Recent Progress in Nanostructured Thermoelectric

Materials

Author: Tian Liu1

1Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4,

9747 AG Groningen,The Netherlands

E-mail: t.liu.4@student.rug.nl

Supervisor: Graeme R. Blake1

1Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4,

9747 AG Groningen, The Netherlands

E-mail: g.r.blake@rug.nl

Abstract. Thermoelectrics have long been recognized as a cost-effective and

pollution-free technology due to their ability to convert heat energy directly into electric

energy. The research on thermoelectric materials keeps exhibiting rapid improvement

and exciting breakthroughs in the past twenty years due to the extensive investigation

on nanostructured thermoelectric materials.More than ten percent in efficiency has

been gained from changes in structural features on a length scale seven orders smaller

than that of the devices. This paper sets out to explore the basic mechanisms of

the thermoelectric effect, summarizes the main methodology for improving the energy

conversion efficiency, critically analyzes measurement accuracy issues, and proposes

thermoelectric systems with novel nanostructures that should exhibit better efficiency.

A discussion of structural design in nanostructured thermoelectric materials is aimed

at enhancing the thermoelectric figure of merit in practical applications.

Keywords: Nanostructured thermoelectric materials, Nanoscience

CONTENTS 2

Contents

1 Introduction 2

1.1 Thermoelectric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Basic Theory for Improving ZT . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Measurement Accuracy in Thermoelectrics . . . . . . . . . . . . . . . . . 7

2 Thermoelectric Materials in Low Dimensional systems 8

2.1 Quantum Well Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 One Dimensional Nanowires . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Bulk Nanostructured Thermoelectric Materials 11

3.1 Progress in Bulk Nanostructured Thermoelectric Materials . . . . . . . . 11

3.2 A Strategy to Improve ZT in Nanocomposites . . . . . . . . . . . . . . . 13

4 Conclusion 15

5 Acknowledgement 16

6 Reference 16

1. Introduction

1.1. Thermoelectric Materials

The global demand for fossil fuels, such as coal and oil, is continuing to increase,

meanwhile the growing speed of non-renewable energy consumption results in inevitable

environmental degradation. The limits of conventional energy and the environmental

concerning both point to find new ways of improving the energy utilization rate.

Thermoelectric materials have attracted increasing attention both from the energy and

environmental aspects over the past few decades due to the promising high efficiency of

converting waste heat into electric energy.

A schematic diagram of the structure of a typical thermoelectric device is shown

in Figure 1. The electrons in the n-type material and the holes in the p-type material

CONTENTS 3

Figure 1. A thermoelectric device with n-type and p-type legs electrically in series

and thermally in parallel. From Shakouri [1].

all carry heat away from the bottom metal-semiconductor contact, by which the hot

side metal-semiconductor junction is cooled[1], and that is the Seebeck effect. Practical

devices are fabricated of multiple pairs of p-type and n-type semiconductor legs to obtain

both high current densities and low voltages. The conversion efficiency of thermoelectric

materials is related to a quantity named the figure of merit (ZT) which is defined by

Altenkirch in 1911 as the relation in Eq. (1).

ZT =S2σT

κ=

S2σT

κl + κe(1)

S is the Seebeck coefficient, σ and κ are the electrical and thermal conductivity of the

materials respectively. Thermal conductivity consists of two contributors (κ): lattice

thermal conductivity (κl) and electron thermal conductivity (κe). The relation between

ZT and efficiency of a thermoelectric device is plotted in Figure 2, where a higher ZT

value is directly related to a high device efficiency.

The first functioning thermoelectric devices were built in the 1950s and 1960s,

with ZT around 1.0 and efficiency about 4%-6% [2]. In the 1990s, materials with

high ZT values were explored in the form of low-dimensional systems and on the

nanoscale [3]. Until now, two different approaches have been investigated to search

for high ZT thermoelectric materials over the past two decades: one is finding and using

new classes of bulk thermoelectric materials with complex crystal structures, and the

other is studying materials in low dimensional systems and bulk structures embedded

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Figure 2. Thermoelectric energy conversion as a function of ZT when the cold side

temperature is 300K. A higher ZT is directly related to a high device efficiency. From

Chen [7].

with nanomaterials. Bulk structures embedded with nanomaterials are usually called

bulk nanostructured thermoelectric materials [4, 5, 6].

