IMPROVED THERMOELECTRIC
PERFORMANCE IN NANOSTRUCTURED CHALCOGENIDES AND PNICTIDES:
SYNTHESIS, STRUCTURE AND TRANSPORT
Federico Serrano Sánchez
Instituto de Ciencia de Materiales de Madrid (CSIC)
Madrid, January 2018
Facultad de Ciencias
Departamento de Física de Materiales
Improved Thermoelectric Performance in Nanostructured Chalcogenides and Pnictides:
Synthesis, Structure and Transport
A Thesis submitted by
Federico Serrano Sánchez
In accordance with the requirements of the degree of Doctor in Philosophy Supervisors
Dr. José Antonio Alonso Alonso Dr. José Luis Martínez Peña
Instituto de Ciencia de Materiales de Madrid (C.S.I.C.)
Madrid, January 2018
To my family
En todos los ámbitos, el consumo energético ha crecido considerablemente durante las últimas décadas. La producción de esta energía, cuya fuente mayoritaria son los combustibles fósiles tradicionales, supone la liberación de grandes cantidades de gases y residuos nocivos para el medio ambiente. Mediante los generadores termoeléctricos gran parte de la energía perdida en forma de calor, tanto en procesos industriales como domésticos, se podría transformar en energía eléctrica, aumentando considerablemente la eficiencia global y reduciendo las emisiones contaminantes. Un generador termoeléctrico es un dispositivo capaz de generar electricidad a partir de un gradiente de temperatura. Estos generadores no presentan partes móviles; tienen una respuesta fiable y una durabilidad mucho mayor que la de otros dispositivos de conversión de energía. Sin embargo, por el momento su fabricación es difícil de amortizar como consecuencia de una baja eficiencia de conversión de los materiales termoeléctricos conocidos. Por esta razón, se emplean únicamente en aplicaciones donde, debido a sus particularidades, su uso es más conveniente que el de otros tipos de generadores. Así pues, para favorecer el uso de generadores termoeléctricos es necesario investigar nuevos materiales que presenten una mayor eficiencia. El rendimiento de un material termoeléctrico respecto a su aplicación como conversor de energía se determina mediante su figura de mérito, definida como 𝑧𝑇 = 𝑆2𝑇/𝜌𝜅, donde S es el coeficiente Seebeck, ρ es la resistividad o inverso de la conductividad eléctrica, κ la conductividad térmica del material y T la temperatura absoluta.
Hasta el día de hoy, los materiales que muestran el mejor compromiso entre las propiedades de transporte son los semiconductores dopados. Asimismo, es conveniente que los materiales sean mecánicamente estables y se puedan preparar mediante procedimientos de bajo coste económico y energético. Por ello esta tesis se ha centrado en la preparación, mediante métodos de síntesis directos como la fusión en horno de arco y la alta presión, y la caracterización de materiales termoeléctricos prometedores, con baja conductividad térmica y aplicaciones desde temperatura ambiente hasta altas temperaturas. Se han medido las propiedades de transporte térmicas y eléctricas mediante diferentes técnicas, con el fin de determinar su figura de mérito con precisión.
Además, se han realizado análisis detallados de la estructura cristalina de los materiales
Con aplicación a temperatura ambiente, y con el propósito de entrar en el campo de los termoeléctricos, se comenzó con la preparación mediante fusión en horno de arco de derivados del conocido Bi2Te3. Se prepararon muestras puras, tipo-n dopadas con Se y tipo-p dopadas con Sb. A causa del método de síntesis, los materiales muestran una nanoestructuración en forma de apilamiento de láminas delgadas de un grosor del orden de 10-30 nm. Esta nanoestructuración produce una reducción de la conductividad térmica como consecuencia del scattering de fonones en los bordes de grano, presente en todas las muestras. En el material Bi2Te3 puro, la orientación laminar de los granos produce un gran aumento de la movilidad electrónica. Por otro lado, una nanoestructuración más pronunciada en las muestras dopadas con Se deteriora las propiedades de transporte electrónico. En el caso de las muestras de tipo-p, la reducción de la conductividad térmica acompañada de buenas propiedades eléctricas resulta en un aumento de la figura de mérito.
Por el mismo método de síntesis se prepararon derivados del SnSe, para aplicaciones a alta temperatura (>800 K). Éste es un material cuyas propiedades termoeléctricas se redescubrieron hace pocos años, cuando en 2014 se definió una figura de mérito récord de 2.6 en una muestra monocristalina. Sin embargo, estas propiedades no se han podido reproducir en muestras policristalinas. En esta tesis se han preparado por horno de arco derivados de Sn1-xMxSe (M = Sb, Ge, Pb, In) en los que se ha encontrado la misma nanoestructuración laminar que tiene lugar en los compuestos de Bi2Te3. Los compuestos muestran una conductividad térmica extremadamente baja y unos coeficientes Seebeck prometedores, que con una mejora de la conductividad eléctrica podría suponer una enorme mejora de la figura de mérito a altas temperaturas.
En cuanto a materiales para aplicaciones a temperaturas intermedias (500 – 800 K), se han preparado los derivados de las skutteruditas RCoSb3 (R = La, Yb, Ce) mediante una técnica de síntesis a alta presión. Debido a las condiciones de preparación, se observa en la muestra sin “rellenar”, CoSb3, la presencia de vacantes de antimonio, responsables de una reducción en la conductividad térmica y una conductividad eléctrica tipo-n. Al rellenar la estructura en la posición 2a con tierras raras R en la estructura cristalina, se
obtener una figura de mérito superior para los compuestos con La y Ce.
Palabras clave: conversión de energía, termoeléctricos, difracción de neutrones en polvo, figura de mérito, Bi2Te3, CoSb3, SnSe, análisis Rietveld, propiedades de transporte, conductividad térmica de la red, coeficiente Seebeck, horno de arco, alta presión.
Worldwide energy consumption keeps growing incessantly in every walk of life. The main sources of energy production are traditional fossil fuels (carbon, oil, and natural gas), which yield huge amounts of green-house gases, and harmful waste. In this context, thermoelectric materials possess the remarkable ability to directly convert heat into electrical voltage. Thermoelectric generators allow us to recover waste heat as a new source of energy, which could mean a significant progress towards a sustainable development. From economic and environmental points of view, a thermoelectric device presents several advantages, such as reliability, endurance, no pollutant emission, quiet operation, and the absence of mobile parts. However, they are not cost-effective yet, due to low conversion efficiencies. The dimensionless figure of merit 𝑧𝑇 = 𝑆2𝑇/
𝜌𝜅, where S stands for Seebeck coefficient, T for absolute temperature, ρ for electrical resistivity, and κ for total thermal conductivity, evaluates the thermoelectric performance of the materials and is used as a reference value in thermoelectric research.
So far, doped semiconductor materials have shown the best compromise between the thermoelectric transport properties. Furthermore, thermoelectric materials must display mechanical stability and should be prepared by direct and economic methods.
