Characterisation of Thermoelectric Properties in R0.65Ca0.35MnO3 Perovskites (R = La, Pr, Nd,

Sm, Y, Bi) and Construction of High Temperature Measurement Setup

by Lee Joon Hon Alvin (A0086862R)

A thesis submitted for the degree of

Bachelors of Science (Honours)

at the National University of Singapore

4 April 2015

Abstract

R0.65Ca0.35MnO3 Perovskites is a class of metal oxide materials that exhibit various interesting

properties. Their ability to remain stable at high temperatures makes them good candidates

for feasibility studies into their potential as thermoelectric materials while their phase

transitions at low temperatures allows us to gain an insight into their electronic transport

properties.

In this article, we will look at the thermopower and resistivity properties of the perovskites

across a wide temperature range of 100K to 700K as well as the interpretation of these

properties. We will also look at the properties of Nd0.65Ca0.35MnO3 within a strong magnetic

field environment to explore the possible phase transitions in the low temperature range.

An unprecedented 1000K High Temperature Measurement setup will also be constructed in

order to study the thermopower, resistivity as well as thermal conductivity properties of

future materials. The progress and challenges of the construction process will be mentioned

for future references in the construction of similar high temperature setups.

Acknowledgements

I would like to thank my project supervisor, Professor Mahendiran Ramanathan, for the

opportunity to work in his lab as well as for the guidance and directions for the project. His

great insights in the results interpretation taught me a lot throughout the course of this project.

I would also like to thank Dr. Pawan Kumar for his countless support in the experimental

methodologies and experimental discussions, especially in the construction of the 1000K

High Temperature Setup. My thanks also go to fellow honours student, Ivan Lee, for the

numerous discussions in measurement results as well as the planning of the project pace and

scope. Last but not least, I would like to thank the fellow lab members, Rubi, Maheswar

Repaka, Amit Chanda and Himadri Roy for the endless support they gave for the success of

this project.

Chapter 1 Introduction and Theory

1. Background of Thermoelectric Effect

Thermoelectric effect mainly consist of the Seebeck and Peltier effects.

The Seebeck effect was discovered in 1821 when Thomas Johann Seebeck discovered that a

coil wound around a compass would deflect the compass when the coil ends were closed with

a dissimilar metal and a temperature difference applied. In other words, a temperature

difference applied across two dissimilar-metal junctions creates an electromotive force.

In 1834, Jean Charles Athanase Peltier discovered the reverse of the Seebeck effect when a

potential difference applied across the junctions gave rise to a temperature difference.

The thermoelectric effect first found commercial use as electronic thermometers in the early

1900s, at a time when voltmeters became increasing more precise. These thermometers have

the advantage of having a wide range of operating temperatures as well as high precision

compared to other thermometers at that time.

Later, at the height of the space race, thermoelectric devices filled an extremely niche role as

the power source of long haul space exploration probes. Today, one such exploration probe,

the Voyager 1, became famous for being the first manmade object to cross the heliopause in

September 2012. These Radioisotope Thermoelectric Devices have the advantage of

operating in high temperatures as well as having no moving parts, allowing it to work with

1

high temperature radioisotope pellets while having high durability.

An increasingly common application of thermoelectric effect today can be found in

refrigeration as Peltier Modules. The high durability and small construct allow these modules

to be used in consumer products such as portable fridge, CPU coolers and even dehumidifiers.

In light of these developments, it is important to characterise and determine the factors that

will allow us to construct increasingly efficient thermoelectric devices and enable us to utilise

the technology more effectively.

1.1 Thermoelectric Basics

The thermoelectric phenomenon of interest in this article can be broken down into two

thermodynamically opposite effects. As mentioned above, they are the Seebeck and Peltier

effects. The Seebeck effect is the emergence of an electromotive force when a temperature

gradient is present on the two ends of a thermoelectric material. On the other hand, the Peltier

effect is the emergence of a temperature gradient when an electric current is passed through a

thermoelectric junction. The Seebeck and Peltier effects can be summarised in the equations

below:

:∇ = − ∇ = −∆∆ = − −−

Where S is the Seebeck Coefficient and ∇ (∆ ) is the temperature gradient (difference)

between the two junctions and ∇ (∆ ) is the potential gradient (difference) generated

between the two ends of a thermoelectric material. The negative sign is present so that a

positive carrier mediated material gives a positive Seebeck Coefficient.

: = Π − Π

Where is the rate of heat pumped from the cold to hot junction, Π and Π are the Peltier

Coefficients of materials A and B respectively and I is the current passing through the

thermoelectric materials.

2

When the Seebeck Coefficient varies with temperature, a variation of the Peltier effect arises.

This is described by the following Thomson effect:

: = −Κ ∙ J ∙ ∇T

Where the Thomson Coefficient, Κ, is related to the Seebeck Coefficient via Κ = .

The coefficients are then related via the two Thomson relations which are given by:

Κ = − and Π =

Since the experiment to be described in this article focuses specifically on the Seebeck effect,

we shall discuss no further on the Peltier and Thomson effects.

1.2 Thermoelectric Unit

To visualise the mechanism that give rise to the thermoelectric effect, it is useful to consider

a simplified conduction model such as the Drude Model. In the simple Drude model [See

Figure 1], the conduction electrons of a metal (as a first consideration) moves around as an

electron gas within the bulk of the material. The electrons’ speed and therefore rate of

diffusion will then be proportional to the temperature of the region of material that the

electrons are in.

When a temperature difference is applied across two ends of a metal [See Figure 2], the

electrons at the hotter end will diffuse away from that end at a higher rate compared to the

electrons at the colder end diffusing away from the cold end. As a result, the colder end will

have a higher density of conduction electron with respect to that of the hotter end and a

potential difference arises. The potential difference will grow until it sufficiently oppose the

effect of electron diffusion as a result of the temperature difference.

Figure 1: Diagram illustrating the random motion and distribution of electrons in a metal, modelled as an electron gas according to the Drude Model. The charge distribution is uniform in the absence of an electric field or temperature gradient.

3

Figure 2: Applying a temperature difference to the material results in the accumulation of charge carriers at the cold end. This give rise to a potential difference that opposes further diffusion and accumulation of charges.

The same visualisation can be made for materials that conducts primarily through holes, with

the effect of reversing the sign of the potential difference. When these two different types of

iers

flow from the hot end to the cold end. Due to the way the thermoelectric materials are

s flow

at

nent of any thermoelectric device and its

efficiency is directly related to the performance of its constituent thermoelectric materials.

thermoelectric materials are arranged as in Figure 3[1], a Thermoelectric Unit is formed.

In Figure 3, when a temperature difference is applied across the junctions, the charge carr

Figure 3: Diagrams showing the inner workings of a Thermoelectric Unit. The diagram on the left shows an electric current being generated as a result of a temperature difference while the diagram on the right shows heat being pumped due to the direction of movement of charges caused by the electromotive force.

arranged, an electrical current flows with which a load can be powered. On the other hand,

when an electromotive force is applied to the ends of the device, the electrons and hole

in the same spatial direction and the device acts as a thermoelectric heat pump, removing he

from one side and depositing it on another.

The Thermoelectric Unit is the basic compo

4

Therefore, it is imperative to choose the right combination of thermoelectric materials

specific application.

1.3 Figu

for the

re of Merit

The fig rformance of thermoelectric materials is the

dimensionless quantity ZT. Its definition is given by:

ure of merit for accessing the pe

= = = +

Where = is the Power bes the absolute power per

squared ure attainabl electrical conductivity of the

Factor of the material which descri

e regardless of efficiency, is the -temperat

material and = + is the thermal conductivity of the material and can be broken

down into the electrically-mediated thermal conductivity and phonon-mediated thermal

conductivity respectively.

It is important to note here that the temperature, T, is present to make the figure of merit

dimensionless, where Z wo

According to the Wiedemann-Franz law

uld otherwise have a dimension of K-1.

= = , the electrical

conductivity, , is directly proportional t al conductivity,

sic

nO3 Perovskites

cture [See

Figure 4][2] and the chemical formula ABO3. In this article, the A atoms are the R atoms and

n this

o the electrically-mediated therm

. Hence, the figure of merit can only be improved by increasing S, which is an intrin

property of the class of thermoelectric material, increasing carrier mobility, which have the

effect of increasing , or by reducing .

2. Focus on R0.65Ca0.35M

Perovskites are a class of metal oxide materials that has the Perovskite Stru

Calcium in stoichiometric ratios and the B atoms are Manganese atoms. The R atoms i

article consists of either La, Pr, Nd, Sm, Y* or Bi.

