s Sb-Sn and Li-Sb-Sn“ - univie.ac.atothes.univie.ac.at/33537/1/2014-07-02_0808386.pdf ·...

MASTERARBEIT

Titel der Masterarbeit

„Phase Equilibria in the Intermetallic Systems Sb-Sn

and Li-Sb-Sn“

verfasst von

Julia Polt, BSc

angestrebter akademischer Grad

Master of Science (MSc)

Wien, 2014

Studienkennzahl lt. Studienblatt: A 066 862

Studienrichtung lt. Studienblatt: Masterstudium Chemie

Betreut von: ao. Univ.-Prof. Mag. Dr. Hans Flandorfer

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Master Thesis, Julia Polt, University of Vienna (2014)

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ACKNOWLEDGMENTS

»A scientist in his laboratory is not a mere technician: he is also a child confronting

natural phenomena that impress him as though they were fairy tales.«

– Marie Curie –

»The most beautiful experience we can have is the mysterious – the fundamental emotion

which stands at the cradle of true art and true science.«

– Albert Einstein –

»’The Answer to the Great Question... Of Life, the Universe and Everything... Is...

Forty-two’, said Deep Thought, with infinite majesty and calm.«

– Douglas Adams, The Hitchhiker’s Guide to the Galaxy –

I thank my parents for encouraging me to follow my dreams in any way possible. Thank

you for creating an oasis of freedom, where I could find the state of mind necessary to put

everything into perspective.

I also thank my friends who inspired me when I needed inspiration, made me laugh when

I needed laughter, hugged me when I needed hugs and celebrated with me when the time

had come. Thank you for being there for me whenever I needed you.

I want to thank my supervisor Hans Flandorfer and my supervising tutor Siegfried

Fürtauer. Thank you for the possibility of conducting my master thesis in this research

group, for always being there to answer my questions and for the great opportunities to

broaden my experience abroad at international conferences.

Finally, I would like to thank all people at the department of inorganic chemistry

(materials chemistry) for providing a stimulating and family-like atmosphere. Thank you!

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TABLE OF CONTENTS

1. Introduction ............................................................................................................. - 7 -

2. Li-Ion Batteries ....................................................................................................... - 9 -

2.1 History ............................................................................................................ - 10 -

2.2 Fundamentals ................................................................................................. - 12 -

2.2.1 The Electrochemical Cell ........................................................................ - 12 -

2.2.2 Thermodynamics ..................................................................................... - 14 -

2.2.3 Battery characteristics ............................................................................. - 15 -

2.3 Basic Concepts of Lithium-Ion Batteries ....................................................... - 18 -

2.4 Battery materials ............................................................................................ - 19 -

2.4.1 Electrolytes ............................................................................................. - 20 -

2.4.2 Electrodes ................................................................................................ - 21 -

3. Literature Review .................................................................................................. - 27 -

3.1 The Elements .................................................................................................. - 27 -

3.1.1 Lithium .................................................................................................... - 27 -

3.1.2 Antimony ................................................................................................ - 29 -

3.1.3 Tin ........................................................................................................... - 30 -

3.2 The binary systems ......................................................................................... - 32 -

3.2.1 Antimony-Tin (Sb-Sn) ............................................................................ - 32 -

3.2.2 Lithium-Antimony (Li-Sb) ..................................................................... - 38 -

3.2.3 Lithium-Tin (Li-Sn) ................................................................................ - 39 -

3.3 The ternary system: Lithium-Antimony-Tin (Li-Sb-Sn) ............................... - 40 -

4. Experimental section ............................................................................................. - 40 -

4.1 Sample Preparation ........................................................................................ - 41 -

4.1.1 Binary system Sb-Sn ............................................................................... - 41 -

4.1.2 Ternary system Li-Sb-Sn ........................................................................ - 45 -

4.2 Analysis Methods ........................................................................................... - 48 -

4.2.1 X-ray Diffraction (XRD) ........................................................................ - 48 -

4.2.2 Difference Thermal Analysis (DTA) ...................................................... - 55 -

4.2.3 Scanning Electron Microscopy (SEM) and

Electron Probe Microanalysis (EPMA) .................................................. - 57 -

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5. Results and Discussion ......................................................................................... - 60 -

5.1 Sb-Sn .............................................................................................................. - 60 -

5.1.1 XRD ........................................................................................................ - 60 -

5.1.2 ESEM/EPMA .......................................................................................... - 69 -

5.1.3 DTA ........................................................................................................ - 75 -

5.1.4 Conclusion .............................................................................................. - 77 -

5.2 Li-Sb-Sn ......................................................................................................... - 81 -

5.2.1 XRD ........................................................................................................ - 81 -

5.2.2 Conclusion .............................................................................................. - 90 -

6. Summary ............................................................................................................... - 92 -

6.1 English ............................................................................................................ - 92 -

6.2 Deutsch ........................................................................................................... - 93 -

7. References ............................................................................................................. - 95 -

8. Appendices .......................................................................................................... - 101 -

8.1 List of Figures .............................................................................................. - 101 -

8.2 List of Tables ................................................................................................ - 104 -

8.3 Curriculum Vitae et Studiorum .................................................................... - 105 -

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1. INTRODUCTION

One of the biggest challenges of our time, which is characterized by an increasing

shortage of fossil fuels and an increasing pollution of the environment, is to improve the

usage of sustainable energy sources. Technologies to use water, wind and solar energy are

up-and-coming, but suitable energy storage components to overcome their temporal and

local limitations are still under development. Another major field of high energy

applications which needs secure and long lasting power supply is transport and mobility.

In order to enable the development of electric vehicles with enhanced cruising range

batteries with prolonged lifetime, high energy and power density as well as charge

capacity are needed.

Despite the disadvantages of fossil fuels as energy carrier and storage media, chemical

energy storage still displays the best solution in terms of energy mass density.

Accumulators (rechargeable or secondary batteries, often referred to as batteries in

common language) however, can provide CO2-neutral, renewable energy with high

conversion efficiency but without pollution of the local environment. In respect to this,

lithium-ion batteries are of special interest due to their high charge capacity, energy and

power density, life time and their low weight. In the early 1990s the commercialization of

lithium-ion batteries with carbon as anode- and CoO2 as cathode material enabled the

miniaturization of mobile devices such as mobile phones, laptops and photo cameras.

However, to achieve the application for high energy devices, Li-ion batteries need further

improvement of energy density, lifetime and operation safety.

For a long time research to improve the performance of Li-ion batteries focused mainly

on the optimization of the existing materials and battery geometry. Only in the past

decade the search for novel electrode materials and improved electrolytes to increase the

battery shelf life and cycle stability gained importance. Promising electrode materials

include lithium alloys of germanium and silicon as cathodes and tin or aluminum as

anode materials. The major drawback of those elements is their large volume change

upon lithiation/de-lithiation which leads to mechanical stress and failure of the material

systems. Possible strategies to overcome the problems arising from large volume change

are variations of the microstructure of the materials, composite materials with a

stabilizing matrix or usage of intermetallic alloys as electrodes prior to lithiation.

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Within the scope of this master thesis the binary phase diagram antimony-tin (Sb-Sn) was

newly investigated and first explorations into the ternary system lithium-antimony-tin

(Li-Sb-Sn) were carried out. Antimony-tin intermetallic alloys have already been under

investigation as possible anode materials for lithium-ion batteries by some research

groups[1-8]

and show promising properties regarding their reversible capacities even after

several charge/discharge cycles. However, for further understanding of the lithiation/de-

lithiation process in this material system and the possible utilization of its principle to

other systems, allowing the design of novel and improved electrode materials, knowledge

about phase relations and thermodynamic properties are mandatory. Consequently, the

aim of this work is to provide an improved phase diagram for the binary system Sb-Sn,

including structural information about the main phase SbSn as well as first results of

phase relations in the ternary system Li-Sb-Sn.

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2. Li-ION BATTERIES

The growing demand on compact, light-weight batteries with high energy and power

densities led to the development of a new battery system with greatly enhanced cell

voltages of ~ 4 V, owing to the use of non-aqueous electrolytes and the possibility of high

temperature operation. The newly developed systems based on the migration of lithium-

ions between the electrodes are characterized by a dramatically improved gravimetric and

volumetric energy density compared to other rechargeable battery systems, see

Figure 1[9]

.

Nevertheless, to be applicable in high-performance electric cars or smart-grids further

improvement of the capacity, energy density, lifetime and operation safety needs to be

achieved. The following chapter gives an overview on the development of lithium-ion

batteries before their commercialization in the early 90s. After that, the fundamental basis

and thermodynamics of batteries and of lithium-ion batteries in particular are explained,

followed by a more detailed description of the design of new battery materials.

Figure 1: Comparison of gravimetric and volumetric energy density of various rechargeable battery

systems. (adapted from Scrosati et al.[9]

)

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2.1 History

The 70s mark the beginning of research on the topic of rechargeable lithium-ion batteries.

In 1976 Whittingham[10]

reported about a new battery system whose underlying

electrochemical reaction on the cathodic side is the intercalation of lithium into titanium

disulfide. However, the proposed anode was metallic lithium constituting severe safety

risks and prohibiting repeated cycling due to dendritic growth of the recrystallizing

lithium. At about the same time Besenhard et al. investigated the intercalation of alkali

metals into graphite and suggested such compounds as electrode material for lithium

cells[11, 12]

. In the late 70s a new synthesis method for lithium intercalated graphite

compounds as well as investigations on their properties including volume change upon

intercalation, electronic conductivity and optical properties were published[13, 14]

.

Goodenough et al.[15]

were the first to use layered LixCoO2 (0 < x ≤ 1) as cathode material

in Li-ion batteries and reported doubled open-circuit voltages of 4-5 V against Li/Li+ in

comparison to LixTiS2 (0 < x ≤ 1). Shortly after that Yazami et al.[16]

demonstrated the

reversibility of lithium intercalation in graphite paving the way for graphite as an anode

material in lithium-ion batteries. These two findings were the basis for Yoshino[17]

to

develop a new set-up for lithium-ion batteries, which is the same as it exists today. He

proposed the combination of a carbonaceous material with a certain crystalline structure

Figure 2: Operating principle of Li-ion batteries (adapted from Yoshino[17]

)

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(vapor-phase-grown carbon fiber) as anode with LiCoO2 as cathode. In this setting both

electrodes serve as host for the intercalating lithium ions and no other chemical reactions

occur. Figure 2 shows the operation principle of this set-up. Additionally, Yoshino

invented some other essential constituent technologies concerning safety, battery structure

and fabrication. These included a multilayer electrode assembly with winded sheets of

electrode materials separated by a membrane[18]

as well as a PTC (positive temperature

coefficient) element[19]

to prevent overcharging. He was the first to use aluminum foil[20]

as current collector at the cathode instead of more precious metals such as gold or

platinum, because he learned that aluminum could withstand the high voltage of 4 V due

to formation of a passivation layer at the surface. On the anodic side copper was used as

current collector, because aluminum would oxidize due to its lower standard electrode

potential compared to carbon. The formation of an oxidic passiviation layer on the carbon

side is not possible due to the absence of oxygen in contrast to the cathode material.

Figure 3 shows the battery and electrode structure proposed by Yoshino.

Based on this developments SONY commercialized the lithium-ion battery in 1991. Since

then the capacity of the batteries almost doubled from 900 mAh to 1600 mAh[21]

and the

number of applications rose dramatically. A variety of other materials have been studied

and developed for electrode applications, but these will be discussed in the later sections

(2.4 Battery materials).

Figure 3: Battery and electrode structure proposed by Yoshino[17]

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2.2 Fundamentals

2.2.1 The Electrochemical Cell

The device that converts chemical

energy into electrical energy or vice

versa is called electrochemical cell.

An electrochemical cell consists of

two half-cells, which on their part

consist of an electrode in contact with

an electrolyte. A schematic diagram of

the electrode processes in an

electrochemical cell is shown in

Figure 4. In case of an open circuit, the metals being in contact with the electrolyte

dissolve to a certain extent and electrons remain at the electrodes. A characteristic

electron density is built up on each side and a potential difference can be measured using

a voltmeter with high internal resistivity. Under these conditions the electrode potentials

are stable, because there is practically no current flow. Upon connection of the two

electrodes with an electronic conductor the electrons start flowing from the anode A

(higher electron density) to the cathode B. As a consequence the less noble metal A

dissolves further providing more electrons and B+-ions are deposited at the cathode

[22].

Anode / Oxidation: (1)

Cathode / Reduction: (2)

Overall reaction: (3)

These reactions continue until either the base metal A is completely dissolved or all

B+-ions are precipitated. In other words the electric current stops when either the

oxidation or the reduction process in one half-cell is completed. Parallel to the electric

current in the external circuit, charge equalization in the electrolyte occurs via diffusion

of negative ions from the positive to the negative electrode. This diffusion is generally the

limiting factor for the current flow in the electrochemical cell, therefore the

resistance ρ [Ω·cm] of the electrolyte needs to be low. To compare different electrolytes

the specific conductivity κ [Ω-1·cm

-1] is used which is defined as the inverse value of the

specific resistance (see Figure 5(a) and (b))[9, 22]

.

Figure 4: Electrochemical Cell (adapted from

Besenhard[22]

)

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The characteristic voltage of a half-cell cannot be determined on its own, but only as a

potential difference to another half-cell. In order to compare different half-cell potentials

a reference system was defined: The standard hydrogen electrode is based on the half-cell

reaction (4) and consists of a platinum electrode with a hydrogen-saturated hydrochloric

acid solution (c = 1 mol·L-1) at standard conditions (T = 25 °C; p = 101.3 kPa)

[22]. The

potential of this reference electrode is normalized to E0 = 0 V.

(4)

The electrochemical series ranks different metal/metal ion couples according to their

standard electrode potentials against the standard hydrogen electrode (see Figure 5(c)).

The obtained potential difference of the overall reaction (3) is calculated by equation (5)

and in case of equilibrium conditions, it is equal to the terminal voltage of the cell.

⁄ ⁄ (5)

Figure 5: (a) Comparison of specific conductivities of different materials and (b) electrolytes used in LIBs

(c) Electrochemical series of different metal/metal-ion couples (adapted from Besenhard[22]

and

Scrosati et al.[9]

).