Therefore, it is necessary to investigate more efficient thermoelectric materials and explore different synthesis techniques. This thesis focuses on the direct preparation by arc-melting and high-pressure synthesis, and the characterization of promising thermoelectric materials with low lattice thermal conductivity, for applications in a wide range of temperatures. Thermal and electrical transport properties have been studied by different measurement techniques in order to assess the figure of merit. Moreover, to optimize these materials, a detailed analysis of the crystalline structure has been performed to establish a connection between the physicochemical properties and the structural features.
To gain traction in the field of thermoelectricity, we have prepared well-known Bi2Te3
derivatives by arc-melting synthesis. This synthesis method is fast and straightforward;
moreover it yields nanostructured samples, with highly oriented and nanometric polycrystalline domains. As a consequence of these features, a strong phonon scattering at grain boundaries produces a reduction of the lattice thermal conductivity, measured in all the samples. Pristine Bi2Te3 shows an enhanced electrical conductivity due to the orientation of the laminar grains, while a more prominent nanostructuration deteriorates
the figure of merit of p-type Bi2-xSbxTe3.
For high-temperature applications (>800 K), we have prepared polycrystalline samples of SnSe, triggered by a report of record-high figure of merit of 2.6 at 913 K in a SnSe single-crystal, although those values have not been reproduced yet. Derivatives of Sn1- xMxSe (M = Sb, Ge, Pb, In) were prepared by arc-melting synthesis, for which we find the same nanostructuration displayed by bismuth telluride samples. Extremely low thermal conductivity and high Seebeck coefficient were measured, which, if accompanied by an improvement of the electrical conductivity, could lead to a significant enhancement of the figure of merit.
Finally, filled skutterudites based on RCoSb3 (R = La, Yb, Ce) with intermediate temperatures of operation (500 – 800 K), were prepared by a high-pressure synthesis method. Under the high-pressure preparation conditions, unfilled CoSb3 showed Sb vacancies that led to a reduction in lattice thermal conductivity and an n-type behavior.
Additionally, R-filled samples display an inhomogeneous distribution of the filling fraction on a nanometric scale, which results in further reduction of the lattice thermal conductivity. The final outcome is a remarkable improvement of the figure of merit in La and Ce skutterudite compounds.
Keywords: energy conversion, thermoelectric, neutron powder diffraction, figure of merit, Bi2Te3, SnSe, CoSb3, Rietveld refinement, transport properties, lattice thermal conductivity, Seebeck coefficient, arc-melting, high-pressure synthesis.
Chapter I. Introduction ... 1
I.1 Motivation ... 2
I.2 Historical Background ... 6
I.3 Transport Properties of Thermoelectric Materials: Basic Principles ... 8
I.3.1 Thermoelectric Effects: Seebeck, Peltier and Thomson Effects ... 8
I.3.2 Transport Properties: Electrical and Thermal Conductivity ... 11
I.3.3 Thermoelectric Devices and Figure of Merit ... 11
I.4 Strategies to Improve Thermoelectric Performance ... 15
I.4.1 Basic Concepts ... 15
I.4.2 Strategies to Improve zT in Thermoelectric Materials ... 19
I.4.2.1 Electronic Band Engineering ... 19
I.4.2.2 PGEC and Complex Crystal Structures ... 20
I.4.2.3 Nanostructuring ... 21
I.5 Synthesis Methods of Bulk Thermoelectric Materials ... 24
I.5.1 Melting Processes ... 24
I.5.2 Mechanical Alloying ... 25
I.5.3 Wet-Chemical Routes ... 25
I.5.4 Solvothermal Synthesis ... 26
I.5.5 Polyol Method ... 26
I.5.6 Microwave-Assisted Synthesis ... 26
I.6 State-of-the-Art Thermoelectric Materials ... 27
I.6.1 Thermoelectric Materials for Room-Temperature Applications ... 28
I.6.2 Thermoelectric Materials for Intermediate-Temperature Applications ... 29
I.6.3 Thermoelectric Materials for High-Temperature Applications ... 31
I.7 References ... 33
Chapter II. Experimental Methods ... 53
II.1 Solid State Reactions/Thermoelectric Materials Preparation... 54
II.1.1 Arc-melting Synthesis ... 54
II.1.2 High-Pressure Synthesis ... 55
II.2 Structural Characterization ... 57
II.2.1 X-ray Powder Diffraction ... 57
II.2.2 XRD Equipment ... 59
II.2.5 Neutron Powder Diffraction ... 61
II.2.6 NPD Instruments ... 64
II.2.6.1 High-Resolution Diffractometer D2B... 65
II.2.6.2 HRPT High-Resolution Powder Diffractometer for Thermal Neutrons . 66 II.3 Rietveld Refinement Method ... 66
II.4 Thermal Analysis ... 71
II.4.1 Differential Scanning Calorimetry (DSC) ... 71
II.5 Surface and Microscopic Analysis ... 73
II.5.1 Scanning Electron Microscopy (SEM) ... 73
II.5.2 Transmission Electron Microscopy (TEM) ... 74
II.6 Thermoelectric Transport Properties Measurements ... 75
II.6.1 Thermal Transport Option (TTO) for PPMS ... 76
II.6.2 High-Temperature Seebeck Coefficient Measured in Micro-Miniature Refrigerator (MMR) Device ... 79
II.6.3 High-Temperature Transport Device: High-Temperature Seebeck Measurements in Homemade Apparatus ... 80
II.6.4 Thermal Conductivity: Laser-Flash Thermal Diffusivity Method ... 87
II.6.5 Hall Measurements ... 89
II.7 References ... 89
Chapter III. Thermoelectric Materials for Room-Temperature Applications: Bi2Te3 Derivatives ... 91
III.1 Introduction ... 93
III.2 Materials Preparation ... 95
III.4 Results and Discussion ... 96
III.4.1 XRD Characterization ... 96
III.4.2 Morphologic Analysis: SEM and TEM ... 96
III.4.3 Structural Analysis of Bi2Te3 Compounds by Neutron Powder Diffraction ... 101
III.4.3.1 Bi2Te3 and Bi2Te2.4Se0.6 ... 101
III.4.3.2 Bi2-xSbxTe3 ... 106
III.4.4 Thermoelectric properties of Pristine Bi2Te3 ... 114
III.4.5 Thermoelectric properties of Bi2Te2.4Se0.6 ... 117
III.6 References ... 124
Chapter IV. Thermoelectrics for High-Temperature Applications: SnSe Intermetallic Alloys ... 129
IV.1 Introduction ... 130
IV.2 Structural Characterization: Motivation ... 131
IV.3 Materials Synthesis of Sn1-xMxSe (M = Sb, Ge, In, Pb) ... 132
IV.4 Results and Discussion ... 132
IV.4.1 XRD Characterization of SnSe Derivatives ... 132
IV.4.2 Morphologic Analysis by FE-SEM... 138
IV.4.3 Structural Evolution of SnSe Derivatives ... 140
IV.4.3.1 NPD Crystal Structure Study of Pristine SnSe ... 140
IV.4.3.2 Thermal Analysis of Pristine SnSe ... 150
IV.4.3.3 NPD Crystal Structure Study of Sb-doped SnSe ... 150
IV.4.3.4 Thermal Analysis of Sb-doped SnSe ... 156
IV.4.3.5 NPD Crystal Structure Study of Ge-doped SnSe ... 157
IV.4.3.6 Thermal Analysis of Ge-doped SnSe ... 164
IV.4.4 Thermoelectric Properties of Pristine SnSe ... 165
IV.4.5 Thermoelectric Properties of Sn1-xSbxSe ... 171
IV.4.6 Thermoelectric Properties of Sn1-xGexSe ... 177
