Index of /rozprawy2/11250

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AGH UNIVERSITY OF SCIENCE AND

TECHNOLOGY

Faculty of Materials Science and Ceramics

Department of Inorganic Chemistry

DOCTORAL DISSERTATION

Functionally graded thermoelectric materials

obtained under strong gravitational field

Kamila Januszko

Supervisor:

prof. dr hab. inż. Krzysztof Tomasz Wojciechowski

Co-supervisor

prof. dr inż. Tsutomu Mashimo

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1

Acknowledgements

I would like to express my gratitude to professors K.T.Wojciechowski of AGH University of

Science and Technology and T. Mashimo of Kumamoto University, for their support, valuable

suggestions and kind guidance and encouragement in carrying out this PhD dissertation.

I would also like to express my gratitude to prof. A. Yoshiasa in Department of Science

and prof. H. Ihara in Department of Applied Chemistry and Biochemistry for their valuable

support, encouragements and suggestions.

Thanks are due to all colleagues in my research group at Kumamoto University

(especially Dr. Ogata, Dr. Rabaya, Mr. Sakata, Mr. Shimowaki, Mr. Tokuda, Mr. J.I.Khandaker,

Mr. Kiyohara and Mr. Jo) and other research groups of Mashimo Laboratory (Prof. Emil, Dr. Chen,

Dr. Zhypargul Abdullaeva

,

Dr. Liu, Dr Zhazgul Kelgenbaeva) from other research groups of

Mashimo Laboratory and Mr Nakatani from Prof. Yoshiasa group.

I would like to express my gratitude to the colleagues from the Thermoelectric Research

Laboratory, especially Dr Juliusz Leszczynski, for his valuable suggestions and encouragement

Rafał Zybała, Artur Stabrawa, Paweł Nieroda, Mr Chetty and Mrs Krishna Raut for their support,

help and advice and all colleagues from the Department of Inorganic Chemistry at AGH

University of Science and Technology.

Thanks are due to Prof. Jaworska and Mr Andrzej Kalinka for help and support for SEM

measurements undertaken in the Institute of Advanced Manufacturing Technology and Mrs

Barbrara Trybalska and Mrs Magdalena Ziąbka for support of SEM measurement at AGH

University of Science and Technology.

I would like to express my gratitude to Dr Konrad Świerczek and his team in Faculty of

Energy and Fuels for his help and support in XRD measurements.

Finally, I would like to thank my parents for their continuous support.

This work has been partially supported by National Science Centre (NCN) as pre-doctoral

grant for research project (

UMO-2012/05/N/ST8/03390

) ‘Thermoelectric graded materials’ in

2013-2016. The part of the research carried out in Japan was also a part of Global Centers of

Excellence program.

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Contents

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List of symbols and abbreviations

SYMBOLS

a0, c0 - lattice parameters

α – Seebeck coefficient cp - specific heat

e –mathematical constant: the base of natural

logarithms, also electron charge

E- electromotive force (EMF),

⃗ - electrical field

I – electrical current l – length

lp – phonon mean free path

L- Lorenz number

- thermal conductivity

N –impurity concentration n - carriers concentration

µ - mean (expectation parameter) v –sound velocity

ηmax – maximum efficiency

ηC –Carnot efficiency

q - heat flux

QP – heat absorbed or emitted at the joints of the

circuit PF – power factor Π – Peltier coefficient R- total resistance ρ – electrical resistivity s- compatibility factor

σ – electrical conductivity; also standard

deviation as stated in text

T- temperature

TC – temperature of hold side in TE

TH - temperature of the hot side in TE

ΔT – temperature difference

x-distance

ZT – non-dimensional thermoelectric figure of

merit

ABBREVIATIONS

a.u. – arbitrary units

FGTM – Functionally Graded Thermoelectric Materials

G –gravity force; also gravitational constant as stated in text

RT – room temperature

SEM –Scanning Electron Microscope, Scanning Electron Microscopy

SPS – Spark Plasma Sintering (also FAST Field Assisted Sintering Technique)

STM - Scanning Thermoelectric Microprobe TE - thermoelement

TEC – Thermoelectric Cooler/Thermoelectric cooling

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Preface

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Preface

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Energy production and energy saving are some of the biggest challenges in the modern world. As energy is still mainly produced using large amounts of resources, saving it seems like the best idea, until new source of energy that would be able to provide desired amount of energy in all the forms needed by humanity could be found.

Thermoelectric materials and devices are meeting quite an amount of expectations in the field of energy saving. Not only could they support other energy –related solutions like solar panels, but these can be used e.g. in waste heat recovery by producing electrical energy with thermoelectric generators TEG using this heat, that usually would be emitted to the atmosphere (in electrical and heat plant or in cars). These devices are practically failure-free and need almost no maintenance. This is why TEGs are used in space probes like Voyager or Curiosity allowing them to work without human intervention for several tens of years. Their main imperfection is their efficiency of only around 10%. In order to improve it many materials scientists are looking for new materials and are trying to improve already known ones for better performance. Optimization of the materials, thermoelectric elements and thermoelectric generators is still an important challenge (even though the first investigations about thermoelectric materials reach XXth century) and leaves some space for improvement.

Until now, many methods of improvement of TE parameters of materials by structural modifications are still under the investigation. One of them is doping of the e materials that are well known or show promising properties, e.g. Bi2Te3–Sb2Te3, Bi-Sb alloys, skutterudites or clathrates, whose size of the unit

cell gives hope to improve some of the transport properties (thermal conductivity is low, however the electric conductivity and Seebeck coefficient are not sufficient). Another method is combining few different materials with relatively optimal thermoelectric properties in certain, but different temperature ranges into one segmented element that could be effective in wider range of working temperatures. Inhomogeneous materials could solve the problems that arise in case of segmented elements preparation and were proposed in XXth century, however obtaining material which is graded in whole sample length with the desired carrier concentration is a task that is yet to be fulfilled. This is a matter, where sedimentation in solid state could be the best solution, if only such a process could be performed in controlled manner.

