synthesis and characterisation of beta-fesi2

8/18/2019 Synthesis and Characterisation of beta-FeSi2

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Synthesis of high density β - FeSi2 : Structural and electrical

characterisation

by Abu Anand ( SB-1312004)

Guide : Prof. Arun M Umarji

Materials Research Centre

Indian Institute of Science (IISc), Bangalore

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Contents

1 Introduction 3

1.1 Thermoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Thermoelectric materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Transition metal silicides as thermoelctric materials . . . . . . . . . . . . . . . . 4

2 Experimental techniques 7

2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Hot pressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Heat treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Characterisation of samples 7

3.1 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Scanning electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Electrical resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3.1 Two probe method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3.2 Four probe methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.4 Seebeck coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Conclusions 14

5 Acknowledgment 14

References 15

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1 Introduction

There has been a dramatic escalation in world’s demand for energy in the past few decades which

resulted in a lot of political and social unrests. Scavenging of waste heat through thermoelectric

generators is a sustainable way of tackling the situation. Home heating,automotive exhaust, and other

industrial processes all generate an enormous amount of unused waste heat that could be converted

to electricity by using thermoelectrics. Since thermoelectric generators are solid-state devices withno moving parts and scalable, making them ideal for small, segmented as well as distributed power

generation.[1]

1.1 Thermoelectric effect

Thermoelectric effect generally deals with the inter-conversion of thermal energy and electrical energy.

The thermoelectric effect arises because the charge carriers in metals and semiconductors are free to

move like gas molecules while carrying charge and heat as well. When a material is subjected to a

temperature gradient, these charge carriers which are mobile will diffuse from hot end to cold end.

This migration will create a build-up of a net charge in the cold end in turn leading to the development

of an electrostatic potential (voltage). At some point, the electrostatic repulsion due to the build-upof charge separation between the hot and cold end will get in equilibrium with the chemical potential

for diffusion. This is called the Seebeck effect. The voltage developed in the material will be directly

proportional to the temperature gradient applied.[2]

∆V = S ∆T (1)

Proportionality constant used here is the Seebeck coefficient (S ) of the material, named after T J

Seebeck who first reported this phenomenon in 1821.

In the other hand, keeping a potential difference between two ends of a conducting material will

lead to generation of a thermal gradient. This phenomenon is called the Peltier effect

Q = πI (2)

π is the Peltier coefficient of the material and Q is the heat flow through the material. Peltier and

Seebeck coefficients can be related as

π = ST (3)

Thermodynamically, these thermoelectric phenomenons are reversible. However, in practice, it is

affected by irreversible phenomenon like electrical resistivity, thermal conduction. The performance of

any thermoelectric device will be dependent on these transport properties. The coefficient of perfor-

mance of a thermoelectric device is given by [1, 3]

COP = T H − T C

T H

√ 1 + zT − 1√

1 + zT − T HT C

(4)

where z is the figure of merit of the material times the operating temperature given as a function of

the transport properties

z = S 2σ

k (5)

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Figure 1.1: Change of transport properties and zT with carrier concentration

In this expression, S 2σ is defined as the power factor of the material.

For the efficient working of a thermoelectric material, its zT value should be maximised.

1.2 Thermoelectric materials

Choosing material for the manufacturing of a thermoelectric device is at-most important thing. The

material chosen should be having maximum zT value as mentioned earlier but along with that for

practical purposes we should also consider the production cost, mechanical strength, chemical and

thermal stability over the operating temperature in which the device manufacture out of the material

is used.Maximisation of zT is a task of mutually conflicting ideas. Looking into the expression of zT, it

could be found that for its maximisation, the Seebeck coefficient and the electrical conductivity should

be increased whereas the thermal conductivity should be decreased. Since these cannot be achieved

simultaneously, there should be an optimum value for the transport properties at which the zT is

maximum. The transport properties are a function of the charge carrier concentration. When we are

plotting carrier concentration and transport properties (Figure 1.1), the zT could be found maximum

when the concentration is in the range of 1019 – 1021. This is the typical carrier concentration of

semiconductors. So semiconductors could be used to get efficient thermoelectric devices.

1.2.1 Transition metal silicides as thermoelctric materials

In the field of high temperature thermoelectric applications, transition metal Silicides are of high

importance due to their thermal and structural stability, high electrical conductivity at elevated tem-

peratures. Also, the elements that are used for the synthesis are naturally abundant and non toxic;

hence the production cost will be low which increases the practical feasibility of the thermoelectric

devices.