IV.5 Conclusions ... 183
IV.6 References ... 186
Chapter V. Thermoelectric Materials for Intermediate-Temperature Applications: CoSb3 Skutterudites ... 189
V.1 Introduction ... 190
V.2 Materials Preparation ... 193
V.3 Results and Discussion ... 194
V.3.1 XRD Characterization of CoSb3 Skutterudites ... 194
V.3.2 Morphologic Analysis by SEM ... 195
V.3.3 Structural Analysis of Skutterudite Compounds via Synchrotron X-ray Powder Diffraction ... 196
V.3.3.1 Unfilled CoSb3 ... 196
V.3.3.2 Filled LaxCo4Sb12 (x = 0.25, 0.5) ... 199
V.3.5 Thermoelectric Transport Properties of Unfilled CoSb3 ... 211
V.3.6 Thermoelectric Transport Properties of Filled LaxCo4Sb12 (x = 0.25, 0.5) . 215 V.3.7 Thermoelectric Transport Properties of Filled R0.5Co4Sb12 (R = Ce, Yb) .. 222
V.4 Conclusions ... 225
V.5 References ... 227
Chapter VI. Conclusions ... 232
VI.1 Summary and Conclusions ... 233
VI.2 Recapitulación y Conclusiones ... 238
Appendix ... 243
Publications ... 276
Chapter I
Introduction
3
I.1 Motivation
Around 19.13 million tons of oil equivalent (Mtoe) of energy were generated with associated 32.3 Gigatons of carbon dioxide emitted worldwide in 2015 (International energy agency[1]). Nowadays our lives are conditioned by an energy demand that has grown continuously and promptly over the years. Traditional fossil fuels, oil, natural gas, and coal are currently the most employed energy sources (Figure 1). These resources are finite and their use in energy production implies a significant pollution waste; in turn the need emerges for renewable energy sources and more efficient technologies. Data on energy usage and consumption show an estimated 60% loss as useless forms of energy (Figure 2). Thus, the recovery of the waste heat produced in energy generation, industrial manufacturing, engine processes etc., dispelled as streams of exhaust gases or liquids, and from heated equipment and products, appears as a possible alternative in order to significantly increase the efficiency of energy generation and many other industrial processes.
Figure 1. World Energy Consumption by Source, Based on Vaclav Smil estimates from Energy Transitions: History, Requirements and Prospects together with BP Statistical Data for 1965 and subsequent[2].
4 Figure 2. Simplified representation of energy use and waste[1].
In this context, the possibility to directly convert temperature gradients into usable electrical energy offered by thermoelectric devices with no inherent pollution emission could play a main role in the development of a sustainable environment. Furthermore, thermoelectric devices are extremely reliable and resilient, require no maintenance expenditures, produce no vibrations and lack moving parts.[3–7] Therefore they are intriguing, among other conversion technologies, as versatile devices in a wide range of applications.
Regardless of these many advantages, thermoelectric devices have only found their place in niche operations due to their low energy conversion efficiency, which currently ranges from 5 to 20%. The conversion efficiency of a thermoelectric material is estimated from its dimensionless figure of merit zT, defined as:
𝑧𝑇 =𝑆2𝜎
𝜅 𝑇 (1)
where S is the Seebeck coefficient, σ the electrical conductivity, κ the total thermal conductivity of the material, which is the sum of lattice and electronic thermal conductivity, and T the absolute temperature. Ideally, for cost-effective applications the figure of merit should be above three[8–13]. It follows from this expression that the optimization of the thermoelectric efficiency requires: (i) a high Seebeck coefficient, for a high voltage output, (ii) high electrical conductivity, to minimize Joule heating losses,
5 and (iii) low thermal conductivity, to maintain a large temperature gradient. This is a challenging task, as all these properties depend on the carrier concentration and the details of the electronic bands near the chemical potential. While metals present high carrier concentration, and therefore, large electrical conductivity, they display almost zero Seebeck coefficients and high thermal conductivity, which significantly decreases the zT. On the other side, insulators show high Seebeck coefficients and low thermal conductivity. However, their poor electrical properties hamper the optimization of the figure of merit. Between these two ends we find doped semiconductor materials, for which the power factor, S2σ, is maximized when carrier concentration is approximately 1019 cm-3. According to the theory of thermoelectricity, zT is directly proportional to the product 𝝁(𝒎∗)𝟑/𝟐where μ is the carrier mobility and m* is the density of states effective mass. Therefore, best thermoelectric materials would have crystal structures with high symmetry that yields multiple equivalent bands contributing to the effective mass, and would consist of elements with similar electronegativity, so the carrier scattering is diminished.[14,15] Yet, this is only half of the solution to the problem. Still, the thermal transport of the materials must be optimized while at the same time avoiding the degradation of the electrical properties. A deep understanding of the phonon transport phenomena have led to many different approaches and guidelines, which have resulted in significant improvements during the last two decades[5,16]. Among them, nanostructuration has been found as one of the most effective methods, predicted to enhance the electrical properties untying the interdependence of the Seebeck coefficient and the electrical conductivity, and it has shown its best efficacy in reducing lattice thermal conductivity.[16–21] Up to now, different families of complex materials have displayed notably high dimensionless figures of merit, such as the long-known Bi2Te3
compounds for room temperature applications, as well as filled skutterudites, tetrahedrites, half-Heusler alloys, rare-earth chalcogenides, clathrates etc. Other novel materials include conductive polymers or carbon based nanomaterials. [22] However, the elaboration methods of highly efficient materials need expensive equipment, several steps of preparation and specific physicochemical conditions. These requirements are one of the main obstacles for the large scale production and general application of thermoelectric materials.[23,24]
For these reasons, this Thesis deals with straightforward and fast techniques based on arc-melting and high-pressure synthesis. We have been able to prepare different families
6 of thermoelectric materials including Bi2-xSbxTe3 and Bi2(Te1-xSex)3 alloys, SnSe and related alloys, and CoSb3 compounds[25–27]. Bismuth tellurides are well-known thermoelectric materials that were first synthesized to acquire thermoelectric background and knowledge about specific features of the methods employed.