* The Y0.65Ca0.35MnO3 sample was prepared but eventually unused due to the unattainably high temperature (1380°C) needed to produce a strong bulk sample for measurement.

5

Figure 4: Diagram of Perovskite Structure. Each B atoms are surrounded by 6 oxygen atoms arranged in an Octahedral manner. Each BO6 group can then be illustrated as being caged by 8 A atoms (a) or 8 BO6 groups caging an A atom (b).

I

o ectively. The substitution of Calcium atoms for the R atoms in this

3

5% in

this research due to the following factors:

While

little focus have been placed on metal oxides as they were thought to be poor

ered

nown at

2) e Ordering (CO) and Magnetic phase

ansitions at various temperatures. It is hoped that we can gain an insight to the

n pure CaMnO3 perovskite, the Calcium, Manganese and Oxygen ions have oxidation states

f +2, +4 and -2 resp

article (R = La, Pr, Nd, Sm, Bi, Y) have the effect of reducing the oxidation state of a

proportion of manganese ions from +4 to +3 as the R atoms commonly form ions in the +

oxidation state. In this case, the proportion of manganese ions would theoretically be 6

the +3 state and 35% in the +4 state. The substitution of Calcium atoms also have the effect

of distorting the Perovskite structure as the replacement ions have different ionic radius

compared to the Calcium ions in the compound.

The R0.65Ca0.35MnO3 Perovskites are of interest in

1) many different types of thermoelectric materials have been studied extensively,

thermoelectric candidates due to their low carrier mobility and high phonon

velocity[3]. This changed in the mid 1990s when the NaxCoO2 oxide was discov

to have anomalously high thermoelectric performance relative to the oxides k

that time. We intend to study the above R0.65Ca0.35MnO3 Perovskites because their

thermoelectric properties are not well studied.

The R0.65Ca0.35MnO3 Perovskites exhibit Charg

tr

electronic transport properties of the thermoelectric materials at these transitions and

perhaps use this knowledge to increase the thermoelectric performance of future

6

materials.

The Perovs

e

3) kites, being metal oxides, have the greatest tolerance for high temperature

nvironments. They are, after all, synthesised using the ceramic-sintering process

ns.

The R a ent consists of La, Pr, Nd, Sm, Y and Bi.

These atoms commonly form ions in the +3 oxidation state and, as mentioned above, would

and

trary, the ionic radius of these R atoms changes as one moves along the series. The

properties of the R atoms are summarised in Table 1[4][5][6][7][8].

For comparison, the ionic radius of Ca2+ ion is 1.14Å and that of Mn3+ and Mn4+ ions are

0.72Å and 0.67Å respectively. O ions have a relatively large ionic radius of 1.26Å.

ns have

bond lengths that are in the specific ratio of √2

which can reach temperatures upwards of 1500 Kelvins. The high temperature

operation not only increase the Power Factor but also increase the thermodynamic

efficiency. This allows metal oxide thermoelectric devices to be powered by high

temperature radioactive sources in niche applications such as deep space exploratio

2.1 About the R Atoms

toms that were chosen for this experim

cause the nominal valence of the Mn ions in the Perovskites to be present in a mix of +4

+3 when replacing the Calcium ions. In this case, the theoretical proportion of Mn ions would

be fixed.

On the con

2-

Strictly speaking, the true Perovskite Structure can only exist when the A, B and O io

:1 (A-O: B-O) at 0K. Only then will the

Table 1: Table summarising the R3+ ionic radii and their associated perovskite structures.

7

compound attain the cubic Perovskite Structure as seen in Figure 1a. This requirement can be

relaxed when the temperature is increased due to the increased flexibility of the ionic bo

angles and lengths.

However, even at ro

nd

om temperatures, the R0.65Ca0.35MnO3 compounds attain either

Orthorhombic or Tetragonal structures which meant that they are strictly distorted

ould increase. However,

the electronic properties of the R ions should

her

2.2 Polaron Conduction M

It is suspected that the perovskites in this experiment conduct via a mechanism called

Polaro i-particles formed from a

distortion in the lattice due to a charge. When a charge, such as an electron, is placed in a

sitive

it

perovskites. An example of the distortion can be seen in Figure 5[9].

As the ionic radii of the R ions decrease, the

amount of distortion sh

not be neglected as this could change the

structure and properties of the compound itself.

In Bi3+ for example, the lone pair of electrons

in the outer shell could contribute some ot

effects to the thermoelectric properties despite

having approximately the same ionic radius as

La3+.

Figure 5: Structure of SrTiO3 below 110K. Each oxygen octahedral rotates with an angle φ away from the ideal alignment.

echanism

n Hopping at room temperature. Polarons are essentially quas

dielectric medium, the electron polarises the ions in the vicinity. This means that the po

lattice ions will move closer to the electron from its equilibrium lattice position and the

negative ions in the opposite direction. This resultant distortion will follow the electron as

moves across the medium.

8

To understand how polarons move within a medium, it is useful to first consider how

conventional Band Transport works. In conventional band transport [See Figure 6], an

electron can be modelled as a ball on a hard surface and a hole can be modelled as a bubble

against a liquid surface. Applying an electric field is akin to tilting the setup, causing the ball

and bubble to move in opposite directions.

A polaron’s potential, on the other hand, is like a ball on a trampoline. The ball sinks as a

result of its presence. When a polaron’s potential is wide and gentle, we call it a Large

Polaron [See Figure 7]. When the potential is narrow and deep, we call it a Small Polaron.

When an electric field is applied, a large polaron can easily ‘roll’ down the gentle potential

and this results in a high mobility. On the other hand, a small polaron is trapped in its deep

well and can only tunnel or thermally hop to the nearest wells.

To determine whether a material conducts via small polaron hopping, we can compare the

properties of its thermopower (S) and its electrical resistivity (ρ). The thermopower and

electrical resistivity of most conductive materials can be described by:

Figure 6: Model of Conventional Band Transport. (a) An electron is like a ball while a hole is like a bubble. (b) Tilting the setup by applying an electric field causes the ball and bubble to move in opposite directions.

(a)

(b)

Figure 7: Model of a polaron’s potential. (a) A Large Polaron (left) has a gentle potential while a Small Polaron (right) has a deep well potential. (b) A large polaron can easily roll down the potential while a small polaron is trapped in the deep well.

(a) (b)

9

= + and =

Where ES and Eρ are the characteristic activation energies of thermopower and resistivity

respectively and α and ρ0 are constants that are dependent on the material.

2.3 Polaron Hopping at H

The signature of small polaron materials is that Eρ is much larger* than ES (by about an order

of magnitude) and we can use this to conclusively determine whether a material conducts via

smal on hopping. In contrast, a material that conducts via large polaron hopping

behaves similar to a conventional band material (Eρ ≈ ES) and they may be indistinguishable

using this method.

*In c onal band transport materials such as extrinsic semiconductors, the thermopower

and resistivity activation energies depend directly on the ionisation energy (E) required to

create a free carrier from a donor. Hence, Eρ ≈ ES ≈ E. In small polaron materials, however,

the resistivity activation energy has an extra Thermally Activated Hopping term (WH). Hence,

E

igh Temperatures

σ

The spin term, Sσ, is given by:

l polar

onventi

ρ=E+WH > ES. [10]

At high temperatures (T above some sample dependent transition temperatures, TC), the

Seebeck Coefficients of small-polaron conduction materials become independent of

temperature. This Seebeck Coefficient at high temperatures, ST large, consists of a spin term S

and a charge-carrier term SC. [11]

= ln 2 + 12 + 1 = −19.2

W th in values of 3/2 and 2 respectively comes from the h

tively. When these value e input into the formula

VK-1

σ1=3/2,σ0=2here e σ1 and σ2 sp igh-spin states of

Mn4+ and Mn3+ respec s ar , a constant value

of -19.2μ is obtained.

On the other hand, the charge-carrier term, SC, is given by the Heikes formula:

10

= − ln 1 − = = 1 −

Where ch is the normalised hole concentration in the material and is mathematically

equivalent to the normalised electron concentration, c, subtracted from unity.

2.4 Seebeck Coefficients of Similar Materials

The thermopower of similar materials were summarised in Table 2 [12][13][14][15][3] to

ast, La0.67Ca0.33MnO3 being very similar to one of the samples we

intend to prepare has a small value at -5μVK-1. Hence, we should expect the samples in this

f the studied

compounds are made xides made up from

such elements due to he thermoelectric

properties are less stu erial usually have a

nstance,

of around

0.1. This is relatively small when compared to commercial compounds with ZT ≈ 1 to 3.

Combining these two terms would give us the total Seebeck Coefficient and since the terms

are temperature independent, so will the total Seebeck Coefficient. This means that if the

material conducts via the small polaron hopping mechanism, we would expect their Seebeck

Coefficients to tend towards a constant value at high temperatures.

give a sense of the typical thermopower values of such materials at room temperature.

