5.5) CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
Analysing thermoelectric transport properties of multiphase materials with the help of these models can offer a vital approach for the zT enhancement in chalcogenides as well as in other multiphase systems.
In this work the models are employed by using the experimental data of both the
PbTe-rich and PbS-rich samples, and then comparing the modelled data to the experimental data from the multiphase sample across the entire temperature range.
5.4 Methods and Experimental Details
The PbTe-rich and PbS-rich samples are fabricated by mixing stoichiometry ratio of high purity Pb (99.999%), Se (99.999%), S (99.99%), Te (99.999+%) and Na
(99.9%) in an evacuated carbon-coated quartz ampoule and heated to 1100° C and held at that temperature for 6 hours to homogenise the melt, followed by water quenching. These samples are then annealed at 550° C for 72 hours. The resulting ingot is then hand ground into a fine powder and sintered using Spark Plasma
Sintering (SPS) under vacuum at an axial pressure of 40 MPa, 520° C for 30 minutes.
The thermal diffusivity of each sample was measured with a Linseis LFA 1000 using the laser flash method, whereby a laser is incident on the sample and a detector is used to capture phonons that are transmitted through the sample. Thermal conductivity is then calculated as
휅 = 퐶푃 × 휆 × 푑 . (5.6)
Samples used for thermal diffusivity measurement were 12mm in diameter and ~2mm in thickness, and these were then cut into a parallelepiped for electrical resistivity and Seebeck coefficient measurement. The density was calculated using CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment the measured weight and dimensions of the sample and the specific heat capacity
(Cp) was estimated using 33:
−4 퐶푃(푘퐵 푝푒푟 푎푡표푚) = (3.07 + 4.7 × 10 × (푇⁄퐾 − 300)) (5.7)
Electrical resistivity and Seebeck coefficient measurements are performed with a Linseis LSR-3 Seebeck Effect & Electrical Resistivity measurement device. The combined uncertainty for all measurements involved in zT determination is ~20%.
X-ray diffraction measurements were performed using a GBCeMMA X-ray diffractometer with Cu Kα radiation (λ = 1.544 Å, 40 kV, 25 mA). These measurements determine the crystallographic structure and composition of the samples, and the lattice parameters are calculated using Rietveld analysis of the X- ray diffraction patterns.
5.5 Results and Discussion
Figure 5.1 shows the XRD patterns of both the PbTe-rich and PbS-rich samples.
Both samples show a single-phase structure, only containing diffraction peaks from their PbTe and PbS matrices respectively, having an NaCl type Face-Centred-Cubic crystal structure.
The PbTe matrix diffractions peaks in Figure 5.1(a) are labelled in black, and the
PbS matrix in Figure 5.1(b) labelled in red. The PbS matrix diffraction peaks have the same Miller indices as PbTe due to the similar crystal structure but occur at slightly higher angles because of the different lattice parameters. These patterns show pure single-phase samples. For multiphase samples, diffraction peaks from both the PbTe matrix and PbS precipitates were observed73. CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
Rietveld refinement was utilised to accurately determine the lattice parameters of the matrix in both the PbTe-rich and PbS-rich samples by extrapolating from high angle diffraction peaks. The PbTe-rich sample has a lattice parameter of 6.38 Å, while the PbS-rich sample has a lattice parameter of 5.96 Å. This agrees well with calculated values of 6.39 Å and 5.98 Å, respectively. The alloying of PbSe and PbS in the PbTe-rich compound causes the overall PbTe lattice to decrease in size due to the alloying effect 10. Since PbS has a smaller lattice parameter (5.36Å) than both
PbTe (6.46 Å) and PbSe (6.12 Å)5; hence, conversely the PbTe and PbSe alloying in the PbS-rich sample causes the PbS lattice to increase in size.
Figure 5.1 Powder XRD diffraction patterns of the PbTe-rich and PbS-rich samples. CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
The resistivity (ρ) and Seebeck coefficient (S) of the PbTe-rich, PbS-rich and multiphase samples are shown as a function of temperature in Figure 5.2. Among the three samples, the PbS-rich sample (shown by red symbols in Figure 5.2(a)) has the highest resistivity over the entire temperature range. The multiphase sample, shown in green solid symbols, has similar behaviour to the PbTe-rich sample at low temperatures, while it shows the lowest resistivity of the three samples after its resistivity plateaus above 650 K.