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2.2.2 Thermodynamics

Just as any other reaction, electrochemical reactions can be described thermodynamically,

making it possible to calculate the standard electrode potentials from thermodynamic data

or vice versa. However, this is only possible if equilibrium conditions exist at the phase

boundaries between electrode and electrolyte. This implies that the cell reaction is

reversible and that there is no concentration gradient in the electrolyte. If these conditions

apply, the Gibbs free energy change of the reaction is equal to the utilizable electric

energy ‘zFE0

rev’ where E0

rev is the electromotive force (emf) at standard conditions (a = 1,

T = 298 K, p = 1 atm), z is the number of exchanged electrons and F is the Faraday

constant (F = 96485 C·mol-1

)[22]

. The Gibbs energy for the cell reaction is negative if the

electrochemical process is exergon, thus equation (6) is valid:

(6)

2.2.2.1 Concentration dependence of the equilibrium cell voltage E0

rev[22]

The chemical potential µi of a species i is defined as first derivative of the Gibbs free

energy with respect to the number of moles ni, if all other components remain constant:

(

)

(7)

At constant temperature and pressure, summation of the chemical potentials of all species

taking part in the reaction results in the molar Gibbs free energy of the reaction:

∑

(8)

where vi is the atomic fraction of compound i, which is positive in case of an educt and

negative in case of a product. The concentration dependence of the chemical potential µi

is given in equation (9):

(9)

where µi0 is the chemical potential at standard conditions and R is the universal gas

constant (R = 8.3145 J·mol-1·K-1

). The combination of equations (8) and (9) results in the

Nernst equation, which is one of the most important relations in electrochemistry, and

describes the concentration dependence of the cell voltage:

Nernst equation:

∑

(10)

Q is the reaction quotient of the electrochemical reaction. In case of a half-cell reaction as

in equation (1) or (2) Q is replaced by ⁄ or ⁄ , respectively[23]

.

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2.2.2.2 Temperature dependence of the equilibrium cell voltage E0

rev[23]

Partial differentiation of the Gibbs-Helmholtz relation (11) with respect to the

temperature T results in the temperature dependence of the Gibbs free energy,

equation (12).

(11)

(

)

(12)

The combination with equation (6) results in the description of the temperature

dependence of the equilibrium cell voltage:

(

)

(

)

(13)

2.2.3 Battery characteristics[22]

There is a large variety of battery systems available for different applications, so in order

to choose the most suitable system it is important to compare their most important

features.

2.2.3.1 Terminal voltage U and open-circuit voltage Voc[22]

The open-circuit voltage Voc is measured at the poles when no external load is connected

to the battery, whereas the terminal voltage U is the voltage measured during charging or

discharging. Due to internal resistance of the battery the terminal voltage during

discharging Udischarge is always smaller than the open-circuit voltage Voc, and the terminal

voltage during charging Ucharge always exceeds Voc. It is possible to calculate Voc, which is

equal to the electromotive force (emf) of an electrochemical cell in thermodynamic

equilibrium, by means of thermodynamics although the calculated value often deviates

from the experimental one due to possible side reaction or other non-equilibrium

conditions.

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2.2.3.2 Charge and discharge characteristic

If the terminal voltage

during charge or discharge

is plotted against the

capacity of the battery the

charge or discharge

characteristic lines are

obtained (see Figure 6[24]

).

In the ideal case, the

discharge curve shows an

extensive flat region with

constant terminal voltage until the last step, when the curve drops to zero and the stored

energy is completely consumed. In reality, the open circuit voltage decreases and the

internal resistance of the battery increases under discharge, explaining the slow decrease

of terminal voltage. The actual course of the graph is dependent on the chemistry and

arrangement of the cell as well as the discharge rate C, which is defined as the reciprocal

discharging time and equal to the discharge current divided by the nominal capacity:

(14)

In a similar way the charge characteristic varies with different currents. Additionally, the

charging procedure has influence on terminal voltage, charging time, number of cycles

and other parameters[22]

.

2.2.3.3 Energy density and power density[22]

Other important characteristics of an electrochemical cell are the gravimetric (Wh·kg-1

) or

volumetric energy density (Wh·L-1

) and the power density P (W·kg-1

) or (W·cm-3

), which

are the available energy or power, related to the battery weight or surface area,

respectively.

Figure 6: Charge and discharge curves of LiNi0.5Mn1.5O4 at different

C rates[24]

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2.2.3.4 Coulometric and energy efficiency

Efficiency in terms of energy conversion is defined as ratio between the energy that is

provided and the energy that is consumed. Due to incomplete conversion caused by side

effects such as heat production, the charge process is always energetically more intensive

than the discharge process, therefore resulting in a lower efficiency.

There are two ways to describe battery efficiency:

Coulometric efficiency:

(15)

where Qdischarge and Qcharge are the charges available or necessary during the

discharging or charging process, respectively. For lithium-ion batteries the

coulometric efficiency reaches nearly 100 percent[22]

.

Energy efficiency:

(16)

where –Udischarge and

–Ucharge are the average terminal voltages during discharging

and charging process. Similar to the available charge during discharge (Qdischarge)

the terminal voltage –Udischarge is lower than

–Ucharge due to internal resistance and

overpotentials[22]

.

2.2.3.5 Cycle life

The cycle life is defined as the number of charge/discharge cycles before a specific limit

of capacity cannot be reached anymore. This level is often set to 80%[22]

of the nominal

capacity of the battery. For comparability reasons the depth of discharge needs to be

taken into account.

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2.3 Basic Concepts of Lithium-Ion Batteries

A lithium-ion battery consists of four main

components: a positive and negative

electrode, an electrolyte and a separator. The

electrodes of lithium-ion batteries act as host

for the reversible insertion/extraction of

lithium-ions. The electrochemical process

accompanying this ion movement comprises

the oxidation/reduction of the host matrix

and an electron flow through the external

circuit[24]

. The separator membrane serves as

electronic isolator between the electrodes,

while the electrolyte, which is contained in

the micro-pores of the separator, enables the

ion-transfer[25]

. Figure 2 and Figure 3 (pages

10 and 11) already show the basic concept and constitution of lithium-ion batteries.

Figure 7[25]

is another graphical representation, where the sequence of current collector,

anode, separator/electrolyte, cathode and again current collector is shown.

Usually, the cathode material is a layered transition-metal chalcogenide, which can

reversibly intercalate lithium-ions (e.g. LiCoO2) and the most commonly used anode is

graphite, which is able to intercalate one lithium-ion per six formula units graphite. The

electrolyte generally comprises a lithium-salt such as LiPF6 dissolved in an organic liquid

carbonate. Detailed requirements of the battery materials are discussed in the next section

(2.4 Battery materials). The associated electrode reactions upon discharging are displayed

in equations (17) and (18):

Anode (graphite):

(17)

Cathode (CoO2):

(18)

where Li(C6) and Li(CoO2) are lithium-ions intercalated into the host matrix, V(C6) and

V(CoO2) are the corresponding vacancies in the structures, Li+(e) is a lithium-ion located

in the electrolyte phase and e-(a) and e

-(c) are electrons flowing through the external wire

which connects the two poles[25]

.

Figure 7: Structure of a lithium-ion battery[25]

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2.4 Battery materials

In order to design an improved battery system regarding high voltage, capacity, energy

and power density and rate capability, some preliminary considerations need to be taken

into account. First of all, the decomposition potential of the electrolyte limits the

open-circuit voltage Voc of the battery system. This was the reason that non-aqueous

electrolytes and as a consequence lithium-salts, which are able to dissolve in non-aqueous

solutions and polymers, were considered for electrolyte-purposes in the first place, since

the decomposition potential of water limits the Voc for aqueous battery systems to

~1.3 V[26]

.

Figure 8 shows a schematic

diagram of the connection

between the highest occupied

molecular orbital (HOMO), the

lowest unoccupied molecular

orbital (LUMO) of the electrolyte

and the chemical potentials µA

and µC of the anode and cathode,

respectively. If the chemical

potential of the cathode µC is

lower than the oxidation potential

(HOMO) of the electrolyte, the

electrolyte will be oxidized

instead of the cathode. This

happens unless a passivation layer – a so called solid/electrolyte interface (SEI) – serves

as mechanic protection and provides kinetic stability[26]

. The same applies for the anode,

with the difference that the chemical potential µA is not allowed to exceed the reduction

potential (LUMO) of the electrolyte.

Keeping this in mind, electrode materials must be designed either with their chemical

potentials perfectly matched to the HOMO and LUMO of the electrolyte or with the

ability to form a stable SEI passivation layer, which heals quickly after being broken by

volume changes of the electrodes occurring upon several charge and discharge cycles[26]

.

Figure 8: Schematic open-circuit diagram adapted from

Goodenough et al.[26]

. ΦA and ΦC are the anode and cathode

work functions. Eg is the window of the electrolyte for

thermodynamic stability. A μA>LUMO and/or a μC<HOMO

requires kinetic stabilisation by the formation of a SEI layer.

- 20 -


2.4.1 Electrolytes

There are manifold requirements an electrolyte of lithium-ion batteries has to meet[26]

,

including:

1) The ability to maintain the contact between electrode and electrolyte interface,

even after many charge/discharge cycles and the thereby occurring volume

change.

2) A Li-ion conductivity of σLi > 10-4

Ω-1·cm

-1,

3) An electronic conductivity of σe < 10-10

Ω-1·cm

-1 over the temperature range of

battery operation,

4) A transference number of σLi/σtotal ≈ 1 (where σtotal contains conductivities of all

ions present),

5) Chemical stability over the temperature range of battery operation,

6) Chemical stability in respect to the electrode materials, including the formation of

a stable SEI passivation layer if necessary,

7) Safe materials, i.e. inflammable, non-explosive and

8) Materials of low toxicity and low cost.

Over the last years, a variety of electrolytes for lithium-ion batteries was proposed. The

most commonly used are organic liquid electrolytes such as propylene carbonate (PC),

ethylene carbonate (EC), diethyl carbonate (DEC), dimethyl carbonate (DMC), or

ethylmethyl carbonate (EMC). They have an oxidation potential (HOMO) of ~4.7 V[27-29]

and a reduction potential of ~1.0 V[30]

(referring to Li/Li+), which is below the

electrochemical potential of graphite, but EC is able to provide a SEI passivation layer

after the first charge/discharge cycle and therefore is added to almost every electrolyte of

lithium-ion batteries. Ionic-conductivities of different organic liquid electrolytes are

shown in Figure 5 (page 13).

Other possible electrolytes include ionic liquids[31-33]

, inorganic liquid electrolytes[34, 35]

,

solid polymer electrolytes[36, 37]

and inorganic solid electrolytes[38-40]

. The latter are of

special interest, because they meet all the requirements mentioned above except the first,

which is their biggest flaw. Nevertheless, a sulphide based solid electrolyte[41]

was

introduced recently, which can maintain the electrode/electrolyte contact and additionally

is not reduced by Li-metal, enabling the construction of an all-solid-state lithium-ion

battery with metallic lithium as anode.

- 21 -


2.4.2 Electrodes

For the design of new electrodes, matching of the chemical potentials µA and µC of anode

and cathode to the “window” of the electrolyte is necessary (remember Figure 8,

page 19). Figure 9(a) shows the relative positions of the Fermi energy of carbon and some

transition-metal/cation couples, which may correspond to their chemical potential, in a

schematic diagram of energy vs. density of states. The energy of any RedOx couple is

influenced not only by the oxidation state of the cation, but also by the amount of

covalent bonding involved and the presence and position of any counter-ions in the

structure[26]

. In Figure 9(b) their terminal voltage against Li/Li+ upon discharging is

shown.

Figure 9: (a) Schematic diagram of corresponding energy vs. density of states, showing the relative

positions of the Fermi energy in an itinerant electron band for different electrode materials (b) Discharge

characteristics of different electrode materials vs. Li/Li+. (taken from Goodenough et al.

[26])

- 22 -


2.4.2.1 Cathode Materials

The search for new cathode materials for lithium-ion batteries started a lot earlier and is

therefore more elaborated than the one for anode materials. Many different materials have

been proposed, but only a few will be presented in the next paragraphs.

The most successful category of cathode materials is the layered transition metal oxide

LiMO2[24, 26]

. Comprising a cubic structure with alternating layers of MO2 and Li,

intercalation and deintercalation of lithium-ions is facilitated in this structure. However,

deintercalation of more than half of the available lithium-ions results in a metastable

compound and/or transformation of the structure, reducing the capacity of the electrode to

approximately one Li-ion for two cobalt-ions. Additionally, cobalt is expensive and toxic,

which is why the development of alternative materials started right after

commercialization of the first lithium-ion battery.

Framework structures such as the cubic spinel A[B2]X4 offer higher stability while still

providing interstitial space for the insertion of Li-ions. Research was done on different

compounds, such as Li[Ti2]S4[42]

and Li[Mn2]O4[43, 44]

. Depending on the compound and

the lithium concentration, the Li-ions intercalate either preferred into the octahedral or

tetrahedral sites, leading to structural distortion of the originally cubic structure. One

major drawback of Li[Mn2]O4 is the dissolution of Mn into the electrolyte, but

improvement of crystallinity solved this problem[45]

.

Other 3D frameworks are the NASICON structure of LixM2(XO4)3[46, 47]

, which is able to

up-take up to 5 Li-ions per formula unit or the olivine structure of LiFePO4 comprising a

flat Voc = 3.45 V versus Li/Li+[48]

.