Nanostructured materials and thermoelectrics have been the subject of significant

research in recent years [5], and it is a challenging topic combining materials science,

nanoscience and physics. Exploring nanostructured thermoelectric materials is not only

useful searching for the next generation of thermoelectric materials exceeding ZT=2.4,

and it is also an inspiration for other research areas of nanoscience by gaining better

material performance from small features [8].

In this review paper, firstly the basic theory and methodology for improving

ZT is introduced, including a discussion of measurement accuracy. After that,

the performances of thermoelectric materials in low dimensional systems and bulk

nanostructured thermoelectric materials are reviewed. Finally, a designed approach

for improving ZT in nanocomposites is proposed.

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1.2. Basic Theory for Improving ZT

Enhancing the figure of merit (ZT) is the common idea for improving efficiency of

thermoelectric materials [9], as explained in Figure 2. From the definition of ZT

in Equation (1), three correlated quantities need to be taken into consideration for

optimizing the value of ZT, and these three factors are a large Seebeck coefficient (S ),

a high electrical conductivity (σ) and a low thermal conductivity (κ). These quantities

are interconnected by the charge carrier concentration n, as plotted in Figure 3. S2σ

is defined as the power factor of thermoelectric devices, which denotes the contribution

of the Seebeck coefficient and electronic conductivity to ZT. The relation between the

Seebeck coefficient and the charge carrier concentration n can be expressed as

S =8π2σk2B

3eh2m∗T(

π

3n)2/3 (2)

where kB is the Boltzmann constant, e is the carrier charge, h is Plancks constant and

m∗ is the effective mass of the charge carrier. Here the charge carriers can be either

electrons or holes. According to Drude’s model, electrical conductivity can be denoted

as

σ = neµ (3)

where µ is the mobility of the charge carrier. The electronic component of thermal

conductivity can be denoted as

κe = LTσ = LTneµ (4)

which follows the Wiedemann−Franz Law. Decreasing the electronic thermal

conductivity results in idecreasing the electrical conductivity, and does not affect ZT

much. The lattice component of thermal conductivity can be estimated as

κl =1

3Cvl (5)

where C is heat capacity of materials, v is the average sound velocity for phonons, and l

is the phonon mean free path (mfp). Compared to the electronic thermal conductivity,

lattice conductivity contributes to the change of ZT much more significantly. There

is a trade-off between the improvement of thermopower and the reduction of thermal

conductivity by charge carrier concentration. Typically, good thermoelectric materials

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Figure 3. Illustration of the variation of the Seebeck coefficient (S ), electrical

conductivity (σ), power factor (S2σ), electronic thermal conductivity (κe), and lattice

(κl) thermal conductivity on the charge carrier concentration n, for a bulk material.

From Shakouri [1].

.

are heavily doped semiconductors with carrier concentration of 1019 − 1021 cm−3 (also

in Figure 3) [10, 7].

As we mentioned before, there are mainly two methods for improving ZT. For

the first appoach, i.e. complex crystal structures, a basic phonon-glass electron-

crystal (PGEC) as a high performance thermoelectric material was proposed by Slack

in 1995 [11, 12]. This idea implies that high thermoelectric performance materials

behave like glass materials regarding their thermal properties and demonstrate electrical

properties as crystalline materials. Materials with ZT>1 have been discovered based

on this idea, for example in skutterudites, clathrates and β-Zn4Sb3 structures [7]. In

particular, a high ZT=1.7 is realized in Ba0.08La0.05Yb0.04Co4Sb12, which is a n-type

skutterudite structure. [13].

However, materials with higher ZT (even more than 2) are normally prepared by

the second approach, i.e. nanostructuring. In the nanostructuring method, the phonon

mfp decreases while the power factor S2σ is maintained at the same level or becomes

even higher than in the original bulk materials. The connection among the above

three factors: Seebeck coefficient S, electrical conductivity σ and thermal conductivity

κ is weaken by the design of nanostrucures. In most cases, only the lattice thermal

conductivity is significantly reduced. Comparing the two approaches, the basic idea for

CONTENTS 7

the first one is trying to find an optimized balance point in the tade-off between these

three factors, while the second approach changes the manner of this trade-off.