Gravity, especially as a tool used for modification of physical and chemical properties of materials, is a field which has a lot to be researched on. Even though in the field of microgravity the amount of the investigations and approaches increased, in case of mega-gravity forces, it is yet barely investigated area, which has a lot of inspiring challenges to overcome. One is of course artificial production of strong gravity forces, as studying the phenomena directly in space on this level is still yet to come. However, as scientist started to investigate the influence of the mega-gravity on the matter, they strived to substitute it by using ultracentrifuge, which could put the accelerations (inertial forces) simulating mega-gravity forces. Currently one of the most successful approaches in extreme-conditions processing of materials are taking place in Japan. At JAEA and Kumamoto University the ultracentrifuges allow proceeding with the centrifugal forces of 106 G, moreover in elevated temperatures that were unobtainable before. Therefore it was possible to obtain the sedimentation of the atoms in the solid state. It is an amazing result, which could allow also other scientists to pursue further investigations that were not possible before, by opening new path.

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Preface

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This could also be a new path for modification of properties of thermoelectric materials. Since as aforementioned, the sedimentation of the atoms in solid state if optimized and controlled could allow creation of desired gradient of chemical composition, resulting in desired carrier concentration profile followed by thermoelectric properties.

It is to be noted that by ‘gravity field’ and ‘gravity force’ in both micro and macro-gravity research that are not being led on in space one commonly refer to conditions (inertial force) corresponding to such fields and forces, as it is in the following doctoral dissertation.

Outline of the present study

In this study, in Chapters 1 and 2 short introduction about the contents of the study is presented and the scientific background is given in order to allow readers to understand motivation, contents and aims of the research clearly. The thesis and goals of the research work formulated by the Author close this part.

In Chapters 3 and 4 ultracentrifuge at Kumamoto University used for gradation process and Scanning Thermoelectric Microprobe (STM) at AGH University and Science and Technology for thermoelectric properties investigation are being described in detail.

Chapter 5 is divided into two parts. First is focused on expanding the matter of obtaining graded structure in Bi-Sb system, followed by obtained results. In second part results of further investigation of Bi-Sb system with the different chemical compositions and gradation profiles and discussion of possible further optimization of the process is presented.

Chapter 6 contains the description of expanding investigation to pseudo –binary Bi-Sb-Te system, which allows unfolding other applications of the gravitational method for thermoelectric materials, altogether with some experimental data.

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Chapter 1 Principles of optimization of thermoelectric properties of materials

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Chapter 1 Principles of optimization of

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Thermoelectric phenomena in solid state

There are known three main thermoelectric phenomena: Seebeck effect, Peltier effect and Thomson effect. However, in this chapter only first two will be briefly explained as these are mainly related to the materials used for this study. The Thomson effect, despite that it is very common, is not practically utilised in devices for energy conversion.

Seebeck effect appears in almost all conductors. The only exceptions are superconductors (where the Seebeck coefficient is equal to 0). The phenomenon is presented at schema 1.1.(a). If two conducting materials are connected and the connections (joints) are being kept in two different temperatures T1 and

T2 a certain voltage is produced causing a flow of electric current within material. This created voltage E

is called electromotive force (EFM) or thermoelectric power and could be presented as: (1.1) E=α(T1-T2)

where:

α – Seebeck coefficient [V/K] T1, T2 – temperatures at joints [K]

Seebeck coefficient (α) is a material parameter depending both on physical properties of two connected materials and temperature.

The set of two connected materials, as shown in Fig. 1.1.(a), is called a thermocouple and is commonly used in sensors of temperature. The Seebeck phenomenon can be also used in creating the electric power from the temperature gradient in thermoelectric generators.

Depending on type of majority current carriers (electrons or holes) the value of Seebeck coefficient varies from negative to positive values. Being slightly negative or positive in metals (e.g. about -70µV/K for Bi and 35µV/K for Sb), whilst for semiconductors it is reaching more than 1mV/K (e.g. for n-type and

p-type Si/Ge alloys).

The Peltier effect appears in form of heat effects (cooling or heating) in result of electrical current passing through the junction of two different conductors. In this case, as presented in Fig. 1.1 (b), absorption and production of heat Q1 and Q2 at the junctions, depending on direction of electrical

current I, can be observed.

The quantity of the heat transported by the carriers (electrons or holes) is described by Peltier coefficient:

(1.2)

where:

Π – Peltier coefficient

QP – heat absorbed or emitted at the joints of the circuit

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It should be noted that in real materials, the total heat generated is not determined by the Peltier effect alone, as it may also be influenced by Joule-Lenz heating caused by electrical resistance of junctions and materials.

The Peltier effect is the opposite to the Seebeck effect. So called ‘Peltier modules’ are used i.a. in devices for cooling purposes like thermoelectric fridges or for cooling the electronic parts inside computers, but also in advanced specialized cooling of the systems in industrial processes or laboratories.

Lord Kelvin found that the Peltier and Seebeck effects are in fact different manifestations of the one thermoelectric effect. Particularly, he has proved that:

(1.3)= T·

This relation expresses fundamental connection between both effects and allows direct calculation of the Peltier coefficient  if the Seebeck coefficient of the material is known.

In the classical approach, the Seebeck and Peltier effect are considered to be a surface phenomena, because they appear at the interface of conductors. Usually materials for conductors are homogeneous, i.e. electrical and thermal properties are not a function of spatial coordinates. However, volume description of these phenomena should be considered in case of inhomogeneous conductors (e.g. functionally graded materials).

Fig. 1.2 shows the occurrence of the Seebeck volume effects in the material with non-uniform distribution of thermoelectric properties due to one-dimensional gradient of doping impurities dN/dx. With the temperature gradient dT/dx thermoEMF dE caused by changes in Seebeck coefficient x, T appears:

(1.4) ∫ ( )

Similarly, volume or so-called distributed Peltier effect appears in inhomogeneous conductor on passing through it the electric current I. In this case Peltier heat dQp is absorbed or emitted heat in the material:

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Electrical resistivity and thermal conductivity

Electrical resistivity and thermal conductivity are irreversible processes lowering performance of thermoelectric devices. The Joule heating caused by resistance R of TE material is proportional to the square of the electric current I but the Peltier effect is linear to the current (eq. 1.6). Therefore, it is not possible to increase the temperature gradient indefinitely simply by the increase of electrical current. In isotropic material the electrical resistivity according to Ohm’s law can be described as:

(1.6) ⃗ where: ρ – electrical resistivity σ – electrical conductivity ⃗ - electrical field I – electrical current

However, in previously described inhomogeneous material (Fig. 1.2) the Ohms low is fulfilled only locally over the distance of dx. Therefore a total resistance R of an inhomogeneous element can be expressed as:

(1.7) ∫ ( )

In any material a temperature gradient causes an irreversible flow of heat in the direction opposing to the gradient due to Fourier’s law. This phenomena leads to the dissipation of heat and lowers effectiveness of TE devices.