Afterwards, the outstanding report of a record figure of merit of 2.6 in SnSe single crystals[28] directed this work towards the study of the structural and physical properties of bulk compounds based on this material. Finally, skutterudite compounds based on the phonon-glass electron-crystal concept[15] were prepared using high- pressure synthesis, which led to the enhancement of the thermoelectric properties. These methods yield highly nanostructured samples prepared in really short times, which require no further processing and are directly implementable into devices. This dissertation addresses the following points:
- Synthesis conditions of the direct preparation by means of arc-melting of known Bi2Te3 and novel SnSe derivatives.
- Preparation under high-pressure and moderate temperatures of filled CoSb3
skutterudites.
- A detailed structural study, performed by Neutron Powder Diffraction (NPD) or Synchrotron X-Ray Diffraction (SXRD) to unveil the relationship between the crystallographic structure and the physical properties of the materials.
- The study of the morphological features of the samples by Field-Emission Scanning Electron Microscopy (FE-SEM) or High Resolution Transmission Electron Microscopy (HRTEM), which has a great influence on the thermoelectric properties.
- Finally, evaluation of the thermoelectric properties of the different materials by various procedures, and discussion of the potential methods to improve the thermoelectric performance.
7
I.2 Historical Background
Two hundred years ago (1821), Thomas J. Seebeck showed that an electrical potential is produced when a temperature difference is established at the junction of two metals.
Sometime later, in 1834 J. Peltier observed how the junction of two different conductors was heated or cooled when a current flows through. It was not until Lord Kelvin (a.k.a.
William Thomson) demonstrated the relationship between the Seebeck and the Peltier effect, and a third thermoelectric effect, the Thomson effect, in 1851, that a connection between these effects was recognized.[3,4]
For several years, thermoelectric materials remained as a mere mean to measure temperature. Alternkirch in 1909-1910 was the first one to correctly deal with the theory of thermoelectric generation and coined the term “figure of merit”. He determined a dependence of the thermoelectric performance on the Seebeck coefficient, the electrical resistivity and thermal conductivity[29]. Later, in 1947, Telkes fabricated a generator with 5% efficiency thanks to the recent developments in the preparation of semiconductors[30].After a Theory of Electronic Semiconductor[31] was published in 1940, Ioffe described a complete model of semiconductor thermoelements and related the atomic weight of the atoms to the thermal conductivity of the materials[32,33]. In 1954 Goldsmith and Douglas prepared a Bi2Te3 based device and discussed the relation between electron mobility and thermal conductivity with atomic weight[34]. The ratio of thermal to electrical conductivity was still too high in semiconductors due to their deficient electrical properties. Nevertheless, in 1956, Ioffe showed how doping with isomorphous compounds decreased the thermal conductivity avoiding any deterioration of the electrical resistivity[35]. In 1959, Chasmar and Stratton[36] expressed the figure of merit in relation to the Fermi-Dirac equations and determined a maximum value of zT. The effects of the band gap on the thermoelectric efficiency were considered. It was in the 50’s when Bi2Te3 and Si-Ge materials were developed and commercialized.
For some period between 1960 and 1990, the interest in thermoelectric research declined due to low conversion efficiencies. It was only developed in an industrial context in situations where the need for energy availability and reliability overcomes energy efficiency and cost. Owing to spacecraft requirements, where there is no refueling and no other device for energy generation is available, radioisotope
8 thermoelectric generators (RTGs) were implemented. Voyager spacecraft were equipped with Si-Ge modules and have been operating uninterrupted since the 70’s[37].
During the 90’s some US funding agencies offered incentives in the thermoelectric research field looking for possible new applications[16]. Then, in 1993, Hicks and Dresselhaus predicted an improvement in the thermoelectric performance by layering a highly anisotropic thermoelectric material, such as Bi2Te3, in the form of quantum-well superlattice structures[38]. They also studied the dependence of thermoelectric properties on the width of a quantum wire and proposed an even larger enhancement of the efficiency[39]. On a different track, Slack proposed the concept phonon-glass electron-crystal (PGEC), defining a crystal structure where heavy atoms in atomic cages act as ‘rattlers’, as phonon scattering centers decoupled from the crystal vibrations, while the electron transport is not affected[15].These predictions boosted the interest in thermoelectric research and divided it into the study of new bulk compounds and low- dimensional systems.
Bulk materials research focused on the study of high atomic weight compounds and the preparation of interfaces in a nanometric scale. In 1996, Mahan and Sofo discussed the transport distribution and the largest figure of merit attainable in terms of the electronic structure. They found that a narrow distribution of the energy carriers increases the thermoelectric performance[40]. New classes of materials emerged, like skutterudites[41], Half-Heusler alloys[42], Clathrates[43] and LAST[44]
(AgPnmSbTe2+m) among others, which fitted into the new approaches that were being developed. Kanatzidis et al. discovered the CsBi4Te6 as a thermoelectric material with promising properties for applications below room temperature[45]. Alongside, low dimensional systems, such as thin films and nanowires[46], were thoroughly investigated[47–49]. Via band engineering Heremans and Snyder improved the thermoelectric properties of known PbTe and proposed directing the convergence of electronic bands by changes in the composition[50,51]. Other approaches emerged from band engineering concepts, such as multivalley-band conduction, directional electronic states and resonant levels[52–55]. In a different line, Biswas et al., considered an all- scale hierarchical scattering, controlling the mesoscale features of nanostructured materials aiming to scatter phonons in a wide range of wavelengths[56]. Other strategies are: the preparation of nanocomposites[57], electron energy filtering and boundary scattering[58], atomic-scale structural engineering of thermoelectrics (ASSET)[59],
9 heavy-band materials[60], bond anharmonicity[61], magnon-drag[62]. The search for novel thermoelectric materials has become a hot topic and the reports of new phases with improved properties occupy an important space in the most reputed scientific journals. Far from exhausted, this exciting field of research deserves much attention, since optimized compositions, probably in novel, more complex, crystal structures, with specifically designed and engineered textures are still to be discovered.
Figure 3. Timeline of the Figure of Merit of different TE materials. Figure adapted from ref.
[63].
I.3 Transport Properties of Thermoelectric Materials: Basic Principles
In this section a brief overview of the main thermoelectric properties is presented. First, the three main thermoelectric coefficients and their connection are explained.
Subsequently, the basic expressions of the electrical conductivity and the thermal conductivity are described. Finally, an overview of the relation between the thermoelectric performance of a material and the efficiency of a thermoelectric device is given.
I.3.1 Thermoelectric Effects: Seebeck, Peltier and Thomson Effects
When a temperature gradient and no electric field are applied to a solid, electrons (or holes) will tend to diffuse from the hot to the cold end, inducing an electrical potential,
10 as they carry both charge and heat. This is a general description of the thermoelectric effect.