Aim of this project is to investigate β -FeSi2 , which is the semiconducting phase of Iron Silicide,

as a potential thermoelectric material and to improve its thermoelectric properties by doping. β -FeSi2is a TMS having large Seebeck coefficient, high electrical conductivity, high thermal stability and low

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Figure 1.2: Fe-Si phase diagram[4]

production cost as well as non toxic in nature. This makes it a potential candidate for a thermoelectric

material for high temperature applications.

From the Fe – Si binary phase diagram (Figure 1.2), β - FeSi2 will get solidified from the peritectoid

decomposition of α-FeSi2 and ε-FeSi, which are metallic phases. Since it is a peritectoid reaction, the

complete conversion of entire ε-FeSi into β - FeSi2 will take lot of time for completion. This is because

of the low rate of diffusion in the solid state.

β -FeSi2 crystallises in orthorhombic structure with 48 atoms per unit cell. It exists in Cmca space

group and have lattice parameters a = 9.863 Å, b = 7.884 Å and c = 7.79 Å.[5] Theoretical calculations

performed suggested that there exists an indirect between Y (valence band) and a non-symmetry point

between Γ and Z (conduction band) with a value of 0.67eV.[6, 7]

Small polaron model has been used to study the conduction mechanism in β - FeSi2 and was found

that there is semiconductor to metal transition at 1259 K. [8] Thermal conductivity as discussed earlier

will have two main contributions, one due to electrons and the other due to the phonon scattering.In β - FeSi2 the phonon contribution is found to be predominant. So in the optimisation of zT, the

main challenge would be the reduction of this lattice contribution of thermal conductivity. Doping in

thermoelectric systems can be used as a tool to optimise the carrier concentration. It can also act as

scattering centres for phonons to reduce lattice thermal conductivity.

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Figure 1.3: Crystal structure β -FeSi2

Figure 1.4: Band diagram of β - FeSi2

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2 Experimental techniques

In this work β - FeSi2 sample with high bulk density is prepared. Doping with phosphorous is carried

out in a sealed tube reaction. Phase characterisation X-Ray diffraction and SEM is carried out.

Electrical characterisation by 4 probe electrical resistivity and Seebeck measurement is done.

2.1 SynthesisInitially, stoichiometric amounts of iron (Sigma Aldrich - 99.98%) and silicon (Alfa Aesar - 99.9999%)

were arc melted in Argon atmosphere. To remove the oxygen content in the chamber, Titanium gutter

was melted before doing the melting Iron and Silicon.

2.2 Hot pressing

Hot pressing is a non equilibrium/ rapid solidification process which is used to make densified samples

out of the arc melted ingot. Since the transport properties are significantly dependent on the density of

the material it is important to obtain dense samples. Ingot synthesised from arc melting was crushed

using a mortar and pestle to get powder. These powdered samples were taken in a graphite die

where the sample was sandwiched between graphite sheets to make the pressure applied uniform. This

graphite die was placed in the middle of the heating coil of the HP apparatus. The heating is happening

in the apparatus due to the induction of eddy currents when the current is passed. Atmosphere inside

the apparatus was maintained inert using Argon in order to avoid oxidation of graphite die. Uni-axially

a pressure of 35 MPa was applied using a hydraulic press at a slow rate to avoid sample breakage for

7 minutes.

Density measurement

Density of the sample pellet synthesised using hot pressing was measured using Archimedes principle.

Here, the weight of sample was measured in air as well as in the liquid. Sample density is calculatedusing the Archimedes equation.

Density = W sW s −W L

ρL (6)

Density of the sample was found to be 4.60 g/cc whereas the theoretical density is 4.80 g/cc.

2.3 Heat treatment

Hot pressed pellets, since the arc melted FeSi2 will be containing α and ε phase, was heat treated.

Heat treatment was done in a vacuum sealed quartz tube at 800oC for 12 hrs. Phosphorous doping

was also tried to study the effect of dopants in the enhancement of thermoelectric properties. This

was done by heat treating the hot pressed samples in a quartz tube containing 20mg of phosphorous

(Merck - 99%).

3 Characterisation of samples

To confirm the presence of expected phases in the synthesised samples powder X-ray diffraction and

Scanning electron microscopy was done.

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Figure 3.1: XRD patterns (Bottom to top) a) Arc melted b) Hot pressed c) Heat treated 800oC/12hrs

Figure 3.2: BSE image and EDAX analysis of heat treated sample

3.1 X-ray diffraction

XRD spectrum was taken using Panalytical X’pert Pro (Cu-Kα source) for the arc melted, hot pressed

and heat treated samples and was compared with the literature spectra for the phase confirmation.

