THESIS. Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Transcription

1 P-type thermoelectric materials for waste heat recovery system : P-type Mg 2 Sn 1-x Si x and Pb 1-x-y Eu x Se:Na y THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Sunphil Kim Graduate Program in Mechanical Engineering The Ohio State University 2014 Master's Examination Committee: Joseph P. Heremans, Advisor Igor V. Adamovich

2 Copyright by Sunphil Kim 2014

3 Abstract The combination of three material properties (Seebeck coefficient, electrical conductivity, and thermal conductivity) defines a thermoelectric materials' efficiency : the figure of merit ( ). The main challenges in the applications of thermoelectric materials are their relatively low efficiency and their cost. For these reasons, we explore two cost-effective thermoelectric materials, namely Mg 2 Sn 1-x Si x and Pb 1-x-y Eu x Se: Na y, which are aimed at high temperature applications, such as waste heat recovery. The primary goal of this study is to have a better understanding on fundamental transport physics in thermoelectricity, to achieving high figures of merit. First, p-type undoped and Ag-doped Mg 2 Sn 1-x Si x (x=0, 0.05, 0.1 ) are synthesized by a co-melting method with sealed crucibles. Thermoelectric, thermomagnetic and galvanomagnetic properties of the samples are investigated. It turns out that while Ag effectively dopes the samples p-type, addition of Si (x) creates additional electrons through native defects. From measured Seebeck coefficient, Nernst coefficient, and mobility, we find that the combination of acoustic phonon scattering (λ = -0.5) and optical phonon scattering (λ = +0.5) is dominant in Ag-doped Mg 2 Sn 1-x Si x (X=0, 0.05, 0.1). Also, effective masses determined from the theoretically calculated Pisarenko ii

4 relation of Ag-doped Mg 2 Sn 1-x Si x (x=0, 0.05, 0.1) vary from 0.5 to 0.7 with respect to hole concentrations. The second project is carried out on Na doped Pb 1-x-y Eu x Se. EuSe is chosen as a nanoscattering agent in PbSe to reduce the lattice thermal conductivity. Compared to Pb 1-y Se : Na y, alloys of Pb 1-x-y Eu x Se : Na y, (y = 0.01) show significant reduction in carrier concentration and mobility. To further study this observed phenomenon, magnetic properties such as Magneto-Resistance, susceptibility, and magnetization are also explored and reported. From the obtained data, several interesting observations are made. First, all the tested samples of Pb 1-x-y Eu x Se : Na y, (y = 0.01; x 0.01) show negative magneto-resistance, indicating scattering of sp hybridized electrons in PbSe on 4f levels of Eu. Second, we fit the magnetization data to a model, which takes into account the antiferromagnetic contributions of singles, pairs, and triplets of Eu atoms to the magnetization. This suggests the existence of antiferromagnetic interactions in Eu atoms. Third, pure Curie-Weiss behavior is observed in all the tested samples with a small negative Curie-Weiss temperature, confirming the existence of weak antiferromagnetic interactions between Eu 2+ ions. Also, the exchange coupling ( ) determined from the Curie-Weiss law was in good agreement with that estimated from magnetization fitting. Last, as the Na doping level, y, is increased in alloys of Pb 1-x-y Eu x Se : Na y, (x = 0.01; y 0), a dramatic decrease in magnetization is observed, suggesting a charge transportation between Na + and Eu 2+. This is also the dominant mechanism that results in decreased carrier concentration with an increase in EuSe in PbSe. iii

5 To my family iv

6 Acknowledgments I was very fortunate to have studied under Prof. Heremans' advise. His profound knowledge and passion in condensed matter physics encouraged me to study fundamental transport physics, led me to explore many projects during my time at the Ohio State University, and gave me more confidence about continuing my graduate study. I would also like to acknowledge my laboratory members: Audrey Chamoire, Christoper Jaworski, Michele Nielsen, Hyungyu Jin, Yibin Gao, Eric Evola, Bin He, Michael Adams, and Sarah Watzman. With their help, I was able to overcome many challenges I faced while working on different projects. These studies were conducted in collaboration with many research groups around the world: Bartlomiej Wiendlocha's theoretical calculations such as Pisarenko relation and band structure were incredibly helpful in completing the projects on p-type Mg 2 Sn 1-x Si x and Pb 1-x-y Eu x Se: Na y. Also, Prof. Vidvuds Ozolins' bandstructure and phonon dispersion calculations in alkali-based I-V-VI 2 were crucial in initiating Li-V-VI 2 project. Lastly, I would like to acknowledge NSF and the DOE EFRC program for their generous funding that supported my study at OSU. v

7 Vita B.S. Mechanical, Seoul National University of Science and Technology(Seoul Tech), Seoul, Korea; B.S. (Dual Degree) Manufacturing System and Design Engineering, Northumbria University, Newcastle, UK to present...graduate Research Associate, Department of Mechanical Engineering, The Ohio State University Publications SP. Kim, H. Jin, B. Wiendlocha, J. Tobola, J. P. Heremans, " Electronic structure and thermoelectric properties of p-type Ag doped Mg 2 Sn 1-x Si x, (x = 0, 0.05, 0.1)", publication in preparation. SP. Kim, Y. Lee, B. Wiendlocha, YB. Gao, B. He, M. G. Kanatzidis, D. T. Morelli, and J. P. Heremans "s-f scattering, Negative Magneto-Resistance, and Eu 2+ - Eu 3+ Transition in Pb 1-xyEu x Se:Na y ", publication in preparation. Fields of Study Major Field: Mechanical Engineering vi

8 Table of Contents Abstract... ii Dedication... iv Acknowledgments... v Vita... vi List of Tables... ix List of Figures... x Chapter 1 : Introduction to thermoelectrics Motivation Thermoelectric effects Seebeck effect Peltier effect Thomson effect Thermoelectric efficiency History and recent advances in thermoelectric materials...10 Chapter 2 : Transport measurement and error analysis...13 Chapter 3 : p-type Mg 2 Sn 1-x Si x (x=0,0.05,0.1) Motivation and literature review...18 vii