The multiphase sample appears to have degenerate semiconducting properties with non-metallic resistivity behaviour above ~600 K, in contrast to the other single-phase samples showing rather metallic-like behaviour with the PbS-rich sample having the most pronounced metallic properties with a linear temperature dependent resistivity. Hence, such resistivity behaviour of the multiphase sample is most likely the result of the alloying PbTe and PbS phases.
The Seebeck coefficient, seen in Figure 5.2(b), increases with temperature for all samples. The increase is linear for PbS-rich sample over the entire measured temperature range and for the other two samples up to ~600 K, which is expected for an extrinsic degenerate semiconductor 81. Above 660 K, for the PbTe-rich sample,
S continues to rise at a slower rate, exhibiting a peak at around 800 K. For the multiphase sample, S shows a maximum at 700 K and decreases levelling at the value similar to the PbS-rich sample.
The maximum in the S behaviour was explained to be due to convergence of the heavy (Σ) and light (L) valence bands 44. The energy of the L band in these two samples is reduced with an increasing temperature until it reaches the Σ band 35, 46. CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
Once these two valence bands converge at higher temperatures, the Σ band is able to contribute to the electronic properties of the alloy, causing a maximum in Seebeck coefficient. At the same time, the PbS-rich sample may have a modified band structure, as indicated by its mostly metallic resistivity dependence in Figure 5.2(a), and/or a compensating effect of the constituents contributing to the Seebeck coefficient81, leading to the linear temperature behaviour. The maximum Seebeck coefficient differs among samples, with the PbTe-rich having a maximum ~275 µV/K at ~825 K, the multiphase having a maximum of ~250 µV/K at ~700 K, while the
PbS-rich attains the value of ~225 µV/K at the maximum measured temperature of
~850 K.
The parallel and series models76 are employed for understanding and ultimately predicting the behaviour of complex multiphase samples. The calculated model curves by using Equations 5.2 and 5.3 are shown by the solid lines in Figure
5.2. Neither fully describe the behaviour of the multiphase sample for its conductivity data (σ = 1/ρ) in Figure 5.2(a). The parallel model (Equation 5.2) approximates the multiphase sample only until ~575 K. By coincidence, the series model (Equation 5.3) for the conductivity well describes the behaviour of PbS-rich sample, while the parallel model (Equation 5.2) approximates the PbTe-rich sample
(Figure 5.2a) over the entire measured temperature range.
The parallel and series models (Equations 5.4 and 5.5, with κ taken from
Figure 5.3) are also calculated for the Seebeck coefficient results shown in Figure
5.2(b). Again, neither of the models fully describe the multiphase sample. However, both models accurately follow its S(T) behaviour until ~650 K. The experimental CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment result deviation from the model curves can be attributed to a step-like increase in
Hall coefficient for highly doped two phase PbTe-PbSe-PbS samples 73 at 600 K that is not accounted for by these models. The PbTe-PbS interface was shown to restructure at high temperatures, contributing to the redistribution of sodium between the PbS secondary phase and PbTe matrix 73. This may lead to the step-like change in Hall coefficient, pointing at corresponding changes in charge carrier concentrations. The drop in Seebeck coefficient is typically associated with the increased concentration of charge carriers81. Notably, the deviation and decrease in
Seebeck coefficient in the multiphase sample from the behaviour of the PbTe-rich sample to the Seebeck coefficient value of the PbS-rich sample, which exhibits the linear metallic-like resistivity, which is the highest among the three samples investigated. CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
Figure 5.2 LSR results for electrical resistivity (a) and Seebeck coefficient (b) of the PbTe-rich,
PbS-rich and multiphase samples. The parallel and series model curves are shown by the solid lines.
In (b), the parallel and series model curves visually overlap. CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
Figure 5.3 shows the thermal conductivity as a function of temperature for the samples measured. Unlike for the resistivity and the Seebeck coefficient, all samples show qualitatively similar behaviour with the desired decreasing thermal conductivity upon increasing temperature up to ~550 K, indicating a typical behaviour of extrinsic semiconductors with the increased carriers scattering off the crystal lattice. However, the thermal conductivity levels out at T > 550 K, pointing at the increasing role of phonons at high temperatures. The experimental data coinciding for the multiphase and PbTe-rich sample indicate that the thermal conductivity in the multiphase sample is dominated by its PbTe-matrix properties.
The calculated parallel model curve accounts well for the behaviour of the multiphase sample over the entire measured temperature range, in contrast to the resistivity and the Seebeck coefficient. The calculated series model curve nearly entirely overlaps with the data for the PbS-rich sample.
CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
2.6
K) 2.4 PbTe-rich 2.2 PbS-rich 2.0 Multiphase Parallel model 1.8 Series model 1.6 1.4 1.2 1.0
Thermal Conductivity (W/m 0.8 300 400 500 600 700 800
Temperature (K)
Figure 5.3 Thermal Conductivity of the PbTe-rich, PbS-rich and multiphase samples. The
calculated parallel and series models are shown by the solid curves.
The calculated parallel model curve accounts well for the behaviour of the multiphase sample over the entire measured temperature range, in contrast to the resistivity and the Seebeck coefficient. By coincidence, the calculated series model curve follows the data for PbS-rich sample.
In Figure 5.4, the experimental data for zT calculated using Equation 5.1 for all the samples are shown along with the calculated results for both models. The figure of merit zT for the multiphase sample is increasing with temperature and is higher than its constituent single-phase samples over the entire measured temperature range, spectacularly reaching the maximum zT of ~ 2 at the highest CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment measured temperature of 850 K. Among the individual phase samples, the highest zT ~ 1.3 is obtained at T ~ 740 K for the PbTe-rich sample. The PbS-rich sample shows a quasi-linear increase with increasing temperature reaching the highest value of zT ~ 0.65. The zT for the PbS-rich sample is consistently well below the other two samples measured.
In general, the parallel and series models, utilised to help in understanding the behaviour of the multiphase sample, dramatically underestimate its zT-values and show no qualitative resemblance to its experimental result. According to
Equation 5.1 and the results obtained in Figures 5.2 and 5.3, the major contributing factor for the spectacularly large value of zT reaching nearly 2 is due to its significantly lower electrical resistivity for T > 570 K (Figure 2a), which is not accounted for by any of the models employed. It may be noted that by coincidence the parallel model somewhat follows the PbTe-rich sample behaviour, showing the maximum zT of 1.4 at T ~775 K, which is still significantly lower than the maximum value for the multiphase sample. CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment
2 PbTe-rich PbS-rich Multiphase Series model Parallel model
T
z 1
0 300 400 500 600 700 800 Temperature (K)
Figure 5.4 Figure of Merit (zT) of the PbTe-rich, PbS-rich and multiphase samples. The calculated
model curves are plotted by the solid lines.
5.6 Conclusions
The PbTe-PbS-PbSe multiphase sample shows a remarkable zT value of ~2, which is one of the highest ever reported. The PbTe-rich and PbS-rich samples resembling the two main phases which comprise the multiphase sample are investigated, with the PbTe-rich composition being the matrix of the multiphase sample, while the PbS-rich composition is dispersed within this matrix. The PbS-rich sample shows the lowest zT values not exceeding 0.65, while the PbTe-rich sample shows a maximum value zT ~1.3 at T ~ 775 K. The results clearly show that the PbTe- rich sample has dominant role in determining the properties of the multiphase sample below 600-700 K. It is worthwhile noting that PbTe-rich phase shows CHAPTER 5 –Thermoelectric Properties of Quaternary Multiphase p-type Lead Chalcogenides: Model Compared to Experiment degenerate semiconductor properties with high charge carrier densities. At the same time, the PbS-rich phase shows rather metallic-like behaviour with a linear temperature dependence of resistance (Figure 5.2a), which has somewhat lower charge carrier densities as may be evident from the Seebeck coefficient results
(Figure 5.2b).
The dispersion of the PbS-phase in the PbTe-matrix leads to the substantial enhancement in the electrical conductivity above ~600 K, which in turn results in the dramatic enhancement of zT (Figure 5.4). The notable degradation of the
Seebeck coefficient above ~700 K (Figure 5.2b) does not compensate the effect of the significant conductivity boost.
Neither series nor parallel model, used to explain heterogeneous systems, is shown to describe the multiphase sample consistently over the entire temperature range for zT and all measured parameters determining zT in Equation 5.1.
Of the two models, the parallel model shows a closer overall behaviour to the multiphase sample properties. The closest match between the multiphase sample and the parallel model is obtained for the thermal conductivity (Figure 5.3).
The parallel model also shows reasonable descriptions for the resistivity below
600 K and for the Seebeck coefficient below 700 K (Figure 5.2). Nevertheless, even the parallel model significantly underestimates zT of the multiphase sample, which is due to peculiarities of the band structure associated effects affecting the general behaviour of the system and the Seebeck effect in particular.