Thermal conductivity  of isotropic materials, in the absence of electric current, is defined as: (1.8)  ( )

where q -heat flux

For inhomogeneous media thermal conductivity  equals: (1.9)  ∫ _{( )}

Thermal conductivity of materials consists of two parts: lattice component latt and electronic

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13 (1.10)  = latt + el

Lattice component latt is related to transport of heat by crystal lattice and for insulators and

semiconductors, like silicon and germanium, plays dominant role in total thermal conductivity. The lattice component can be estimated using the following equation:

(1.11)

where:

cp - specific heat

v –sound velocity

lp – phonon mean free path

Electronic component el is a result of transport of heat by free electrons in materials. Therefore metals,

having high carrier concentrations are usually very good heat conductors.

Thermal conductivity in conductors is closely related to electrical conductivity by Wiedemann-Franz law: (1.12)

where:

L - Lorenz number (equal to 2.44 · 10-8_W2_K-2₎

T – absolute temperature

The Wiedemann-Franz law is applicable to metals and most of classical semiconductors, however some significant exceptions were found in the recent years [1].

Efficiency of the thermoelectric generator and ZT parameter

Thermoelectric properties (α, σ, λ) of the material allow characterization and classifying them into types (n-type, p-type) and groups (low temperature, medium temperature, high temperature) and through this are indirectly informing about possible field of application. Direct and full information, whether the certain thermoelectric material is useful in the selected temperature range and can be successfully applied for the thermoelectric purposes, requires introducing another parameter called non-dimensional thermoelectric figure of merit ZT that combines these properties. ZT parameter is used for material optimization in terms of efficiency of energy conversion (e.g. power generation and thermoelectric cooling). Figure 1.3 presents simplified schema of the single-stage thermoelectric generator TEG composed of two semiconductors (so-called thermoelectric legs). The maximum efficiency (ηmax) of the

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14 (1.13)

where

TC, TH - are temperature at cold and hot shoe

ηC = (TH - TC )/ TH – Carnot efficiency

Equation 2.13 contains the material parameter ZT defined as [2]: (1.14) where: α – Seebeck coefficient σ – electric conductivity λ – thermal conductivity T - average temperature

The mathematical analysis 1.13 shows that growth in the ZT value leads to the increase of the efficiency of thermoelectric generator.

The numerator of the fraction 1.14 is called the power factor (PF): (1.15) ,

This coefficient is usually applied if the main focus on the material optimization is enhancing electrical properties. Both ZT and PF parameters are temperature dependent. Figure 1.4 [3] presents temperature dependences of thermoelectric figure of merit ZT for selected (a) n-type and (b) p-type thermoelectric materials. It should be noted that the ZT curves have maximum values in the relatively narrow temperature range and for different materials highest values of ZT are reached at different temperatures.

It may seem that the best solution to increase efficiency is to increase the temperature range in which TEG would work (as both ZT and Carnot efficiency are dependent on temperature). However, materials can work in the limited temperature range due to their chemical and mechanical stability.

From the eq. 1.13 one can conclude that the higher is ZT parameter (in selected temperature range), the higher efficiency max of the thermoelectric generator. In the Fig. 1.5, calculated dependences of

the efficiency of the material on this parameter for selected difference in temperature T are presented.

It should be pointed out that the efficiency curves were calculated for assumed constant ZT values over given temperature range T. However, as it was mentioned above, in real materials ZT parameters

significantly change with the temperature. Even if physical properties of the material allow applying of

𝜂

√1 + 1

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high temperature difference between the joints of the TE element, if the ZT parameter is low increase in

ΔT will not have large impact on materials efficiency. In order to obtain highest efficiency of TE

generator it is important to apply material that will have high ZT parameter in wide temperature range (see Fig. 1.6, red line).

Inhomogeneous thermoelectric materials

In the real TE device each thermoelectric element operates in the gradient of temperature covering wide temperature range. Therefore, in uniform thermoelectric element material only narrow region with optimal carriers’ concentration, has maximum ZT values. There are known following concepts to improve the efficiency of the TE leg:

 development of so-called segmented thermoelectric legs

 construction of legs from functionally graded thermoelectric materials (FGTM)

Both concepts allow obtaining multiple regions with maximum ZT parameter, so overall ZT in such material can be enhanced (Fig. 1.6 and 1.7). As a result relatively constant ZT parameter could be obtained in wide temperature range and whole TE element.

Thermoelectric materials were firstly produced in the form of crystals, as bulk uniform materials. Ioffe in his works [2] suggested preparation of inhomogeneous materials, with controlled carriers concentration along the length of the material. Various approaches in that matter resulted in increasing values of ZT parameter of many thermoelectric materials from less than 1 up till even 2.0 [4]

Theoretical calculations show that maximum possible ZT values for the optimally doped TE single-crystals could reach around 3.0. It is possible to enhance the properties by introducing controlled inhomogeneity in carrier concentration to the material. It can be made by either proper doping of the material or the distribution of the chemical composition within the material, which is equivalent to the distribution of the current carriers concentration. However, it has to be properly optimized; otherwise the improvement of the properties cannot be realized.

Preparation of the segmented materials for the thermoelectric generation of energy is another approach that is based on similar idea. By preparation of the legs for thermoelectric modules, from more than one TE material, where each of the materials is optimal in the different temperature range, it is possible to increase the efficiency of the prepared module by widening working temperature range of the module. In order to properly optimize such modules usually numerical models are being prepared in advance. These include equations related to proper heat flow, electric current, heat distribution, etc.

It is reasonable and effective method (regarding e.g. costs) for conventional use. However, it also has its drawbacks, especially on the joints of the materials, which need as low resistivity as possible in order to limit the losses of at junctions, therefore preparation of very good segmented module is still a challenging task.

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Discovery of the volume effects in the inhomogeneous thermoelectric materials suggested the fact that thanks to the internal inhomogeneity additional temperature gradients were present, increasing efficiency of the materials. Explanation of origins of the volume effects: Seebeck effect, Peltier effect and Thomson effect and resulting changes in Seebeck coefficient, thermal and electrical conductivity resulted in significant enrichment of the knowledge in the thermoelectric field.

According to theoretical calculation preparation of the material with desired profile of carrier concentration would lead to significant improvement on the efficiency and ZT of the material (around 50%) in comparison to uniform material.