9 3.2 Sample preparation of Mg 2 Sn 1-x Si x (x=0,0.05,0.1) Result and discussion Undoped Mg 2 Sn 1-x Si x (x=0, 0.05, 0.1) Ag doped Mg 2 Sn 1-x Si x (x=0, 0.05, 0.1) Chapter 4 : Pb 1-x-y Eu x Se : Na y Motivation and literature review Sample preparation of Pb 1-x-y Eu x Se : Na y Results and discussion Thermoelectric properties of Pb 1-x-y Eu x Se :Na y Magnetization of Pb 1-x-y Eu x Se : Na y...41 Conclusion...52 References...54 viii

10 List of Tables Table 1. Actual Eu 2+ obtained from magnetization data fitting ix

11 List of Figures Figure 1.Annual energy flow diagram during 2013 in the US, adapted from Ref.[1] Figure 2. Schematic drawing of a device that demonstrates the Seebeck effect... 3 Figure 3. Commercially available thermoelectric module for cooling or heating application... 5 Figure 4. Schematic drawings of (a) TE power generator with n- and p- type legs (b) its Seebeck(α = S/e) - temperature(t) thermodynamic cycle (c) entropy(s)-temperature(t) relation in Carnot cycle... 6 Figure 5. Thermoelectric properties as a function of carrier concentration... 7 Figure 6. Normalized thermoelectric efficiency of thermoelectric generator as a function of for various temperature difference... 8 Figure 7. Evolution of the maximum ZT from 1940 to present. The figure shows significant improvement in after the contribution of Hicks and Dresselhaus to the field. Blue dots represent thermoelectric cooling while red ones are for power generation, adapted from Ref. [6] Figure 8. An actual picture of a cryostat. The cryostat was used to measure thermoelectric properties of a material x

12 Figure 9. (a) A mounted sample to measure thermoelectric properties. (b) A schematic drawing of a mounted sample. This mounted sample was placed in the cryostat to measure its thermoelectric properties Figure 10. A Quantum Design PPMS puck with a mounted sample. Magnetoresistance (MR) measurements were conducted in a longitudinal external magnetic field Figure 11. Binary phase diagram of Mg and Sn, adapted from Ref. [31] Figure 12. Obtained Mg 2 Sn ingot fabricated by co-melting method with a sealed graphite crucible Figure 13. (a) Powder XRD pattern for Mg 2 Sn 1-x Si x (x = 0, 0.05, 0.1) (b) DSC latent heat trace of Mg 2 Sn Figure 14. Temperature dependent thermoelectric properties of undoped Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) (a) Seebeck coefficients (b) Resistivity (c) Hall resistivity of undoped Mg 2 Sn from 120K to 180K (d) Inverse ρ H divided by electric charge of the undoped samples Figure 15. Temperature dependent thermoelectric properties of Ag doped Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) (a) hole concentration (b) Seebeck coefficient (c) resistivity (d) mobility Figure 16. (a) Scattering parameter of Ag doped Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) calculated from measured Seebeck(α), Nerst(N), and Mobility(μ) (b) The obtained data from this work and previously reported values of Seebeck(α) and hole concentration(p) at 300K plotted on the calculated Pisarenko plot with λ = xi

13 Figure 17. Theoretically calculated effective masses (m*) as a function of carrier concentration (p) Figure 18. Power factor of Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) doped with Ag for different hole carrier concentration, p Figure 19. Temperature-dependent thermoelectric properties of Pb 1-x-y Eu x Se : Na y Figure 20. Schematic drawings of the alignment of magnetic moments in paramagnetic material, adapted from Ref.[56] (a) Disordered arrangement of magnetic moments in the absence of an external field. (b) The response when a field of moderate strength is applied Figure 21. Magnetoresistance of Pb 1-x-y Eu x Se : Na y (x =0, y = 0.01) from -70kOe to 70kOe at 2k, 4k, 6k, and 8k Figure 22. Magnetoresistance of alloys of Pb 1-x-y Eu x Se : Na y at each temperature (2k,4k,8k, and 16k). The sample label is (y = 0.01; x= 0.01( ), 0.02( ), 0.03( ), 0.04( ), 0.09( ), and 0.12( )) Figure 23. Magnetoresistance as a function of inverse temperature (1/T) for Pb 1-x-y Eu x Se : Na y (y = 0.01; x = 0.04, 0.09, and 0.12) Figure 24.(a) Magnetization of Pb 1-x-y Eu x Se : Na y (y = 0.01) with varying Eu level (x) as a function of magnetic field (b) Magnetization of Pb 1-x-y Eu x Se : Na y (x = 0.01) with varying Na doping level (y) as a function of magnetic field Figure 25. Comparison between a model with a Brillouin function, M BR,which considers no interaction between Eu ions (Brillouin function) and a model, M AF_BR, which xii

14 considers each contribution of singles, pairs, triplets (open, closed) to the magnetization in the cubic structure (calculated from the sample with 0.9 at% of Eu 2+ at 2 K) Figure 26. Magnetization of two samples (Pb 1-x-y Eu x Se : Na y ) as a function of magnetic field. Solid lines of (a) (c) are the curves of the calculated magnetization with a Brillouin function. Solid lines of (b) (d) are the curves of a model that considers the antiferromagnetic contributions of singles, pairs, and triplets in nearest neighbor Eu atoms to the magnetization Figure 27. Inverse susceptibility of three samples(pb 1-x-y Eu x Se : Na y ) as a function of temperature. The solid lines are obtained from the Curie-Weiss low Figure 28. Comparison between estimated X 3+ Eu (X 3+ Eu = 1-X 2+ Eu where X 2+ Eu is obtained from the fitting of Pb 1-x-y Eu x Se : Na y (x= 0.01; y = 0.01, 0.02, 0.03, and 0.04) magnetization data, and carrier concentration at 300k of Pb 1-x-y Eu x Se : Na y (y = 0.01; x = 0.01, 0.02, 0.03, and 0.04) xiii

15 Chapter 1: Introduction to thermoelectrics 1.1 Motivation Figure 1.Annual energy flow diagram during 2013 in the US, adapted from Ref.[1]. According to the Energy diagram (Figure 1), more than 50% of the total energy produced during 2013 was wasted as heat in the US. For this reason, using the produced energy with a proper energy conversion system is critical in the modern day energy system. This 1