2.4.2.2 Anode Materials

Lithium metal was the first material used for anodes in lithium-ion batteries and exhibits a

theoretical specific capacity of 3862 mA·h·g-1[49]. However, due to safety issues and

instability of the electrode/electrolyte interface, caused by its high reactivity, lithium was

replaced by carbonaceous materials, which enabled the commercialization of lithium-ion

batteries in the early 90s. Although some other compounds were investigated as possible

anode materials, including lithium-aluminum alloys[50-52]

and lithium-silicon alloys[53-56]

,

research in the following years focused on the improvement of existing materials instead

- 23 -


of finding new ones. Only in the last decade the interest in alternative anode materials,

such as lithium alloys and metal oxides was revived. Investigations of possible alloy

systems included the binary systems Li-Si, Li-Sn[57, 58]

, Li-Sb[59-61]

, Li-Bi[61]

and some

others[62, 63]

, as well as some ternary systems[64, 65]

. The biggest drawback of most lithium

alloys is the large volume change involved in the formation of the compound and the

following failure of the anode due to lack of contact between the particles. Figure 10

compares the theoretical capacities of some lithiated compounds with their volume

change upon lithiation/de-lithiation[66]

. Due to the huge amount of information, the

following paragraphs will concentrate on Li-Sn alloys, intermetallics and composites as

anode materials in an exemplary manner.

Upon electrochemical lithiation a variety of intermetallic compounds between lithium and

tin is formed (see phase diagram in section 3.2.3 Lithium-Tin (Li-Sn)). The compound

richest in lithium (Li22Sn5 / Li4.4Sn) has a theoretical capacity of 994 mA·h·g-1[66]

,

therefore being of huge interest as anode material. To overcome the large volume changes

during lithiation/de-lithiation, caused by the large density differences of lithium and tin,

several solutions have been considered[67]

. i) A smaller potential window excluding

Figure 10: Comparison of theoretical capacity (mAhg-1

), volume change (%) and potential vs. Li (~V) of

different anode materials (data taken from Zhang et al.[66]

)

- 24 -


lithium-alloys with higher lithium content reduces mechanical stress on the electrode[68]

.

ii) Smaller particle sizes improve the battery performance (see Figure 11 for comparison

of nano-[69]

and micron-Sn particles[70]

), but fail to improve the cycling stability. iii) The

introduction of a second phase, which is not involved in the actual electrochemical

reaction, but assures electronic and ionic conductivity[71]

.

The last bullet point yields the best results for reduction of volume change and as a

consequence several different Sn-based composite materials have been studied as anode

material for lithium-ion batteries. The second phases of those composites are manifold

and include disordered carbon[72-78]

, graphite[76, 77, 79]

, single-walled carbon nanotubes[80,

81], multi-walled carbon nanotubes

[82-84], semi-amorphous carbon

[85], TiO2 nanotubes

[86],

and semi-amorphous copper[87]

. Figure 11 shows the electrochemical performances of the

composites, but although there are some very promising candidates, e.g. tin-filled carbon

nanofibers or nanotubes, their complicated multi-step production process keeps them

from being realizable in industrial scale.

Figure 11: Comparison of reversible capacities (mAhg-1

) vs. cycle number of different Sn-based composite

anode materials (taken from Kamali et al. [67]

; references correspond to Kamali et al. [67]

)

- 25 -


A fourth possibility to overcome the volume changes upon lithiation/de-lithiation is the

use of intermetallic alloys and their composites. A high number of compounds was

investigated for this purpose, including tin-based intermetallics in the systems Cu-Sn[88,

89], Sb-Sn

[5, 7, 90-96], Co-Sn

[97-99], Fe-Sn

[100-102] and many others. Figure 12 shows the

electrochemical performance of some Sn-based intermetallic anodes. Most noteworthy for

this thesis are the high and – over a large number of cycles – stable reversible capacities

of two different SnSb composites[92, 93]

.

The advantage of the intermetallic alloy SnSb is that it consists of two active components

and reaction with lithium can yield in two lithiated phases Li3Sb and Li22Sn5. The

involved reactions, theoretical capacities and terminal voltages against Li/Li+ were

investigated previously and are shown in equations (19) and (20)[67]

.

↔

334 mA∙h∙g

-1 (19)

↔

↔

↔

825 mA∙h∙g

-1 (20)

As can be seen in Figure 12, both research groups[92, 93]

reported a considerable reversible

capacity of 550 – 600 mAh.g-1

even after several charge/discharge cycles. The proposed


) of different Sn-based intermetallic and/or

composite materials (taken from Kamali et al. [67]

; references correspond to Kamali et al. [67]

)

- 26 -


explanation of this is, that the volume expansion during the first step caused by Li3Sb is

buffered through the formation of ductile Sn[67]

. Wachtler et al.[92]

showed furthermore

that additives such as ethylene carbonate (as filming agent) and saturated

phosphatidylcholine (as surfactant) in the electrolyte improve the electrochemical

performance of the battery.

- 27 -


3. LITERATURE REVIEW

3.1 The Elements

3.1.1 Lithium

Greek lithos = stone

Chemical symbol: Li

Atomic number: 3

Relative atomic mass:

(C12

=12.0000) 6.941

Radii /pm: Li+ 78; atomic 152; covalent

123

Electronegativity: 0.98 (Pauling)

Electron configuration: [He] 2s1

Oxidation states: LiI

Melting point /°C: 180.69

Boiling point /°C: 1347

Density /g·cm-3

: 0.534 [20 °C]

Photo taken from periodictable.com with permission of Theodore Gray

Lithium was first discovered in 1817 by the Swedish chemist Johan August Arfedson in

Stockholm, Sweden. Shortly after that, small amounts of metallic lithium were obtained

through electrolysis by William Thomas Brande and Sir Humphrey Davy in 1818[103]

.

Lithium is a soft, silver-white metal and the first element in the group of alkali metals in

the periodic system. It is the lightest metal of all solid elements with a density of

0.534 g·cm-3

(20 °C). The loss of one electron leads to the noble gas configuration

2s2 [He] (oxidation state Li

I) explaining the high electropositivity and reactivity. Under

ambient conditions lithium reacts readily with oxygen, hydrogen, halogens etc. to form

Li2O, LiOH, LiH, LiCl, LiNO3 and others[104]

.

Due to its high reactivity, lithium never naturally occurs in its elemental form, but only

bound in minerals such as spodumene LiAl[Si2O6], petalite LiAlSi4O10[105]

or lepidolite

K(Li,Al)3(Si,Al)4O10(F,OH)2[106]

. Secondary deposits of lithium are seawater (less than

1 ppm[104]

) and salt lakes such as Salar de Atacama in Chile which contains 27% of the

world’s lithium reserve[107]

. Lithium is the 34th

most abundant element with 0.0017% of

the earth’s crust[108]

. Despite that, the Handbook of Lithium and Natural Calcium

Chloride[109]

states: “Lithium is a comparatively rare element, although it is found in

- 28 -


many rocks and some brines, but always in very low concentrations. There are a fairly

large number of both lithium mineral and brine deposits but only comparatively few of

them are of actual or potential commercial value. Many are very small; others are too

low in grade.” The growing demand of lithium, resulting from increasing usage of

lithium-ion batteries, caused many companies to expand their extraction efforts. There are

different prospects for the future lithium production[110, 111]

. The latest however,

conducted by the Lawrence Berkeley National Laboratory and University of California

Berkeley presents a confident view asserting that “there is sufficient availability of the

elements for battery deployment in grid-scale applications.”[111]

The extraction of lithium is either done by mining of spodumene-containing petalite

followed by chemical processing with chalk and precipitation as carbonate or by

concentrating lithium-containing brine and subsequent reaction with soda to yield lithium

carbonate (Li2CO3). After conversion of the carbonate with hydrochloric acid (HCl) to

form lithium chloride (LiCl), metallic lithium is obtained via a molten electrolysis process

of a eutectic mixture of lithium chloride and potassium chloride (KCl).

Nevertheless, the largest share of produced lithium-salts is not reduced to the metal but

used directly or converted to other useful compounds. The largest proportion of lithium is

used in the field of ceramics and glass[112]

, where lithium aluminum silicate is used as

additive to improve the thermal expansion coefficient[104]

. This application is closely

followed by the application of lithium in batteries (see section 2. Li-Ion Batteries) Other

common uses for lithium are in greases, which are characterized by high temperature-

resistance[113]

and as alloy components of ultra-light alloys for high performance aircraft

parts[114]

. In organic chemistry lithium is used as reduction agent in the form of lithium

aluminum hydride (LiAlH4) or lithium borohydride (LiBH4). Organolithium compounds

such as butyllithium are used as catalysts for polymerization reactions. Lithium has no

biological relevance in the human body, however, lithium carbonate and other

compounds are used as antidepressants and treatment for mental diseases such as bipolar

disorder or schizoaffective and schizophrenic disorders[115]

.

- 29 -


3.1.2 Antimony

Greek anti + monos = not alone

Chemical symbol Sb: latin stibium = german Grau/Spießglanz

Chemical symbol: Sb

Atomic number: 51


(C12

=12.0000) 121.75

Radii /pm: Sb5+

62; Sb3+

89; atomic 182;

covalent 141


Electron configuration: [Kr] 4d10

5s2 5p

3

Oxidation states: SbIII

, SbV



Density /g·cm-3

: 6.691 [20 °C]


In the early Bronze Age, antimony was already used as alternative or complementary

alloy component for bronzes. Since antiquity, antimony and its compounds were used in

cosmetics by Egyptians and the Chinese[104]

. In 1540 Vannoccio Biringuccio mentioned

antimony as means to separate gold and silver in his book 'De la Pirotechnia'[116]

, which is

considered the first book of metallurgy published in Europe. Antimony is a silvery, hard,

brittle and toxic heavy-metal belonging to the 15th

group of the periodic table. Due to its

low electronic conductivity of only 4% compared to copper, it is sometimes referred to as

metalloid.

Antimony is a rather rare element with only 2x10-5

% of the earth's crust (rank: 64th

)[108]

.

The predominant ore mineral of antimony is the sulfide stibnite (Sb2S3), however in some

areas it is also found as native metal[104]

. Production of antimony can be done either by

direct reduction of the sulfide with scrap iron or by a carbothermal reduction of the oxide

Sb2O3, which is obtained through roasting[117]

. The republic of China owns the largest

antimony reserves of the world and is also the largest antimony producer of the world[112]

.

As a consequence, a report published by the EU in 2014[118]

identifies antimony as one of

twenty critical raw materials.

The largest market for antimony is the production of flame-retardant materials[117]

.

Antimony oxide (Sb2O3) in combination with halogenated substances is used in textiles,

- 30 -


plastics and resins to inhibit ignition and prevent flames from spreading. Furthermore,

antimony is used as alloying constituent in bearings (Sn-Sb-Cu(-Pb)-alloys, so called

Babbitt metals), some “lead-free” solders and battery electrodes (Sb-Pb-alloys in lead-

acid batteries), improving their charging characteristics as well as hardness and

mechanical strength[119]

. Other applications for antimony oxide (Sb2O3) are the catalysis

of polyester polymerization, opacification of glasses and its conversion to antimony

chromate which is used as yellow pigment. Antimony salts are also components of

pesticides, mordant and fireworks[104]

.

3.1.3 Tin

German Zinn: old high german Zein = rod

Chemical symbol Sn: latin stannum

Chemical symbol: Sn

Atomic number: 50


(C12

=12.0000) 118.710

Radii /pm: Sn2+

93; Sn4+

74; atomic 140.5;

covalent 140


Electron configuration: [Kr] 4d10

5s2 5p

2

Oxidation states: SnII , Sn

IV



Density /g·cm-3

: 7.310 [20 °C]


The first usage of tin dates back to 3000BC in the Bronze Age, when it was discovered

that smelting of copper ore together with small amounts of tin ore yields an alloy with

greatly improved properties in terms of hardness, ductility and corrosion resistance. In

principle, this discovery built the foundation for the development of the advanced ancient

civilizations of Egypt, Mesopotamia, Greece, China and Central- and South America[104]

.

In the 14th

century it was discovered that coating of iron with tin was a reliable protection

of corrosion. In the 20th

century the production of tinplate changed from a rolling-mill

process to electroplating, which is still used up to now.

- 31 -


Tin is a silver-white, shining, very soft and ductile metal in the 14th

group of the periodic

system. There are two modifications of tin: Below 13.2 °C there is α-tin, which is brittle

and not electronically conductive due to its diamond cubic crystal structure and above

that there is β-tin crystallizing in a tetragonal structure. The decay of β-tin at low

temperatures is known as “tin pest”[103]

. As a result of passivation, tin is stable against air

and water, but dissolves in acids and bases. It has two possible oxidation states (SnII and

SnIV

) and forms various compounds such as SnCl2, SnO, SnO2, SnCl4 and SnF4 as well as

salts and complexes. There is also the possibility of covalent bonding between the metal

and other elements (Sn-Sn, Sn-H, Sn-Cl, Sn-F, Sn-C, Sn-O, etc.)[104]

.

Tin ranks 47th

among the most abundant elements in the earth's crust (2.2x10-4

%)[108]

and

is scarcely found as native metal in nature. The main tin ore is cassiterite SnO2, which is

the raw material for carbothermal reduction to produce metallic tin. The countries most

important for primary production of tin are China, Indonesia and Peru[112]

, however,

secondary production i.e. recycling of scrap tin gained importance over the last years.

More than half of the extracted tin in the world is used in solder materials[120]

. The rest

divides between tin plating, which mainly serves the production of food preservation

cans, tin chemicals, such as organotin compounds for the stabilization of PVC or used as

fungicides, pesticides, algaecides and antifouling agents, and special alloys such as

various white brasses and bronzes. Another area of application is the field of electrode

materials for lithium-ion batteries. The phase diagram of lithium and tin shows several

binary phases, making tin a promising material for lithium-ion battery electrodes (see

sections 2.4.2.2 Anode Materials and 3.2.3 Lithium-Tin (Li-Sn)).

- 32 -


Figure 13: Phase diagram by Gallagher[122]

3.2 The binary systems

3.2.1 Antimony-Tin (Sb-Sn)

As early as in the 19th

century investigations on the binary alloys of antimony and tin

started. In 1900 Reinders[121]

presented a cooling curve exhibiting three peritectics and

two intermetallic compounds namely SbSn and Sb4Sn3 (or Sb5Sn4). Six years later the

first complete phase diagram was published by Gallagher[122]

(see Figure 13) including an

intermetallic compound with large homogeneity range and a high and low temperature

configuration. His version of the phase diagram, however, did not satisfy the phase rules,

which were already known at that time. For example, at 430°C there are four compounds

in equilibrium instead of three allowed compounds, and the solidus line of the δ-phase is

missing. For this reasons, Williams[123]

conducted his own survey of the Sb-Sn system,

discussing the results of Reinders and Gallagher, concluding that only one intermetallic

compound without a temperature dependent change of its crystal structure exists. In 1912

Konstantinow and Smirnow[124]

were the first to mention an intermetallic compound –

namely Sb2Sn3 – additionally to SbSn. Their findings were based on measurements of

electrical conductivity and they stated that Sb3Sn2 can only be found after long thermal

annealing of the samples. Later Broniewski and Sliwowski[125]

claimed that Sb3Sn2 is the

only stable compound in the binary system Sb-Sn, but Jones[126]

and Bowen[127]

disagreed

and insisted that it is SbSn nevertheless.