Table 2 a imilar materials. : T ble summarising the Seebeck coefficients of s

In Table 2, we can see that the Seebeck coefficients of similar compounds range largely

within ±300μVK-1. In contr

article to present roughly simila values. In Table 2, we can also see that most or

up of La or Sr atoms. This is due to the interest in o

their interesting phase transition effects. However, t

died. This is compounded by the fact that these mat

low ZT value and is often unsuitable for commercial thermoelectric generation. For i

La1-xSrxCrO3 while having rather high Seebeck coefficients only have ZT values

11

Ch Key Experimental Procedures and Methodology

1. Investigation Objectives

e es

2) Low temperature with magnetic field (77K to 300K at up to 7T for one sample)

3) High tempe

p

t. If

the construction of the high temperature setup was not successful, a lower range of 300K to

700K could still be measured using an alternative setup that was under construction at the

start of the project.

apter 2

In this experiment, we are interested to find out how various properties (thermopower S,

resistivity ρ, thermal conductivity κ and other associated quantities) of the perovskite

materials vary as we move along th seri of R atoms.

We are interested in characterising these properties within three main experimental

configurations. They are:

1) Low temperature region (77K to 300K)

The first two regimes utilises experimental setups that were available in the lab. However, the

third regime requires the design and construction of an unprecedented high temperature setu

and it was expected that this would take up a significant proportion of effort in this projec

rature region (300K to 700K or 1000K if possible)

12

2. Key Experimental Procedures

2.1 Sample Preparation

nO3 Perovskites were produced by a high temperature sintering

s the Solid State Process. [See Figure 8] In this method, high

rity (>99.9%) precursor nanopowders of CaCO3, Mn2O3 and the oxide of the R atom (such

La2O3 for the Lanthanum sample) were weighed and mixed in stoichiometric ratios.

s,

ecome a crumbly pellet that contains a mixture of the target perovskite

and the unreacted precursors.

The samples of R0.65Ca0.35M

process that is also known a

pu

as

Figure 8: Sequence showing the Solid State Pr The procesweighing o

ocess.

s consists of three main steps, namely the f reactants, grinding and mixing as well as

sintering at high temperatures of 1000°C to 1200°C.

intering at 1200°C. Afterwards, the sample was cut and polished

The cycle was repeated 3 times with a final s

before applying conductive silver paint.

The mixed powder was then physically grounded in a pestle and mortar (for at least 30

minutes) to maximise homogeneity and subsequently transferred to an alumina (Al2O3)

crucible. The crucible containing the powder was then placed in a high temperature furnace

and sintered at 1000°C (950°C for the Bismuth sample) for 12 hours at a heating and cooling

rate of 3K per minute from and to room temperature. At the end of the first sintering proces

the powder would b

13

The grinding and sintering process was then repeated once more during which most of the

unreacted precursors would have been consumed. Finally, the pellet was ground again and

this tim e compacted into a green pellet (a fragile

unsinter then placed in the furnace and sintered at

r t is

into the shape required to fit into the measurement setup. After cutting and polishing,

electrical contact surfaces were added by applying a uniform silver paint over a cellophane

mask. An example of a prepared sample that is ready for measurement is shown in Figure 9.

About the stoichiometry:

e placed in a high pressure pelletiser to b

ed pellet) at 2000bar. The green pellet was

1200°C (980°C fo he B muth sample) for at least 24 hours at a heating and cooling rate of

1.5K per minute from and to room temperature.

The final product of sintering would be a strong solid pellet that has to be cut and polished

Figure 9: Picture of the final standardised sample for immediate mounting onto the measurement setups.

The sintering process was conducted in common atmosphere with oxygen readily available.

We can write the chemical reaction as: (for R = La, Nd, Sm, Bi and Y)

(1-x)R2O3 + Mn2O3 + 2xCaCO3

2R1-xCaxMnO3 + 2xCO2.

Where x = 0.35. Notice that in this chemical equation, we have only taken the heavier R, Mn

se

the R, Mn and Ca elements were non-volatile a .

The carbon atoms would be readily emitted as CO during calcination at high temperatures

and the oxygen being in excess would be free t

and Ca elements in the product into account for the ratio of the reactants. This was becau

nd will remain in the mixture during sintering

2

o enter or exit the mixture.

14

For the Praseodymium sample, due to its oxide occurring as Pr6O11 instead of the usual R

it has a slightly different chemical reaction: 2O3,

⅓(1-x)Pr6O11 + Mn2O3 + 2xCaCO3

2Pr1-xCaxMnO3 + 2xCO2

As usual, x = 0.35 for this reaction.

About the sintering process:

Sintering is a chemical process whereby the solid reactants were heated to a temperature

below the melting points of the reactants. At this temperature, although the reactants remai

as solids, the constituent atoms can diffuse within the mixture towards homogeneity. As the

reaction proceeds, only the most stable compound grow while the reactants are consumed.

Because the diffusion is largely localised, the gri

n

nding and sintering process has to be

During the holding phase (constant high temperature phase), the target compound will grow

crys lly get

consumed. This essentially mini ount of amorphous compound (to almost none

repeated several times.

Figure 10: Figure showing the sintering process as the reaction proceeds. (a) Initial nanometre-sized grains of the precursor powders. (b) Physical compaction results in the deformation of the grains and smaller air gaps. (c) Neck growth between grains as the sintering process initialises. (d) Final sintered piece showing a great reduction of air gap and grain boundary. The pellet shrinks as this happens.

in grain size and the grain boundaries will diminish [See Figure 10]. In effect, the larger

crystals become larger while the smaller tals become smaller and eventua

mises the am

15

present)[16]. The slow cooling rate helps in relieving stress, not unlike the tempering process

used in metallurgy.

2.2 X-Ray Diffraction (XRD)

After preparing the sample through sintering, we needed a way to determine the quality of the

his check works because the impurities exist in

structures that may be different from ompound or that they may exist in the same

er distinct phases

r impurities, such as unreacted reactants,

were present and whether the resultant compound exists in a second undesired phase.

, we would regrind the sample and re-sinter for a longer

The actual experimental procedures for this step were fairly straight forward. A small portion

of the final pellet was ground into a fine powder and placed in an XRD sample holder. The

holder was then placed in the XRD machine and a scan was conducted in the Gonio mode

where the incident beam angle equals the receiving detector angle. The X-rays used for the

scan comes from the copper K-α line (produced in an X-ray tube), with the other modes

filtered away by a band pass filter within the machine. The scan was performed for 2θ set

between 20° and 80° (θ being the incident beam angle) at a scan rate of 1.00 second per 0.05°

scan step.

The resultant XRD data was plotted on a graph and analysed for structure identification and

to determine whether other distinct phases were present.

final product. To achieve this, we used X-Ray Diffraction (XRD) to check whether the

sample exist only in a single distinct phase. T

the target c

structure but having different lattice constants. By looking for signs of oth

ine whethepresent in the XRD, we could determ

If we did find other distinct phases

duration and/or at a higher temperature. This process may be repeated several times if

necessary. In contrast, if we only find a single distinct phase, we could conclude that the

impurities were beyond the detectable range and that the amount was satisfactorily

insignificant. In practice, we would simply sinter the samples for a longer duration than was

necessary in order to avoid this problem in the first place.

16

2.3 Low Temperature Measurement Setup

The low temperature setup was capable of concurrently measuring the resistance R an

thermopower S from 350K down to 55K. A simple diagram of the sample platform is shown

in Figure 11.

d

simple *

am).

nsor.

rs. These

t.

el-Constantant junctions)

thermocouple wire to provide differential temperature readings.

erior

Figure 11: Diagram of the Low Temperature Measurement Setup. The setup was used for the measurement of resistance (and resistivity) as well as thermopower from 350K to 55K.

In Figure 11, two copper blocks were soldered on top of a base plate which contained a

heating and refrigeration core for temperature control. The heating was provided by a

heater coil made from nichrome wire wound around a ceramic core and refrigeration was

provided by a helium refrigerator that was capable of reaching 55K (not shown in diagr

Temperature feedback was provided by the Pt-1000 Platinum Resistance Temperature Se

On top of each copper blocks were heaters made from 24.0 Ω surface mount resisto

heaters were used to provide a temperature difference of 2-3K for thermopower measuremen

The copper blocks were also linked with a Type E (Chrom

Insulation of the conductive copper blocks was achieved using Kapton® Tape on the top

surface. The sample was mounted onto the insulated copper blocks using silver paint to

maximise thermal conductivity. Next, the 4 wire contacts were fixed to the contact surfaces

using silver paint. After drying, a steel shell was secured over the setup and a vacuum int

was achieved using a turbo pump. The vacuum was used to minimise heat flow to and from

the setup to achieve stable operating temperatures.