16 is where thermoelectric devices can play an important role because thermoelectric generators (TEG), also known as solid state energy convertors, can directly generate electricity by temperature gradient. The efficiency of TEG, in general, is much lower when compared to other thermodynamic systems such as Rankine and Stirling. 2 However, there are unique advantages to TEG, such as high power density, long-term reliability, and less maintenance, which are important properties for remote and mobile applications. The applications of thermoelectric devices can range from waste heat and solar energy converters 3 to cooling and heating devices. 1.2 Thermoelectric effects Seebeck effect ( ) In 1821, Thomas J. Seebeck, a German physicist, discovered that there exists a small current across a junction of two different metal wires when there is a difference in temperature of the two ends (Figure 2). 4 This phenomenon was later named the Seebeck effect. This observation empirically proves that heat energy can be directly converted to electricity. The mathematical definition of the Seebeck effect is: (1.1) 2

17 Figure 2. Schematic drawing of a device that demonstrates the Seebeck effect Assuming reversible process and one single and free electron, the Seebeck effect can be described as: 5 (1.2) where S is entropy and e is electric charge. This expression has many interesting implications. Since entropy goes to zero when the temperature approaches 0K (the third law of thermodynamics), the same phenomenon holds for the Seebeck coefficient:. Also, since entropy is a state function, which depends only on initial and final states, the Seebeck coefficient is also a state function. It only matters what the resulting potentials and temperatures are at two different destinations. 3

18 1.2.2 Peltier effect ( ) Another important thermoelectric phenomenon- later called the Peltier effect- was observed three years after the Seebeck effect was reported. Jean Peltier discovered that when a current flows in an isothermal sample, temperature gradient is generated between the two ends of the sample. The Peltier effect is the reverse of the Seebeck effect and can be expressed as: (1.3) where Q is the heat flow and I is the electrical current. In 1831, Heinrich Lenz demonstrated freezing of a small quantity of water with a bismuth-antimony (Bi-Sb) thermocouple, and melting of the created ice by reversing the current direction Thomson effect ( ) In 1851, William Thomson discovered the third thermoelectric effect, which is now known as the Thomson effect: when current flows in a material with a temperature gradient, heat emission or absorption, other than previously known Joule heating, can occur depending on the material. The Thomson coefficient is defined as: 4

19 (1.4) where 1.3 Thermoelectric efficiency Figure 3 shows a typical thermoelectric device where n- and p- type materials are connected electrically in series and thermally in parallel. The commercially available thermoelectric material is Bi 2 Te 3, which has zt value around 1 for cooling and heating applications near the room temperature. Alloys of SiGe have also been used as high temperature regime thermoelectric materials in the applications for space missions. Figure 3. Commercially available thermoelectric module for cooling or heating application 5

20 Thermoelectric device can have the ideal thermodynamic cycle, known as the Carnot cycle, if it follows reversible process. 6 Figure 4a shows diagram of a thermoelectric device with a single n and a single p leg, and Figure 4b shows the relationship between the Seebeck coefficient and temperature in the ideal thermoelectric cycle assuming that both legs have temperature- independent Seebeck coefficient. When the Seebeck coefficient is expressed in terms of entropy, entropy-temperature diagram of an ideal thermoelectric device (Figure 4b) is identical to that of the Carnot cycle (Figure 4c). Figure 4. Schematic drawings of (a) TE power generator with n- and p- type legs (b) its Seebeck(α = S/e) - temperature(t) thermodynamic cycle (c) entropy(s)-temperature(t) relation in Carnot cycle However, heat conduction through the device and joule-heating make the whole system irreversible; and therefore, the ideal Carnot cycle cannot be achieved. The actual efficiency can be expressed as below: (1.5) 6

21 . From the equation (1.5), we find that the efficiency is limited by dimensionless unit, where,. Hence, any increase in leads to higher efficiency of a thermoelectric engine. According to the equation of to get a high efficiency, one can maximize α 2 σ, known as the power factor, and minimize κ. However, is composed of inter-related material properties, and therefore, improving one property can degrade another. 7 To further explain, Figure 5 shows the fundamental relation of carrier concentration(n) and α 2 σ. An increase in n leads to a decrease in α, and also an increase in σ. Consequently, α and σ are inter-related in terms of carrier concentration, n: (Pisarenko relation) and (Drude theory) (1.6) Figure 5. Thermoelectric properties as a function of carrier concentration 7

22 In addition, electronic thermal conductivity (κ e ) and σ are mutually contra-indicated by the Widmann-Fraz law. The lattice thermal conductivity (κ L ) and the mobility (μ) are also mutually contra-indicated. In a mathematical form with, where is the electric charge, we can express as: zt 2 n qt (1.7) L where is lattice thermal conductivity and It can be assumed that L is dominant, which is typical for thermoelectric materials. The mutually contra-indicated properties are grouped in the parenthesis. 7 Figure 6. Normalized thermoelectric efficiency of thermoelectric generator as a function of for various temperature difference 8

23 Figure 6 shows normalized efficiency of thermoelectric generator with respect to for each temperature difference ( ). It is shown that the larger the temperature difference, the higher the efficiency of thermoelectric materials is. Since is a combination of material properties, it is important to select the right material in the first place. Typically, metal shows good electrical conduction, but the thermal power is too low to be a good thermoelectric materials. On the other hand, insulator has ideal thermal power, but the electrical conductivity is too low. For this reason, good thermoelectric materials in general are found from the semiconductors and semimetals. 9

24 1.4 History and recent advances in thermoelectric materials After the development of PbTe and Bi 2 Te 3 as efficient thermoelectric materials by Ioffe and Goldsmid respectively, semiconducting materials began to be intensely studied and to this date have continued to be studied as a possible thermoelectric material. Many attempts to increase with semiconductors have been made to increase the thermoelectric efficiency. Before 1970s, empirical searching for better thermoelectric materials was the main theme in thermoelectrics community. When it was discovered that the lattice thermal conductivity could be engineered, the emphasis had been placed on the reduction of the lattice thermal conductivity by alloy scattering to obtain high, which likely reduces mobility of the sample. 8 The key to this approach was engineering nanostructures that scatter phonons more than electrons, thereby increasing the ratio of µ to κ. The idea of using voids in lattices filled with small ions that scatter high phonon energy (occurring within such materials as skutterudites 9, clathrates 10, and zintl phases 11 ) was heavily studied as another way to reduce lattice thermal conductivity. However, when it was realized that there was a limitation in reducing thermal conductivity - a minimum in thermal conductivity is reached when phonon's mean free path approaches interatomic 10