The band structure effects are obviously not taken into account by such rather simplistic mixture models. Hence, in the case of this complex system, the models are unreliable for predictions of thermoelectric properties and functionalities.
CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
CHAPTER 6 – Characterisation of the Undoped
PbTe-PbSe Series
CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
6.1 Motivation
The study of lead chalcogenides forms the basis of this thesis, and while they are well researched as high performing thermoelectric materials when combined with suitable dopants, the study of many of these compounds as undoped alloys has not been performed. There has been research performed on pure PbTe and PbSe, but not the series as a whole82.
Here, the undoped PbTe-PbSe series is characterised, and knowing the fundamental thermoelectric properties of this system will be instrumental in deciding what further research to do with lead chalcogenides, with the possibility of achieving a zT above 2, and future work can be done on implementing these compounds in a thermoelectric device.
6.2 Abstract
The undoped series (PbTe)1-x(PbSe)x was synthesized and its thermoelectric properties measured. These compositions are promising thermoelectric materials and understanding the behaviour of their properties is important to increase the zT for lead chalcogenides and their alloys. Adding PbSe to PbTe significantly altered the
Seebeck coefficient, decreased the thermal conductivity, with a minimum for the x = 0.70 sample and increased the resistivity, with a maximum for the x = 0.50 sample. Using these results to optimise the material’s properties, and additionally further introducing appropriate doping, it is possible to increase zT for lead chalcogenides. CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
6.3 Introduction
Thermoelectric devices have been established as a useful candidate for harnessing waste heat. Their ability to convert heat to electricity has widespread applications, and a better understanding of how these materials work could lead to an improvement in efficiency. The conversion efficiency of a thermoelectric material is defined by the dimensionless figure of merit,
zT = (S2σT/κ) (6.1)
where T is the operating temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity. Lead chalcogenides have had recent improvements in efficiency due to alterations in band structure and by using nanostructured multiphase materials to achieve a zT of ~2, which is one of the highest in the mid-range temperature region (600–900 K). The ternary PbTe-PbSe and PbS-PbSe systems have been shown to have high zT due to band structure engineering increasing the power factor and by decreasing the lattice thermal conductivity. The multiphase PbTe-PbS and system has shown to decrease thermal conductivity by the use of nanostructuring and have a higher Seebeck coefficient with increased PbS content 25, 69.The fabrication of PbTe-PbSe-PbS simultaneously to form a quaternary system with both n- and p-type doping has been shown to combine the benefits35 of the ternary systems.
The PbTe-PbSe system is a solid solution across the entire composition range70, with an NaCl type Face-Centred-Cubic crystal structure. The lattice parameter of PbTe (6.46 Å) is larger than PbSe (6.12 Å) and so as PbSe is added to
PbTe the lattice parameter linearly decreases. A greater understanding of the PbTe-
PbSe system will lead to improvements in the thermoelectric performance of lead CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
chalcogenides, as it can be further alloyed with PbS to form a quaternary PbTe-PbSe-
PbS26, 69 system as well as introducing p- and n-type doping to increase zT.
X-ray diffraction (XRD) measurements were performed on the PbTe-PbSe series by Patterson et al.70, and the results show a single-phase solid solution across the whole system with a linear decrease in lattice parameter with increasing amounts of PbSe. In the same work, measurements of the band gap indicate a bowing, with a maximum band gap for the (PbTe)0.50(PbSe)0.50 composition.
6.4 Method and Experimental Details
The (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70, 0.85, 1) samples are fabricated by mixing a stoichiometric ratio of high purity Pb (99.999%), Se
(99.999%) and Te (99.999+%) in an evacuated quartz ampoule, heated to 1100° C and held at that temperature for 6 hours to homogenise the melt, followed by furnace cooling. The resulting ingot is then hand ground into a fine powder and sintered using Spark Plasma Sintering (SPS) under vacuum at an axial pressure of 40 MPa,
550° C for one hour.
A Linseis LFA 1000 is used to measure the thermal diffusivity, which utilizes the laser flash method. A laser is incident on the sample and a detector is able to capture phonons transmitted through the sample. The thermal conductivity is then calculated by
휅 = 퐶푃 × 휆 × 휌 (6.2)
Samples used for thermal diffusivity measurement were 12mm in diameter and ~2mm in thickness, and these were then cut into a parallelepiped for electrical resistivity and Seebeck coefficient measurement. The density was calculated using CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
the measured weight and dimensions of the sample and the specific heat capacity
(Cp) estimated using:
−4 33 퐶푃(푘퐵 푝푒푟 푎푡표푚) = (3.07 + 4.7 × 10 × (푇⁄퐾 − 300)) (6.3)
The electrical resistivity (ρ) and Seebeck coefficient (S) are measured in a
Linseis LSR-3 Seebeck Effect & Electrical Resistivity measurement device. The combined uncertainty for all measurements involved in zT determination is ~20%.