Arc melted and hot pressed samples where showing α and ε phase as expected from the binary

phase diagram of Iron and Silicon since these processes where happening above the peritectoid point.

XRD patterns (Figure 3.1) of heat treated sample was showing β phase with slight presence of ε phase

since the peritectoid reaction is solid state diffusion process which will be happening in very slow rate.

3.2 Scanning electron microscopy

The SEM (JEOL JXA-8530F Electron Probe Micro analyzer) images and EDAX analysis of the heat

treated sample is shown in Figure 3.2. The existance of ε-FeSi in β - FeSi2 matrix is clealy seen. This

is further clarified elemental analysis by EDAX for the grey and dark region.

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3.3 Electrical resistivity

Resistivity measurement techniques

According to Ohm’s law, the current flowing through a substance will be directly proportional to the

potential difference applied across it.

V = IR (7)

The constant of proportionality used in this statement is the resistance of that material which

depends on the microscopic as well as the geometric properties of it. So even for the same composition

sample the resistance will be different according to the dimensions of the sample. The dependence of

sample geometry in the resistance is as follows

R = ρl

A (8)

where ρ is the resistivity of the material. Inverse of resistivity is termed as the conductivity (σ). In

calculating the zT of a thermoelectric material it is very important to have accurate measurements of

the electrical conductivity. There are various methods used for the conductivity measurement which

can be broadly classified into two.

3.3.1 Two probe method

In this method a current is passed through the sample and the potential drop across the sample will

be measured using a voltmeter. This method can be adopted only if the sample resistance is high.

It is because the resistance that we are measuring includes the resistance of the contacts made by

the probes also. So, if the sample is having low resistance, then the contact resistance will mask the

resistance of the sample.

3.3.2 Four probe methods

3.3.2.a Linear four probe

This method was first reported by L. B Valdes in 1954. In this method, the probes will be kept collinear

as the name suggests. The outer probes are to pass current and the inner probes are used to measure

the voltage as shown in the figure. The calculation of resistivity from the readings of this method is

done by the following equation [9]

ρ = V

I 2πs (9)

The equation is derived using the method of images in electrostatics assuming the sample is having

semi-infinite volume i.e. of infinite area but the thickness is very small. So in reality there should be

some correction factors introduced to rectify the errors caused by the geometry as well as the thicknessof the sample. This correction factors were calculated by F M Smit in 1958. [10]

A C programme code was written for generating the correction factors in linear four probe when

the sample dimensions are provided (Appendix 1). In the code correction factors given in the Smit’s

paper was taken as data points to generate Lagrangian interpolating functions[11] and the geometrical

dimensions given by the user will be evaluated using these Lagrangian functions to get the correction

factors.

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3.3.2.b Van der Pauw method

Van der Pauw method is a four probe resistivity measurement method which can be used to obtain

the resistance values of arbitrary shaped samples. Experimental setup is as shown in the figure.

Van der Pauw method was used to calculate the sample resistivity with temperature, in the home

built apparatus. A resistive furnace was used to reach higher temperature values. Four electrical

contacts made where of pressure contact type using platinum wires and the resistivity was calculated

using the Van der Pauw equation. β -FeSi2 shows the same trend of general p-type semiconductors.

Band gap of the sample was calculated by linearly fitting the intrinsic region of the curve.[12]

3.4 Seebeck coefficient

Seebeck coefficient metrology techniques can be broadly divided into two types

• Integral method

• Differential method

– Steady state method

– Quasi steady state method

– Transient method

Integral method can be used when the temperature gradient is very high. Here, we plot thermo emf

generated as a function of temperature and the Seebeck coefficient at any particular temperature is

given by the slope of the curve at that particular point.

Differential methods can be used when the temperature gradient is small so that the coefficient

can be determined directly. In this type of measurements, we can wait for the achievement of a steady

state (ie the rate of change of the heat flux through the sample is zero). This is called the steady state

differential method. This method will be more accurate but will take lot of time for the measurement

to get completed. Since the gradient should be holded for a long time span it cannot be implementedwhere the sample is not thermally very stable. [13]

In quasi steady state differential method, we will not wait for the constant heat flux condition. This

method will be less accurate but is more practical in scenarios like sample with less thermal stability.

Transient method is the one in which the direction of thermal gradient is cycled as a function of time

inorder to make Seebeck measurements. This is to get rid of some offset thermal emfs generated in

some materials due to the unidirectional heat flow[14, 15].