25 distance 12,13 - the attention was diverted to maximizing properties on the numerator of, such as Seebeck coefficient. In 1993, Hicks and Dresselhaus suggested that low dimensional thermoelectricity could increase the figure of merit by two ways: first, the control of the Seebeck coefficient and electrical conductivity by quantum confinement (increasing effective mass by density of state change), and second, by providing interfaces that scatter high energy phonon while allowing low energy electrons to pass through. 14,15 It has been proven that the low dimensional thermoelectric materials such as Bi nano wire indeed increase their efficiencies. 16,17 In real application, however, only bulk materials can be used because it generates large amount of power at once. 6 In 1996, Mahan and Sofo reported that the best bulk thermoelectric materials has delta like DOS near the Fermi level and suggested that distorting localized density of state could enhance the thermoelectric efficiency. 18 About 12 years later, the concept called resonant level was experimentally proven with PbTe:Tl, which doubled the efficiency of the materials. 19 Recently with an improvement in the field of nano-technology, a new interesting approach to improving thermoelectric efficiency of PbTe was made. Biswas et al. investigated PbTe- SrTe system synthesized by Spark Plasma Sintering. SrTe was used as the nanostructuring agent while using powder-sintering with SPS for meso-scale 11

26 architecture in the samples. They obtained one of the highest zts ever reported from p- type thermoelectric materials in lead salts. 20 This suggested that properly designed concurrent nano- and meso- structure system- the so called panoscopic approach- can boost the thermoelectric efficiency of materials. Fig.7 shows the history of the advance in thermoelectric material. From this figure, it is shown that how well nano-technology played a role in the field of thermoelectrics. Figure 7. Evolution of the maximum ZT from 1940 to present. The figure shows significant improvement in after the contribution of Hicks and Dresselhaus to the field. Blue dots represent thermoelectric cooling while red ones are for power generation, adapted from Ref. [6]. 12

27 Chapter 2: Transport measurement and error analysis Transport properties were measured by customized cryostat with an AC bridge. Figure 8 shows the actual picture of a cryostat. Figure 8. An actual picture of a cryostat. The cryostat was used to measure thermoelectric properties of a material. All the samples tested were cut into parallelepipeds with dimensions width (w) thickness (th) length (L) to measure thermoelectric properties (Figure 9). 13

28 Figure 9. (a) A mounted sample to measure thermoelectric properties. (b) A schematic drawing of a mounted sample. This mounted sample was placed in the cryostat to measure its thermoelectric properties. The experimental ρ was measured using the four probe ( 4 copper wires ) method with an AC bridge. The major errors in ρ stem from geometrical errors. In this case, the total estimated error from geometry is about 10%. We neglect errors from current and voltage measurements since they are much smaller than geometrical errors. The experimental α values were measured using the conventional static heater and sink method. In this study, very thin wires (diameter =0.0025mm) of copper and constantan 14

29 were used as thermocouples to minimize heat losses. Thus, the estimated error in measuring α is about 10% mostly due to noises in the voltage measurements. Hall resistivity and adiabatic Nernst Ettingshausen voltage were also measured with customized cryostat in transverse magnetic fields, sweeping from -14kOe to +14 koe. Origin of errors is mainly in measuring sample's geometry. Estimated errors for Hall and Nernst are 5%. Magnetoresistance (MR) is the change in resistivity when an external magnetic field is applied following the equation: (2.1) In this study, MR measurements were conducted using Quantum Design PPMS in a longitudinal magnetic field sweeping from -70 koe to 70 koe at each temperature ( 2K, 4K, 8K, and 16K ) as shown in Figure

30 Figure 10. A Quantum Design PPMS puck with a mounted sample. Magnetoresistance (MR) measurements were conducted in a longitudinal external magnetic field. Magnetization (M) can be expressed as the magnetic moment per unit volume. When a very small magnetic field (H) is applied to a paramagnetic material, M is linearly proportional to H. And the ratio M to H is called susceptibility (χ) : (2.2) The susceptibility of a paramagnetic material varies on χ Two experimental measurements for M were conducted using Superconducting Quantum Interference Device (SQUID). The first measurement of M was performed by applying a low magnetic field (5 koe) from 2K to 300K. From the obtained data, the magnetic 16

31 susceptibility χ was calculated. The susceptibility of Eu 2+ was then obtained by subtracting the diamagnetic susceptibility of the PbSe lattice. The second measurement of M was carried out by varying H from 0 to 60 koe at each temperature ( 2K, 4K, 6K, and 8K), where (2.1) breaks down and M becomes a more complicated function of T and H, known as a Brillouin function. The errors described above are not reflected in these measurements. 17

32 Chapter 3: P-type Mg 2 Sn 1-x Si x 3.1 Motivation and literature review One of the promising thermoelectric materials for power generation is Mg 2 X (X= Sn, Si), because of its low cost, non-toxicity, and abundance. Also, high zt values have been numerously reported on n-type Mg 2 Sn 1-x Si x. 21,22 In contrast, only a limited number of studies has been reported on p-type Mg 2 Sn 1-x Si x. Studies about the band gap, electrical conductivity, and hall resistivity on pure Mg 2 Sn had been conducted and reported in 1948 by Robertson 23 and in 1955 by Blunt 24. According to Blunt, the band gap of Mg 2 Sn is about 0.33eV at 0 K. 24 Later, thermal conductivity of pure Mg 2 Sn was also reported in 1968 by Martin and Danielson. 25 However, doping studies on p-type Mg 2 Sn and alloys of Mg 2 Sn 1-x Si x have only been recently reported. Chen et al. and Savvides et al. investigated various properties on Agdoped Mg 2 Sn grown by Bridgmann technique and RF induction melting. 26,27,28 Isoda et al. studied effects of double-doping on Mg 2 Sn 0.75 Si 0.25 with Ag and Li that was synthesized by liquid solid reaction followed by hot pressing technique. 29 Also, Tada et 18