Up to then, the only crystallographic information about an intermetallic compound in this

system was one about a cubic structure of NaCl-type[126, 127]

. Only in 1935, Hägg and

Hybinette[128]

described a splitting of lines in the X-ray powder diffractograms according

- 33 -


to a distortion of the cubic lattice and introduced a rhombohedral crystal structure with a

rhombohedral angle α=89.38°. In accordance with Iwasê, Aoki and Osawa[129]

Hägg and

Hybinette supported a transformation of the phase SbSn at 320°C and suggested a similar

structure such as an undeformed NaCl-type for the high temperature configuration, see

Figure 14. Another explanation for the invariant reaction at ~320°C was proposed by

Stegherr[130]

, who suggested a phase diagram with the non-stoichiometric SbSn phase

showing an inverse miscibility gap, but did not deny the possibility of an existing second

intermetallic compound.

The compilation of Massalski for binary alloys[131]

includes the phase diagram assessed

by Predel and Schwermann[132]

shown in Figure 15. They performed metallographic and

thermoanalytical investigations including DTA and calorimetric measurements. The

results showed extended mutual solid solutions of Sb and Sn (up to 10.0 at% Sb in pure

Sn and 12.6 at% Sn in pure Sb) and two binary compounds SbSn (β-phase) and Sb2Sn3.

SbSn reaches over a large homogeneity range from 43 to 60 at% Sb and Sb2Sn3 is

Figure 14: Phase diagram by Hansen, based on work of Iwase et al.[129]

- 34 -


represented as a line compound stable between 242 and 324°C. For Sb2Sn3 no crystal

structure is given and SbSn was assumed to be of cubic NaCl-type.

About ten years later, Jönnson and Ågren[133]

did another assessment of the system and

included calculations based on thermochemical and phase diagram information which

were developed by Jansson[134]

. Their result was very similar to the phase diagram

published by Predel and Schwermann with the difference of expecting a smaller

homogeneity range for SbSn (approximately 48 to 55 at% Sb) and lower mutual

solubilities of the pure elements at low temperatures, respectively (0 at% Sb in pure Sn

and 2 at% Sn in pure Sb). Ohtani et al.[135]

on the other hand reported a slightly different

phase diagram, which was published in a supplemental literature review done by

Okamoto[136]

. They proposed a metatectic decomposition Sb2Sn3 ↔ L + SbSn at ~250 °C

instead of the eutectoid decomposition Sb2Sn3 ↔ β-Sn + SbSn at 242 °C.

In order to resolve the uncertainties regarding the phase diagram and crystal structures of

SbSn and Sb2Sn3, Allen et al.[137]

performed detailed investigations on two samples of

composition Sn-54.5 at% Sb and Sn-43.5 at% Sb. Both samples were analyzed by in situ

high temperature X-ray diffraction at different temperatures ranging from 20 to 375 °C.

Figure 15: Phase diagram by Predel and Schwermann[132]

in Massalski's compilation for binary alloys[131]

- 35 -


Neither of the obtained patterns showed additional reflections, which would have

explained structural changes or the formation of a second phase such as Sb2Sn3 at

elevated temperatures. However, they observed a decrease in splitting of reflexes

characteristic for rhombohedral SbSn at high temperatures in the sample with lower

Sb-content, which was explained with the possible existence of a high temperature phase

with cubic NaCl-structure referring to Hägg and Hybinette[128]

.

A completely different proposition was made by Vassiliev et al.[138]

. EMF-measurements

on various samples made them assume that four line compounds, SbSn (β), Sb13Sn12 (β´),

Sb3Sn2 (β´´) and Sb2Sn (β´´´) exist within the β-phase homogeneity range (see Figure 16).

Their crystal structures all being closely related to one another via a variation of stacking

periodicity along the c-axis. However, a more detailed description of the crystal structures

was not given in the article. Oberndorff et al.[139]

, who studied Sb/Sn diffusion couples in

order to construct an isothermal section of the ternary system Ag-Sb-Sn at 220 °C,

reported two line compounds Sb3Sn4 and Sb4Sn3 in the binary system Sb-Sn.

In 2006 an Australian group of scientists reinvestigated the structure of the β-phase

(SbSn) using X-ray, synchrotron and electron diffraction as well as electron probe

microanalysis (EPMA)[140]

. Their conclusion was a rhombohedral parent structure which

is incommensurately modulated along the c-axis. However, the proposed explanation for

the modulated structure, implying a strict correlation between the primary modulation

Figure 16: Phase diagram by Vassiliev et al.[138]

- 36 -


wave vector qh and the chemical composition of the crystal, was not reflected in their

experimental data, which showed a very well defined primary modulation wave vector of

qh = 1.3109(9 regardless of compositional changes. A few years later a similar

investigation was carried out using single crystal X-ray diffraction and energy dispersive

X-ray spectroscopy (EDX)[141]

. In this survey a linear relationship between q-vector and

composition was found based on measurements of four samples in the composition range

from 35 to 55 at% Sn.

Shortly after that, an extensive study of the Sb-Sn system including CALPHAD modeling

was conducted by Chen et al.[142]

. Several samples in a composition range from 15 to

80 at% Sb were prepared, annealed at different temperatures between 160 to 300 °C and

investigated using X-ray diffraction, thermal analysis and electron probe microanalysis.

These results together with thermodynamic properties taken from literature were used as

basis for thermodynamic modeling of the phase diagram. As can be seen in Figure 17

they reported two binary compounds: The β-phase SbSn, but without a order-disorder

transformation and with a smaller homogeneity range at lower temperatures compared to

previously published phase diagrams and the line compound Sn3Sb2 stable even below

room temperature. Although they admitted that the differentiation between rhombohedral

SbSn and cubic Sn3Sb2 is hard, they claimed to be able to distinguish between the two in

Figure 17: Phase diagram by Chen et al.[142]

- 37 -


optical micrograph pictures and in X-ray diffraction patterns. The latter are shown in

Figure 18. According to Chen et al. the difference between β-SbSn and Sn3Sb2 in these

patterns are the peaks near 2θ=51°. The rhombohedral β-SbSn phase has two reflections

at 51.1° and 51.7° belonging to the [003] and [021] planes respectively, whereas cubic

Sn3Sb2 has only one reflection at 51.7°. Their experimental data of differential thermal

analysis (DTA) exhibited no effect within the homogeneity range of β-SbSn

corresponding to an order-disorder

transition. Also there was only one

thermal effect at 243 °C arising from the

peritectic reaction L + Sn3Sb2 ↔ Sn

contradicting the phase diagram of Predel

and Schwermann.

Investigations of the thermochemical data

in the system were done by several

research groups[143-150]

. Calorimetric

measurements covered the determination

of enthalpy of mixing of the liquid phase

at various temperatures ranging from

532 °C to 834 °C[143-146, 148, 150]

.

Vassiliev et al.[138]

applied EMF methods

to derive the enthalpy of mixing at

527 °C. In 1991 Tomiska et al.[149]

reported a clear temperature and

concentration dependence of ΔmixH in the

liquid phase and proposed a new

evaluation technique for the simultaneous

determination of both dependencies.

However, in the most recent assessment

of the system by Chen et al.[142]

a regular

solution model assuming no temperature

dependence for the enthalpy of mixing of

the liquid phase was used for the Figure 18: XRD patterns of Sb-Sn intermetallic alloys

with (a) 30 at% Sb at 280 °C (b) 30 at% Sb at 210 °C

and (c) 70 at% Sb at 300 °C. (taken from Chen et al. [142]

)

- 38 -


thermodynamic modeling. Values for the integral excess entropy of liquid alloys at

632 °C were derived from previously published thermochemical data by Hultgren

et al.[147]

.

Alloys of antimony and tin especially the compound SbSn have been suggested for

applications such as lead-free solders[151, 152]

and electrode materials for lithium-ion

batteries[1-8]

. The application for lithium-ion batteries was already discussed in section

2 Li-Ion Batteries.

In order to use the binary phase diagram as basis for CALPHAD modeling of higher

order systems and to understand the insertion mechanism of lithium-ions into the phase

SbSn, further investigations of the phase diagram are mandatory. The remaining

ambiguities in the system include the exact phase boundaries, the number of actually

existing phases, their limits of stability and a detailed description of their crystal structure

in dependence on composition.

3.2.2 Lithium-Antimony (Li-Sb)

There is only very little information available about the binary system lithium-antimony.

Massalski’s compilation of binary phase diagrams[131]

includes a phase diagram

assessment by Sangster et al.[153]

which is highly hypothetical, because it is based on

calculations assuming that the thermodynamic properties of liquid Li-Sb alloys are the

same as for Li-Bi alloys. Furthermore, the estimated error limits of the calculated melting

point of Li3Sb (1150°C) are +150°C and –50°[154]

. The polymorphic transformation

temperature of Li3Sb is assumed to be >650°C[154]

. It is reported that the phase Li2Sb is

stable at 1000°C, but decomposes at 1200°C[155]

. The resulting phase diagram, which was

used as basis for the investigation of the ternary system Li-Sb-Sn, is shown in Figure 19.

Due to lack of data on this system a detailed investigation is currently under development

in the research group of H. Flandorfer.

- 39 -


3.2.3 Lithium-Tin (Li-Sn)

First investigations of this system were conducted by Masing and Tammann in 1910[156]

.

Many other research groups followed with investigations of the whole[157, 158]

or part of

the phase diagram[57, 65, 159, 160]

. In 1998 Sangster and Bale[161]

reinvestigated the Li-Sn

phase diagram and reported seven intermetallic compounds Li22Sn5, Li7Sn2, Li13Sn5,

Li5Sn2, Li7Sn3, LiSn and Li2Sn5. Gasior et al.[162]

performed emf measurements and found

an additional phase Li8Sn3. X-ray single crystal diffraction and neutron diffraction

investigations by Goward et al.[163]

and Lupu et al.[164]

lead to the proposition of a

different crystal structure for Li22Sn5, with the more appropriate stoichiometry Li17Sn4.

Figure 20 shows the phase diagram of Li-Sn assessed by Li et al.[165]

, which was used as

basis for the investigation of the ternary system Li-Sb-Sn.

Several research groups investigated thermodynamic properties of the system, including

activities of Li and Sn[57, 166]

, enthalpies of formation[57]

, enthalpies of mixing[166-168]

and

Gibbs energies[166]

. A CALPHAD assessment of the phase diagram was performed by

Gasior et al.[169]

, Yin et al.[170]

and Du et al.[171]

.

C alcu lat ed assessed L i -Sb p h ase d iag r am . Jou r n al o f Ph ase E q u i l ib r ia, 14 (4 ), (19 9 3)

Figure 19: Phase diagram of Li-Sb from Massalski's Binary Alloy Phase Diagrams[131]

(assessed by

Sangster et al.[153]

)

- 40 -


Application of Li-Sn alloys as electrode material for lithium-ion batteries have already

been discussed in section 2.4.2.2 Anode Materials.

3.3 The ternary system: Lithium-Antimony-Tin (Li-Sb-Sn)

There are no literature data available for the ternary phase diagram of lithium-antimony-

tin (Li-Sb-Sn). There is one structural description of a ternary compound Li(2+x)Sn1-xSb

which was synthesized by electrochemical lithiation of Ag36.4Sb15.6Sn48[172]

. The therein

proposed structure of Li(2+x)Sn1-xSb is face-centered cubic and has a close resemblance to

the binary phase SbSn. This research group also investigated the differences of

mechanical and electrochemical lithiation of different alloys and proposed an insertion

mechanism for lithium-ions into SbSn. Other investigations of lithium insertion

mechanisms were conducted by Ru et al.[173, 174]

. Sb-Sn alloys and composite materials

with SbSn have also been studied as electrode material of lithium-ion batteries in several

publications[175-177]

, which were discussed previously (see section 2.4.2.2 Anode

Materials).

In order to conduct CALPHAD modeling of the system, some basic experimental data

about the system is mandatory. Therefore, the aim of this work is the investigation of

phase relations in this system, starting with the solubility of lithium in the phase SbSn.

Figure 20: Phase diagram of Li-Sn by Li et al.[165]

- 41 -


4. EXPERIMENTAL SECTION

4.1 Sample Preparation

4.1.1 Binary system Sb-Sn

Primarily the phase diagram, which was published by Predel and Schwermann[132]

(see

section 3.2.1 Antimony-Tin (Sb-Sn), Figure 15. page 34) was used as basis for the

selection of suitable samples. However, the more recently assessed phase diagram by

Chen et al.[142]

(Figure 17, page 36) was always kept in mind for comparison. Table 1

summarizes the chosen sample compositions and lists their IDs, which will be used

throughout the following chapters.

Table 1: Sample compositions of binary Sb-Sn samples

Sample ID

atomic percentage[%]

weight percentage [%]

Sb Sn Sb Sn

SS01 70.00 30.00 70.51 29.49 SS02 55.00 45.00 55.40 44.23 SS03 50.00 50.00 50.37 49.14 SS04 45.00 55.00 45.33 54.06 SS05 30.00 70.00 30.22 68.80 SS06 52.00 48.00 52.38 47.18 SS07 42.00 58.00 42.31 57.01 SS08 40.00 60.00 40.29 58.97

SS09 47.00 53.00 47.35 52.09 SS10 62.00 38.00 62.46 37.35

SS11 58.00 42.00 58.43 41.28

To calculate the corresponding weight percentages to the chosen atomic percentages the

following equations were used:

(21)

( ) (22)

where at%x is the atomic percentage of component x in %, wt%x is the weight percentage

of component x in %, nx and ny are the molar amounts of substance x and y and Mx and

My are the molar masses of x and y in g·mol-1

, respectively. For the original sample

weight the calculated weight percentage was related to 2g total mass of the sample,

- 42 -


respectively 4g total mass in case of sample SS06, which was also used as master alloy

for the preparation of ternary Li-Sb-Sn samples.