80% nickel and 20% chromium. * An alloy of

17

The operation of the setup starts by seeking the target temperature appointed by the

experimenter. This was done by varying the heating and cooling power to the base plate and

k. Once the target temperature

was reached, a 1 mV current was passed through the end electrodes (force connections) from

the left to the right for 10.0 seconds. Towards the end of the 10.0 seconds, the voltage across

the middle two electrodes (sense connections) were read and recorded. This was then

repeated for a current passing from the right to the left. The knowledge of the force currents

and the sense voltages allowed us to calculate the resistance across the sense connections and

subsequently, the resistivity of the sample.

After this 20.0 seconds sequence, the left heater would be supplied with 70.0 mA of current

for 60.0 seconds. This would heat up the left side to about 2-3K warmer than the right side.

Towards the end of the 60.0 seconds, the voltage across the end electrodes (previously force

connections) and the thermocouple wire voltage were read and recorded. The thermocouple

voltage was converted to temperature and the thermopower S was obtained by dividing the

thermovoltage by the temperature difference. This step was then repeated for the right heater

for 60.0 seconds before the whole cycle repeats for the next target temperature.

In both measurements of resistance and thermopower, the experiment was repeated for both

directions to minimise any effects due to the geographical irregularities in temperature and

electrical contact biases. This was done by averaging the two obtained values.

The low temperature setup for the 7T magnetic field measurement works in a similar way to

the setup described above. The setup was simply housed in the core of a superconducting

solenoid (PPMS*) charged to 7T during measurement. In addition, the magnetic moment of

the sample can be measured with a Vibrating Sample Magnetometer (VSM) used in

conjunction with the PPMS.

using the calibrated Pt-1000 reading for temperature feedbac

* PPMS refers to Physical Properties Measurement System®, a commercial system by Quantum Design™ that allows one to measure various properties at low temperatures and under strong magnetic fields. An additional component called the Vibrating Sample Magnetometer allows one to measure the sample’s magnetic moment.

18

Chapter 3 1000K High Temperature Measurement Setup

1

o

.

rrently.

e

. Introduction

The High Temperature Measurement Setup was a 3-months long project that was intended t

achieve the measurement of electrical properties at the high temperature regime that was

unavailable at that time.

The aims of the setup were as follows:

1) To enable the measurement of electrical properties (resistivity and thermopower) in the

high temperature region (300K – 1000K).

2) To enable the measurement of thermal conductivity in the high temperature region

3) Ideally to perform the above two types of measurements concu

This project was started roughly simultaneously with another setup that aims to achieve th

above objectives up to a lower temperature of 700K using more conventional building

resources. This other setup was built by then PhD student Dr. Pawan Kumar and the

experiences gained from the setup would help in the success of the 1000K setup.

19

2. Design and Principles of Operation

The design of the High Temperature Measurement Setup was shown in Figure 12.

Figure 12: Diagram of the High Temperature Measurement Setup. The setup was designed to measure resistance (and resistivity), thermopower as well as thermal conductivity from 300K up to 1000K. A full page diagram was provided in the annex. The actual setup is shown in Figure 13 below.

Figure 13: Picture of the actual High Temperature Measurement setup, showing the steel liquid nitrogen chamber, Heating Platform and the Base Platform as well as the associated components.

In Figure 12, a liquid nitrogen reservoir to the left provided the required cooling to the entire

etup. This cooling action was pposed by the heating tubes on the Heating Platform so that

the temperature of the setup could be adjusted by varying the power supplied to the heating

tubes. A low conductivity thermal lag material (Al2O3 ceramic hollow tubes) was sandwiched

between the liquid nitrogen reservoir and the Heating Platform to slow down the removal of

thermal energy to the level where the heating tubes can keep up (<75W). In order to provide

temperature feedback, a Type K thermocouple (Chromel-Alumel junctions) was placed on

s o

20

th

th

e Heating Platform. This temperature feedback was used to control the power supplied to

e heating tubes in order to achieve temperature regulation.

ith the temperature of the setup regulated and stabilised, measurements could proceed on

e Base Platform. The Base Platform featured its own set of Type K thermocouple that acted

ontrast to the temperature feedback of the Heating Platform

ely regulate the temperature of the setup, the thermocouple on the

se Platform was placed very near to the samples in order to sense the immediate

perature of the running experiment.

e Low Temperature

power S, with the

erature tolerant materials. This

wire experiment was performed with the same principles as the Low Temperature

easurement Setup.

he thermal conductivity experiment which simply consists of a

heater assembly, a Type K thermocouple and a sample mount. A user-defined amount of

sample was simply measured and the thermal conductivity of the

mple could be determined based on the knowledge of the heat current and temperature

etup was none

other than the high temperature environment of the experiments. At the intended range of

C

rvive in

ve at

°C (1273K) in order to pr vide a safe margin. For instance, the usual Type E

thermocouples were replaced with Type K thermocouples that could survive up to 1533K

instead of 963K, electrical insulations gave way to Al2O3 ceramics and silver paint was used

W

th

as a temperature sensor. In c

which served to approximat

Ba

tem

On the top of the Base Platform was the 4-wire experiment similar to th

Measurement Setup that served to measure the resistivity ρ and thermo

difference that the components were built out of high temp

4-

M

Below the Base Platform was t

power was first supplied to the heater assembly for an amount of time sufficient for the

temperature gradient in the sample to reach quasi-steady state. The temperature difference

across the two ends of the

sa

difference.

3. Design Challenges

The main challenge to the design of the High Temperature Measurement S

high temperatures, conventional electrical insulators would start to decompose and the usual

method of joining components via soldering fails as solder melts at approximately 350°

(623K). To overcome this challenge, high temperature tolerant materials that could su

that temperature range had to be used. In fact, the setup was overdesigned to survi

1000 o

21

to join the copper components together (silver forms strong Cu-Ag-Cu alloys at high

temperatures). With the use of these materials, the setup could be satisfactorily built, although

cs were

impossible to machine without diamond tools and this sometimes require slight modifications

to the design.

Besides material considerations, at this range of high temperatures, heat loss and oxidation of

components became the next source of concern as heat loss would lead to inaccurate

measurements and oxidation would cause damage to the setup. These problems were solved

by performing the experiments in vacuum, eliminating conduction and convection and

and the experimental

setup, the components in the setup was polished to a high shine to minimise emissivity.

Finally, a calibration of the setup could be done to minimise the residual systematic errors.

4. Experience from 700K Setup

The 700K setup initially produced several useful measurements before running into durability

issues near the end of January. Access to the setup was granted for two weeks in February

during which the causes of the measurement problems were studied extensively. The

experience gained with the 700K setup helped avoid some initial design flaws in the 1000K

setup.

It was determined that the setup suffered from a slow breakdown of insulation and binding

nish,

omposed at high

some of these materials were difficult to work with. For example, the Al2O3 cerami

limiting oxygen presence. At the very high temperatures, radiation loss became an issue. To

minimise radiation transfer between the walls of the vacuum chamber

materials at temperatures above 550K. First, the General Electric 7031 Varnish (GE Var

composed of Phenolic Butvar Resin), used to join components, rapidly dec

temperatures causing a black residue to deposit on the setup. Discontinuation of the use of

GE Varnish immediately solved this problem. However, the setup has to be sanded to restore

the shine. Second and more importantly, the polyamide-imide insulation of the Kapton®

Tape slowly decomposed at high temperatures, causing it to outgas and expand [See Figure

14]. This compromised the thermal conduction between the sample and the copper blocks,

causing the temperature difference across the sample to be smaller than expected which

resulted in unreliable measurements in thermopower.

22

The problem was solved by replacing the insulation with Al2O3 ceramics and binding the

copper blocks directly onto the base using silver. This, however, caused the heat flow out of

the copper blocks to become too rapid, resulting in large temperature gradients which also

s

o the

ree

adversely affected the measurements.

Figure 14: Four pictures showing the successive modifications to the 700K setup. The picture on the top left shows the unmodified setup. The dark colouration was due to oxidation and the decomposition of the Kapton®

cture on the top right, the copper blocks were joined directly rature gradients. The picture on the bottom left showed the introduced. The setup also has a spacer tube in between the

copper blocks and wires anchoring the experiment. The bottom right picture shows the silicone adhesive failure

tape was indicated by the discolouration. In the pionto the Base Plate but this resulted in large tempecurrent stable version, with Kapton® insulation re

at high temperatures in the first few modifications.