33 al. most recently reported thermoelectric properties of sodium acetate and metallic sodium doped Mg 2 Sn 0.75 Si However, to our best knowledge, no systematic doping studies have been performed with varying x in Mg 2 Sn 1-x Si x. In this study, we report thermoelectric, thermomagnetic, and galvanomagnetic properties of undoped and Agdoped Mg 2 Sn x Si 1-x (x = 0, 0.05, 0.1). 3.2 Sample preparation of Mg 2 Sn 1-x Si x (x = 0, 0.05, 0.1) Figure 11. Binary phase diagram of Mg and Sn, adapted from Ref. [31] 19

34 High purity Mg(99.98%), Sn(99.999%), Si( %), and Ag( %) were prepared to fabricate Mg 2 Sn 1-x Si x : Ag (x=0, 0.05, and 0.1). While melting the elements, Mg generated unacceptable high vapor pressure and reacted with ampoules. To compensate the loss of Mg from the evaporation, excess Mg was added. It should be noticed that too much excess Mg leads to the formation of a Mg+Mg 2 Sn eutectic phase, while not enough excess Mg leads to Sn + Mg 2 Sn eutectic phase. 27 The phase diagram of Mg and Sn (Figure 11) shows two Mg + and Sn + eutectic phases at 551 o C and 204 o C respectively. Hence, one of the challenges in fabrication of pure Mg 2 Sn is to determine the excess amount of Mg needed with a proper heat treatment. To minimize the loss of Mg and protect samples from any reaction with quartz ampoule, sealed graphite or boron nitride crucibles were used. Stoichiometric amounts of raw elements with appropriate excess Mg (8 to 10 at.%) were loaded in the crucibles inside of quartz ampoules that were sealed under a pressure less than 10-6 torr. The samples were slowly heated up to 1123K and cooled down to 923K at 1K/min and annealed for 2 days. To keep the experimental consistency, three parameters -amount of Mg (1.4g), melting and annealing temperatures, and durations- were maintained the same for all material synthesis. Figure 12 shows the actual picture of a Mg 2 Sn sample. The resulting samples were cut into parallelepipeds to measure thermoelectric properties. 20

35 Figure 12. Obtained Mg 2 Sn ingot fabricated by co-melting method with a sealed graphite crucible. The purity of the obtained Mg 2 Sn samples were checked by two methods : powder X-Ray Diffraction (XRD) to check the atomic structure of the material and Differential Scanning Calorimetry (DSC) to check the presence of eutectic phase. Figure 13a shows X-ray Diffraction (XRD) patterns of Mg 2 Sn 1-X Si X (x =0, 0.05, and 0.1). Only clear Bragg peaks of anti-fluorite structure (space group, Fm3m) were shown with no secondary phases such as Sn. With the addition of Si, because of its smaller ionic radius than Sn, the peaks were shifted to the right according to the amount of Si, indicating that Si successfully replaced Sn-site. Differential Scanning Calorimetry (DSC) were used to trace the latent heat of Mg 2 Sn, Since loss of Mg is likely to form Sn or Sn-Eutectic phases. In this study, 21

36 absence of Sn or Sn-eutectic peaks at the melting and eutectic temperature of 503 K and 475 K, respectively, were verified in Figure 13b. Above 600 K, Mg 2 Sn was oxidized. Hence, no further study to search for Mg + eutectic phase (824 K) with DSC was conducted. Figure 13. (a) Powder XRD pattern for Mg 2 Sn 1-x Si x (x = 0, 0.05, 0.1) (b) DSC latent heat trace of Mg 2 Sn 22

37 3.3 Results and discussion Undoped Mg 2 Sn 1-x Si x (x=0, 0.05, 0.1) Figure 14. Temperature dependent thermoelectric properties of undoped Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) (a) Seebeck coefficients (b) Resistivity (c) Hall resistivity of undoped Mg 2 Sn from 120K to 180K (d) Inverse ρ H divided by electric charge of the undoped samples 23

38 Undoped Mg 2 Sn shows temperature-independent, large, and positive α from 120 K to 180 K (Figure 14a). The corresponding hole concentration is about 8.0 x (Figure 14c). However, above 180 K, the α tends to decrease rapidly due to thermal excitation of minority carriers and becomes negative near 280 K. The α values obtained here are in good agreement with that reported by Chen & Savvides. 27,28 Since the low temperature carrier concentration in this sample is very small, the reason for thermopower turnover is likely to be bipolar conduction effect. On the other hand, Mg 2 Sn 0.95 Si 0.05 and Mg 2 Sn 0.9 Si 0.1 show fairly small positive α at low temperatures compared with that of Mg 2 Sn. ρ of the undoped samples is also reported in Figure 14b. All samples show typical semiconductor-like behavior: ρ decreases as temperature increases. With the increase in substitutional Si level (x), samples become more conductive at low temperature. Figure 14d shows the measured of each samples where e is the electric charge and is the hall voltage. The dominant carriers in Figure 14d are electrons, since α of all three samples show negative values in the given temperature range. Change of sign of the Hall voltage (pure Mg 2 Sn), thermopower (all samples), and strongly temperature-dependent behavior show that both types of carriers, holes and electrons, are present. It is clearly shown that the increase in x leads to increase in the number of electrons in the samples. This explains the decreases in both α and ρ with increasing x shown in Figure 14a and 14b, respectively. 24

39 3.3.2 Ag doped Mg 2 Sn 1-x Si x (x = 0, 0.05, and 0.1) Figure 15. Temperature dependent thermoelectric properties of Ag doped Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) (a) hole concentration (b) Seebeck coefficient (c) resistivity (d) mobility 25