For the sample preparation tin-ingot (99.999% pure) and antimony (99.999% pure),

which was melted and filtrated through glass-wool to remove any surface oxides, was

used. First tin was roughly weighed and the amount of antimony was calculated based on

this value. Then antimony was weighed as exactly as possible and added to the sample.

This proceeding yielded a maximal deviation from the supposed atomic percentage of

0.01%, which is considered to be negligible.

The weighed metals were sealed in quartz glass tubes under vacuum, which were purged

thrice with argon gas before final sealing. The quartz ampoules were put into a muffle

furnace at 700 °C for ~24 hours in order to melt the metals. For better mixture of the

elements the quartz ampoules were shaken every 3 hours during the first 8. On the next

day the samples were allowed to furnace cool (fc) and the obtained alloy-pill was

reweighed. Total mass loss after the melting process constituted 0.4% at most, which was

explained through the loss of small alloy droplets formed upon shaking of the quartz glass

tubes.

Figure 21: Graphical representation of the binary Sb-Sn samples and their annealing temperatures (phase

diagram taken from Predel and Schwermann[132]

)

- 43 -


In order to anneal the samples at different temperatures the pills were carefully broken

into smaller pieces. Two fragments were separately sealed into quartz glass tubes as

described before and put into the muffle furnace again. The chosen annealing

temperatures were 400/300°C and 220/170°C, respectively, and the samples were kept at

these temperatures between 20 and 94 days, depending on composition and annealing

temperature. When the annealing duration was over the quartz glass tubes were thrown

into a cold water bath to quench the equilibrium state at the elevated temperature.

Figure 21 shows the positions of the sample composition and their annealing temperature

in the phase diagram of Predel and Schwermann[132]

.

For the preparation of the samples for the different analysis methods, each of the sample

pieces was cut into three fragments using a diamond saw. One fragment was embedded

into a synthetic resin with added carbon for conductivity reasons. The embedded samples

were grinded and polished with an automatic grinding machine, using commercially

available grinding papers (roughness from 600 - 1200 mesh, starting with the roughest,

600, to the finest, 1200) and corundum powder (Al2O3, ∅=1µm) on a soft fabric plate. In

both cases water was used as dispersion and cooling agent. The embedded samples were

analyzed by EPMA.

The samples which were annealed at the lower temperature of each composition were

prepared for differential thermo analysis (DTA). From those samples a piece with a mass

between 100 – 150 mg was chosen and sealed in a special DTA-quartz glass ampoule.

The DTA-quartz glass ampoule has a diameter of ∅=0.8cm and a smaller quartz glass

tube (∅=0.5cm) is attached at the bottom. This attachment is necessary to fix the quartz

glass ampoule in the DTA instrument.

A small fraction of the remaining sample fragments was pulverized with a DURIT

(tungsten-carbide) mortar to get a fine powder. These powders were used for X-ray

powder diffraction measurements. The evaluation of the diffraction patterns led to the

doubt that the samples reached equilibrium state. Therefore some of the samples were

crushed to reasonably small particles, pressed to pellets using a hydraulic press to apply a

load of ~15N and were again annealed in a quartz glass tube at 300°C. The ID of these

samples was extended with the previous annealing temperature, p (for powdered and

pressed) and the subsequent annealing temperature. See Table 2 for a summary of the

annealing temperatures and applied analysis methods of all binary Sb-Sn samples.

- 44 -


Table 2: SbSn samples - annealing temperature and applied analysis

Sample ID atomic percentage[%] annealing

temperature [°C] annealing

duration [d] Analysis Methods

Sb Sn XRD SEM DTA

SS01 70.00 30.00 fc x x

400 30 x x 300 30 x x x

SS02 55.00 45.00

fc x x 300 30 x x

220 30 x x x 300,p,300 45 x x

SS03 50.00 50.00

fc x x 300 30 x x 220 30 x x x

300,p,300 45 x x

SS04 45.00 55.00

fc x x 300 30 x x

220 30 x x x 300,p,300 45 x x

SS05 30.00 70.00 fc x x

300 30 x x 220 30 x x x

SS06 52.00 48.00

fc x x 300 20 x x

170 50 x x x 300,p,300 45 x x

SS07 42.00 58.00

fc x x 300 20 x x 170 50 x x x

300,p,300 45 x x

SS08 40.00 60.00 fc x x

300 20 x x 170 50 x x x

SS09 47.00 53.00

fc

x 300 94 x x 220 89 x x

fc,p,300 42 x x

SS10 62.00 38.00

fc

x 300 94 x x

220 89 x x

fc,p,300 42 x x

SS11 58.00 42.00 fc x x

fc,p,300 45 x x

- 45 -


4.1.2 Ternary system Li-Sb-Sn

Since to date no phase diagram was published for the ternary system Li-Sb-Sn, the chosen

sample compositions were distributed over the whole composition range (see Figure 22).

The first three samples (LSS01-LSS03) were prepared to analyze the solubility of lithium

in the phase SbSn. These three and the sample LSS09 were prepared from the previously

prepared master alloy Sb52Sn48 (SS06). All 15 samples were annealed at 300°C for

different duration. Table 3 lists the compositions of the prepared ternary Li-Sb-Sn

samples and the corresponding annealing durations.

Table 3: Sample composition of ternary Li-Sb-Sn samples

Sample ID

atomic percentage[%] weight percentage [%] annealing duration [d] Li Sb Sn Li Sb Sn

LSS01 10.00 46.80 43.20 65.82 17.56 16.62 22

LSS02 20.00 41.60 38.40 81.25 9.63 9.12 22 LSS03 30.00 36.40 33.60 88.13 6.10 5.77 22 LSS04 5.00 65.00 30.00 47.80 35.43 16.77 28 LSS05 20.00 27.00 53.00 81.18 6.25 12.58 28 LSS06 20.00 76.00 4.00 81.41 17.64 0.95 28 LSS07 30.00 50.00 20.00 88.18 8.38 3.44 28 LSS08 45.00 20.00 35.00 93.39 2.37 4.25 28 LSS09 51.00 25.50 23.50 94.75 2.70 2.55 not finished LSS10 10.00 20.00 70.00 65.65 7.48 26.87 37 LSS11 65.00 32.00 3.00 97.02 2.72 0.26 not finished

LSS12 60.00 30.00 10.00 96.32 2.75 0.94 not finished LSS13 20.00 5.00 75.00 81.07 1.16 17.78 37 LSS14 45.00 5.00 50.00 93.34 0.59 6.06 40 LSS15 60.00 5.00 35.00 96.26 0.46 3.28 40

The equations used for the calculation of the weight percentages from the chosen atomic

percentages are similar to the ones used in case of the binary system:

(23)

( ) (24)

Generally, the total mass of the prepared samples was 1 g, except for samples with higher

lithium content. Due to the low density of lithium and a limited volume of the tantalum

crucibles in which the samples were molten, the total mass of the samples with a lithium

content > 45 at% was limited to 0.5 g.

- 46 -


The ternary alloys were prepared with the same tin-ingot (99.999% pure) and filtered

antimony (99.999% pure) that was used for the other binary alloys. The used lithium

(99.999% pure) was stored in petroleum-ether under argon atmosphere in a glove-box.

Prior to usage it was cleaned by sonication in an acetone bath and any surface oxides

were scratched off with a scissor.

Due to the high reactivity of lithium, also the sample preparation had to be done in a

glove-box under argon atmosphere. First, the amount of lithium was roughly weighed and

this value was used for the calculation of the amount of antimony and tin. The latter were

weighed under normal atmosphere as exactly as possible and introduced into the glove-

box. There, the three metals were combined and put into tantalum crucibles which were

provisorily closed with a tantalum lid. The tantalum crucibles were welded in an arc

furnace under argon atmosphere.

Figure 22: Graphical representation of the compositions of the ternary Li-Sb-Sn sample; the binary phase

diagram data were taken from Predel and Schwermann[132]

(Sb-Sn), Li et al.[165]

(Li-Sn) and

Sangster et al.[153]

(Li-Sb).

- 47 -


The arc furnace has a water-cooled copper plate with a special supplementary part to fix

the tantalum crucible on the plate. After closing the furnace chamber and purging it three

times with argon, the arc was ignited through contact between the moveable negative

electrode made of a thin tungsten rod and the tantalum crucible which served as positive

electrode. By following the gap between tantalum crucible and its lid, they were welded

together. To protect the crucibles from oxidizing at elevated temperatures, they were

additionally sealed in quartz glass ampoules. The in this way sealed samples were

annealed at 300°C in a muffle furnace for 22 to 40 days. Figure 22 shows the positions of

the samples in an isothermal section at 300 °C of the phase diagram.

After the annealing duration the samples were quenched, the quartz glass tubes were

broken and the crucibles were reintroduced to the glove-box. In the glove-box the

crucibles were opened with a bolt cutter, and through careful deformation of the crucible

with flat pliers the sample was extracted. In some cases (LSS05, LSS08, LSS10) only a

very small amount of sample could be removed from the crucible, because the alloys

were stuck to the crucible wall. The samples LSS10 and LSS13 were additionally very

ductile and could not be appropriately grinded to powders.

The other samples (except LSS09, LSS11 and LSS12, which are still in the muffle

furnace for annealing, see section 5.2.1 XRD) were pulverized with a DURIT mortar

under argon atmosphere to yield a fine powder. These powders were analyzed by X-ray

powder diffraction, using a special sample holder with a plastic dome, to prevent the

powders from oxidizing during the measurement.

- 48 -


4.2 Analysis Methods

4.2.1 X-ray Diffraction (XRD)

4.2.1.1 Basic principles

Diffraction is generally a combination of scattering and interference of waves. The

requisite is that the wavelength has to be in the same range as the distances between the

scattering centres. X-ray diffraction is a combination of interaction of X-rays with the

electrons localized at the atoms of a crystal. It utilizes the fact that the wavelengths of

X-rays have the same order of magnitude as the distances between the lattice planes in a

crystalline solid, which is the reason for occurring diffraction. By evaluating the obtained

diffraction patterns information about the crystal structure can be drawn.

4.2.1.1.1 X-rays

The wavelengths of X-rays lie within a range of 10-8

m to 10-12

m, which corresponds to

an energy of 200 eV to 1 MeV (1 eV = 1.602·10-19

J)[178]

. X-rays are produced in an X-ray

tube by collision of high speed electrons with matter. The general structure of an X-ray

tube is shown in Figure 23. Electrons, which are produced by heating of a tungsten

filament cathode, are accelerated towards a water cooled anode. Most of the energy that is

transferred upon collision of electrons and anode is transformed into heat and only a small

part (less than 1%)[178]

is emitted in form of X-rays.

A typical X-ray spectrum is shown in Figure 24(a). The spectrum consists of the

continuous spectrum (or white radiation) and some characteristic wavelengths. The

continuous part of the X-ray spectrum originates from electrons losing their energy upon

Figure 23: Schematic diagram of an X-ray tube (adapted from Suryanarayana[178]

)

- 49 -


several different collisions with atoms,

therefore emitting a variety of

wavelengths. Whereas the characteristic

lines are caused by the ejection of an

inner-orbital electron in an atom and the

subsequent reoccupation of the obtained

hole with an outer-orbital electron, which

is accompanied by the emission of an

X-ray photon with an energy equal to the

corresponding difference of the energy

levels. Dependent on the energy levels

involved, one can distinguish between

particular characteristic lines, Figure 24(b).

The most important lines for X-ray

diffraction are the Kα and Kβ-lines, which

arise from a transition to the K-shell

starting from the L or M-shell,

respectively. This nomenclature is based

on the Bohr model of atoms, were

electrons are orbiting the nucleus in shells

of different distance to the centre. In

addition to this differentiation, the Kα

radiation itself splits up into two separate

lines (Kα1 and Kα2). This is caused by the presence of subshells in the L-shell, which

correspond to the 2p-orbitals (LII and LIII). The intensities of the characteristic lines are

calculated based on the following equation:

(25)

where B is a proportionality constant, i is the tube current corresponding to the number of

electrons per second hitting the target, V is the applied potential, VK the potential required

to eject an electron from the K-shell and n a constant with a value between 1 and 2,

corresponding to a particular value of V.

The relative intensities of the characteristic lines can be calculated based on the

Figure 24: (a) characteristic X-ray spectrum and (b)

possible electron transitions based on Bohr’s model

(adapted from Suryanarayana[178]

)

- 50 -


probabilities of the electrons to be in a particular energy level. A transition from the 2s

orbital to 1s is forbidden. The p-orbitals contain six electrons overall and are splitted in

two narrow levels LII and LIII. Two electrons occupy LII and four electrons are located in

LIII, making a transition starting from the LIII-level more probable in comparison to the

LII-level. A transition from the M-level is again less likely and occurs with only one fifth

of the probability of a 2p–1s transition. The expected relative intensities for the K-series

are therefore Kα1:Kα2:Kβ = 4:2:1[179]

.

For the purpose of X-ray diffraction monochromatic radiation (radiation with only one

characteristic wavelength) is preferred. Table 4 lists the characteristic wavelengths of

different metals which are commonly used for X-ray diffraction. The most commonly

used is copper Kα radiation. Due to its higher energy compared to Lα-radiation, absorption

is less likely and scattering is preferred. The easiest way to filter out unwanted

wavelengths is the usage of particular metal foils, with an absorption edge between the Kα

and Kβ-lines. In case of copper radiation nickel foil is used to remove the Kβ-radiation.

Another possibility is the usage of a single crystal monochromator. It consists of a crystal

with known lattice spacing which is oriented in a specific way so that only Kα1-radiation

is diffracted.