In the final modification, thermal lag materials were sandwiched between the copper block

and base and the temperature stabilisation period was more than doubled from 180 seconds to

420 seconds. This increased the time taken to perform an experiment from 11 hours to 25

hours but resulted in exceptionally stable measurements.

In summary, the experience with working with the 700K setup served as a prelude t

problems that would come when running the experiments at high temperatures. Th

important modifications could be applied to the 1000K setup in order to improve

23

measurement results:

1) Sandwiching thermal lag materials between the copper block and Base Platform to

minimise temperature gradients.

2) Increasing the time allowed for temperature stabilisation to take place.

3) Placing the differential thermocouples as close as possible to the sample with the help of

ceramic tubes acting as the sample insulation and thermocouple anchor.

een the

ard compatibility to be able to fit into the 7 Tesla superconducting solenoid for future

ide

Finally, even though good results could be obtained, there would be mismatches betw

Low Temperature Measurement Setup and the 700K setup due to systematic errors. In order

to correct for this error, a standard material such as Constantan was used to calibrate the

setups by producing a correction term with which the systematic error could be subtracted.

Further notes about the 1000K Setup: The steel shell was designed by Dr. Pawan Kumar

for forw

experiments involving high temperature measurements in the presence of a strong magnetic

field. In line with this design specification, the materials used in the 1000K setup were of

relatively non-magnetisable materials, principally copper, silver and aluminium oxide.

While the liquid nitrogen reservoir was ultimately not used in the pilot test of the setup

described later in this article, the reservoir served as a means to be able to cool the

experiment down to 77K when required. As a result, the setup can technically measure a w

temperature range from 77K to 1000K with or without the presence of a magnetic field.

Hence, the names High Temperature Measurement Setup and 1000K Setup may be an

understatement of its capabilities.

24

Chapter 4 Results and Discussion

1. XRD and EDS Results

The XRD results are summarised in Graph 1.

Graph 1: Graph of Normalised Intensity VS 2θ for the XRD results. The graph shows the plots for the La, Pr, Nd, Sm, Y and Bi samples stacked vertically.

25

In Graph 1, we can see

all exist in the Perovskite structure at room temperature. In fact, we can try to group th

into several sets at 2θ positions of

the peaks of the 110, 111, 200 and 211 cubic structure signature. However

note that the samples were actually distorted perovskites at room temperature and can only

attain a tetragonal or octahedral structure. This can be seen from the grap

that each of the samples give a roughly similar XRD pattern as they

e peaks

around 32°, 40°, 48° and 60°. These positions correspond to

, it is important to

h that the La, Pr and

Nd samples contain two peaks splitting (tetragonal) while the Sm, Bi and Y contain three

parameter is slightly different (a = b ≠ c). This results in a single splitting of the peaks

associated with the cubic structure which would be detectable in the higher order diffraction

eaks, such as the 211 peaks.

an orthorhombic structure, the angles still remain at 90° but this time, the lattice

parameters are all different (a ≠ b ≠ c). This results in two splitting of the cubic peaks which

ecomes more obvious as the difference in lattice parameters increases. In light of this, it is

o longer meaningful to label each individual peaks with its associated Miller Indices.

However, since we know where the splitting comes from, we could still label each group with

ium

be

the case.

laced) at

ucture where the three lattice parameters do not differ by

oo much. This makes them lo k like cubic structures on the XRD result as the peaks cannot

peaks splitting (orthorhombic)*. This result was consistent with that reported in the literature.

In a cubic structure, the lattice parameters and angles are uniform at a = b = c and

α = β = γ = 90°. In a tetragonal structure, the angles remain at 90° but a single lattice

p

In

b

n

its corresponding cubic structure peaks.

As we move along the series, from R = La, Bi, Pr, Nd, Sm, and Y, we would expect the

lattice distortion to change uniformly as the ionic radius mismatch of the R atom and Calc

atoms increases [See Table 1 above]. Curiously however, this does not always appear to

Pr3+ has an ionic radius of 1.13Å that is closest to that of the Ca2+ ions (which it rep

1.14Å so we would expect the Pr sample to show the least structural deviation from CaMnO3

which exists in the cubic structure at room temperature. In the XRD result, the La, Pr and Nd

samples all exist in the tetragonal structure at room temperature. In fact, the La and Pr

samples exist in a pseudo-cubic str

t o

* This may be difficult to see if one only considers the 110 group.

26

be

in

well resolved, and was why the La and Pr samples were labelled with the cubic miller

dices. The peak splitting can only be seen in the higher order peaks and more clearly in the

sample (labelled with tetragonal miller indices).

we move along the series, the Sm and Y samples reflected a stronger orthorhombic

that the structural deviation increases with decreasing ionic

le Bi3+ at 1.17Å has an ionic radius close to La3+ at 1.172Å

d should also show a tetragonal structure, the XRD result showed instead an orthorhombic

aracteristic. This shows that the factors that goes into the determination of the final

ms alone but may also be

mselves.

1.1 Using the XRD Result to Detect Impurities

t is to check for impurities within the final

compound before measurement. This impurity can be in the form of unreacted reactants,

reactants forming undesired compounds or having the compound in an undesired secondary

phase.

Unreacted reactants and unwanted products would show up in the XRD graph as they either

have a different crystal structure compared to the target Perovskite compound or they may

have the same structure but with different lattice parameters. For example, the Yttrium

sample has the tendency to form hexagonal YMnO3 when the Yttrium content is increased[6].

If this happens, there would be detectable peaks corresponding to a hexagonal signature in

the XRD and further actions would have to be taken to ensure that the final sample only

contain the desired compound. Likewise, if there are unreacted reactants, for example CaCO3

having the trigonal structure, it would be detected in a similar way.

More importantly, the XRD result helps to check for secondary crystal phase which signals

that the sintering process is either incomplete or that the cooling rate is too fast. The reason

this happens is that the high cooling rate or incomplete sintering causes the compound to be

stuck in a higher temperature metastable phase which is similar to quenching in metallurgy.

Since, f a crystal structure different from

o not see a significant splitting that might

Nd

As

signature. Thus, it is expected

radius from Pr3+. However, whi

an

ch

perovskite structure depend not only on the ionic radius of the R ato

further dependent on other internal characteristics of the R atoms the

One of the most important use of the XRD resul

from the XRD graph, we do not find the signature o

cubic, tetragonal or orthorhombic and that we d

27

have been from a compound with cubic, tetragonal or orthorhombic structure but with

different lattice parameters, we conclude that the presence of impurities in the samples were

beyond the detectable range of the X-Ray Diffraction technique.

The only sample that might seem doubtful was the Yttrium sample. In the XRD plot for the

Yttrium sample, we can clearly see peaks that deviate from the respective peak groups by a

significant degree. However, a check through the existing literature showed that the lattice

parameters do indeed deviate greatly from one another at the Yttrium content of 65%. This

deviation can be seen in Graph 2 and provides a satisfactory explanation for the presence of

Co cerns have been raised about the accuracy of the target com und stoichiometry that was

p

the large splitting.[17]

Graph 2: Graph showing the increasing deviation of the a lattice parameter as the Yttrium concentration increases. The large deviation results in a significant peak splitting.

1.2 Energy-Dispersive X-Ray Spectroscopy (EDS)

n po

em irically determined through the weighing of the reactant powders. The primary concern

was that the empirical formula derived from the reactant ratio may not actually reflect the

stoichiometry of the target compound and that a direct measurement, if possible, would

provide greater confidence in the stoichiometry. In an attempt to answer this concern, the

samples were sent for an EDS measurement in the Chemistry department to determine the

ratio of the elements within the sample and derive a second source of empirical formula.

28

The EDS results are summarised in Table 3.

Table 3: Table showing the EDS results and the implied empirical formula. The EDS measuremparticularly inaccurate for the Yttrium and Bismuth samples.

ent was

The ED measurements

ineffective. Firstly, the EDS equipment cannot detect light elements such as Oxygen. This

ber

g radiation spectrum. This meant that different elements, having different response

positions on the X-ray spectrum, would be measured on different baselines of background

n

to

is beyond the scope of this project.

S equipment presented 2 very significant limitations that rendered the

meant that the exact oxygen content of the sample cannot be determined and the

stoichiometry was forced to be based on manganese instead (having a stoichiometric num

of 1). Secondly, and more importantly, the EDS technique was sensitive to the background

breakin

noise. Since the background intensity varies across the spectrum, elements with characteristic

X-ray peaks far from each other would experience significantly different zero errors that

would distort the element content.