40 In this study, Ag is used as an acceptor in Mg 2 Sn 1-x Si x (x = 0, 0.05, and 0.1). Carrier concentrations of seven samples are reported in Figure 15a. The hole concentration of 0.5 at. % Ag-doped Mg 2 Sn sample (6.0 x at 300 K) is almost identical what was reported by Chen (6.1 x at 300K). 28 An interesting finding is that roughly 4 times the amount of Ag is required in order to obtain a similar order of hole concentration in Mg 2 Sn 0.95 Si 0.05 :Ag (2at.%) and Mg 2 Sn 0.9 Si 0.1 :Ag(2at.%) when compared to Mg 2 Sn: Ag (0.5at.%). Presumably, the substitution of Si creates more electrons (Figure 14c) in Mg 2 Sn, causing an increase in the amount of Ag required to compensate and convert the sample into the p-type semiconductor. The hole concentrations of Mg 2 Sn 1-x Si x : Ag (x = 0, 0.05, 0.1) are almost temperature independent up to 300K, except for the Mg 2 Sn 0.95 Si 0.05 : Ag(0.5at.%) and Mg 2 Sn 0.95 Si 0.05 : Ag(1at.%) samples. The hole concentration of those samples gradually increases as temperature increases mostly -due to the generation of holes caused by thermal excitation. For simplicity of discussions, we will adapt the hole concentration at 80K as a label for each sample henceforth. In Figure15b, experimentally measured Seebeck coefficients as a function of temperature are shown and all the data follows typical Pisarenko relation: α is inversely proportional to logarithm of carrier concentration (p). All the samples above hole concentration shows linear behavior in temperature- dependent α. Two samples 26

41 with order of hole concentration have α data bending over around 200K, as mentioned above, due to the thermally excited minority carriers. All of the Ag doped samples with hole concentration above show increasing ρ with increase of temperature (Figure 15c), showing the typical heavily doped semiconductor behavior, as opposed to the undoped Mg 2 Sn 1-x Si x samples (Figure 14b). Accordingly, the mobility decreases with increasing temperature (Figure 15d). When mobility decreases with an increase in temperature, the predominant mechanism is a phonon scattering. Also, it is observed that Mg 2 Sn 0.95 Si 0.05 : Ag (p = 6.5x10 19 ) displays nearly the same mobility as that of Mg 2 Sn: Ag (p = 6.0x10 19 ) with the almost identical carrier concentration. On the other hand, Mg 2 Sn 0.9 Si 0.1 : Ag (p = 6.7x10 19 ) shows the lowest mobility and the highest ρ among all the samples with p > cm -3. Presumably, the difference of the electronegativity between Sn and Si increases alloy scattering rate of the sample, causing the decrease in mobility of Mg 2 Sn 0.9 Si 0.1, 32 since the Pauling electronegativity of Sn is 1.96 and that of Si is

42 (a) 1 p =6.0x10 19 p =7.7x10 19 Si 5%, p =6.5x10 19 Si 5%, p =7.1x10 19 Si 10%, p =6.7x10 19 at 300 K Theoretical pisarenko plot 35 Exp. this work, (Ag) Exp. this work, (Si x :Ag, x = 0.05,0.1) Exp. Chen et al. 28 (Ag) 300 (b) 0 Exp. Isoda et al. 29 (Si x : Ag, Li, Ag+Li, x = 0.25) Exp. Tada et al. 30 (Si x : Na, x = 0.25) 200 ( V/K) T (K) 1 10 p (10 19 cm -3 ) Figure 16. (a) Scattering parameter of Ag doped Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) calculated from measured Seebeck(α), Nerst(N), and Mobility(μ) (b) The obtained data from this work and previously reported values of Seebeck(α) and hole concentration(p) at 300K plotted on the calculated Pisarenko plot with λ = 0. The relaxation time scattering parameter λ, defined as (acoustic phonon scattering is while polar optical phonon scattering is ) can be calculated from α, N, and μ calculated from measured ρ and p for parabolic band model: 33 (3.1) The values of λ for the Ag-doped Mg 2 Sn 1-x Si x (X=0, 0.05, 0.1) samples show various values from +0.5 to -0.5 (Figure 16a), indicating that the combination of acoustic phonon and optical phonon scatterings is acting dominant in the samples. "Pisarenko relation" by Ioffe 34 defined as the Seebeck coefficients plotted against the hole 28

43 concentrations (p) is used to determine the effective masses of the samples. Theoretically calculated Pisarenko plot with λ=0 is shown in Figure 16b. 35 The experimental data in this study as well as in previous studies 28,29,30 are also plotted. Both sets of experimental data show fairly good agreement with the theoretically calculated Pisarenko curve. Hence, we were able to obtain the hole- concentration dependence of the valence band density of state effective masses of the samples from the theoretically calculated pisarenko curve. Figure 16 shows the calculated effective masses in terms of hole concentration. Figure 17. Theoretically calculated effective masses (m*) as a function of carrier concentration (p) Since our obtained hole concentrations range from 1 x to about 8 x at 300K, the effective masses of the samples vary from 0.5 to 0.7 as shown in Figure

44 Figure 18. Power factor of Mg 2 Sn 1-x Si x (x=0, 0.05, and 0.1) doped with Ag for different hole carrier concentration, p. The power factor of the tested samples is shown in Fig.18. The maximum power factor of 22 μwcm -1 K -2 at 380K has been obtained for the Mg 2 Sn: Ag with p = 6.0 x cm

45 Chapter 4: Pb 1-x-y Eu x Se:Na y 4.1 Motivation and literature review Pb-salts have been of great interest as potential high-temperature regime thermoelectric materials since the development of PbTe by Goldsmid. Since then, many interesting studies on Pb-salts have been conducted and reported with high thermoelectric efficiencies. 19,36,37 Recently, another interesting approach to improving thermoelectric efficiency of PbTe was made. Biswas et al. 20 investigated PbTe- SrTe system synthesized by Spark Plasma Sintering (SPS). SrTe was used as the nanostructuring agent while using powder-sintering with SPS for meso-scale architecture in the samples. They obtained one of the highest zts ever reported from p-type thermoelectric materials in lead salts. This suggested that properly designed concurrent nano- and meso- structure system- the so called panoscopic approach- can also boost the thermoelectric efficiency of the materials. However, applications of the material in real thermoelectric devices are limited, even with the highest zt, due to the limited availability of Te in the earth's crust. Therefore, many researchers have been studying Te-free materials, such as PbSe, and have shown 31