Segmented thermoelectric materials

In order to enhance the thermoelectric materials and elements doping, creating the segmented materials, searching for new material and structures are the common approaches these days and some of these are pursued since many years. One of the most common approaches is, construction of segmented thermoelectric legs.

As a result of preparation composite of two or more segments (Fig 1.6) made of different materials it is possible to significantly increase efficiency of the obtained thermoelectric legs. Each of the segment is prepared for gaining the optimal working performance in a certain (narrow, but subsequent) temperature range. Combination of the two of such segmented thermoelectric elements, so-called TE legs in thermoelectric generators, with all connections and joints form a module, that can be used e.g. for waste heat recovery.

For the design of the segmented TE elements, the compatibility of the TE parameters is as important as selection of materials with subsequent maximum ZT in the temperature range of the segmented element. Estimation of these parameters would require a sufficient model, however knowledge of compatibility factor described s in [5] could be enough for the conformity analysis.

(1.16) √

This s factor is temperature dependent (as ZT and α coefficients); for the segmented leg to work efficiently, the selected materials should have similar compatibility factors and coefficients of thermal expansion, good thermal and chemical stability. For application purposes also additional factors are being taken into account like materials costs, availability and toxicity of the elements.

The amount of materials used for preparation of the segmented material may vary. For example Caillat in his work [6] presented complex segmented TE legs based on Bi2Te3, Zn4Sb3, CoSb3, CeFe4Sb12 materials,

with expected efficiency of energy conversion reaching 15%. Results on skutterudite segments prepared by hot-pressing shown in this work, confirmed over 10% energy conversion efficiency. Calculations of

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efficiency, as a functions of temperatures of cold Tc and hot TH side of the thermoelement, as well as

geometrical parameters of the thermoelements were made using Swanson model [7]. The crucial data required for proceeding with this model are thermoelectric properties measured as a function of temperature, as the model is semi-analytical.

There are several problems connected with technology of production of segmented materials. One is preparation of proper junctions that would not cause losses of efficiency.

The junctions are required to have low electrical resistivity (otherwise the Joule’s heat will be produced on the junction and the efficiency of the thermoelement will drop with each junction), low thermal resistivity (or ΔT would decrease with each junction), good mechanical properties (thermally induced mechanical tensions are present during the work of TE), high thermodynamic stability in time (reciprocal diffusion at junction could degenerate thermoelectric materials)[8]. More details concerning designing of segmented elements, especially multiple ones and TEG design can be found in other works [9].

It would be favourable to prepare materials that could have enhanced ZT value over wide temperature range, without limitations caused by junctions. Gradation of the materials offers such a possibility.

Functionally graded thermoelectric materials (FGTMs)

If the inhomogeneity in material is properly controlled and the desired carriers concentration (e.g. by chemical composition control) is reached it is possible to obtain more than one maximum ZTmax for

the material in the certain temperature range [2]. Schematic adjustment of the carriers concentration within the sample length could be seen in the Fig 1.7.[10]. The model with multiple maximum ZT values leads therefore to higher average ZT in the whole region. Shift of the ZTmax temperature with

the chemical composition can also be found in the work of Jiang [11], where with change of chemical composition in Bi-Sb-Te material, maximum ZT value was reached in slightly different temperatures in the samples (see also Chapter 6, Fig. 6.3).

Progress in research on inhomogeneous materials for the energy generation in TEG, started around 1990s [12,13]. Theoretical calculations at that time suggested that the gain on TEG can reach 25% for Bi2Te3 material, as reported in [12]. Mahan work [13] shows the calculations e.g. for the doped Bi2Te3

material, with around 7% increase in efficiency and it is also noted there that even if the doping profile is not very precise at some point there will be no additional effect on the efficiency of the TE made of the material, therefore the devices should be easier to construct.

There are numerous methods of preparation FGTMs [14], however doping during synthesis of starting material is the most common. Dashevsky [15] described preparation of PbTe-based FGTM materials by doping the PbTe crystal grown by Czochralski method with Indium (0.1-4% dopant in the obtained sample) diffused from the gaseous source. Efficiency of manufactured material was stated as 10.66%. Alternative method proposed in this work was sintering few polycrystalline samples of PbTe with different amounts of dopant (Indium) in order to obtain gradient of carrier concentration.

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Kuznetsov [16] in one of his works on Bi2Te3 system compared functionally graded materials with

segmented ones. In samples with double doping of the material (with SbI3 and excess of Te), made by

Bridgman method, efficiency of over 10% was reached for both segmented materials and FGTMs (with temperature difference reaching 200K), with graded materials presenting slightly better performance. However, it is also noted that the efficiency of TE element produced might suffer from change in the profile of dopant concentration after extended working time of the material (the material will become more homogeneous with time due to diffusion processes).

Optimization of thermoelectric properties

Each thermoelectric material can be characterized by a set of thermoelectric properties which are dependent on concentration of current carriers. In most of the cases with the increase of the electrical conductivity, Seebeck coefficient decreases, which is related to their dependence on carrier concentration, as it is displayed in Fig. 1.8 [17]. As can be noticed, in insulators carrier concentration is low therefore they have low electrical conductivity and high Seebeck coefficient. On the contrary, metals are characterised by high carrier concentration thus they are good conductors both for current and heat. Unfortunately, the Seebeck coefficient in metals is very low.

Taking the maximum value of ZT parameter as an optimisation criteria one can find the optimal carrier concentration, at which each of transport parameters () has balanced value. As a result ZTmax is

obtainedaccordingly toeq. 1.14. Optimal value of the concentration of carriers depends on the material and working conditions, however usually the best profile of thermoelectric properties is reached in semiconductive region, with carriers concentration of around 1019 order of magnitude (Fig 1.8).

The procedure of development of materials with optimal carrier concentration (to gain the maximum efficiency or ZT value) is called the optimisation of thermoelectric materials. Manipulation of the carriers concentration by doping or preparation of inhomogeneous material is used for enhancing thermoelectric properties. It is a complex matter, as the influence of carrier concentration on properties may differ also depending on electronic structure of material, type of dopant or the location of dopant in the crystal structure of doped material.

Another important matter related to optimization process is selection of the proper temperature range for optimized material.

Bi2Te3 and Sb2Te3 are one of the best commercially used thermoelectric materials for low temperatures.

The application is either cooling, as a component of the Peltier module or power generation in low temperature. The peak of ZT value in these materials is around 1.0 at 400K in bulk uniformly doped material (or undoped), therefore proper optimization of dopant distribution would allow increasing this value, however for similar temperature range.