Table 4: Commonly used X-ray wavelengths of different metals[178]

Element X-ray wavelength [nm]

Kα (weighted average) Kα1 Kα2 Kβ

Co 0.179026 0.178897 0.179285 0.162079 Cu 0.154184 0.154056 0.154439 0.139222 Mo 0.071073 0.070930 0.071359 0.063229

When X-rays hit an atom they are diffracted by the electrons around the nucleus. This

process is actually a combination of absorption and reemission (scattering) of the incident

radiation and subsequent interference of the electromagnetic waves scattered by electrons

located at the atoms. Statistically one can consider the atoms as scattering centres in the

lattice planes of the crystal. The angle at which constructive interference occurs is called

Bragg angle θ and the relation between wavelength λ of the incident beam, interplanar

spacing d of the lattice planes and the Bragg angle is given by equation (26):

Bragg’s law: (26)

As can be seen in Figure 25 the lattice planes of the crystal act as reflective mirror for the

- 51 -


incidents X-rays. The condition to obtain a diffracted wave is that the scattered waves of

different lattice planes are in phase with each other. Therefore the path difference δ

(δ = DC + ED) has to be an integral multiple of the wavelength λ (see left side of

Bragg’s law (26)). By means of trigonometry the path difference δ can also be

represented as a function of the interplanar spacing d (right side of Bragg’s law (26)).

In the crystal structure the lattice planes are described by the Miller indices (hkl) which

are derived from the reciprocal intersections of the lattice planes with the lattice

parameters a, b and c. For example a plane is intersecting the lattice parameters at a=1,

b=2 and is parallel to c. First the reciprocal values are determined and then the fractions

are eliminated, resulting in the Miller indices (210), see also Table 5.

Table 5: Derivation of Miller indices[22]

a b c

Intercepts 1 2 ∞

Reciprocals 1 ½ 0 Clear fraction 2 1 0

4.2.1.2 Bruker D8 Powder X-ray Diffractometer

The diffractometer used during this work was a Bruker D8 powder diffractometer with

θ/2θ-geometry. This means that X-ray source, specimen and X-ray detector all lie on the

circumference of the focusing circle (see Figure 26(a)), and that the X-ray source is fixed

while specimen and detector move. If the specimen is rotated by an angle of θ the detector

Figure 25: Diffraction of X-rays by a crystal (adapted from Suryanarayana[178]

)

- 52 -


needs to rotate by an angle of 2θ, which is accompanied by a change of the radius of the

focusing circle. However, the radius of the diffractometer circle or goniometer circle is

fixed. The specimen is located in the centre of the diffractometer circle, whereas X-ray

source and detector are located on its circumference.

The utilized radiation was produced in an X-ray tube with a copper target at an

accelerating voltage of 40 V and an electronic current of 40 mA. To filter out unwanted

wavelengths a nickel-filter was used, so that only Kα1 and Kα2-lines remained. With the

aid of some vaseline the powdered sample was loaded onto a specimen holder, consisting

of a silicon mono-crystal cut in a certain direction in order to avoid diffraction lines from

the Si-crystal. During the measurement the specimen holder was rotated around its own

Figure 26: (a) Geometry of an X-ray diffractometer and (b) arrangement of slits in an X-ray diffractometer

(adapted from Suryanarayana[178]

)

- 53 -


axis in order to provide even irradiation of the specimen and additional averaging over the

randomly distributed powder particles.

Before and after the interaction with the sample the X-rays pass several slits in order to

define and collimate the radiation. Figure 26(b) illustrates the arrangement of slits in an

X-ray diffractometer. The soller slits ensure parallel alignment of the X-rays, while the

divergence slit limits the divergence (= width) of the incident beam. Before the X-rays are

registered by the detector they pass an anti-scatter slit to improve the signal to

background ratio, a receiving slit to define the width of the beam that enters the detector

and another set of soller slits. The wider the receiving slit, the higher is the intensity of

the reflections, but this is also accompanied by some loss of resolution.

The diffracted X-rays are finally registered in a detector. During this work a “Lynx eye”-

strip detector was used. This detector comprises several parallel arranged silicon strips,

which detect an X-ray quant by formation of electron-hole pairs creating a charge pulse

that can be measured. The advantage of a strip-detector compared to a usual point

detector is, that a certain range of diffraction angles is counted simultaneously and the

obtained intensities at a specific angle are added up while the detector is moving. This

results in high resolution X-ray patterns in much shorter measurement times. The

obtained diffraction pattern is a diagram of peak intensity vs. diffraction angle, 2θ. The

evaluation of the patterns was done with the software Topas3® provided by Bruker AXS.

4.2.1.3 Rietveld Refinement

Topas3® uses the Rietveld refinement for the interpretation of X-ray diffraction patterns.

The Rietveld refinement is a mathematical least square method to compare calculated

diffraction patterns based on previously entered structure files with experimental patterns.

To improve the fit of the calculated pattern, several parameters are available for

adjustment. The most important equations involved in the calculations are given below

(equations (27) to (30)).

Intensity: | | (

)

(27)

Structure

Factor: ∑

(28)

- 54 -


Square error:

∑

∑ (29)

Calculated

intensity

(at point i):

∑| |

(

)

(30)

p................................. Multiplicity factor of an hkl plane set

(

).............. Lorentz-polarisation factor

................... Temperature factor

yOi............................... Observed intensity at point i

wi............................... Weight factor ⁄

yBi............................... Background at point i

S…………………… Scaling factor (for each phase)

Φ................................ Profile function

Phkl.............................. Factor for preferred orientation

A................................ Absorption function

Sr................................ Function for surface roughness

E................................. Extinction factor

The refinement process was usually done in the following order:

1. Set-up of instrumental data and measurement parameters.

2. Generation or loading of structure files for the expected structures. Structure data

were obtained from databases such as Pearson’s Handbook of Crystallographic

Data for Intermetallic Phases or the ICSD database (FindIt® software).

3. Calculation of the theoretical pattern and refinement of the provided structural

parameters:

a. Scale factor

b. Lattice parameters

c. Crystal size

d. Atom sites (if required)

4. Checking of the Rw-value of the refinement.

- 55 -


4.2.2 Difference Thermal Analysis (DTA)


The measurement of a temperature difference occurring between a test sample and an

inert reference material upon application of an identical temperature program is called

difference thermal analysis (DTA). This thermoanalytical technique is based on the

absorption or emission of heat that accompanies a transformation process of the test

sample. Therefore DTA is a useful method for the determination of phase transformations

and their corresponding temperatures. A phase transformation can be either exothermic

(release heat) or endothermic (absorb heat) and is based on an invariant or non-invariant

reaction. Invariant reactions are characterized by the absence of degrees of freedom

according to the Gibbs phase rule (31)[180]

:

Gibbs Phase Rule: if (31)

where P is the number of phases, F are the degrees of freedom, C is the number of

components and p is the pressure. In case

of an invariant reaction (F=0) the

temperature has to be constant until the

transformation process is finished.

The distinction between invariant and

non-invariant reactions is important for

the evaluation of the obtained diagram.

The signal of an invariant reaction is

characterized by a sharp and linear

increase, which is evaluated by the onset

or extrapolated onset of the peak, whereas

non-invariant reactions have a more

Gaussian looking signal and the first

deviation from the base line (cooling) or

the peak maximum (heating) are used as

characteristic temperature.

Figure 27 shows the general structure of a differential thermal analyzer[181]

. It is

comprised by a tubular furnace and a ceramic specimen holder with thermocouples at the

ends to measure the temperature difference between sample and reference. Usually the

Figure 27: Schematic diagram of a differential

thermal analyzer (adapted from Speyer [181]

)

- 56 -


difference thermocouple voltage is not converted into a temperature, but directly plotted

against the temperature to obtain the DTA-curve.

4.2.2.2 Differential Thermal Analysis Netzsch 404 S

The DTA Netzsch 404S was used for the measurements on the binary system Sb-Sn. The

samples were sealed in evacuated DTA-quartz glass crucibles (see section 4.1.1 Binary

system Sb-Sn) and the reference material was zirconium. Due to the closed quartz glass

crucibles a protective argon-gas flow was not required. The device was calibrated using

the melting temperatures of four different metals: indium (In), tellurium (Te), antimony

(Sb) and silver (Ag). The applied temperature program is illustrated in Figure 28. Starting

at room temperature the sample was heated to the annealing temperature with a rate of

15 K.min-1

, the temperature was kept there for 30 minutes, followed by heating to the

maximum temperature (between 450 and 700 °C) and cooling to Tmin = 100 °C with a

slope of 5 K.min-1

. The heating and cooling cycle was repeated one more time before

cooling down to room temperature.

The software Calisto®

provided by Setaram was used for the evaluation of the DTA-

signals. It enables the evaluation of overlapping peaks with the included peak

deconvolution tool.

Figure 28: Temperature program for the DTA

- 57 -


4.2.3 Scanning Electron Microscopy (SEM) and Electron Probe

Microanalysis (EPMA)


Scanning electron microscopy

(SEM) and electron probe

microanalysis (EPMA) are non-

destructive analysis techniques

that enable the visualization of

the surface of a sample similar

to optical light microscopy, but

with much higher

magnification, and the analysis

of the composition of small

areas (1-2 µm2) of the sample.

Both techniques use an electron

beam to scan the surface of the

sample and to cause a variety of scattering effects. The electron beam can be produced

either by a thermionic cathode, which consists of a tungsten filament or LaB6 tip and

emits electrons upon heating or by a field-effect cathode that emits electrons upon

application of a high electric field strength[180]

. The acceleration voltage of the electron

beam varies between 5 and 40 kV, dependent on the elements present and the excited

spectral lines.

In Figure 29 the general instrumental setup of a scanning electron microscope / electron

probe micro-analyzer is shown. After passing some electron optics to focus the beam and

direct it to a specific area, the electrons hit the sample surface and cause a range of

effects, such as secondary electrons, backscattered electrons, Auger electrons, continuous

X-rays (white radiation), characteristic X-rays and fluorescent X-rays[180]

. The interaction

volume, from which these effects originate, is dependent on the material, the electron

energy and the type of effect. For example backscattered electrons (BSE) have a higher

penetration depth and leave the sample after some elastic and inelastic scattering with

energy of 80 to 90 % of the incident beam. Whereas secondary electrons (SE), which

result from atom ionization along the path of the incident beam, have lower energy and

Figure 29: EPMA - instrumental setup (taken from lecture material

of K. Richter[180]

)

- 58 -


can only leave the sample when they

are produced in close proximity to the

surface (Figure 30).

The contrast arising from secondary

electrons is based on the topography of

the specimen surface, resulting in a

micrograph showing the heights and

depths of the sample surface. The

contrast of backscattered electrons

arises from the (average) atomic

number of the atoms located in the scanned area. A higher atomic number and therefore

higher backscattering coefficient, results in a brighter BSE image. Imaging with back

scattered electrons can therefore provide a phase contrast depending on the sample

composition. It gives a similar picture to a conventional light microscopy image, but

much higher magnification can be achieved.

There are two different detection techniques for the determination of the specimen

composition. The first one is energy dispersive spectroscopy (EDX) and the second one

wavelength dispersive spectroscopy (WDX). Both are based on the analysis of the

characteristic X-ray lines after excitation by the incident electron beam. In the EDX

method the X-ray photons are counted by a solid state detector by formation of

electron/hole pairs in semiconducting silicon. The detection occurs fast enough to be able

to distinguish single photon impacts. Thus it provides information about the energy as

well as the intensity of the X-ray radiation. Cobalt or copper are usually used to calibrate

the electron current as well as the X-ray spectral resolution. The formation energy of

electron/hole pairs in silicon is ε = 3.8 eV and the maximum number of pairs is therefore

⁄ [180]. This limits the resolution of this method due to the possible overlap of the

characteristic lines of different elements. However, the advantage of this method in

comparison to WDX is the faster acquisition of the spectra.

The WDX detector avoids the problem of interfering spectral lines by using a

monochromator crystal and counting the signals in a conventional scintillation detector.

Another advantage is the possibility of analyzing light elements down to beryllium which

is not possible with an EDX detector. On the other hand different wavelength ranges need

Figure 30: Production and path of backscattered and

secondary electrons in the specimen (taken from lecture

material of K. Richter[180]

)

- 59 -


different monochromator crystals making this detector more expensive. Additionally,

crystal and detector need to move along the focusing circle in order to detect the different

wavelengths, resulting in much longer acquisition times compared to EDX.

Just like any other analysis technique, EPMA needs calibration with standard substances.

The calibration substances need to be homogeneous, very well characterized and their

measurements need to be done at the same conditions as the samples. Furthermore,

occurring matrix effects, arising from the different behavior of electrons and X-rays in

different materials, need to be corrected using the ZAF matrix correction, equation (33):

“k-ratio”:

(32)

ZAF matrix correction:

[ ] (33)

Here Cx and C(x) are the mass concentrations of the element x in the sample and standard

substance, respectively. Ix and I(x) are the intensities of the characteristic lines of the

element x in the sample and standard substance. As a consequence, the “k-ratio” gives a

first approximation of the ratio of mass concentrations of the element x in the sample and

standard. This value has to be corrected with the ZAF matrix correction, which includes

coefficients corresponding to the average atomic number (Z), the absorption (A) and the

fluorescence (F) of the sample matrix. These terms are calculated by mathematical

models in an iterative manner. The correction yields in an improved value for the weight

percentage of the elements in the analyzed area. Their sum which should be close to 100

weight percent is an important quality criterion of the measurement.

4.2.3.2 Scanning Electron Microscope

Zeiss Supra 55 VP

During this work the scanning electron

microscope Zeiss Supra 55 VP was used,

see Figure 31[182]

. The acceleration voltage

was 15-20 kV and an EDX detector was

used for EPMA. The calibration was

carried out with tin and an alloy of indium

and antimony (InSb, 1:1).

Figure 31: Scanning electron microscope Zeiss

Supra 55 VP (taken from Faculty Centre for Nano

Structure Research[182]

)

- 60 -


5. RESULTS AND DISCUSSION

5.1 Sb-Sn

5.1.1 XRD

In the binary antimony-tin system 10 samples in the composition range of 30 to

70 at% Sb were prepared and annealed at two different temperatures (170 and 300 °C,

220 and 300 °C or 300 and 400 °C). After an annealing duration of 20 to ~90 days the

samples were quenched and analyzed by X-ray powder diffraction. The obtained results

are summarized in Table 6. The generally rather broad peaks observed in all the

diffraction patterns raised concerns whether the samples reached full equilibrium state or

not. To resolve this uncertainty an additional sample and some of the previously prepared

and annealed samples were ground to reasonably small particles, presses to pills and

annealed at 300°C (section 4.1.1 Binary system Sb-Sn), see Table 7 for the XRD-results.