1.3. Measurement Accuracy in Thermoelectrics

Nevertheless, before starting the introduction to exciting and high performance

nanostructured thermoelectric materials, the author would like to mention that there

are serious measurement issues for most thermoelectrics. The measurement issues arise

because of the complexity of fabricating devices, measurement uncertainty and materials

complications [14]. Moreover, inaccurate carrier concentration measurement can also

result in wrong Seebeck factor enhancement [8, 15]. Direct efficiency measurements

require nearly as much complexity as building an entire device [14].Therefore the figure

of merit is obtained by measuring thermal conductivity κ, Seebeck coefficient S and

electrical conductivity separately.

Thermal conductivity values κ are normally calculated from thermal diffusivity α,

while thermal diffusivity measurement exhibits considerable inaccuracy. The relation

between thermal conductivity and thermal diffusivity is defined as

α =κ

ρCp

(6)

where ρ is the material density and Cp is the specific heat capacity. Furthermore, in this

calculation, there is also an approximation that the specific heat capacity constant in the

material according to the Dulong−Petit Law.. This approximation brings uncertainty

to the final result, especially in complex nanosctructured materials. The inaccurate

measurement in thermal diffusivity and and the approximation of a constant specific

heat results in uncertainty around 15%-20% in thermal conductivity calculation. The

error for the Seebeck coefficient is around 5% (it may be up to 10%), and the inaccuracy

for electric conductivity measurement is also 2%-3%. The final ZT value therefore

exhibits significant uncertainty, which can be up to around 30%.

Besides the simple superposition of errors due to measurements and the

approximation, the final result can be more inaccurate because it originates from

the process of separate measurements. Firstly, the inside grain sizes and shapes of

thermoelectric materials are changed by annealing, which occurs after each measurement

CONTENTS 8

is performed. Therefore separate measurements do not measure the properties of the

exact same sample, and there are slightly difference in each measurement. Secondly,

the grains in a ceramic material can align in a preferential direction, and the physical

properties can exhibit anisotropy such that the sample exhibits better performance when

measured along a particular direction. These preferred directions also add difficulties to

the ZT measurements. The final errors of ZT can be up to even 50% in some cases.

These measurement inaccuracies are directly linked to the reproducibility of

experimental results. Currently, the reproducibility of thermoelectric materials with

high performance is poor and many excellent results haven’t been proved by a second

research group [2]. As Snyder and his coworker mentioned, one should be encouraged

by results of ZT exceeding 1.5 but remain wary of the uncertainties involved to avoid

pathological optimism [14].

2. Thermoelectric Materials in Low Dimensional systems

The great pioneers Hicks and Dresselhaus proposed a few types of thermoelectric

materials in low dimensional systems, including 1D conductors, quantum wells and

semimetal-semiconductor transition in quantum-well superlattices in 1993 [3, 16, 17].

Later in 1996, they experimentally realized a ZT of 2.0 in 2D multiple-quantum-well

structures (PbTe/Pb1−xEuxTe) by Molecular Beam Expitaxy (MBE) [18]. That value

of ZT iis still one of the highest reported until now. This excellent research guided the

journey toward nanostructured thermoelectric materials in the past twenty years.

2.1. Quantum Well Superlattices

The original idea of applying quantum well structures to thermoelectric materials is that

an enhancement of the power factor S2σ could be realized through quantum confinement.

Additionally the lattice thermal conductivity could be significantly reduced by the

interface scattering in the direction perpendicular to the quantum wells , especially in

atom thick layers. The predicted ZT in 2D as a function of layer thickness is plotted in

Figure 4. Based on this idea, high ZT values are realized not only in PbTe/Pb1−xEuxTe

systems [18], but also in PbTe/PbSe0.2Te0.8 by MBE [19]. In 2001, Venkatasubramanian

CONTENTS 9

Figure 4. Calculated ZT as a function of layer thickness a in a quantum well structure

for layers parallel to the ab plane (1)and b-c plane (2). The dashed line represents the

optimized ZT forbulk Bi2Te3. From Hicks[16] and Chen[7].

and his coworkers reported the highest ZT=2.4 in Bi2Te3/Sb2Te3 (p-type) quantum well

superlattices [20]. Further explanation about the increased power factor is proposed by

Shakouri. The improvement of power factor is due to sharp features in the electronic

density of states of quantum-confined structures (Figure 5(b)). It enables a doping-level-

tunable increase in the asymmetry between hot and cold electron transport, leading

to a large average transport energy and a carrier concentration (i.e., a large Seebeck

coefficient and electrical conductivity) [21].