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Even though properties of these materials can be still enhanced, for commercial use, usually materials with ZT over 0.5 are applied if their physical properties are favourable for the estimated working conditions [17].

The lowest values of the ZT parameter exist in undoped materials, with the one temperature where ZT parameter reaches maximum value. To optimize it segmented material might be constructed from more than one material giving two or more maximum ZT regions in wider temperature range. It is effective, but complicated method, and much better would be preparation of graded structure in one material, widening the maximum ZT region.

However, the efficiency of such material is higher than in uniform material, however the graded material, with profile of carrier concentration changing along materials length, is expected to have it even higher than segmented one.

If the material is uniform - efficiency of TE is the highest only in a certain temperature range, that is rarely located near junctions. In such material in the highest and lowest working temperatures the efficiency will significantly drop. Moreover, mentioned thermoelectric properties are all temperature dependent, and that dependence might not be linear in the selected temperatures, or even non- monotonic.

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References

[1] Wakeham, N. et al. Nat. Commun. 2:396, 1406 (2011).

[2] Ioffe A.F.: Semiconductor Thermoelements and Thermoelectric Cooling, Infosearch, London, 1957

[3] Snyder G.J and Toberer E.S., Nature Mater., 7 (2), 2008, pp.105-114

[4] L.I.Anatychuk, L.N.Vikhor in Thermoelectricity, Vol 4 Functionally graded thermoelectric materials, Bukrek Publishers, Chernivtsi, Ukraine (2012)

[5] G.J. Snyder, in Thermoelectric Handbook, Macro to Nano,ed. by D.M. Rowe (Boca Raton: CRC Press, 2006), pp. 9–1

[6] Caillat et al, in IEEE 20th International Conference on Thermoelectrics (ICT '01),Beijing 2001, p. 282

[7] B. W. Swanson, E. V. Somers, R. R. and Heike, Journal of Heat Transfer, 1961, p. 77-82

[8] R.Zybala, High-temperature segmented thermoelectric module, PhD dissertation (in Polish), (2012)

[9] Rowe D.M. ed.: CRC Handbook of Thermoelectrics, CRC Press, Ch.37, 1995

[10] Graded material based on: K.T. Wojciechowski, Modelling of physical properties of functional gradient thermoelectric materials, DIMAT 2014, Münster,Gemany, 19th August 2014

[11] J.Jiang , L.Chen, S.Bai, Q.Yao and Q.Wang, J. Cryst. Growth 227, 258 (2005)

[12] L.I.Anatychuk, V.P.Bulat, V.A. Semenyuk, Thermoelectric Material for Thermogenerators as Optimal Control Object, Doklady An Ukr. SSR Ser. Fuz-Mat and Tekhn. Nauki, 10, p.48-52, 1988 (in Russian)

[13] G.D. Mahan, J. Appl. Phys. 70, 4551 (1991).

[14] Shiota, Nishida, in IEEE 16th International Conference on Thermoelectrics (ICT '97), Dresden,

August 1997

[15] Z. Dashevsky, Y. Gelbstein , I.Edry, I.Drabkin, M.P.Dariel, in IEEE 22nd International Conference on Thermoelectrics (ICT '03), La Grande Motte, August 2003, p. 421

[16] V.L. Kuznetsov, L.A. Kuznetsova, A.E. Kaliazin, and D.M.Rowe, J. Mater. Sci. 37, 2893 (2002) [17] Wojciechowski K.T., Influence of structural modifications of thermoelectric properties of

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Figures

(a)

(b)

Figure 1.1. Simplified schema of (a) Seebeck and (b) Peltier effects in uniform materials.

electric contact dN T 1 T₂

x

0 _l

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Figure 1.4. Temperature dependences of ZT for selected (a) n-type and (b) p-type thermoelectric materials [3].

(a)

(b)

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(b)

Figure 1.6. Uniform, segmented and graded thermoelement – comparison; (a) ZT curves in temperature range (b) construction of elements . Graph (a) based on[17]

(a)

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Figure 1.7. Dependence of carrier concentration and temperature on ZT parameter [10]

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Chapter 2 Concept of Functionally Graded Thermoelectric Materials (FGTMs); Thesis & aims of the dissertation

25

Chapter 2 Concept of Functionally Graded

Thermoelectric Materials (FGTMs);

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Idea of Functionally Graded Thermoelectric Materials (FGTMs)

The idea of functionally graded thermoelectric materials was introduced by Ioffe in 1950s [1]. Through the years this idea is pursued by many scientists till this day. The main drawback of thermoelectric materials is relatively low efficiency of energy conversion of thermoelements (TEs) made from these materials, and their high effectiveness only in a narrow temperature range. By construction of the FGTMs it is possible to widen the temperature range.

Mahan in one of his work [2] points out that by applying certain inhomogeneous doping to the thermoelectric material it is possible to increase the efficiency of thermoelectric element made from such a material by 10% comparing to the undoped one. The other approach mentioned by the author is preparation of the segmented device, which could also be considered graded material. In such case the TE is composed of different segments – from either different materials or differently doped materials (usually semiconductors), connected together using various methods e.g. soldering or hot-pressing. However, utilizing bonding comes with difficulties in regards to interfaces between the segments. Therefore in this work of Mahan [2] it is also noted that variation of the doping along the length of the TE leg benefits without the limitations of joints. Calculated ZT values of the expected results of doping are presented in figure 2.1. One can conclude that with the inhomogeneous doping it is possible to obtain higher ZT throughout almost whole device; therefore the efficiency of the TE element would increase. Shiota, and Nishida explain the matter of FGTMs [3] from experimental point of view. In one of their works they focus on how the change in carrier concentration, e.g. in PbTe material, is enhancing the energy conversion efficiency in comparison to monolith element. As presented in the Figure 2.2 a [3], with change of carriers concentration in the material one can observe shift of the narrow maximum of figure of merit to different temperature (Z (1/K). If the carrier concentration is fitted to the temperature gradient, the energy conversion within the material will be enhanced. Authors stated that by preparation of the elements from PbTe with carrier concentration distribution as given in Figure 2.2a it is possible to increase the TE performance even 50% comparing to monolith one and the maximum thermoelectric efficiency in TEG of 19% could be reached.