The first thing to notice in Table 6 is the absence of the binary phase Sb2Sn3 in the

samples SS04, SS05, SS07 and SS08. All reflections in their powder diffraction patterns

could be described using the binary phase SbSn in cubic or rhombohedral structure.

Additionally, the samples SS07 and SS08 contained tin, originating from the quenched

liquid phase, although they should be located in the two phase field of SbSn and Sb2Sn3,

according to Predel and Schwermann[132]

. It has to be mentioned that the cubic structure

of SbSn was preferably found at higher temperatures (and in the quenched samples);

however, a detailed discussion about the crystal structure of SbSn will follow later in this

section. The number of phases found in all of the four samples satisfied the Gibbs phase

rule for binary systems.

The samples SS02, SS03, SS06 and SS09 are located in the homogeneity range of the

SbSn phase and should therefore contain only one phase. Despite that the sample SS06

annealed at 170 °C showed small intensities of Sn in the diffraction pattern, suggesting

that the sample was not in equilibrium. The as cast samples (without annealing) did not

reach the equilibrium state and hence show the phase SbSn with Sn or Sn and Sb,

respectively. The last samples that were analyzed during the first run were SS01 and

SS10 (annealing temperatures, see Table 6), which are placed in the two phase field of

SbSn and solid solution of Sn in Sb. They both satisfy the Gibbs phase rule and are in

good agreement with the previously published phase diagram.

- 61 -


Ta

ble

6 :

XR

D r

esu

lts

of

the

bin

ary

Sb

-Sn

sa

mp

les

ord

ered

fro

m l

ow

est

to h

igh

est

an

tim

ony-f

ract

ion

R

-Bra

gg

6.8

36

4.7

50

6.2

98

4.2

97

6.6

89

9.8

43

6.0

15

4.4

10

5.8

90

5.0

44

3.5

9

5.2

52

6.0

70

5.2

79

5.5

85

3.5

96

3.8

42

3.0

83

3.9

63

4.3

20

3.2

43

5.0

64

7.7

84

8.3

16

Latt

ice

Par

ame

ters

[Å

] c

(13

)

(42

)

(15

)

(11

)

(55

)

(33

)

(11

)

(18

)

(49

)

(37

)

(10

)

(40

)

(37

)

3.1

81

46

3.1

80

94

5.3

39

82

3.1

83

07

3.1

80

63

3.1

80

49

5.3

31

56

3.1

80

33

3.1

81

39

3.1

82

35

5.3

32

46

3.1

80

54

3.1

81

76

a

(17

)

(17

)

(79

)

(51

)

(85

)

(14

)

(90

)

(65

)

(80

)

(39

)

(47

)

(22

)

(83

)

(59

)

(16

)

(46

)

(47

)

(48

)

(16

)

(45

)

(13

)

(79

)

(79

)

(99

)

6.1

27

84

5.8

36

66

6.1

27

69

7

5.8

34

88

4.3

25

36

9

5.8

40

2

6.1

30

53

8

5.8

34

16

6.1

28

3

5.8

35

03

4.3

23

60

8

5.8

34

87

6.1

30

14

6

5.8

35

97

6.1

32

84

5.8

39

88

4.3

23

97

2

5.8

35

47

6.1

33

32

5.8

38

97

6.1

37

29

6.1

26

86

6

6.1

30

97

2

6.1

33

18

2

Nr.

22

5

14

1

22

5

14

1

16

6

14

1

22

5

14

1

22

5

14

1

16

6

14

1

22

5

14

1

22

5

14

1

16

6

14

1

22

5

14

1

22

5

22

5

22

5

22

5

Spac

e G

rou

p

F m

-3

m

I 41

/a m

d S

F m

-3

m

I 41

/a m

d S

R -

3 m

H

I 41

/a m

d S

F m

-3

m

I 41

/a m

d S

F m

-3

m

I 41

/a m

d S

R -

3 m

H

I 41

/a m

d S

F m

-3

m

I 41

/a m

d S

F m

-3

m

I 41

/a m

d S

R -

3 m

H

I 41

/a m

d S

F m

-3

m

I 41

/a m

d S

F m

-3

m

F m

-3

m

F m

-3

m

F m

-3

m

Stru

ctu

re

Typ

e

NaC

l

Sn

NaC

l

Sn

Hg

(LT)

Sn

NaC

l

Sn

NaC

l

Sn

Hg

(LT)

Sn

NaC

l

Sn

NaC

l

Sn

Hg

(LT)

Sn

NaC

l

Sn

NaC

l

NaC

l

NaC

l

NaC

l

Frac

tio

n [

%]

87

13

96

4

75

25

96

,67

3,3

3

94

,26

5,7

4

94

,56

5,4

4

96

,08

3,9

2

95

,76

4,2

4

96

,98

3,0

2

97

3

10

0

10

0

10

0

10

0

Ph

ase

SbSn

_cu

b

Sn

SbSn

_cu

b

Sn

SbSn

_rh

om

Sn

SbSn

_cu

b

Sn

SbSn

_cu

b

Sn

SbSn

_rh

om

Sn

SbSn

_cu

b

Sn

SbSn

_cu

b

Sn

SbSn

_rh

om

Sn

SbSn

_cu

b

Sn

SbSn

_cu

b

SbSn

_cu

b

SbSn

_cu

b

SbSn

_cu

b

Tem

pe

ratu

re

tre

atm

en

t [°

C]

fc

30

0

22

0

fc

30

0

17

0

fc

30

0

17

0

fc

30

0

22

0

30

0

22

0

Co

mp

osi

tio

n [

at%

]

Sb

30

40

42

45

47

Sn

70

60

58

55

53

ID

SS0

5

SS0

8

SS0

7

SS0

4

SS0

9

- 62 -


Ta

ble

6:

XR

D r

esu

lts

of

the

bin

ary

Sb

-Sn

sa

mp

les

ord

ered

fro

m l

ow

est

to h

igh

est

an

tim

ony-f

ract

ion

(co

nti

nu

ed)

R-B

ragg

2,8

62

3,4

86

3,1

03

5,6

60

4,5

57

2,2

76

3,0

68

3,4

68

5,1

55

4,1

38

3,9

90

2,7

44

3,5

00

2,9

14

3,5

90

4,5

62

4,4

86

9,0

87

3,6

66

3,3

55

4,1

47

2,3

41

3,9

12

2,3

25

Latt

ice

Par

ame

ters

[Å

] c

(12

)

(15

)

(20

)

(18

)

(11

)

(18

)

(18

)

(31

)

(15

)

(15

)

(15

)

(13

)

(77

)

(12

)

(13

)

(78

)

(72

)

(20

)

(53

)

(18

)

3,1

81

3

5,3

45

22

11

,43

92

5,3

49

15

3,1

81

7

5,3

46

97

5,3

42

3,2

25

8

11

,43

65

5

,34

43

2

5,3

60

97

5,3

55

02

11

,44

76

2

5,3

67

85

11

,45

01

11

,43

75

3

11

,45

16

4

5,3

90

04

11

,44

23

6

5,3

62

68

a

(20

)

(15

)

(87

)

(22

)

(43

)

(97

)

(13

)

(98

)

(78

)

(37

)

(33

)

(20

)

(63

)

(91

)

(59

)

(15

)

(56

)

(24

)

(21

)

(25

)

(18

)

(13

)

(11

)

(83

)

6,1

36

04

5,8

38

9

4,3

27

69

9

6,1

33

42

4,2

57

94

4,3

27

57

0

5,8

41

1

4,3

28

75

5

4,3

24

15

2

5,8

60

4

4,2

56

07

6,1

34

21

4,3

23

55

7

4,3

25

92

4,3

23

39

4,2

61

34

4,3

22

4,2

58

99

4,2

65

66

1

6,1

38

27

01

4,2

59

84

4,3

23

76

4,2

60

05

98

4,3

21

98

46

Nr.

22

5

14

1

16

6

22

5

16

6

16

6

14

1

16

6

16

6

14

1

16

6

22

5

16

6

16

6

16

6

16

6

16

6

16

6

16

6

22

5

16

6

16

6

16

6

16

6

Spac

e G

rou

p

F m

-3

m

I 41

/a m

d S

R -

3 m

H

F m

-3

m

R -

3 m

H

R -

3 m

H

I 41

/a m

d S

R -

3 m

H

R -

3 m

H

I 41

/a m

d S

R -

3 m

H

F m

-3

m

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

F m

-3

m

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

Stru

ctu

re

Typ

e

NaC

l

Sn

Hg

(LT)

NaC

l

As

Hg

(LT)

Sn

Hg

(LT)

Hg

(LT)

Sn

As

NaC

l

Hg

(LT)

Hg

(LT)

Hg

(LT)

As

Hg

(LT)

As

As

NaC

l

As

Hg

(LT)

As

Hg

(LT)

Frac

tio

n [

%]

98

2

10

0

10

0

8

91

1

10

0

98

,89

1,1

1

16

84

10

0

10

0

83

,15

16

,85

93

,32

6,6

8

47

53

27

73

31

69

Ph

ase

SbSn

_cu

b

Sn

SbSn

_rh

om

SbSn

_cu

b

Sb

SbSn

_rh

om

Sn

SbSn

_rh

om

SbSn

_rh

om

Sn

Sb

SbSn

_cu

b

SbSn

_rh

om

SbSn

_rh

om

SbSn

_rh

om

Sb

SbSn

_rh

om

Sb

Sb

SbSn

_cu

b

Sb

SbSn

_rh

om

Sb

SbSn

_rh

om

Tem

pe

ratu

re

tre

ate

me

nt

[°C

]

fc

30

0

22

0

fc

30

0

17

0

fc

30

0

22

0

30

0

22

0

fc

40

0

30

0

Co

mp

osi

tio

n [

at%

]

Sb

50

52

55

38

70

Sn

50

48

45

62

30

ID

SS0

3

SS0

6

SS0

2

SS1

0

SS0

1

- 63 -


Ta

ble

7:

XR

D r

esu

lts

of

the

add

itio

na

lly

po

wd

ered

. p

ress

ed a

nd

rep

eate

dly

ann

eale

d b

inary

Sb

-Sn

sa

mp

les

ord

ered

fro

m l

ow

est

to h

igh

est

an

tim

on

y-f

ract

ion

R-B

ragg

7.2

08

3.8

39

5.1

92

9.3

26

7.0

42

3.5

09

3.3

59

4.2

38

3.5

9

4.5

62

Latt

ice

Par

ame

ters

[Å

] c

(11

)

(23

)

(93

)

(22

)

(10

)

(84

)

(11

)

(14

)

(13

)

(77

)

5.3

30

37

3.1

80

48

5.3

25

31

1

5.3

26

45

5.3

41

37

5.3

45

22

9

5.3

45

82

5.3

54

88

5.3

55

01

11

.44

76

2

a

(48

)

(28

)

(43

)

(95

)

(47

)

(39

)

(48

)

(62

)

(59

)

(15

)

4.3

26

60

4

5.8

36

97

4.3

30

04

2

4.3

27

38

8

4.3

23

51

6

4.3

23

16

2

4.3

22

84

5

4.3

22

45

1

4.3

23

39

4.2

61

34

Nr.

16

6

14

1

16

6

16

6

16

6

16

6

16

6

16

6

16

6

16

6

Spac

e G

rou

p

R -

3 m

H

I 41

/a m

d S

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

R -

3 m

H

Stru

ctu

re

Typ

e

Hg

(LT)

Sn

Hg

(LT)

Hg

(LT)

Hg

(LT)

Hg

(LT)

Hg

(LT)

Hg

(LT)

Hg

(LT)

As

Frac

tio

n [

%]

93

.15

6.4

9

10

0

10

0

10

0

10

0

10

0

10

0

83

.14

16

.86

Ph

ase

SbSn

_rh

om

Sn

SnSn

_rh

om

SbSn

_rh

om

SnSn

_rh

om

SbSn

_rh

om

SbSn

_rh

om

SbSn

_rh

om

SbSn

_rh

om

Sb

Tem

pe

ratu

re

tre

atm

en

t [°

C]

30

0, p

, 30

0

30

0, p

, 30

0

fc, p

, 30

0

30

0, p

, 30

0

30

0, p

, 30

0

30

0, p

, 30

0

fc, p

, 30

0

fc, p

, 30

0

Co

mp

osi

tio

n [

at%

]

Sb

42

45

57

50

52

55

58

62

Sn

58

55

43

50

48

45

42

38

ID

SS0

7

SS0

4

SS0

9

SS0

3

SS0

6

SS0

2

SS1

1

SS1

0

- 64 -


The distinction between cubic and rhombohedral structure of the phase SbSn was based

on the splitting of certain reflections in the diffraction pattern, see Figure 32. The

reflections corresponding to the hkl-planes (022) and (222) in the cubic structure (see

sample SS07 in Figure 32) split up into two reflections, (012), (110) and (003), (021), in

the rhombohedral structure (see sample SS01 in Figure 32), respectively. A closer look on

the structures revealed that rhombohedral SbSn is a slightly distorted version of the cubic

NaCl-type structure. The structural information used in the refinement of the diffraction

patterns is based on the hexagonal description of this rhombohedral version. The detailed

structure information of the cubic and rhombohedral versions of SbSn is presented in

Table 8 and Table 10. As can be seen in Table 10 the Sb and Sn atoms occupy the same

atomic position, but with a site occupancy factor (SOF) of 0.49 and 0.51[140]

, respectively.

This is legitimate, because Sb and Sn are neighbors in the periodic table of elements, and

therefore exhibit a very similar scattering factor, which makes it impossible to distinguish

between the ordered and disordered structure by Powder-XRD-analysis. For the same

reason a simple-cubic Po-type structure (disordered) instead of the ordered NaCl-type

structure could not be distinguished by refinement of the diffraction patterns.