Steady state method was used to measure the Seebeck coefficient in room temperature. Undoped

sample was showing a positive Seebeck coefficient whereas the doped sample was giving negative. This

suggests the undoped sample is p-type (positive charge carriers) and the phosphorous doped ones are

n-type (negative charge carriers).S undoped = +180 µV/K

S P doped = −198µV/K

Power factor Γ = S 2σ was found to be for each samples

Γundoped = 1.19µW/mK 2

ΓP doped = 1.44µW/mK 2

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Figure 3.3: Two probe method

Figure 3.4: Linear four probe schematic[9]

Figure 3.5: Resistivity vs Temperature – Undoped beta-FeSi2

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Figure 3.6: log resistivity vs 1000/T – Band gap determination

Figure 3.7: Van der Pauw method : Schematic experimental setup[16]

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Figure 3.8: Van der Pauw method : Sample orientation and connections

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4 Conclusions

High density β -FeSi2 was prepared by arc melting followed by hot pressing. Inclusion of -FeSi phase

in matric of β -FeSi2 is revealed by SEM and XRD results.

A C programme to obtain bulk resistivity from surface resistance obtained from linear four probe

electrical resistance measurement is written and implemented.

The power factor S 2

σ for β -FeSi2 (undoped) and phosphorous doped samples are shown to beΓundoped = 1.19µW/mK 2 and ΓP doped = 1.44µW/mK 2.

5 Acknowledgment

I would like to express my sincere gratitude to Prof. Arun M Umarji, Materials research centre, IISc

Bangalore for his invaluable guidance in my summer term 2015. I thank Rajasekar P and other lab

mates in AMU lab for their guidance and affection they have shown during my stay. I would also like

to thank Kishore Vaigyanik Protsahan Yojana (KVPY), Department of Science and technology, Govt.

of India for providing me an oppurtunity to do this summer project.

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References

[1] David Michael Rowe. CRC handbook of thermoelectrics . CRC press, 1995.

[2] G Jeffrey Snyder and Eric S Toberer. Complex thermoelectric materials. Nature materials ,

7(2):105–114, 2008.

[3] Glen A Slack and DM Rowe. Crc handbook of thermoelectrics. CRC, Boca Raton, FL, 407440,1995.

[4] Ortrud Kubaschewski. Iron Binary phase diagrams . Springer Science Media, 2013.

[5] Y Dusausoy, J Protas, R Wandji, and B Roques. Structure cristalline du disiliciure de fer, fesi2.

Acta Crystallographica Section B: Structural Crystallography and Crystal Chemistry , 27(6):1209–

1218, 1971.

[6] SJ Clark, HM Al-Allak, S Brand, and RA Abram. Structure and electronic properties of fesi 2.

Physical Review B , 58(16):10389, 1998.

[7] Tribhuwan Pandey, David J Singh, David Parker, and Abhishek K Singh. Thermoelectric prop-erties of β -fesi2. Journal of Applied Physics , 114(15):153704, 2013.

[8] U Birkholz and J Schelm. Mechanism of electrical conduction in β -fesi2. physica status solidi (b),

27(1):413–425, 1968.

[9] Leopoldo B Valdes. Resistivity measurements on germanium for transistors. Proceedings of the

IRE , 42(2):420–427, 1954.

[10] FM Smits. Measurement of sheet resistivities with the four-point probe. Bell System Technical

Journal , 37(3):711–718, 1958.

[11] William H Press. Numerical recipes 3rd edition: The art of scientific computing . Cambridge

university press, 2007.

[12] LJ Van der Pauw. Determination of resistivity tensor and hall tensor of anisotropic conductors.

Philips Research Reports , 16:187–195, 1961.

[13] J Martin, T Tritt, and Ctirad Uher. High temperature seebeck coefficient metrology. Journal of

Applied Physics , 108(12):121101, 2010.

[14] Joshua Martin. Apparatus for the high temperature measurement of the seebeck coefficient in

thermoelectric materials. Review of Scientific Instruments , 83(6):065101, 2012.

[15] V Ponnambalam, S Lindsey, NS Hickman, and Terry M Tritt. Sample probe to measure resistiv-

ity and thermopower in the temperature range of 300–1000k. Review of scientific instruments ,

77(7):073904, 2006.

[16] T Das Gupta. PhD Thesis . IISc, Bangalore, 2007.

synthesis and characterisation of beta-fesi2

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