The first of them, the Seebeck effect, is associated with an electromotive force proportional to the temperature difference in an open circuit situation. Figure 4 shows a simple device that consists of two different conductors, A and B, joined at one end. If a heat source is applied to the junction, while the free ends are maintained at a certain temperature, charge carriers diffusion will generate a voltage drop, ΔV, between the free ends. The differential Seebeck coefficient is defined as the ratio between the voltage and the temperature difference:
𝑆𝐴𝐵=∆𝑉
∆𝑇 (2)
Figure 4. Basic thermocouple scheme.
The differential Seebeck coefficient of the thermocouple is equal to the difference of the absolute Seebeck coefficients of the conductors, which is characteristic of each material and depends on the temperature. It is denoted as S or α and also called thermopower or thermoelectric power. Typical values of the Seebeck coefficient in semiconductor materials are around hundreds of microvolt per Kelvin (μV K-1).
11 In a similar diagram (Figure 5), the differential Peltier coefficient, πAB, is defined when a current flows through two different joint conductors. Depending on the current direction, a reversible cooling or heating is generated at one junction, while the opposite effect takes place at the other. The heat flux density is proportional to the current density by:
𝜋𝐴𝐵 =𝑄
𝐽 (3)
Figure 5. Simplified sketch of the Peltier effect.
Again, the differential coefficient is determined as the difference between the absolute Peltier coefficients of each conductor 𝜋𝐴𝐵= 𝜋𝐴− 𝜋𝐵. This effect is related to the heat driven per charge carrier in each material and the energy released or absorbed when it passes through the junction.
One of the relations introduced by Lord Kelvin established a connection between the Seebeck coefficient and the Peltier coefficient. As the latter is much harder to quantify, this equivalence allows us to conduct our research only in terms of the Seebeck coefficient:
𝜋𝐴𝐵 = 𝑆𝐴𝐵𝑇 (4)
The Thomson effect arises from the temperature dependence of the Seebeck coefficient when a current flows through a conductor where a temperature gradient is established within. It is defined as the rate of heating or cooling per unit of temperature gradient and per unit current:
12 𝜏𝐴= 𝑇𝑑𝑆𝐴
𝑑𝑇 (5)
These two essential relations permit us to characterize the thermoelectric properties of a given material only by its Seebeck coefficient.
I.3.2 Transport Properties: Electrical and Thermal Conductivity
As well as the thermoelectric coefficients, the electric and thermal transport properties of the materials play a major role in the efficiency of a thermoelectric device. While the three thermoelectric effects are reversible phenomena, electrical and thermal resistances result in irreversible thermodynamic losses.
The electrical conductivity () is the reverse of the electrical resistivity and is defined as:
𝐼 =𝑉𝜎𝐴
𝐿 (6)
where I is the current that flows through a conductor with cross-section A and length L when a voltage V is applied.
Similarly, the thermal conductivity is defined for a conductor with unit cross-section perpendicular to the heat flow:
𝜅 = − 𝑄⃗
∇⃗⃗ T (7)
where 𝑄⃗ would be the heat flow through the conductor when a temperature gradient ∇⃗⃗ T is set.
Thermal conductivity is determined by many different factors. It is sensitive to crystalline defects, like dislocations and point defects, the grain boundaries and morphology, strength and anharmonicity of the chemical bonds, carrier-phonon interactions and magnetic elements among others. The contribution of the electronic thermal conductivity to the total thermal conductivity is described below.
I.3.3 Thermoelectric Devices and Figure of Merit
Seebeck, Peltier and Thomson effects are the spine for the production of energy as thermoelectric generators (TEG), and controlled cooling or heating, as thermoelectric
13 Peltier coolers (TEC). A thermoelectric module can perform both tasks depending on the configuration (Figure 6). It consists of a pair of n- and p-type thermoelectric materials, usually bar-shaped, connected electrically in series and thermally in parallel.
To build the module, they are packed in between two thermally conducting and electrically insulating ceramic plates. If an electric current flows through the module, heat will be released or absorbed in one of the ceramic plates, depending on the current direction. On the contrary, electric energy is generated when the module is connected to an electrical load and a temperature gradient is established between the plates.
Figure 6. (a) Simple representation of a TEC, (b) simple representation of a TEG.
Concerning the estimation of the module performance, it is assumed that there is no thermal resistance between the thermoelectric conductors and the heat source or sink.
Besides, any kind of thermal conduction of the surrounding is not taken into account, and all the heat flow would theoretically take place within the thermoelectric materials.
In this scenario, the primary irreversible energy losses arise from the electrical resistance, in the form of Joule heating, and Fourier heat conduction, which is proportional to the thermal conductance of the device and originates from the thermal gradient set between the source and the sink.
The quantity of interest for a TEC is referred to as the coefficient of performance (COP), which is the ratio of the heat extracted from the source to the expenses of electrical energy. When the current is optimized, the maximum COP is defined as:
a) b)
14 𝜙𝑚𝑎𝑥 = 𝑇𝐻
𝑇𝐶− 𝑇𝐻
(1 + 𝑍𝑇𝑚)1/2− (𝑇𝐶/𝑇𝐻)
(1 + 𝑍𝑇𝑚)1/2+ 1 (8)
Likewise, the thermoelectric efficiency of a TEG is the ratio of the energy delivered to the electrical load to the total heat flow. When the relation of the load resistance with the module resistance is optimized:
𝜂𝑚𝑎𝑥 =𝑇𝐻− 𝑇𝐶 𝑇𝐻
(1 + 𝑍𝑇𝑚)1/2− 1
(1 + 𝑍𝑇𝑚)1/2+ 𝑇𝐶/𝑇𝐻 (9)
In both cases, if the form factor is optimized, the module figure of merit is:
𝑍𝑇𝑚 = (𝑆𝑝− 𝑆𝑛)2
[(𝜅𝑝𝜌𝑝)1/2+ (𝜅𝑛𝜌𝑛)1/2]2
𝑇𝑜𝑝 (10)
It can be observed that when Z tends to infinity, the efficiency approaches the Carnot limit: TH/(TC-TH) and (TH-TC)/TH. Figure 7a shows the generator efficiency as a function of ZTm for different heat source temperatures.
This value is only useful to determine the performance of a thermoelectric couple of materials. Thus, it is more convenient to define a figure of merit for a single thermoelectric material than for a module, as it is not common to investigate a pair of materials at a time:
𝑧𝑇 =𝑆2𝜎
𝜅 (11)
It is not accurate to calculate the efficiency of a module using solely z, however the average of zp and zn usually lies near Z. Therefore the figure of merit of a single material becomes meaningful in order to distinguish materials with higher performance.