In same works of Shiota and Nishida [3] discuss improvement of the thermoelement by preparation of the segmented TE, and the advantages of forming FGTM from these materials. It is concluded that significant improvement of maximum efficiency can be achieved in segmented element from graded materials reaching 22.3% for temperature range of 300 to 1400K. In comparison, for monolithic samples of PbTe and SiGe with slightly smaller temperature range (500K to 1400K), it reaches only 12% and 14%, respectively. In the Figure 2.2 b, comparison of the gains on the FGTM forming from these materials is presented.

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Bi-Sb and Bi

2

Te

3

-Sb

2

Te

3

based thermoelectric materials for thermoelectric

cooling

Bi-Sb alloys, Bi2Te3 –based and Sb2Te3 – based thermoelectric materials are widely known and applied for

either cooling or energy generation in low temperatures. These are known for their relation between rhombohedral structure and anisotropy in thermoelectric properties mentioned by many authors [4, 5, 6].

The anisotropy has been approached in various ways. Kitagawa et al. [6] mentions employment of various preparation methods such as unidirectional crystal growth by melt-growth as one of usual means to control the crystal orientation of these materials, but also solidification under centrifugal pressure (for thick film, by Kinemuchi et al.[7]) or preparation of polycrystalline materials. In his work Kitagawa et al. [6] focuses on preparation of the Bi0.5Sb1.5Te3 samples with controlled carrier concentration using

liquid-phase growth (LPG) in sliding boat process, with excess of 1 to 10% wt. tellurium as a dopant and then compares the obtained results with hot-pressed sintered materials. Experimental setup of LPG method is displayed in the figure 2.3. Tungsten weight, separated by mica from the surface of the sample, was used to increase the wettability of samples during process. Majority of the crystals grown using this method were align in the same, laminar structure. Thermoelectric properties measurements indicate that majority of the carriers are holes and with increase in Te (up to 6%), concentration of these carriers decreases. Good compatibility of thermoelectric properties, especially Seebeck coefficient (α, in that work S) and electrical resistivity (ρ) with carrier concentration profile in the wide range is confirmed in this work. However there are some deviations of ρ-x dependences, comparing with the sintered samples, which is explained as a result of obtaining one general alignment of the crystals in the LPG samples. These samples exhibit lower resistivity than sintered samples, which leads to conclusion that carrier concentration control together with preferable crystal orientation lead to obtaining samples with better overall performance.

On the other hand in works of J.Jiang et at.[8, 9] two different approaches are considered. One is texture modification and in this work [8] as in work of Kitagawa, authors obtained preferable crystal orientation, however by using spark plasma sintering technique (SPS).

The change of sintering conditions resulted in corresponding change in orientation factor (from 0.4 to 0.85) of (0 0 l) planes. The optimal figure of merit ZTopt was stated to be comparative to that of the zone

melted materials with the same crystallographic parameters, however with bending strength 7-8 times higher (even 80 MPa) than in zone melted samples. Influence of the method on mechanical stability was also investigated as Bi2Te3-Sb2Te3 solidified ingots are regarded as brittle materials with relatively low

mechanical properties. The relative densities of the sintered samples were stated as 98% and increase of mechanical resistivity was correlated with decrease of starting particle size.

Another benefit of using [8] spark plasma sintering is rapid heating and shorter sintering period which allows avoiding compositional change in material, in comparison to other methods that require temperatures near potential recrystallization temperature. Thermal conductivity in the obtained samples was lower than in zone-melted samples which might have been caused by increase in phonons scattering

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thanks to dense grain boundaries in the sintered polycrystalline materials. However, electrical properties of samples prepared by SPS method were slightly worse as a result of increase in carrier concentration. Authors stated that sintered samples with highly preferred orientation of crystals from Bi2Te3 materials

exhibited better mechanical properties than zone-melted samples, but only comparable thermoelectric properties (ZT of the sintered samples reached 90% of the zone-melted samples ZT).

Zone-melted samples prepared by the same authors [9] were made in form of p-type ingots with different chemical composition (Bi2Te3)x(-Sb2Te3)1-x, where x=0, 0.5, 0.1, 0.16, 0.20, 0.24 and 0.26. By

change of Bi content, the carrier concentration was controlled. The authors stated that with increase of x decrease in hole concentration was observed, resulting in decrease of electrical conductivity and increase of Seebeck coefficient. Highest ZT values of 1.14 were reached for sample with x=0.24 and 3 wt.% excess Te, measured at temperature around 350K. Similarly to the sintered samples, thermal conductivity decreased in samples prepared by zone-melting, however this was explained to be a result of two contributions: increase in phonon scattering and decrease in electrical component of thermal conductivity related to decrease of electrical conductivity (caused by antistructural defects).

Thick films of bismuth telluride alloys mentioned above, made by Kinemuchi at al. [7] were prepared using unique method of solidification under centrifugal pressure. In this work deposition was made on zirconia polycrystals. According to authors, starting powders were charged in the groove patterns of the substrates and after melting solidified under centrifugal acceleration of 104 m/s. Obtained films were

c-axis oriented and over 100µm thick (up to 200µm). In accordance to their orientation thick films of p-type and n-type were prepared with power factors reaching 4.2 mW/mK2 and 2.7 mW/mK2 (in plane), which in case on p-type materials is comparable to results obtained using other preparation methods and confirms good quality of the obtained thick films.

The process is presented in the figure 2.4. Ceramic rotor, driven by inverter motor has been placed in chamber of especially designed furnace. Depending on the required experimental conditions, atmospheric pressure or vacuum, the maximum rotation reaches from 1000 m/s2 to 10 000m/s2 and from 1000m/s2 to 100 000m/s2 respectively. Moreover two types of heating materials can be used: silicon carbide (up to 1000°C) or graphite (1200°C) and the water flow cooling is applied. Along the radial direction of the rotor, with the radius of 15 cm, temperature gradient of around 6°C/cm is obtained (lower temperature is exhibited near the center of the rotor). Given temperature profile was confirmed for the steady-state conditions. During the experiment, dried powder of processed bismuth telluride alloy was charged firstly into a dry-etched pattern on the zirconia polycrystalline material. Patterned substrate was covered with a flat substrate that was then wrapped together using aluminum foil, placed in ceramic rotor and subjected to heat treatment under the centrifugal force. Then, the pressure of the chamber was decreased and when it dropped below 10 Pa acceleration was applied in the thickness direction of the substrate and the heating procedure under centrifugal force was started. Authors state that using that method allows precise shape forming; moreover they point out benefits of good composition control of solidification process, especially in case of volatile materials, like tellurium, and increase in growth rate as a result of applying centrifugal force.