This gave rise, for instance, to the observation that there was more Bismuth and Yttrium tha

manganese in the Bi and Y samples respectively. This result was obviously incorrect due

the inherent impossibility of forming such compounds. As a result, the EDS measurements

became a failed attempt.

An alternate solution to EDS would be to perform several titrations of the samples to

determine the amounts of Mn3+, Mn4+, Ca2+ as well as the R3+ present in the sample and with

the result, indirectly determine the oxygen content and the empirical formula. This, however,

required some specialised equipments as well as more extensive knowledge in Chemistry and

29

On the positive side, the EDS measurements helped a colleague uncover that he had sw

his Bi0.7Sr0.3MnO3 sample with one containing Ba1-xEuxTiO3 due to the fact that his EDS

measurement for that sample only registered Barium, Europium a

apped

nd Titanium. The EDS

measurements also provided the opportunity to photograph the samples using the built-in

Scanning Electron Microscopes (SEM). The SEM images are shown in Figure 15.

Figure 15: SEM images of the compounds used in the experiment. The Yttrium sample showed distinct grains while all other samples showed ex nsive melding of the grains. te

30

One of the most interesting feature of the SEM images was that the Yttrium sample showed

discernible grains while the other samples seemed to have the individual grains melded

extensively together. In fact, the reason that the Yttrium sample was not used in the later

thermopower and resistivity measurements was that the sample had failed to achieve a strong

bulk strength* despite being sintered multiple times. The SEM image served to confirm the

fragile nature of the bulk sample by showing the weakness in the microstructure.

2. Combined Thermopower and Resistivity Results

The results from the Low Temperature Measurement Setup as well as the 700K Setup for the

for their zero errors and plotted in Graph 3 and

La, Pr, Nd, Sm and Bi samples were corrected

Graph 4.

Graph 3 shows the variation of the Seebeck Coefficient S over a temperature range of 100K

to 700K.

* The prepared Yttrium sample had around subsequent drops shatter the pellet. At Yttriu

the same strength as powdered cosmetic. A drop results in cracks and m concentration of 65%, the sintering temperature has to be at least

1380°C [5]. The strongest furnace in the lab was only capable of reaching 1300°C.

Graph 3: Graph of Thermopower against Temperature for the five measured samples from 100K to 700K. The inset shows the behavior at the higher temperature range.

31

From Graph 3, we can see that as the temperature increased, the Seebeck Coefficients of all

samples approached a constant value of roughly -25μVK-1. This agrees with the high

temperature polaron hopping model where the Seebeck Coefficient reaches a temperature

independent value at high temperatures. However, the rate at which each sample approach

this constant varied and this might be due to the difference in the characteristic activ

ation

energies ES and the sample dependent α parameters [See Table 4 below]. For instance, the Sm

sample only reached -22μVK-1 at 700K.

In the lower temperatures of below 400K, the Seebeck Coefficients seemed to increase in

value as one moved across the series (La, Pr, Nd, Sm, Bi). However, The Nd sample showed

an unexpectedly lower Seebeck Coefficient compared to the Pr sample while that of the Bi

sample was exceptionally high. Besides these observations, the Seebeck Coefficients of the

samples also showed gradient changes at various temperatures. In particular, the La sample

showed a drastic increase in thermopower at around 260K. This corresponds to the

Paramagnetic-Ferromagnetic transition for La0.65Ca0.35MnO3.

32

Graph 4 shows the variation of the Resistivity ρ over a temperature range of 100K to 700K.

Graph 4: Graph of Resistivity against Temperature for the five measured samples from 100K to 700K. The inset shows the behavior at an expanded range in order to present the features of the La sample.

In Graph 4, the most intriguing feature was that the La sample showed an Insulator-to-Metal

transition at around 260K. This conclusion was reached because the resistivity of the La

sample initially increased as the temperature decreased, indicating an insulator behaviour, but

showed a significant gradient change and a subsequent peak at around 260K and 210K

respectively. Thereafter, its resistivity decreased as the temperature decreased, indicating a

metallic behaviour.

On the other hand, the resistivity of all other samples seemed to be an exponentially

increasing curve as temperature decreased, also indicating an insulator behaviour.

33

2.1 High Temperature Polaron Analysis

tic

In Graph 5, we can see that the plots reveal linear relationships between S and 1/T at the high

temperature region of 1/T < 0.0036K-1. In some of the plots, there are jagged lines due to

noise in the measurement setup. These noise became noticeable when the small variation in

Seebeck Coefficient was comparable to the magnitude of the noise level, which was around

±0.5μVK-1.

The graphs of Seebeck Coefficient against 1/T and the logarithm of Resistivity/T against 1/T

were plotted in Graph 5 and Graph 6 respectively in order to determine the characteris

activation energies, ES and Eρ, and the sample dependent constants α and ρ0. We shall note

here that only the high temperature region of the graphs (1/T < 0.0036K-1) are valid in the

discussion of the Polaron model.

Graph 5: Graph of Thermopower against the reciprocal of Temperature for the five measured samples. The inset shows the behavior at the full temperature range.

34

Graph 6: Graph of ln(Resistivity/Temperature) against the reciprocal of Temperature for the five measured samples.

In Graph 6, we can see significantly cleaner plots and that the linear relationships between

of

aight

ln(ρ/T) and 1/T in the high temperature region can be clearly seen. The cleaner plots were

due to the lower level of noise in the resistivity aspect of the experiment compared to that

the thermopower. In the graph, we can also see a gradient change for all the plots around

1/T = 0.004K-1 and subsequent straight lines in the lower temperature regions. These str

lines, however, cannot be used in the polaron model analysis as it does not apply in that

temperature range.

35

The parameters derived from Graph 5 and Graph 6 were tabulated in Table 4 below.

In Table 4 we can clearly see that the Resistivity Activation Energies Eρ were always

significantly higher than that of the Thermopower Activation Energies ES for all the samples.

This indicates that the samples were all conducting via the small polaron model in the high

temperature region. However, across the series, we do not see any remarkable trend in the

parameters that varies linearly with the ionic radius.

In the high temperature region of Graph 3 above, we have seen that the Seebeck Coefficients

of the samples approached a constant value of roughly -25μVK-1. Using this value, we could

correct for the spin term, Sσ, and use the Heikes formula to determine the normalised hole

concentration, ch, in the material. The normalised hole concentration was calculated to be

ch = 48.3%. This value was remarkable as it meant that the concentration of holes and

electrons were roughly equal.

This result was contrary to the theoretical expectation that the proportion of the holes was

ds

In the Crystal Field theory, the 5 degenerate d-orbitals of the manganese atoms would split

into 2 higher level orbitals (eg orbitals) and 3 lower level orbitals (t2g orbitals) when the

manganese atoms are placed in the center of an octahedral crystal bond. In Mn4+ ions having

3 valance electrons, these electrons will occupy all 3 lower level t2g orbitals while the Mn3+

ions having 4 valance electrons will have an extra electron occupying the higher level eg

Table 4: Table listing the parameters derived from the curve fitting of the high temperature data with respect to the polaron model. The values in parentheses indicates the uncertainty in the last one or two digits of the value. Uncertainties with leading digit “1” have an extra significant figure.

equal to the proportion of the Mn4+ ions at 35% in the Nominal Valence model, which buil

on top of the Crystal Field theory.

36

orbitals. Inserting the Polaron model this picture, the Mn4+ ions would act as hole polaron

sites where hole polarons could hop to the nearest Mn3+ sites*.

Now, in the Nominal Valence model, the stoichiometry of the Ca2+ ions at 35% would induce

an Mn4+ prop 4+ortion of 35% in order to balance the charge. The Mn ions behaving as hole

polaron sites would give the theoretical hole concentration, ch, at 35%. However, the large

iscrepancy between this model and the result (35% VS 48.3%) suggests that the Nominal

Valence model was incomplete.