15 Figure 7. (a) TEG efficiency as a function of ZTm, (b) State-of-the-art zT for bulk TE materials[28,44,56,60,64–78].
Nowadays many promising materials have shown zT>1, which yield conversion efficiencies around 10%, however a figure of merit above 3 would be needed for cost- effective applications from a technological point of view[12]. Furthermore, a large
a)
b)
16 average figure of merit in a wide temperature range and stable and mechanically robust materials are necessary for adequate practical applications, which make finding a suitable TE material for generalized implementation of devices a challenging task.
Figure 7b shows some state-of-the-art zT as a function of temperature for different materials. Bismuth telluride and lead telluride compounds are still the best option for room and middle temperature applications respectively. Nevertheless in high temperature applications Si-Ge modules has lost its dominant spot, as new promising materials have emerged during the last years.
I.4 Strategies to Improve Thermoelectric Performance
The thermocouples are made of metallic elements, which present negligible Seebeck coefficients and high thermal conductivities. Therefore they are not appropriate for thermoelectric applications. It was after Ioffe’s theory on thermoelectric semiconductors that Bi2Te3 and Si-Ge materials were developed and the figure of merit improved to values close to one. Since the theoretical predictions on low-dimensional systems and nanostructured materials in the 90’s, efforts in the thermoelectric field have significantly grown over the past years[79]. Due to environmental concerns and technological advances, the production and development of enhanced thermoelectric materials has experienced a revival. Nowadays there are many different lines of research for the improvement of the figure of merit[54,79,80]. In this introduction, approaches used in bulk thermoelectric materials research will be briefly described.
The beginning of this chapter revises the fundamental notions necessary to recognize the features that affect the transport properties. Then, the main approaches that are currently exploited aiming to improve the figure of merit of bulk thermoelectric materials will be described.
I.4.1 Basic Concepts
In order to deal with the optimization of the figure of merit, it is imperative to understand the interdependence that is characteristic of its components: the Seebeck coefficient, the electrical conductivity and the thermal conductivity. These three parameters are not entirely independent as they all are linked to the crystallographic and electronic structure of the material.
17 A first suitable condition is that only one kind of charge carriers should intervene in the transport properties at the temperature of operation. If both, holes and electrons, diffuse equally towards the cold end of a solid, the Seebeck effect would be cancelled. In degenerate semiconductors and using single-parabolic band approximation:
𝑆 =8𝜋2𝑘𝐵2𝑚∗𝑇 3𝑒ℎ2 (𝜋
3𝑛)
23 (12)
where kB is the Boltzmann constant, T the absolute temperature, m* the density of states effective mass, h the Plank constant, e the electron charge and n the carrier concentration. This equation follows the general rule that establishes a reverse relation between charge carrier concentration and Seebeck coefficient, which is called Pisarenko relation after Mr. N. L. Pisarenko, and was reported in the seminal monograph on thermoelectricity by Abram Ioffe[33].
At the same time the electrical conductivity is directly related to the carrier concentration, n, through the carrier mobility, μ:
𝜎 = 𝜇𝑒𝑛 (13)
As shown in equations 12 and 13, carrier concentration optimization is one of the main challenges in thermoelectric research. There must be a compromise between Seebeck coefficient and electrical conductivity in order to maximize the power factor, which is usually achieved for heavily doped semiconductors with carrier concentration in the range 1019-1021 cm-3[4].
Besides, the effective mass m* plays a relevant role in the transport properties. Large effective masses are associated with peaks in the density of states (DOS) and localized electronic bands, which could result in low carrier mobility but high Seebeck coefficient. This relation is complex and depends on the anisotropy, scattering mechanisms and the electronic structure[81]. Commonly, ionic compounds formed of elements with large electronegative differences present high effective masses, while materials made of elements with small electronegativity difference usually show large mobility and small effective masses.
Though the electron mobility and carrier concentration depend mainly on the structure of a material, other aspects can play an important role determining the electrical conductivity in bulk systems, such as grain connectivity, morphology or density.
18 Figure 8. Carrier concentration dependence of the Seebeck coefficient, electrical conductivity, power factor and thermal conductivity. Adapted from ref [12].
Moreover, it is important to realize that the thermal conductivity comes from two different sources: electrical carriers transporting heat (κele) and phonons that circulate through the structure (κlat). There is a fundamental relationship between the electronic contribution to the thermal conductivity and the electrical conductivity, the Wiedemann- Franz law:
𝜅𝑒𝑙𝑒= 𝐿𝜎𝑇 = 𝐿𝜇𝑒𝑛𝑇 (14)
where L is the Lorentz number and T the absolute temperature. The Lorentz number depends on the particular band structure and carrier concentration of a material, however is identical for metals. Kim et al. proposed a suitable approximation that allows an estimation of the Lorentz number with no further calculations[82]:
𝐿 = {1.5 + exp [− |𝑆|
116]} ∗ 10−8 𝑊𝛺𝐾−2 (15) This approximation yields much better results than using a constant value. It presents a 5% error compared to the SPB-AS method. The Wiedemann-Franz law displays another
19 of the intrinsic conflicts towards the optimization of the figure of merit, as a high electrical conductivity is directly related to a high electronic thermal conductivity.
A wide spectrum of phonon frequencies and mean free paths, from 1 nm to 10 μm, are responsible for the lattice thermal conductivity[3]. This diversity makes it hard to find effective phonon scattering mechanisms. A simple kinetic approximation defines the lattice conductivity of a crystal structure as a function of the sound velocity in the material, vs, heat capacity at constant volume, Cv, and the average phonon mean free path, lph:
𝜅𝑙𝑎𝑡 =1
3𝐶𝑣𝑣𝑠𝑙𝑝ℎ (16)
As heat capacity and sound velocity are invariant at high temperature, optimization approaches are directed towards the reduction of the phonon mean free path. The crucial obstacle to address this task is the possible deterioration of the charge carriers’ mobility due to common scattering mechanisms of phonons and electrons (or holes). The lower limit of the lattice thermal conductivity is associated with amorphous materials, such as glasses, where the random distribution of atoms disrupts phonon transport at any wavelength. The concept of phonon-glass electron-crystal (PGEC) originates from the idea of a crystalline material where “phonon mean free paths are as short as possible and in which the electron mean free paths are as long as possible”[15]. Usually, scattering mechanisms are introduced in the crystal lattice as structural defects, mass fluctuation via isoelectronic substitution, dislocation, grain boundaries or phase separation.
Upcoming sections will discuss some of the current strategies to manage all the difficulties that lie in the way towards optimized thermoelectric transport properties.
Research on low-dimensional systems, such as nanowires, thin-films and quantum dots is not covered in this work.
I.4.2 Strategies to Improve zT in Thermoelectric Materials I.4.2.1 Electronic Band Engineering
The approach about Electronic Band Engineering focuses on the enhancement of the electronic properties by modifications of the band structure of a material. The most representative example is the enhancement of the Seebeck coefficient in PbTe using Tl
20 as dopant reported by Heremans et al. in 2008[50,83,84]. When Tl is introduced in the crystalline structure, the dopant element states are in resonance with the host material valence or conduction bands. This alteration has a concomitant increase of the density of states effective mass, which results in an enhanced Seebeck coefficient that deviates from the Pisarenko relationship. The same effect has been found in other thermoelectric materials, such as Sn-Bi2Te3[85], SnTe-AgInTe2[86], In-doped SnTe[87] and Al-doped PbSe[88].