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Bi-Sb alloys, in comparison to the Bi2Te3-Sb2Te3, since the 1950s are commonly prepared by crystal

growth methods, but modification of these techniques allows improvement of their TE properties. also nowadays. For instance, in his work Kozhemyakin et al. [10] proposed modifications of the Czochralski method for growing graded Bi-Sb single crystals with desired carrier concentration distribution. Samples with Sb content up to 18 at %. were prepared and the influence of the growth parameters: the pulling rate, Sb feeding rate and melt depth on the properties of obtained crystals were investigated. Distribution coefficients of Sb were calculated according to the Ostrogorsky-Müller model [10] and the change in lattice parameter c as well as spacing between crystalline planes and dislocation density were measured. In this work a solid Sb feed is being used. Authors also state that for practical purposes the suggested Ostrogorsky-Müller model shows the best agreement with the experimental data.

In the figure 2.5 Czochralski pulling apparatus is shown. Authors of the work [10] mention possibilities of control of the temperature gradient in pulling crystal and the sinking speed of a solid Sb feed in the melt for the growth of their crystals as some of the advantages of the method. The samples were prepared with the average puling rate of 0.01- 0.02 mm/min. In order to obtain reduced dislocation density three different regions of 3mm in length in each crystal were grown with different pulling rates (0.05, 0.035 and 0.02 mm/min, respectively), which resulted in the decrease in dislocation density by 30-75%. Important factor was optimum axial gradient of temperature in the pulling crystals as it influences quality of the crystals significantly. Authors [10] mention also the need of reducing of the pulling rate for the samples with high Sb concentration gradient, in order to obtain proper antimony distribution within the crystals. This method has proven good control over the carrier concentration gradient, as almost linear distribution could be obtained with the lattice parameter gradient equal to 0.66%/cm and gradient of the antimony concentration reaching 14.4 at.%/cm. The highest achieved gradient in Sb concentration was 17.6 at.%, however it was also confirmed that the change of the gradient crystal diameter increased Sb segregation, causing non-linear dependence of the lattice parameter.

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PbTe based thermoelectric materials for thermoelectric generation

Lead telluride based compounds are typical p-type and n-type materials for thermoelectric generation the middle-temperature (50-600°C) applications. In his work Gelbstein [11] proposed doping PbTe with Sn to get p-type functionally graded Pb1-xSnxTe, using powder metallurgy processing. As applying this

method might result in atomic defects and local strains authors propose annealing procedures for reduction of the mentioned effects and in order to obtain desired carrier concentration along the profiles of obtained samples. It is also noted how this process can decrease hole concentration of a sample saturated e.g. with excess Te (when annealing is proceeded at high temperatures in Te-rich atmosphere). Even short heat treatment can reduce the effects significantly, which is one of the advantages of using given method. It is important, as in these materials with the powder processing one can change carrier sign of the material, resulting in changing the conductivity type (from p-type to n-type) and also material instability. The effects of annealing in these materials are known as ‘strain induced compensation’. Potential of PbTe as a FGTM material is already known for n-type TE legs. In a p-type PbTe gradation was usually applied in a form of segmented TE as monolith layers with different compositions. In presented work [11] authors aimed to optimize such TE by adapting the annealing processes for the increase in TE’s efficiency. Starting materials were made by simultaneous cold compaction of powder layers, containing different Sn content, followed by sintering treatment in argon atmosphere. Then samples were annealed in cycles of 600°C/24h in argon. Homogeneous samples made from single layers and graded samples made from three layers with different Sn contents were prepared using same method. Two segmented thermoelements were prepared: with the equi-wide and an optimal ZT envelope layers. In both cases annealing processes allowed stabilizing these materials for thermoelectric applications. Step like characteristic of the thermoelectric properties, with desired profile of carrier concentration, was confirmed within sintered samples after annealing for not more than 168 hours. Further annealing did not affect Seebeeck coefficient further. The temperature dependence of figure of merit Z for the material did not exceed 0.8 in the stated work. However samples displayed a promising potential for improved efficiency using FGM configuration. Good thermal stability of the samples has been also confirmed by the authors [11].

Cui and Zhao [12] decided on applying pressureless sintering (PS) with Ag doping. The samples were optimized to fit the FGTMs composition. Preparation of the TE in accordance to the proposed chemical composition, thus carrier concentration allowed widening working temperature range to 500K (between 200K and 700K). Calculations have shown that the maximum power output of prepared samples could reach even 21% increase comparing with monolith samples. Experimental values measured by the authors confirmed maximum power output to be at least 16% higher than in uniform samples. Imai et al. [13] in one of earlier works, focused on optimizing n-type, segmented PbTe. Prepared TE made of segments with two carrier concentrations 1x1025 and 3.0x1025 m-3 made by hot pressing (HP) had different length ratios. Carrier concentration in the samples was controlled with PbI2 dopant and the

starting powders were separated by 25µm Fe foil in order to avoid uncontrolled mixing. The length ratios between divided parts were 44, 50 and 62%. The highest power factor PF or the single segments was reached at 500K for the lower carrier concentration and around 700K, and the different length ratios

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were obtained by cutting the length of the segment with higher carrier concentration. It was concluded that within the samples, length of 50% ratio has shown best performance, however further increase might be observed in case of sample with 75% length ratio.

Presented sintering and pressing methods all allow obtaining materials with good mechanical properties, densities and desired carrier concentration, however the spark plasma sintering SPS is the most beneficial in the terms of density of prepared samples and sintering quality. Moreover, reduced time of sample preparation allows faster quality control and further investigation of e.g. stability of the samples. Schema of the spark plasma apparatus used for such processing is presented in the figure 2.6 [14].

Prospective FGTMs processing methods

FeSi2 materials are being of some interest in recent years. These might be used for example in

the segmented TE, as presented in the work of Cui [15], but also in the form of graded TE as it is presented in the work of Müller et al. [16] . In this work [16], for the thermoelement preparation new method, referred as Doping by Intermixes Additives Sintering (DIAS), has been used. This method required gas-atomized FeSi2 powders along with elemental additives to be ball-milled, layered with

doping variations (in case of segmented samples), hot pressed and hot-treated for the preparation of the samples (hot –treatment of the samples is necessary to incorporate dopants onto proper lattice positions). Only short time milling of the starting powders, filled together with oxygen-free milling liquid, was required for sufficient intermixing. Moreover, it limited iron abrasion of the milling balls that would cause non stoichiometry (Fe excess) in the obtained materials. The obtained TE performances depend sensitively on the powder preparation, especially milling time and atmospheric environment. Authors [16] concluded that obtained samples exhibit thermoelectric properties comparable to materials obtained by standard hot pressing processes.