One way to explain this discrepancy may be to use the Charge Disproportionation model[18]

which suggested that a proportion of the Mn3+ ions further split into a population of Mn2+

ions and Mn4+ ions in order to remove the unstable degeneracy. This gives a higher hole

concentration:

[Mn2+] = 0 [Mn2+] = 0 + δ

[Mn3+] = 1-x ,

d

[Mn3+] = 1 – x - 2δ

[Mn4+] = x [Mn4+] = x + δ

In the above illustration, x represents the concentration of the Ca2+ ions while δ represents

the Charge Disproportionation factor. In our experiment, x = 0.35. The concentrations on the

left indicates the predictions of the Nominal Valance model where the concentration of the

Ca2+ ions directly influence the concentration of the Mn4+ ions. On the right, the splitting of

the Mn3+ ions by a factor of δ removes 2δ of Mn3+ and redistributes them evenly in the

concentrations of the Mn2+ and Mn4+ ions. Since the hole polaron hopping is still between the

Mn4+ and Mn3+ sites, ie. = = , the Charge Disproportionation factor can

ined from this analysis and it is calculated to be δ = 0.0897 = 8.97%. This meant 3+ to

al

be determ

that Charge Disproportionation would cause roughly 18% of the Mn ions to split in order

account for the remaining hole concentration.

While this model provides a possible mechanism to explain the large value of hole

concentration, it was felt that this analysis was ad hoc in nature; We need other experiment

evidence for Charge Disproportionation as the discrepancy could be due to some other more

complex factors in the Perovskite itself.

ote that we can also treat the Mn3+ ions as electron polaron sites and use c instead of ch for the Heikes rmula analysis. There is no differ ce in these two different perspectives.

* Nfo en

37

3. Thermopower and Resistivity Under Magnetic Field

After the zero magnetic field measurements were done, the Nd sample was chosen for further

study in the in the magnetic field environment.

The Magnetic Susceptibility, Seebeck Coefficient and Resistivity were plotted against

Temperature in Graph 7.

Graph 7: Graph of Thermopower, Resistivity and Magnetic Susceptibility against Temperature. The first inset shows the magnetic transition in greater detail while the second inset shows the resistivity values for 0T and 3T. The thermopower and resistivity curves were all measured during cooling.

38

In Graph 7, we can clearly see that in the presence of a strong magnetic field, the Seebeck

Coefficient of the Nd sample would undergo a transition where the increasing thermopower

will slow down its rate of change and finally peak with decreasing temperatures. In addition,

tr d

ficant changes. While the Resistivity of the sample under

3T was similar to that of the 0T measurement, at 5T and 7T, the sample showed an insulator

c

al under an applied magnetic field is an example of the Colossal

Magne

In the M ibility ks , as

well as In

particular, the peak positions correspond to the Charge Ordering transition and

Field

greater magnetisation w f hyster is between the cooling and

see first inset] as the peak changes into a

featureless slope with increasing magnetic field. This is also attributed to the emergence of

wer and resistivity measurements.

the temperatures at which the peaks occur seemed to increase with increasing magnetic H

Field s ength, with the peak positions being around 80K, 130K and 150K for the 3T, 5T an

7T magnetic fields respectively.

The Resistivity also showed signi

to metal transition, similar to that of the La sample mentioned above. In addition, the

temperatures at which the peaks occur also in rease with increasing magnetic fields, being at

95K and 135K for 5T and 7T respectively. At the same temperature, the change from

insulator to met

toresistance Effect found in some antiferromagnetic compounds.

agnetic Suscept graph, we can clearly see two pea near 230K and 150K

two troughs at 200K and 120K for all 3 magnetic fields of 0.1T, 5T and 7T.

Paramagnetic-to-Antiferromagnetic transition with decreasing temperatures for 230K and

150K respectively[7]. The values of the magnetic susceptibilities seemed to be identical for

all three magnetic fields down to about 150K where the plots start to diverge.

This divergence can be attributed to a stronger alignment of domains under a stronger H

where the antiferromagnetic state of the material gradually becomes more ferromagnetic

under the influence of the strong H Field. The increased ferromagnetic property results in a

hich leads to the presence o es

warming curves as can be seen in the graph. The increased ferromagnetic property also

causes the 150K transition to be more blurred [

stronger magnetisation as the material becomes more ferromagnetic.

However, there appears to be no direct relationship between the susceptibility transitions and

the transitions occurring in the thermopo

39

In Graph 8 below, the percentage change of Seebeck Coefficient and Resistivity as well as

molar Magnetic Moment were plotted against the Magnetic H Field.

Graph 8: Graph of the percentage change of Thermopower and Resistivity with reference to the zero field value and Molar Magnetisation against the driving H Field. Note that 1T = 10,000Gauss.

40

In Graph 8, the percentage change of the Seebeck coefficient and resistivity with respect to

their zero magnetic field values show a larger change as the temperature decreases from

result was consistent with Graph 7 above. In addition, the

d thermal

reviously

Nd

producible in

t

eral

h

ctivity measurement

180K to 80K. The general shape of the change appears to be half-bell shape in nature and is

always negative for all temperatures measured. This meant that the presence of a magnetic

field would always give rise to Seebeck coefficient and resistivity values that were smaller

than the zero field values. In particular, the resistivity values at 80K and 100K showed the

largest change of up to -99.999%, indicating an extremely strong Colossal Magnetoresistance

effect at those temperatures*. This

magnetic moment also showed larger values at lower temperatures. In all three graphs,

hysteresis can be clearly seen due to the significant difference between the field ascending

part of the graph and the field descending part.

4. High Temperature Setup Results and Performance

The Nd sample was used as a pilot sample in the testing of the High Temperature

Measurement Setup. The results of the Seebeck coefficient, resistivity an

conductivity were plotted against Temperature in Graph 9.

In Graph 9, we can see that the thermopower and resistivity of the Nd sample behave

identical to that reported earlier in Section 2. However, a new feature that was p

unknown was present in the thermopower result. At around 765K, the thermopower of the

sample underwent a drastic gradient shift and troughed, causing the thermopower to increase

in value beyond this temperature. This feature was not an anomaly as it was re

the subsequent cooling curve. In addition, the shape of the graph suggests that this feature

would not be anticipatable by using the 700K setup. The consequence of this feature mean

that the Nd sample underwent a phase change at 765K which suggests a more complex

behaviour from the simple small polaron model.

The thermal conductivity of the sample was also plotted in the graph and it showed a gen

increasing trend as the temperature increased. However, the absolute value of this

measurement cannot be taken at face value as the measurement setup was not calibrated wit

a known standard sample owing to time constrain. The thermal condu

* The effect was so strong because of the insulator to metal transition, causing the resultant resistivity to be extremely small.

41

also showed increasing noise level as the temperature increased beyond 600K and 725K. This

It should be noted here that the largest control temperature achievable was 845K and the

largest sample temperature achievable was 804K. This was about 150K lower than the target

temperature of 1000K. This temperature ceiling could be increased with a more powerful

could be attributed to the weakening of the silver contacts as the temperature increased.

Graph 9: Graph of Thermopower, Resistivity and Thermal Conductivity against Temperature for the Nd sample, measured using the High Temperature Setup.

temperature controller and a refinement in the thermal lag arrangement. For instance, the

42

mounting screws’ lengths could be increased to allow for a second or third layer of Al2O3

thermal lag tubes to be inserted between the coolant and the platform to reduce heat loss.

In general, the limitations of the current measurement could be easily overcome with simple

modification to the thermal lag arrangement, refinement in the silver contacts, replacing the

current temperature controller with a more powerful one and doing one round of calibration

for the thermal conductivity experiment. Taking the current results into consideration, the

High Temperature Setup performed satisfactorily well and could be considered as a success.

5. La0.65Ca0.35MnO3 Magnetic Measurements

After observing several interesting results in the

Nd sample for the low temperature region,

der

ithin

lotted

he thermopower and resistivity

d

an

sceptibility also displayed a small amount of

ncrease in

material, in contrast to that of the Nd sample which found no direct relationship.

interest arose about how the La sample, being a ferromagnetic material, would behave un

the same conditions. As a result, the properties of the La sample was briefly measured w

a few days despite time limitations.

Graph 10 shows the Magnetic Susceptibility, Thermopower as well as Resistivity p

against Temperature from 10K to 350K, similar to Graph 7. T

curves were measured during cooling.

In Graph 10, the first thing we notice is that there was a sharp increase in magnetic

susceptibility around 265K with decreasing temperatures and the values before and after this

transition remained largely constant. This transition corresponds to the Curie temperature of

the material (Paramagnetic-to-Ferromagnetic transition). The magnetic susceptibility value

also reached a large value of around 460 emu/mol·T in contrast to 11.2 emu/mol·T achieve

by the Nd sample under 7 Tesla of H Field; While the Nd sample was becoming increasingly

ferromagnetic at strong magnetic fields and low temperatures, it was nowhere as strong as

intrinsic ferromagnetic material. The magnetic su

hysteresis at this transition temperature and at lower temperatures.