In a similar way, lead telluride has provided the basis for the convergence of electronic bands concept. PbTe electronic structure presents two valence bands close to the Fermi level, one of them is a light hole band at the L symmetric point, significantly higher in energy than the other, a heavy band at the Σ point[89,90]. When the system is alloyed in the Pb sublattice, the energy offset between the bands is reduced and the charge carriers are distributed among them, increasing valley degeneracy and density of states effective mass. PbTe alloyed with Mn and Mg[53,91], as well as other systems such as PbSe- SrSe[92] and SnTe[93] have shown this behavior.
Figure 9. Representation of the valence bands relative energy of PbTe, where solid solutions of Mg or Mn[53,91] push both L and Σ down, situating them closer in energy (adapted from ref [54]).
I.4.2.2 PGEC and Complex Crystal Structures
As described above, the concept PGEC introduced by Slack in 1995 involves the search of new thermoelectric materials with electrical conductivity is as high as in crystalline materials and lattice thermal conductivity as low as in amorphous solids. There is no clear path to find an ideal thermoelectric material that fulfills this description, but there
21 are different strategies that can be followed and have resulted in distinct novel families of materials. The most characteristic materials associated with the PGEC concept are the skutterudites[41,94,95], clathrates[5] and Zintl compounds[96]. The notion behind these materials is a crystalline structure where two distinct regions could be electronically and thermally disconnected. A sublattice providing strong phonon scattering would be entangled within another one providing high carrier mobility.
Skutterudites and clathrates present voids within the unit-cell where caged atoms can be placed. In this scenario the charge carriers’ transport occurs through the cage framework while phonons are scattered by the isolated ‘rattling’ atoms inside the cage. Experiments have shown how this approach is able to maintain a high power factor while the lattice thermal conductivity is lowered[97–101]. Recent inelastic neutron scattering studies of these materials’ phonon spectra have described the interaction of the rattlers with the phonon dispersion process, showing a coupling between the main grid and the caged atoms[99,102,103]. Another type of materials, Zintl compounds, shows the two distinct sub-structures in a different way. They are composed of an anionic sublattice covalently bonded that can adopt many different complex substructures. The charges are balanced by a cationic sublattice for which the interactions are mainly electrostatic. Disorder in this second region would yield the phonon-glass character while the covalent grid provides suitable electronic properties. Zintl compounds, Zn4Sb3 and CaxYb1–xZn2Sb2
have shown surprisingly low thermal conductivity in the mid temperature range and a high figure of merit due to disorder at very different length scales in the cationic framework[77,104].
Based on similar concepts, numerous materials with complex crystalline structures have been investigated. Yb14MnSb11 presents an extremely low lattice thermal conductivity resulting from its large molecular weight and complex unit-cell in the space group I41/acd[105,106]. In CsBi4Te6, a more complex structure than Bi2Te3 and the formation of new Bi-Bi bonds shift the maximum figure of merit to below room temperature, where it reaches values close to 0.8. The unit-cell of Ag9TlTe5 consists of 180 atoms and 12 molecules weakly bonded in a hexagonal crystalline structure in the R-3c space group. Despite its intrinsic low carrier mobility, it shows a figure of merit as high as 1.23 at 700 K thanks to a glass-like thermal conductivity[75].
22
Figure 10. Crystal structure of a) Yb14MnSb11[96] and b) Ag9TlTe5[75].
I.4.2.3 Nanostructuring
Reducing the dimensionality of thermoelectric materials should yield enhanced properties by various means. Quantum confinement is predicted to enhance the power factor through new density of states peaks near the Fermi level and a more independent behavior of the electrical conductivity and Seebeck effect, which results in a dimensionality dependence of the figure of merit (Figure 11). Besides, interfaces on a nanometric scale close to the phonon mean free path would significantly increase boundary scattering and affect a wide range of the phonon spectrum[79,80,107].
Figure 11. Two- and one-dimensional zT dependence on the layer thickness and nanowire diameter, adapted form ref [38].
a) b)
23 Even though the reduction of the thermal conductivity through nanostructuration has been proven experimentally[16,108], quantum confinement predictions on the power factor are still to be demonstrated. Advances in the field of nanotechnology have made it possible to develop new synthesis methods, in which the morphology of the materials can be controlled in a nanometric scale. The main difficulty in the preparation of bulk nanostructured materials is the possible simultaneous decrease of carriers’ mobility and lattice thermal conductivity, consequence of boundary scattering at grain interfaces.
One representative example of nanoparticles in a matrix are the LAST (AgPbmSbTe2+m) compounds. At certain Ag and Sb compositions, nanoscale constituents precipitate in the matrix, which results in a marginal deterioration of the electrical properties overcome by the reduction of the lattice thermal conductivity[17,109,110].
The formation of bulk samples formed of nanosized grains has led to improved performance in nanostructured BiSbTe alloys. Nanocrystalline Bi-Sb-Te alloys synthesized by ball milling and hot-pressing have shown zT as high as 1.4.[111] In order to reduce bulk thermal conductivity, bismuth-antimony-telluride alloys were synthesized from their oxide reagents in a high temperature melting and reduction process, which allows control of microstructure morphology, reaching values of zT=0.7 for Bi0.4Sb1.6Te3.[112] Zhang et al. achieved a zT=0.51 in optimized Bi0.5Sb1.5Te3 by a controlled synthesis of nanoplatelets and its sintering through SPS to form bulk nanocomposites, as a scalable bottom-up process.[57] In these examples, a more extended grain interface increases phonon scattering and induces electron energy filtering[83], leading to enhanced power factor and reduced thermal conductivity. A natural continuation of this approach is to target the whole phonon spectrum. Using the synthesis control of all-scale hierarchical structures[56] that constitute the materials, and considering all length scales of phonon mean free path, is suggested to maximize lattice thermal conductivity reduction. This is achieved by the introduction of defects or disorder on an atomic scale[113] and nanometric inclusions[114–116] to mesoscale grain interfaces[117–122]. These three scales are targeted by alloying, formation of solid solutions, point defects, nano-precipitates or nano-inclusions and synthesis methods that yield fine-grained materials with appropriate connectivity. A huge 55%
reduction of the thermal conductivity of Na-doped PbTe has been reported by addition of SrTe nanoinclusions and further grain boundary scattering by nanostructuration, leading to a figure of merit as high as 2.2 at 915 K[56].