MBE is not the only frabrication technique in quantum well superlattices for

thermoelectric materials. Ohta and his coworkers reported ZT=2.4 in a two-dimensional

electron gas in SrTiO3/SrTi0.8Nb0.2O3 superlattices [22], where this sample was

fabricated by pulsed laser deposition (PLD). The quantum well thickness was only

0.3905nm. One should note that this high value of ZT is calculated from the assumption

that electrons are strictly confined in that thin layer [1].

Although high ZT values have been discovered in artificial superlattice structure,

there is still a long way to go for practical applications for waste heat power generation,

since it is difficult to fabricate large area devices for fitting in practical devices. Moreover

the stability of the thin layer needs to be investigated for real applications [11].

Larger area and lower cost techniques than MBE and PLD such as Chemical Vapour

CONTENTS 10

Figure 5. Schematic illustration of the density of states (DOS) as a function of energy

for: (a) a bulk material (3-D), (b) a quantum well (2-D), (c) a nanowire (1-D)

Deposition (CVD) have not been well developed for allowing high quality film growth

with atomic precision. Fabrication techniques like CVD need to be improved in the

fulture especially for the growth of crystalline chalcogenides, which is necessary for

many high-performance thermoelectric materials.

Thermal conductivity reduction is found to be the main reason behind the enhanced

ZT in superlattices. Studies on the heat-conduction mechanisms in superlattices

demonstrate that periodic structures are not necessary for thermal conductivity

reduction [23]. To overcome the scaling-up problems and find materials for commercial

applications, combining bulk nanomaterials and nanostructures seems to be a reasonable

solution, which will be introduced later in this paper.

2.2. One Dimensional Nanowires

Theoretical calculations predict a large improvement of ZT in one-dimensional

nanowires, even higher than in 2D quantum well superlattices. The reasons for

this enhancement are the change of DOS (Figure 5(c)) due to the strong quantum

confinement and the reduced lattice thermal conductivity due to the high surface to

volume ratio [3]. The thermoelectric figure of merit of a one-dimensional conductor or

quantum wire depends strongly on the radius of the wire [3]. Theoretical studies on III-

V semiconductor nanowires also indicate that InSb seems to be a promising candidate

for a reasonably high figure of merit for nanowires around 10nm thick. Some materials

(such as GaAs) show calculated high ZT values with diameters which are experimentally

unattainable [24]. However, in experiments InSb nanowires exhibit even lower ZT values

CONTENTS 11

than their bulk materials [25, 26]. The unexpected reduction of ZT also arises in Bi2Te3

nanowires [27]. The reason for this unexpected reduction has not been fully understood,

but may originate from the impurities in nanowires [28, 29, 30].

Improved ZT values are found for some nanowires in experiments, but in general

high ZT materials as 2D quantum well superlattice systems have not yet been

fabricated.. For example, silicon nanowires demonstrate a ZT=0.25 [31] for rough silicon

nanowires of 50 nm in diameter and 0.6 [32] for rough silicon nanowires of 50 nm in

diameter, while the bulk ZT for silicon is only around 0.01[33, 34]. Cylindrical Bi

nanowires are predicted to have a significantly improved Seebeck coefficient, because

a semimetal-semiconductor transition can occur below a critical wire diameter due to

quantum confinement [35]. The critical wire diameter at 77 K is found to be between

39nm and 55nm, and it depends on the crystal orientation of the wire axis [35]. High-

quality Bi nanowires are difficult to fabricate and they are often fabricated in porous

anodic aluminium oxide (AAO) or quartz (SiO2) templates [30]. Large enhancement

in the thermoelectric power of Bi nanowires embedded in porous alumina and porous

silica was reported by Heremans [36] in 2002, where the nanowires are with diameters

of 9nm and 15nm and the thermoelectric power is enhanced by two or three orders in

the temperature range of 100-300K.