46 that they can also be excellent thermoelectric materials. 38,39 For example, PbSe has several advantages over PbTe. Not only does it have similar chemical and electronic structures as compared to those of PbTe but it is also cheap and readily available. Furthermore, the higher melting temperature and forbidden gap of PbSe make the material ideal for applications in thermoelectric generators (TEG). In this study, alloys of Pb 1-x-y Eu x Se : Na y samples were synthesized by the SPS technique. EuSe was chosen as the nano-structuring agent in PbSe (conceptually similar to the PbTe-SrTe system mentioned previously), since EuSe and PbSe both have rock-salt structures and have approximately 1% lattice mismatch. 40 Another advantage of the addition of EuSe is that it increases the band gap of the sample, which is a desired property for high-temperature thermoelectric materials. 40,41 Unlike the continuous and extensive magnetic studies that have been performed on Pbsalts with rare earth elements for the application of infrared diode lasers 42,43 and transistors 44, studies on Pb-salts with rare earth elements as a thermoelectric material have begun only recently. 45 No studies on thermoelectric properties along with magnetic properties of Pb 1-x-y Eu x Se : Na y and very few studies on magnetic properties of Pb 1- xeu x Se have been reported so far, because EuSe has a very complicated magnetic phase diagram compared to the ones of EuTe and EuS. 46,47 In this study, we report our findings on thermoelectric, galvanomagnetic, and magnetic properties in paramagnetic alloys of Pb 1-x-y Eu x Se : Na y. 32

47 4.2 Sample preparation of Pb 1-x-y Eu x Se : Na y Details of sample preparation such as heat treatment and synthesis methods are not reported here because all the samples of Pb 1-x-y Eu x Se : Na y were synthesized by Yeseul Lee at Northwestern University. 33

48 (ohm m) p (10 19 cm -3 ) 4.3 Results and discussion Thermoelectric properties of Pb 1-x-y Eu x Se : Na y, (a) x = 0 x = 0.01 x = 0.02 x = 0.03 x = 0.04 x = 0.06 x = 0.12 T(K) Pb 1-x-y Eu x Se: Na y (y =0.01) T (K) Pb 1-x-y Eu x Se: Na y (y =0.01) (b) ( V/K) 4 50 (c) E-3 1E-4 Pb 1-x-y Eu x Se: Na y (y =0.01) Pb 1-x-y Eu x Se: Na y (y =0.01) (d) (cm 2 /v/s) 1E E T (K) p (10 19 cm -3 ) 0 Figure 19. Temperature-dependent thermoelectric properties of Pb 1-x-y Eu x Se : Na y (a) Carrier concentration(p) (b) Seebeck coefficient(α) (c) Resistivity( ρ) (d) Mobility( μ) comparison at 300k. The back dotted line represents mobility of PbSe with differing Na doping level. 34

49 Thermoelectric properties of Pb 1-x-y Eu x Se : Na y, (y = 0.01; x = 0, 0.01, 0.02, 0.03, 0.04, 0.06, 0.12), are shown in Figure 19. x is the stoichiometric ratio of Eu, and y is the stoichiometric doping level of Na. From Figure 19, two significant observations are made. First, the substitution of EuSe greatly reduces the carrier concentration. The sample with (x = 0, y = 0.01) shows highly degenerate semiconducting properties with approximately 1.8x10 20 cm -3 hole concentration at 300K. The hole concentration of (x = 0.01, y = 0.01) sample is about 8.0x10 19 cm -3 at 300K. The continuous reduction in carrier concentration with higher EuSe level in ( y = 0.01; x > 0.01) samples is also apparent, although to a lesser degree. Also, the sample with (x = 0.12, y = 0.01) was too resistive and did not give measurable Hall data. For this reason, the hole concentration of (x = 0.12, y = 0.01) is not reported here. Another interesting observation is that the mobility decreases dramatically with the substitution of EuSe when compared to the typical PbSe with differing Na-doping levels (Figure 19d). The black dotted line shows the mobility of PbSe with differing Na concentration at 300K. Clearly, the mobility of EuSe substituted (y=0.01; x = 0.01, 0.02, 0.03, 0.04, and 0.06) samples is significantly lower than that of the PbSe doped with different Na levels. It cannot be definitively concluded, however, that the increase in EuSe level continuously decreases the mobility of the samples, even though such a trend is suggested in Figure 19d. It should be noted that all the samples are synthesized with the same conditions(such as melting temperature and Spark Plasma Sintering (SPS) conditions). There are two possible factors that can cause the decrease in mobility of the 35

50 samples (y = 0.01; x = 0.01, 0.02, 0.03, 0.04, and 0.06), the first being the large electronegativity difference between Pb and Eu. Pauling electro-negativity, X Pb, is 1.87 while that of Eu (X Eu ) is only 1.2. The net difference, X, is around This big electronegativity difference results in higher alloy scattering rate, thereby decreasing mobility. 32 Another possible reason for the mobility decrease is s-f magnetic scattering. The conduction and valence band edges are composed mostly of sp hybridized electrons that are likely to be scattered by f electrons of Eu. One can verify the existence of s-f magnetic scattering by measuring the magneto-resistance (MR) of the samples. Figure 20. Schematic drawings of the alignment of magnetic moments in paramagnetic material, adapted from Ref.[56] (a) Disordered arrangement of magnetic moments in the absence of an external field. (b) The response when a field of moderate strength is applied. Figure 20 shows schematic drawings of the alignment of magnetic moments in paramagnetic material. The arrow represents magnetic moments. In Figure 20a, the randomly distributed magnetic moments are presented in typical paramagnetic materials 36

51 and since electrons are scattered by magnetic moments, it can explain decreasing mobility of the EuSe substituted samples (y = 0.01; x 0.01). Figure 20b explains what happens when magnetic field is applied in the paramagnetic material. The magnetic moments would be aligned along with the magnetic field. Hence, electrons will less scatter by magnetic moments, causing an increase in mobility proportional to the field and showing negative MR. Thus, if s-f magnetic scattering is present, the MR should be negative Pb 1-x-y Eu x Se: Na y 0.04 x = 0, y = K K 8K K H (KOe) Figure 21. Magnetoresistance of Pb 1-x-y Eu x Se : Na y (x =0, y = 0.01) from -70kOe to 70kOe at 2k, 4k, 6k, and 8k The MR of the sample with (x = 0, y = 0.01) sample is positive as expected (Figure 21). The maximum change in positive MR is roughly 5% with PbSe at 7T. 37