The crystallographic structure and composition were determined using X-ray diffraction (XRD) with a GBCeMMA X-ray diffractometer with Cu Kα radiation (λ =
1.544 Å, 40 kV, 25 mA). The lattice parameters are calculated using Rietveld analysis of the X-ray diffraction patterns. 83
6.5 Results and Discussion
The resistivity and Seebeck coefficient of all samples are shown as a function of temperature in Figure 6.1(a) and (b), respectively. Across the entire temperature range pure PbSe and PbTe have the lowest resistivities, with PbSe having the lowest resistivity of ~2 mΩcm, PbTe is the next highest of ~8 mΩcm and both increasing to
~13 mΩcm at 850 K. The carrier mobility in the PbTe-PbSe system is lower than that in pure telluride or selenide5, which leads to the increase in resistivity for the alloyed samples. For these alloyed compositions, the resistivities at maximum temperature increase with added PbSe content, starting at ~13 mΩcm for x = 0.10 and increasing to ~24 mΩcm for x = 0.85. CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
500 125 (PbTe) (PbSe) a) (PbTe) (PbSe) b) 1-x x 400 1-x x
cm) x = 0 x = 0
V/K) x = 0.10 x = 0.10 100 300 x = 0.15 x = 0.15 x = 0.35 200 x = 0.35 75 x = 0.50 x = 0.50 x = 0.70 100 x = 0.70 x = 0.85 x = 0.85 50 x = 1 0 x = 1 -100 25 -200
Seebeck Coefficient ( Electrical Resistivity (m 0 -300 300 400 500 600 700 800 300 400 500 600 700 800 Temperature (K) Temperature (K)
500 125 (PbTe) (PbSe) a) (PbTe) (PbSe) b) 1-x x 400 1-x x cm) x = 0 x = 0
V/K) x = 0.10 x = 0.10 100 300 x = 0.15 x = 0.15 x = 0.35 200 x = 0.35 75 x = 0.50 x = 0.50 x = 0.70 100 x = 0.70 x = 0.85 x = 0.85 50 x = 1 0 x = 1 -100 25 -200
Seebeck Coefficient ( Electrical Resistivity (m 0 -300 300 400 500 600 700 800 300 400 500 600 700 800 Temperature (K) Temperature (K)
Figure 6.1 (a) Resistivity of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70, 0.85, 1); (b)
Seebeck Coefficient of (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70, 0.85, 1) Coloured lines
connecting data points are fitted as a visual guide. CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
Table 6.1 contains the band gaps of all samples. The band gap increases with
addition of PbSe to PbTe up to a maximum with the x = 0.50 sample and then
decreases with further PbSe. This bowing coincides with the maximum resistivity in
the x = 0.50 composition and high absolute Seebeck coefficient of ~250 μV/K.
Table 6.1 Band Gap of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70, 0.85, 1)
Composition x = 0 x = 0.10 x = 0.15 x = 0.35 x = 0.50 x = 0.70 x = 0.85 x = 1
Band Gap (eV)70 0.293 0.2975 0.296 0.2925 0.2985 0.288 0.2795 0.27
Figure 6.2 shows the thermal conductivity as a function of temperature for all
compositions. All samples show typical behaviour of intrinsic semiconductors,
where the thermal conductivity decreases with increasing temperature followed by
an increase at higher temperatures due to the influence of minority carriers10. A
decrease in thermal conductivity with alloying is attributed to phonon scattering
from the disorder arising from the introduction of solute atoms46. CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
2.2 0.6 (PbTe) (PbSe) (PbTe)1-x(PbSe)x x = 0 1-x x 2.0 x = 0 x = 0.10 0.5 x = 0.10 1.8 x = 0.15 x = 0.15 x = 0.35 1.6 0.4 x = 0.35 x = 0.50 x = 0.50 1.4 x = 0.70 T 0.3 z x = 0.70 x = 0.85 1.2 0.2 x = 0.85 x = 1 x = 1 1.0 0.1 0.8 0.0
Thermal Conductivity (W/m.K) Conductivity Thermal 0.6 300 400 500 600 700 800 300 400 500 600 700 800
Temperature (K) Temperature (K)
Figure 6.2 Thermal Conductivity of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70,
0.85, 1) Coloured lines connecting data points are fitted as a visual guide.