High quality nanowires of these materials are generally quite challenging to

synthesize. Moreover, the unexpected reduction of ZT also needs to be investigated

to find the mechanisms behind it.

3. Bulk Nanostructured Thermoelectric Materials

3.1. Progress in Bulk Nanostructured Thermoelectric Materials

Bulk nanostructured thermoelectric materials[23] are bulk materials embedded with

nanoparticles or interfaces with nanometer size. These materials demonstrate improved

thermoelectric properties similar to the low dimensional systems, where the lattice

thermal conductivity is reduced due to designed phonon scattering. Compared to those

thermoelectricswith low dimensions, bulk nanostructured thermoelectric materials can

CONTENTS 12

be produced in a form suitable for current thermoelectric device configurations [5]. This

type of materials are also called nanostructured composite materials or nanocomposites.

In some high performing thermoelectric nanocomposites, the main contribution

to improved ZT is the reduction of lattice thermal conductivity. The mfps of phonons

typically range from several nanometers up to a few hundred nanometers, while the mfps

of carriers are much shorter, only a few nanometers [37]. Therefore, nanocomposites offer

the possibility for the effective scattering of phonons with long mfps without hindering

charge current conduction. Additionally, the Seebeck coefficient can also be lifted due to

electron filtering at grain boundaries in nanocomposites [11]. Furthermore, it is desirable

to have nanostructural features on different size scales, ranging from single atomic point

defects to nanoscale second phase inclusions to grain boundaries / twin boundaries on

the hundreds of nm scale. This helps to scatter phonons over their entire wavelength

range. A strategy based on this idea is illustrated later in this paper.

There have been three main strategies for bulk thermoelectric nanocomposites, as

demonstrated schematically in Figure 6[11]. One strategy is to form thermoelectric

nanocomposites with single-phase nanograins, which only involves reduction of the

thermal conductivity. The other two stratigies are to form second-phase nanoinclusions

(Figure 6 (b), (c)), where a large number of interfaces are formed between the

thermoelectric material and the nanoinclusions. The interfaces can be either incoherent

or coherent, which corresponds to the second and third strategies respectively. A

coherent nanoinclusion demonstrates good lattice matching with the matrix phase due

to similar lattice constants, while an incoherent nanoinclusion shows a clear boundary

between the matrix phase and the dispersed phase for the embedded nanostructures [11].

The Seebeck coefficient is enhanced for the last two approaches, in addition to the

reduction of thermal conductivity.

Typical strategies to synthesize nanocomposite thermoelectric materials are the

powder metallurgy method and melt metallurgy method, which are inspired by classic

metallurgical approaches. The powder metallurgy method is to prepare pre-synthesed

nanoparticles by physical or chemical routes with fast powder compaction to avoid grain

growth. For example spark plasma sintering is a direct current induced hot pressing

CONTENTS 13

Figure 6. Approaches for bulk thermoelectric nanocomposites: (a). nanograined

composite, (b). nanoinclusion composite with an incoherent interface, and (c).

nanoinclusion composite with a coherent interface[11]

technology, and it can create extensive interfaces between the neighbouring nanoparticles

and lower the thermal conductivity. The melt metallurgy method usually applies melting

and quick cooling to obtain small grain size or even amorphous powders [11, 7, 38].

The improvement of ZT has been investigated in a wide range of bulk

nanostructured material families, including Bi2Te3-based nanocomposites, PbTe-based

nanocomposites and SiGe-based nanocomposites. For a detail overview of these three

families of bulk nanostructured thermoelectric materials, the reader is referred to the

recent review article by Chen et al [7]. In this paper, the author proposes an idea for

improving ZT by the detailed design of a more efficient way of scattering phonons, i.e.

by adjusting the distribution of the nanosize dots or interfaces along the temperature

gradient in practical devices.