Next, we can see that the thermopower curve for the 0T measurement had a sharp i

value, in conjunction with the magnetic transition of the material. This suggests that the

electronic transport properties of the material are coupled to the magnetic ordering of the

43

Graph 10: Graph of Thermopower, Resistivity and Magnetic Susceptibility against Temperature for the Lsample. This graph was plotted in the same style as Graph 7.

a

If this coupling of electronic and magnetic properties is true, then the spread and slow

increase for the 5T thermopower curve with decreasing temperature wouldn’t come as a

surprise. At the stronger magnetic H Field of 5 Tesla (which is a very strong field), the

domains in the material have a very large incentive to align with the magnetic field due to the

much lower energy they would possess during alignment. This means that the activation

energy needed to break away from alignment is much larger than without a field and as a

44

result, the Paramagnetic-to-Ferromagnetic transition should happen at a higher temperature

and at a more gradual rate. In addition, the magnetic susceptibilities at different H Fields

away from this transition should behave largely the same after the transition has completed.

Finally, we look at the resistivity behaviour which exhibited Colossal Magnetoresistance

oincides with the

insulator-to-metal transition, as indicated by the peaks at that temperature. At this

e La sample exhibits transitions at the same temperature

regardless of the external magnetic field while the Nd sample exhibits changing transition

d a

ted identical start and end values around the transition

a result,

e resistivity of the La

sample became less negative as the temperature was increased from 225K to 310K. This was

at

Since we have assumed that the electronic and magnetic properties are coupled, the exact

same effect for the magnetic property should happen to the thermopower behaviour, and this

was what we observed. Unfortunately, we do not have enough time to measure the magnetic

susceptibility curve at 5 Tesla to prove this point experimentally.

below around 300K. This effect was the strongest at around 225K which c

temperature, the magnetic H Field of 5T caused a reduction in resistivity by around 45%.

Comparing the resistivity and thermopower behaviour between the La and Nd sample, the

most notable observation was that th

temperatures with varying external magnetic fields. For resistivity, the La sample exhibite

constant transition temperature while that for the Nd sample increase with increasing H Field.

For thermopower, the La sample exhibi

while the Nd sample exhibited varying thermopower values at different H Fields. As

we can conclude that the La sample was much less complex in phase transitions compared to

the Nd sample.

Graph 11 below shows the percentage change of Seebeck Coefficient and Resistivity against

the Magnetic H Field, similar to Graph 8 but without the data for Magnetic Moment. The

graph offers another perspective to Graph 10 regarding the changes in resistivity and

thermopower as the magnetic field strength changes from 225K to 310K.

From Graph 11, we can clearly see that the percentage change of th

reflected in Graph 10 where the difference between the 0T values and 5T values became

smaller as the sample was warmed from 225K to 310K. In addition, it should be noted th

the cooling and warming curves matches each other almost exactly and there was no

significant hysteresis.

45

Graph 11: Graph of the percentage change of Thermopower and Resistivity with reference to the zero field value against the driving H Field. Note that 1T = 10,000Gauss. This graph was plotted in the same style as Graph 8. The percentage change in Seebeck Coefficient is negative due to the Seebeck Coefficient being negative at 0T. The magnetic moment data was unavailable due to the lack of time to conduct the required measurements.

As for the thermopower result in Graph 11, we can clearly see that the percentage change in

thermopower became more negative as the sample warms from 225K to 270K but became

less negative thereafter as the sample was further warmed to room temperature. This was also

es

increase initially from 225K to around 270K but decrease after around 270K to room

reflected in Graph 10 where we can see that the envelop between the 0T values and 5T valu

temperature. The thermopower curves also does not exhibit significant hysteresis.

46

Chapter 5 Conclusion

eld measurements of the Nd sample revealed several interesting properties

ibilities in these

temperatures. These features could be explored in greater detail in future studies.

a

K

hich

e lab. Finally, the limitations of the current setup could be overcome

with simple modifications and the 1000K Setup could be considered a success.

Samples of R0.65Ca0.35MnO3 (R = La, Pr, Nd, Sm, Y, Bi) were prepared and measured in the

Low Temperature Measurement Setup (50K - 310K) and a high temperature setup

(300K - 700K), with the exception of the Y0.65Ca0.35MnO3 which failed to achieve sufficient

bulk strength. The high temperature results revealed that the samples conduct via the small

polaron mechanism. The existence of a weekly temperature dependent Seebeck coefficient

value at high temperatures suggests a hole concentration of approximately half which may be

explained by the Charge Disproportionation model.

The magnetic fi

which included a Colossal Magnetoresistance effect, Insulator-to-Metal transitions as well as

several phase transitions; The magnetic susceptibility graph revealed Charge Ordering

transition as well as magnetic ordering (antiferromagnetic) below 230K and 150K

respectively, as evidenced by the presence of peaks in the magnetic suscept

The pilot test result of the 1000K Setup with the Nd sample revealed an additional phase

transition feature at 765K which would be immeasurable with the 700K Setup. The clean dat

also suggests that the setup performed satisfactorily well at the high temperatures. The 1000

Setup also provided an avenue to measure the thermal conductivity of future samples w

was unprecedented in th

47

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[2] D. Fu and M. Itoh, Ferroelectricity in Silver Perovskite Oxides, Ferroelectrics - Material Aspects, Dr. Mickaël Lallart (Ed.) ed., 2011.

[3] M. Ohtaki, "Recent aspects of oxide thermoelectric materials for power generation from mid-to-high temperature heat source," Journal of the Ceramic Society of Japan, vol. 119, pp. 770-775, 2011.

[4] R. D. Shannon, "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides," Acta Cryst, vol. A32, p. 751–767, 1976.

[5] J. Loudon, "An Investigation of the Unconventional Phases in the La1-xCaxMnO3 System," 2003.

[6] E. Pollert, S. Krupička and E. Kuzmičová, "Structural study of Pr1−xCaxMnO3 and Y1−xCaxMnO3 perovskites," Journal of Physics and Chemistry of Solids, vol. 43, no. 12, pp. 1137-1145, 1982.

[7] D. Hsu, Y. C. Shih, W. T. Wang and J. G. Lin, "Magnetotransport Behaviour and the Phase

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ters,

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Diagram of Nd1-xCaxMnO3," IEEE Transactions on Magnetics, vol. 45, no. 10, pp. 4345-4347, 2009.

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[9] A. Putnis, "An Introduction to Mineral Sciences," Cambridge University Press, 1995.

[10] N. F. Mott and E. A. Davis, "Electronic Processes in Non-Crystalline Materials," Oxford Classic Texts in the Physical Sciences, 2012, p. 91.

[11] D. Emin, "Thermoelectric Power Due to Electronic Hopping Motion," Physical Review Letvol. 35, no. 13, p. 882, 1975.

[12]

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48

49

2005.

] M. Jaime, M. B. Salamon, K. Petit, M. Rubinstein, R. E. Treece, J. S. Horwitz and D. B. Chrisey, "Magnetothermopower in La0.67Ca0.33MnO3 thin films," Applied Physics Letters, vol. 68, p. 1576, 1996.

ebert and V. Hardy, "Colossal magnetoresistance manganites: ative phenomena," The Royal Society of Chemistry, vol. 17, pp. 5023-

] H. Mesbah, M. A. Wilson, M. A. Carter and J. Shackleton, "Effect of prolonged sintering time at 1200°C on the phase transformation and reactivity with moisture of fired kaolinite," in 11th Int.

nce, 2010.

D. Vega, G. Polla, H. Aliaga and M. T. Causa, "Ca1-xYxMnO3 manganites: Synthesis and ESR characterization," Physica B: Condensed Matter, vol. 320, no. 1-4, pp. 47-50, 2002.

515,

[14

[15] A. Maignan, C. Martin, S. Himportance of the cooper5031, 2007.

[16

Conf. on Ceramic Processing Scie

[17] O. Agüero, A. G. Leyva, P. König,

[18] J. J. Neumeier and M. F. Hundley, "Thermoelectric power of La1−xCaxMnO3+δ: Inadequacy of the nominal Mn3+/4+valence approach," Physical Review B, vol. 55, no. 17, pp. 11511-111997.

A

nnex

Figu

re 1

2: D

iagr

am o

f the

Hig

h Te

mpe

ratu

re M

easu

rem

ent S

etup

. The

setu

p w

as d

esig

ned

tes

ista

nst

ivity

),w

er a

s w

ell a

s the

rmal

con

duct

ivity

from

300

K u

p to

100

0K.

o m

easu

re r

ce (a

nd re

si th

erm

opo

Picture A: Picture showing the full setup including the steel shells with lab colleague Ivan Lee holding up the top half containing the experiment setups. The slender shape of the lower section is designed to fit into the 7 Tesla superconducting solenoid.