The calculated zT of all samples using the experimental data is shown in
Figure 6.3. Pure PbSe has the highest zT over the entire temperature range as it has a significantly lower resistivity compared to all other compositions. The high PbTe content samples (x = 0, 0.10, 0.15) have higher zT at room temperature whereas the high PbSe content samples (x = 1, 0.85, 0.70) have higher zT’s at high temperature due to an improved thermal conductivity. CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
0.6 (PbTe)1-x(PbSe)x
0.5 x = 0 x = 0.10 x = 0.15 0.4 x = 0.35 x = 0.50 T 0.3 z x = 0.70 x = 0.85 0.2 x = 1 0.1
0.0 300 400 500 600 700 800
Temperature (K)
Figure 6.3 zT of undoped (PbTe)1-x(PbSe)x (x = 0, 0.10, 0.15, 0.35, 0.50, 0.70, 0.85, 1) Coloured lines
connecting data points are fitted as a visual guide.
6.6 Conclusions
The alloying of PbTe with PbSe decreases the thermal conductivity compared to the individual compounds, increases the resistivity and significantly changes the
Seebeck coefficient.
By choosing an alloy such as the x = 0.50 composition, which has a low thermal conductivity and relatively high Seebeck coefficient, and adding a suitable dopant there may be a large increase in zT for thermoelectric power generation. Although this composition has the highest resistivity, the addition of a dopant would significantly decrease this and make it a viable candidate with high thermoelectric CHAPTER 6 – Characterisation of the Undoped PbTe-PbSe Series
performance. Future work could consist of optimization of this doping, and possibly trialing these compositions as both n- and p-type semiconductors.
CHAPTER 7 – Thesis Conclusions and Future Work
CHAPTER 7 – Thesis Conclusions and Future
Work
CHAPTER 7 – Thesis Conclusions and Future Work
7.1 Thesis Conclusions and Future Work
Lead chalcogenides are versatile compounds with a wide range of applications as thermoelectric materials. Chapter 4 looked at single-phase quaternary PbTe-PbSe-PbS with the aim of increasing zT, however it did not increase compared to similar multiphase compositions. The addition of PbS in fact decreased the Seebeck coefficient significantly, so that the maximum zT across the compositions investigated was only ~1.4. These alloys would likely not be used in a thermoelectric device as there are better performing materials.
Chapter 5 investigated multiphase lead chalcogenides, specifically the quaternary PbTe-PbSe-PbS system whereby the material has already shown to have extremely high performance. Looking at the multiphase material as the summation of two single-phase materials, more information can be determined about the thermoelectric properties of lead chalcogenides. Interestingly, the models significantly underestimated the performance of the multiphase material, with a low resistivity leading to the high zT in the multiphase sample. Comparing this multiphase sample to the single-phase composition in Chapter 4, it is clear that multiphase lead chalcogenides are a viable candidate for use in thermoelectric devices. Future research into the optimisation of these multiphase compounds with different alloying and doping could lead to a further increase in zT.
Chapter 6 characterised the PbTe-PbSe undoped series, and these alloys form the basis of lead chalcogenides as thermoelectric materials. Alloying these compounds greatly changes all of the thermoelectric properties in different ways, and it is important to know how these compositions will behave in order to choose CHAPTER 7 – Thesis Conclusions and Future Work
a suitable option for use in a thermoelectric device. Future work could consist of adding different dopants and different amounts of dopant to this system to increase zT, however this would again change the thermoelectric properties, requiring further research to find the optimal doping concentration for a given composition.
There are a large variety of lead chalcogenide compositions that have been studied, however there are still further combinations of alloys that have not been looked at. Adding to the fact that lead chalcogenides can be both p- and n-type semiconductors, there are endless combinations of alloys and dopants that can be investigated with the possibility of achieving a zT higher than any current thermoelectric materials. Using the knowledge obtained from the experiments and results in this thesis, further research can be done on lead chalcogenides as thermoelectric materials to improve their performance and increase zT to a point where these materials can be applied in many more thermoelectric devices, and efficient renewable energy can be created and used around the world.
CHAPTER 8 – References
CHAPTER 8 - References
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