3.2. A Strategy to Improve ZT in Nanocomposites

Current research in nanostructured composites for thermoelectric materials combines

low-dimensional and bulk materials for thermoelectric applications. As we mentioned

before, nanocomposites (in Figure 6) contain a high density of second-phase

nanoinclusions, and they are powerful tools for improving ZT. For example, Girardin

et al. reported PbTe bulk materials with homogeneous distributed PbS nano-size dots

that improves ZT into 1.4 at 750K in the PbS(8%)-PbTe materials system by lattice

thermal conductivity reduction [38]. Biswas et al reported a figure of merit of 1.7 at

800K in PbTeSrTe (SrTe=0.52mol%) materials doped with 1mol% Na2Te [39]. Also in

CONTENTS 14

Na1−xPbmSbyTem+2 systems, ZT=1.7 at 700 K was reported by Poudeu [40]. These

nanostructured thermoelectric systems exhibit better ZT than simple bulk materials

mainly due to the scattering of long mfp phonons by nano-scale features.

The mean free path of phonons in nanocomposites based on bulk materials is

determined by two factors:one is scattering from nanosize particles and grain boundaries

of the sample and the other is scattering with other phonons.. Current studies

have focused on the first factor and improve ZT by optimizing compositions of the

materials that can scatter phonons more effectively. In the second factor, the interaction

between phonons can also change the mfp by the Umklapp process. The probability

that a phonon undergoes a collision is directly proportional to the number of other

phonons present and the number of phonons at high temperature is proportional to

kBT/~ω, according to the Bose-Einstein Distribution. Therefore the mfp l in the

system is approximately proportional to 1/T. In thermoelectrics, a pronounced gradient

of temperature is required, meanwhile phonon mfps increase along the temperature

gradient. Therefore it is reasonable to propose a model which varies the nano-size

features of thermoelectrics along the temperature gradient and gains better scattering

results for phonons over their entire mfp range corresponding to different temperatures.

A schematic figure is plotted to illustrate this idea in Figure 7, where an increased

trend in size for nanoparticles is demonstrated. The homogeneous size distribution (in

Figure 7.a) only obtains an average optimized scattering rate for phonons with different

mfps. Our designed system (in Figure 7.b.) can optimize the scattering of phonons over

their entire mfp range along the temperature gradient, and therefore it could achieve a

higher ZT value in the end.

One reasonable way to realize this model is applying ferromagnetic nanoparticles

with a wide range of sizes in bulk materials. By applying a magnetic field in the

molten state of the bulk matrix, a size distribution can be established. For example,

one can control the size distribution of magnetite (Fe3O4) nanoparticles embedded in

GST (Ge2Sb2Te5) matrices. There are two shortcomings of this idea. One is that the

ferromagnetic nanoparticles need a high melting point, which limits the materials that

CONTENTS 15

Figure 7. Schematic pictures of: (a). homogeneous size distribution for nanoparticles

in a bulk thermoelectric material compared with (b). increased size distribution along

the thermal gradient for nanoparticles in a bulk thermoelectric material. The latter

model can scatter phonons over their entire mfp range.

can be combined with each other.Another difficulty is that the crystal types (or space

groups) of the nanoparticles and matrices need to be same or compatible.

4. Conclusion

Over the past twenty years, thermoelectric nanomaterials and materials embedded

with nanostructures have been extensively investigated and and have shown promising

potential promising potentials for waste heat utilization. ZT values of thermoelectric

materials have been increased from 1.0 in the 1950s to around 2.4 nowadays. In this

paper, an idea of adjusting nano-scale structures along the temperature gradient is

proposed. This strategy could be a fruitful way to enhance thermoelectric device

performance for practical applications. Measurement accuracy and reproducibility of

high-performance thermoelectrics are also critically analyzed. Measurement issues of

thermoelectrics are very serious (even with errors around 30%-50%) and worth attracting

attention from academia for bridging the gap from high-performance materials to

practical devices. Moreover, applying thermoelectric materials with a ZT value

exceeding 2.0 in commercial devices is still a challenging topic, especially for materials in

CONTENTS 16

low dimensional systems. To solve the measurement inaccuracy and apply the excellent

breakthrough of ZT into waste heat utilization, scientists from academia and industry

need cooperate together for fabricating practical devices and improving efficiency in an

accurate way.

5. Acknowledgement

This review paper is finished under the guidance of Dr. Blake. The author thanks

him for his supervision and suggestions during very useful discussions. The author also

appreciates the workshops given by Prof. Chiechi and Dr. Pchenitchnikov and especially

thanks Dr. Kaverzin for his teaching in writing skills.

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