Yasuda et al. [17] in his work decided to obtain porous FGTMs, using FeSi2, PbTe and materials based on

bismuth and antimony tellurides. Such materials could be used for novel TEG and TEC systems (figure 2.7 a) that would base on thermo-fluid mechanics, and could be used for utilizing heat convection. For that authors [17] developed enhanced hot press method. Porosity of the obtained materials was up to 35% and permeability 10-9 to 10-10m2. Firstly, the starting samples of FeSi2 materials doped with Mn (with

Cu as catalyst) were prepared using rotating-water atomization equipment; obtained particles were conventionally hot pressed. PbTe and (Bi,Sb)2Te3 porous thermoelectric were prepared by hot pressing

of crushed, synthesized powders with KCl particles, that were removed afterwards by water thanks to large water-solubility of KCl. The process of revised hot pressing is shown in figure 2.7 b. FGTMs were obtained by hot pressing obtained porous materials into segments. Authors stated that the addition of KCl did not affect the thermoelectric power of the materials obtained using this method and that by control of the KCl particles size it is possible to control the porosity of obtained thermoelectric materials.

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Thermoelectric materials could be also obtained in a form of thin films. In the work of Cho et al. [18] thin films of Bi-Sb alloy, were grown on CdTe by molecular beam epitaxy (MBE) method. There were two groups of thin films: undoped and doped by Sn or Te. Using tin as a dopant resulted in sign change of thermopower (from negative to positive) and allowed control of this power maximum values. The authors note that too high doping levels (with Sn or Te) might cause samples degeneration. The method is very accurate; however for the application of the thermoelectric materials in order to obtain certain gradient of temperature within the sample it is necessary to obtain samples of larger thickness like ones described above in the work of Kinemuchi [7].

High gravity sedimentation method

In this work original method to obtain functionally graded thermoelectric materials is developed. Therefore, in this part the brief explanation of the sedimentation mechanism of atoms in the gravitational field will be introduced. The original concept of the method was developed by T. Mashimo [19,20]. The ultracentrifuge giving the acceleration of 106 G in elevated temperatures up to 500 °C is in his laboratory at Kumamoto University.

The usage of the gravity of the presented magnitude in elevated temperature allows sedimentation of atoms in the solid state. In the ultracentrifuge the sample is put inside one of the capsules, which are placed inside the rotor as could be seen in Fig. 2.8.(a). When the centrifuge acceleration simulating gravity force is applied, the heavier atoms are being pulled by that force accordingly to the force direction, whilst the lighter atoms are moving in opposite direction (as presented in Fig. 2.8 (b). The grain refinement and confirmation of the phenomena is presented in works made in JAEA and Mashimo Laboratory in Japan [21,22]. There are some exceptions from this rule if the difference in atomic masses of the elements are small, whilst the differences in densities large [23]. In such case it is possible that the atoms with higher density will move in the direction of the applied force.

The details of the theoretical part of the sedimentation of atoms in gravitational field were explained quite recently in other works of Mashimo [19,22].

High acceleration that could be obtained on the level of 1 million G and the possibility of performing the experiment in temperature up to 500°C is unique worldwide, allowing synthesis of many new materials with very unique properties [20,24].

For the thermoelectric materials usage of the gravitational method could give numerous new possibilities. The advantages of the method are i.a. performing sedimentation of atoms in whole sample depth which allows bringing the doping into whole another level or modification of the crystal structure and microstructure that would affect transport properties of the materials (electrical conductivity, thermal conductivity). For that kind of investigation selection of the materials with relatively low melting temperature and with atoms of significantly different atomic masses, in order to observe effect of diffusion forced by gravity.

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Sedimentation under large gravitational field has many advantages; the most important for this investigation is the fact that the diffusion of atoms in solid state can be observed in whole sample depth. Moreover, process could be precisely controlled by altering 3 independent parameters: acceleration, time and temperature. Thanks to the non-equilibrium thermodynamic conditions it is possible to produce new materials by modification of lattice constants, obtaining requested gradient of dopant concentration, production of new phases, etc.

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Previous studies on preparation of FGTMs by sedimentation method

The investigation of the sedimentation of atoms in metallic and semi-conductive materials has already been started. Few examples of the research in this field in Japan (in JAEA and Kumamoto University) will be presented next. The selected ones are In-Pb-Te and Se-Te systems.

In-Pb

In the case of In-Pb material investigation [24] atomic scale gradation was confirmed after processing in the ultracentrifuge as well as phase transition was observed. The sample with starting composition of 80 at. % indium and 20 at.% lead was processed in an ultracentrifuge under the conditions of 155 000 rev/min, which caused the acceleration of even 820 000 G, in 150°C (423.15 K) for 100h. After the experiment the chemical composition was confirmed by electron probe microanalysis (EPMA) to be changing almost linearly from 94 at.%. to 55 at.% for indium and from 6 at. % to 45 at.% for lead. Three separate regions of differing properties could be seen from the microphotograph and EPMA mapping in Fig. 2.9. These correspond to different phases that occurred in the analysis fcc (Pb-rich phase), fct (



phase) and tetragonal (In-rich phase), whilst in the starting material only one phase was present (single fct phase (



phase)).

Moreover, change in lattice parameters (a0 and c0), reaching the values of even 1% has been observed in

the sample with the increase of Pb in phases, especially in In-rich region.

Se-Te

The aim of the study on this material was investigation of the sedimentation mechanism and creation of graded band gap from direct band gaps that exist in both semiconductive materials, Se and Te. Samples of Se-Te were prepared with the starting composition of 70 at.% Se and 30at.% Te in a form of cylinder: one with the height of 5mm and diameter of 4mm and second one with height of only 0.6mm but the diameter of 5mm [25]. These were encapsulated in rod type and plate type capsules; the setting could be seen in Fig. 1.9. X-ray photoelectron spectroscope (XPS) was used for determining binding energies in the samples and electron probe micro analyzer (EPMA) for chemical composition investigation.

For the rod type sample, in the Fig. 2.10, two regions with different size crystals could be clearly observed, which correspond to low and high gravity regions, with grain refinement occurring in the latter. The SEM line data of Se and Te content confirms significant gradation of the sample, which in low gravity region seems almost linear.