24 Apart from bulk thermoelectric materials with nanoscale constituents, much effort has gone into the field of low-dimensional systems. Pioneering breakthroughs have been achieved since 1993, when Dresselhaus and Hicks predicted an exciting enhancement of the figure of merit by reducing the dimensionality of the materials to a quantum regime[38]. Besides, quantum-confinement phenomena are supposed to allow the independent treatment of the transport properties and yield a sharp increase of the density of states distribution. Urged by these predictions, thermoelectricity researchers have used new technologies and methods to design these systems, such as superlattices, nanowires and quantum-dots[16,47,123].
Most attempts to implement these theoretical predictions into actual materials are carried out in superlattices and nanowires. Supperlattice usually refers to periodic structures which are formed of alternating nanometric layers of different thermoelectric materials. Depending on the current direction, they can take advantage of interface phonon scattering, electron energy filtering and quantum size effects[47]. A study on Bi2Te3/Sb2Te3 has shown an impressive figure of merit of 2.4[124] due to reduction of thermal conductivity, however it has not been reproduced yet. Enhancements of the zT in different materials’ superlattices have invariably been reported mainly as a consequence of the reduction in thermal conductivity[125–127]. Nevertheless, transport properties values must be carefully considered due to the measurement difficulties in nanometric systems.
The largest effect predicted due to quantum confinement on the thermoelectric properties would occur in 1D system such as nanowires. Singularities, increasing enormously the density of states, appear when the diameter of the nanowires is sufficiently decreased. Bismuth nanowires were extensively studied because of the predicted transition from a semimetal to a semiconductor driven by two-dimensional quantum confinement effects, which was observed in 1998[128]. Owing to the inherent difficulties of the transport property measurements of one-dimensional systems, not much information about the thermoelectric properties is reported in the literature[129].
One of the most common methods of preparation is carried out in alumina templates by electrochemical deposition, as shown in Figure 12. This procedure has been successfully used to form nanowires of several different materials, such as Bi2Te3[130], Bi1-xSbx[131] or PbTe[132], with a diameter as low as 15 nm. In nanowires as well as in superlattice structures, an enhancement of the thermoelectric performance is observed
25 due to the reduction of the thermal conductivity, and a further reduction of the nanowire size is needed to observe the quantum confinement phenomena in the transport properties[47].
Figure 12. Porous alumina templates of different diameters synthesized by anodization, adapted from ref [47].
I.5 Synthesis Methods of Bulk Thermoelectric Materials
In this section a brief overview of the most common synthesis procedures currently used to prepare thermoelectric materials is given. There are several factors that must be taken into account in order to prepare the materials with the desired morphology and properties. Moreover, the wide range of elements and systems that form thermoelectric materials makes it necessary to develop synthesis methods adequate for each aspect.
Therefore, different chemical and physical routes have been used to understand the particular effects of the synthesis conditions on the specific features of the materials with the ultimate purpose of modifying the transport properties.
I.5.1 Melting Processes
Perhaps the simplest and most straightforward method is when stoichiometric powders of the constituent elements are directly melted at high temperature, to finally slowly cool or quench them to room temperature. There are different melting techniques convenient for different purposes. Traditional melting consists of heating a mixture of
26 the reacting powders above the melting temperature inside sealed ampoules. It is useful for initial preparation, however it does not allow controlling either grain morphology or other features such as anisotropy. This difficulty is usually overcome by zone melting, in which the melting process is carried out by moving the sample inside a furnace where a temperature gradient is stablished and where temperature and growth are carefully controlled[133]. Condition temperatures and cooling rate are selected depending on the phase diagram of the compounds to yield the desired alloy composition and these differ for each different doping element[53,134]. In levitation and arc melting techniques an instantaneous melting of the elements is achieved at high temperatures, by means of an oscillating magnetic field or a high-current electron beam. These methods are fast and useful for the preparation of intermetallic compounds[135,136]. A method for rapid cooling is melt spinning, in which a molten stream of material is dropped onto an internally cooled and rotating wheel. High-performance Bi-Sb-Te alloys have been obtained by this method[68,137,138]. After melting, materials are usually annealed to remove unwanted impurities and defects, and finally compacted by hot-pressing (HP) or Spark Plasma Sintering (SPS)[136,139,140].
I.5.2 Mechanical Alloying
Mechanical alloying comprises the high-energy ball milling process of the thermoelectric materials or stoichiometric mixtures of elemental powders. It is used either to synthesize materials, requiring long periods of time, or in order to reduce grain size to a nanometric range, as per the nanostructuring approach. Afterwards, the powders are compacted into ingots by HP or SPS. Reports on Pb0.98Tl0.02Te, Cu2Se and La3-xTe4 are some examples of thermoelectric materials that have shown high figures of merit through the preparation by this procedure[65,134,141].
I.5.3 Wet-Chemical Routes
The different methods encompassed in wet-chemical routes are based on chemical reactions in a liquid phase or solution at various temperatures that use many different precursors to prepare nanoparticles. Ligand-assisted chemical methods are useful to obtain small particle size, shape and crystallinity. Nevertheless, the insulating organic capping ligands must be completely removed from the nanocrystals before bulk pellets can be formed. The zT values of most chemically prepared materials are low, affected
27 by inappropriate carrier concentrations and lousy intergranular connectivity[23,24].
Other important chemical techniques are the solvothermal and microwave synthesis, and the polyol method.
I.5.4 Solvothermal Synthesis
A precursor solution made of the reacting compounds and a specific solvent is sealed in an autoclave. It is exposed to high-temperature conditions, which are meant to create a controlled situation of high-vapor pressure. The main experimental parameters used to regulate the process are reaction time and temperature, solvent and precursor type and temperature program. Thus, this method allows controlling grain shape, crystallinity and distribution of nanostructured particles. When an aqueous solution is employed, this method is called hydrothermal synthesis. PbTe powder can be prepared from lead acetate, Te, NaOH and NaBH4 in an ethanol/glycol/acetone mixture by this method[142]. Moreover, many Bi2Te3 derivatives have been prepared by this method[107].
I.5.5 Polyol Method
Another synthesis technique is based on specific precursors dissolved in an alcohol solution, commonly ethylene glycol (EG) or hexadecadiol, which act as reductant and surface protecting agents for nanoparticles. A moisture assisted solid-state reaction takes place using different energy sources, to yield the desired nanocrystals. This method allows control of the nucleation, grain shape and size on micro- and nanometric lengths with a low grade of agglomeration[107,143,144].
I.5.6 Microwave-Assisted Synthesis
Molecules in a solution are excited by an external electromagnetic source, microwave radiation. It is a reliable method for which the reaction rates are rather enhanced.
Typically the precursors are sealed in an ampoule or autoclave and exposed to microwave radiation[145]. Half-Heusler alloys TiNiSn have been prepared by microwave synthesis leading to special microstructures and a figure of merit enhancement up to 0.44 at 723 K[146]. Lead acetate and thiourea have been used to prepare PbS nanoparticles with particle size in the 30-200 nm range, in ethanol, water, ethylene glycol and polyethylene glycol-200 solutions[147].