52 In contrast, all Pb 1-x-y Eu x Se : Na y, (y = 0.01; x = 0.01, 0.02, 0.03, 0.04, 0.09, and 0.12), show negative MR (Figure 22). This indicates magnetic scattering of Eu. The higher the EuSe level of the sample, the more negative the MR. Since the carrier concentration and mobility change with the EuSe level from one sample to another, the exact comparison of the MR at each temperature in terms of EuSe level alone cannot be determined. However, it can be said that as temperature increases, the negativity of MR tends to weaken because of the increase in phonon scattering. The sample with (x = 0.01, y = 0.01) shows slight negative MR up to 4T then positive MR all the way up to 6T at 2K. Also, as temperature increases, MR changes from negative to positive at 8K and stays positive up to 16 K (Figure 22). The maximum change in negative MR is about 25% shown in (x = 0.12, y = 0.01). 38

53 / K 4K K 16 K H (koe) H (KOe) Figure 22. Magnetoresistance of alloys of Pb 1-x-y Eu x Se : Na y at each temperature (2k,4k,8k, and 16k). The sample label is (y = 0.01; x= 0.01( ), 0.02( ), 0.03( ), 0.04( ), 0.09( ), and 0.12( )) However, other mechanisms have also caused negative MR in impurity-doped semiconductors. 48 One way to check the presence of magnetic scattering is to plot the values of inverse temperature (T -1 ) with resulting MR data at each fixed applied field. If it truly is magnetic scattering dominant, a linear relation (Curie-Weiss law) would be shown according to the mathematical relation shown below 49 : (4.1) 39

54 Figure23 shows the linear relationship between MR and inverse temperature (T -1 ) at 5 koe and 10 koe in samples with (y = 0.01; x = 0.04, 0.09, and 0.12). (a) 0.00 (b) Pb 1-x-y Eu x Se: Na y at 5 koe x = 0.04, y = 0.01 x = 0.09, y = 0.01 x = 0.12, y = / T (K -1 ) Pb 1-x-y Eu x Se: Na y at 10 koe x = 0.04, y = 0.01 x = 0.09, y = 0.01 x = 0.12, y = / T (K -1 ) Figure 23. Magnetoresistance as a function of inverse temperature (1/T) for Pb 1-x-y Eu x Se : Na y (y = 0.01; x = 0.04, 0.09, and 0.12) This linearity can support the presence of magnetic interaction in s-f level. So, in our case, it seems reasonable to conclude that the dominant mechanism causing the negative MR is s-f magnetic scattering. In this section, we discuss the decrease in mobility with the addition of EuSe because: (i) big electro-negativity of Pb and Eu may suggest an increase in alloy scattering in the samples, and (ii) observation of negative MR may suggest that s-f magnetic scattering is dominant and scatters electrons by magnetic moments. 40

55 M (emu/g) M (emu/g) Magnetization of Pb 1-x-y Eu x Se : Na y (a) Pb 1-x-y Eu x Se: Na y (y=0.01) at 2k Pb 1-x-y Eu x Se: Na y (x=0.01) at 2k (b) x = 0.01 x = 0.02 x = 0.03 x = 0.06 x = 0.09 x = 0.12 y = 0 y = 0.01 y = 0.02 y = 0.03 y = H (koe) H (koe) Figure 24.(a) Magnetization of Pb 1-x-y Eu x Se : Na y (y = 0.01) with varying Eu level (x) as a function of magnetic field (b) Magnetization of Pb 1-x-y Eu x Se : Na y (x = 0.01) with varying Na doping level (y) as a function of magnetic field 0.0 The measured magnetization curves (emu/g) of (y = 0.01; x = 0.01, 0.02, 0.03, 0.04, 0.06, 0.09, and 0.12) and (x = 0.01; y = 0, 0.01, 0.02, 0.03, and 0.04) as a function of magnetic field at 2K are displayed in Figure 24a and Figure 24b respectively. As the Eu level, x, increases in (y = 0.01; x 0.01 ) samples, the magnetization also increases (Figure 24a). This verifies that Eu indeed gets incorporated into each sample proportionally to the amount of Eu added. Interestingly, the sample with (x = 0.01, y = 0) shows a significant decrease in magnetization with each increasing Na doping level starting from the undoped (x = 0.01, y = 0) as shown in Figure 24b. The difference in 41

56 M (emu/g) magnetization between undoped (x = 0.01, y = 0) and (x = 0.01, y = 0.01) is significant. However, the continuous increase in Na level by the same amount does not result in an equal reduction in magnetization each time, but rather decreases to a lesser degree with each increasing level of Na. This observation is very similar to the reduction characteristic in carrier concentration (Figure 19a). Detailed discussion for this observation is present later in this section Singles, M s Pairs, M p Open triplets, M ot Closed triplets, M ct M AF_BR =M s +M P +M ot +M ct M BR (Brillouin) H (koe) Figure 25. Comparison between a model with a Brillouin function, M BR,which considers no interaction between Eu ions (Brillouin function) and a model, M AF_BR, which considers each contribution of singles, pairs, triplets (open, closed) to the magnetization in the cubic structure (calculated from the sample with 0.9 at% of Eu 2+ at 2 K) 42

57 Figure 26. Magnetization of two samples (Pb 1-x-y Eu x Se : Na y ) as a function of magnetic field. Solid lines of (a) (c) are the curves of the calculated magnetization with a Brillouin function. Solid lines of (b) (d) are the curves of a model that considers the antiferromagnetic contributions of singles, pairs, and triplets in nearest neighbor Eu atoms to the magnetization The actual amount of Eu 2+,, in each sample is deduced based on the saturation of experimental magnetization data at low temperatures using the contribution of the single Eu 2+ ions ( ), as given by (4.2) 43