Figure 32: Part section of the diffraction patterns of the binary Samples SS01, SS03 and SS07 (annealed at

300 °C), depicting the splitting of reflexes that occurs upon distortion of the cubic to the rhombohedral

structure of SbSn.

- 65 -


Table 8: Structural details for the cubic phase SbSn

Phase: SbSn_cub

Structure Type: NaCl

Space Group: F m-3m (166)

Pearson Symbol: cF8

Lattice Parameters [Å]: a(Lit.) = 6.132

a(exp.) = 6.13342

Atom Nr OX Site x y z SOF

Sn 1 0 4b 0.5 0.5 0.5 1

Sb 1 0 4a 0 0 0 1

Table 9: Structural details for the small simple-cubic (Po-type) and large rhombohedral (GeTe-type)

structures of the phase SbSn

Phase: SbSn_rhom_large

Structure Type: GeTe (supercell)

Phase: SbSn_cub_small

Space Group: R -3mR (166)

Structure Type: Po

Pearson Symbol: hR8

Space Group: P m-3m (221)

Lattice Parameters: (rhombohedral)

a(Lit.)= 6.132

Pearson Symbol: cP

ϕ(Lit.)= 89.708

Lattice Parameters: a(Lit.)= 3.066

Lattice Parameters: (hexagonal)

a(Lit.)= 8.6502


c(Lit.)= 10.6752

Sn 1 0 1a 0 0 0 0.5

Sb 1 0 1a 0 0 0 0.5


Sn 1 0 4b 0.5 0.5 0.5 1

Sb 1 0 4a 0 0 0 1

Table 10: Structural details for the disordered rhombohedral phase SbSn

(hexagonal and rhombohedral description)

Phase:

SbSn_rhom

Structure Type:

Hg (LT)

Space Group:

R -3mH (166)

Pearson Symbol: hR1

Lattice Parameters [Å]: (hexagonal)

a(Lit.) = 4.3251 c(Lit.) = 5.3376

a(exp.) = 4.323516 c(exp.) = 5.34137

Lattice Parameters [Å]: (rhombohedral)

a(Lit.) = 3.066 ϕ(Lit.) = 89.708

a(exp.) = 3.0661 ϕ(exp.) = 89.67


Sb 1 0 3a 0 0 0 0.49

Sn 1 0 3a 0 0 0 0.51

Figure 33: Scheme for the sequence of distortion and loss of order in the phase SbSn to get from the not

distorted, ordered structure (NaCl-type) to the distorted and disordered structure (Hg(LT)-type). Literature

data of the lattice parameters was taken from Noren et al.[140]

.

1a) Loss of order 1b) Distortion

2b) Loss of order 2a) Distortion

- 66 -


Figure 33 shows a schematic diagram, where the sequence of distortion and loss of order

in the phase SbSn is illustrated. Starting from the cubic NaCl-type structure, there are two

possibilities: a) loss of order, resulting in the simple-cubic Po-type structure, where Sb

and Sn atoms are statistically occupied, or b) distortion, resulting in a large rhombohedral

structure. After subsequent distortion of the Po-type structure or loss of order in case of

the large GeTe-supercell the resulting structure is in both cases the smaller rhombohedral

cell (Hg(LT)-type structure) that is used in the refinement throughout this work.

With the help of some simple mathematical expressions the lattice parameters of the

cubic and rhombohedral unit cells can be converted into each other, see equations (34)

and (35). Figure 34 illustrates the distortion of the cubic cell to get the rhombohedral cell

and the conversion of both into the hexagonal cell description.

√

(34)

√

(35)

The distortion of the cubic unit cell can be either described by the rhombohedral angle φ

or as ratio ch/ah of the hexagonal lattice parameters. In case of the cubic unit cell with

φ = 90° the ratio ⁄ √ . The angle φ (rhombohedral setting) or the ratio

ch/ah (hexagonal setting) decrease with increasing distortion of the unit cell.

As can be seen in Figure 32 the reflections of the SbSn phase were rather broad in

comparison to others such as the reflections of Sn. This gave rise to the concern that the

samples did not reach full equilibrium state but exhibit small concentrational scattering.

Figure 34: Cubic (left) and rhombohedral structure (right) of SbSn with the respective hexagonal cell

inscribed. Sb = blue, Sn = orange, hexagonal unit cell = pink.

- 67 -


Therefore additional samples were prepared as was described before and in section

4.1.1 Binary system Sb-Sn. The XRD-results of these samples are presented in Table 7.

Figure 35 shows the higher resolution of diffraction patterns after the additional treatment

for different samples located within the homogeneity range of SbSn (SS02, SS06, SS03,

SS09, and SS04) as well as two samples (SS10 and SS07) located shortly outside of the

single phase field. The figure illustrates that the splitting and hyperfine structure of the

samples SS10, SS02, SS06 and SS03 is definitely more pronounced, providing evidence

that the phase SbSn is definitely rhombohedral in the entire homogeneity range. The

samples SS09, SS04 and SS07 show a clearly decreased, however still undeniable

broadening of the peaks due to the splitting.

As a consequence of the variation of the splitting in the different samples, the distortion

and lattice parameters were compared as a function of alloy composition. The resulting

graphs are shown in Figure 36 and exhibited clear composition dependence, where the

less distorted SbSn is located on the antimony poor side of the homogeneity range and

more distorted SbSn on the antimony rich side. It seems that the SbSn structure

approaches the angles in the crystal structures of the respective pure elements: β-Sn

Figure 35: Diffraction patterns before (black) and after (blue) the additional treatments of different

samples ordered from low antimony content (top) to high antimony content (bottom).

- 68 -


crystallizes in a tetragonal (nearly cubic) and Sb in a rhombohedral crystal structure. This

analysis is taken as first indication that the cubic NaCl-type structure of SbSn or the

supposedly cubic compound Sb2Sn3[128]

might correspond to that. Thus it is considered

that Sb2Sn3 does not exist at all at 300 °C, but further evidence is needed to prove this

statement.

Figure 36: Change of lattice parameters ah and ch as well as ratio ch/ah over a certain composition range.

- 69 -


5.1.2 ESEM/EPMA

In order to investigate the maximum solubilities of antimony in tin and tin in antimony as

well as the exact phase boundaries of the binary phase SbSn, electron probe microanalysis

(EPMA) was carried out. In contrast to Powder-XRD the neighbourhood of Sb and Sn in

the periodic table is not a problem in the quantitative EPMA measurements. The chosen

L-lines of both elements (Lα(Sb) = 3.604 keV and Lα(Sn) = 3.443 keV) are far enough

apart to ensure unambiguous allocation of the quantum energies with the EDX detector.

Nevertheless, the contrast of different phase composition in the SEM images is rather low

and overlayered by other effects such as orientation contrasts. The results of all

measurements are given in Table 11.

Generally, the analysis yielded in good results regarding the sum of weight percentage

(maximum deviation of 2 wt% from 100 wt%), which was used as criteria for the quality

of the measurements. For most samples the standard deviation of the mean values of the

repeatedly measured phase compositions did not exceed 0.5 at%. The exceptions were the

furnace cooled samples, which could not have reached equilibrium state and therefore

contained a variety of phase compositions. Also samples that were annealed at lower

temperatures, such as SS03 (220°C), SS02 (220°C) and SS01 (300°C) have not been in

full equilibrium. However, the standard deviation of the average compositions in the

samples SS03 (220°C) and SS01 (300°C) was around 1 at%, justifying their consideration

in the analysis of the phase boundaries.

Other samples such as SS05 (220 and 300°C), SS08 (300°C), SS07 (300°C and 300°C, p,

300°C), SS10 (220 and 300°C) and SS01 (400°C) were in good agreement with each

other and served as basis for the determination of the phase boundaries of SbSn and the

solubility limits of antimony in tin and tin in antimony, respectively. Unfortunately, only

one of the additionally treated samples (powdered, pressed and annealed at 300°C) which

were located in the two phase fields of SbSn with Sb and Sn, respectively, could be used

for this purpose. The sample SS10 (fc, p, 300°C) showed a large variation in the

composition of the phase SbSn. A possible explanation for this is the fact that this sample

was not annealed before the additional treatment and the furnace cooled-sample, which

was used as starting material, was too far from equilibrium state.

- 70 -


Table 11: EPMA results of the binary Sb-Sn samples ordered from lowest to highest antimony-fraction

ID Composition [at%] Temperature

treatment [°C] Phase

EPMA [at%] Std. dev. [ at%] Sb Sn Sb Sn

SS05 30 70

fc SbSn 45.22 54.78 0.9617

300 SbSn 44.44 55.56 0.0850

Sn 0.00 100.00

220 SbSn 43.53 56.47 0.1686

Sn 9.74 90.26 0.4101

SS08 40 60

fc SbSn 45.31 54.69 0.2890

Sn 8.71 91.30 0.2899

300 SbSn 44.58 55.42 0.1639

Sn 8.03 91.98 0.9907

170 SbSn 43.37 56.63 0.8959

Sn 6.04 93.97 0.1768

SS07 42 58

fc SbSn 45.61 54.39 0.6055

Sn 9.51 90.49 0.5422

300 SbSn 44.37 55.63 0.2737

Sn 4.93 95.08 0.2616

300, p, 300 SbSn 44.73 55.27 0.2249

Sn 6.02 93.98 1.4861

170 SbSn 43.68 56.32 0.1537

Sn 6.39 93.61 0.1109

SS04 45 55

fc SbSn 46.17 53.83 2.0805

300 SbSn 45.14 54.86 0.1938

300, p, 300 SbSn 45.60 54.40 0.2488

220 SbSn 45.10 54.90 0.4311

SS09 47 53

fc

SbSn 47.47 52.53 2.8703

SbSn 60.16 39.84 2.8491

Sn 8.14 91.86 0.9906

300 SbSn 47.94 52.06 0.4025

fc, p, 300 SbSn 48.05 51.95 0.4443

220 SbSn 47.77 52.23 0.1420

SS03 50 50

fc SbSn 48.39 51.61 5.3102

Sn 9.39 90.61

300 SbSn 50.53 49.47 0.3245

300, p, 300 SbSn 50.43 49.57 0.2369

220 SbSn 48.69 51.31 0.9578

- 71 -


Table 10: EPMA results of the binary Sb-Sn samples ordered from lowest to highest antimony-fraction

(continued)

ID Composition [at%] Temperature

treatment [°C] Phase

EPMA [at%] Std. dev. [ at%] Sb Sn Sb Sn

SS06 52 48

fc SbSn 45.49 54.51 0.5117

Sn 9.17 90.83 2.4287

300 SbSn 51.66 48.34 0.4520

300, p, 300 SbSn 51.73 48.27 0.2568

170

SbSn 59.73 40.27 3.5221

SbSn 47.23 52.77 2.3572

Sn 6.05 93.95

SS02 55 45

fc SbSn 49.89 50.11 3.9530

300 SbSn 52.62 47.38 0.2624

300, p, 300 SbSn 52.84 47.16 0.3081

220

SbSn 50.35 49.65 0.9578

SbSn 57.47 42.53 1.9313

Sb 85.65 14.36 0.1768

SS11 58 42 fc

SbSn 54.13 45.87 5.5141

Sb 84.20 15.80 0.3676

Sn 7.26 92.74 1.7311

fc, p, 300 SbSn 58.52 41.48 0.4599

SS10 62 38

fc

SbSn 53.28 46.72 5.1214

Sb 88.29 11.71 0.9822

Sn 6.37 93.63 1.6847

300 SbSn 61.37 38.63 0.2912

Sb 88.06 11.94 0.3282

fc, p, 300 SbSn 57.32 42.68 2.9538

Sb 88.78 11.22 0.4213

220 SbSn 60.72 39.28 0.2000

Sb 87.57 12.43 0.1774

SS01 70 30

fc SbSn 46.42 53.58 0.4835

400 SbSn 64.71 35.29 0.1358

Sb 88.17 11.83 0.3156

300 SbSn 60.72 39.28 0.0153

Sb 89.79 10.21 1.1427

- 72 -


Table 12: Summary of the determined phase boundaries in the binary system Sb-Sn

Phase Phase boundary [at% Sb]

400 °C 300 °C 220 °C 170 °C

Sn

9.74 ± 0.41 6.24 ± 0.22 SbSn

44.56 ± 0.24 43.53 ± 0.17 43.46 ± 0.75

(lower limit) SbSn

64.71 ± 0.14 61.19 ± 0.39 60.72 ± 0.20

(upper limit) Sb 88.17 ± 0.32 88.06 ± 0.33 87.57 ± 0.18

The samples lying within the homogeneity range of the phase SbSn, SS04, SS09, SS03,

SS06, SS02 and SS11 were single phase and showed good agreement between the

nominal and measured composition. Especially the additionally treated samples exhibited

excellent correlation to the supposed sample compositions. A summary of the single

phase compositions and determined phase boundaries is given in Table 11 and Table 12,

respectively.

Figure 37 shows micrographs of two sample compositions SS02 and SS07, located in the

single phase and two phase field, respectively. Since the electron number of antimony and

tin varies only by one, the achieved phase contrast in the BSE-images is rather low.

Despite that, the BSE-images show a variety of gray shadings, suggesting the presence of

different compositions even in the single-phase field, where SS02 is located. However,

according to the EPMA-analysis this contrast is not depending on concentration, see

Table 11. The explanation for the observed grains of different shades of gray is an

orientation contrast. Dependent on the plane that lies on the surface of the specimen, the

packing of antimony and tin is different, resulting in a different appearance in the EDX

EPMA.

- 73 -


(a) BSE-image of SS02 (annealed at 300°C)

(d) BSE-image of SS07 (annealed at 300°C)

(b) BSE-image of SS02 (powdered, pressed and

annealed at 300°C)

(e) BSE-image of SS07 (powdered, pressed and

annealed at 300°C)

(c) SE-image of SS02 (powdered, pressed and

annealed at 300°C)

(f) SE-image of SS07 (powdered, pressed and

annealed at 300°C)

Figure 37: Different micrographs of the binary Sb-Sn samples SS02(a-c) and SS07(d-f); BSE = Back

Scattered Electron; SE = Secondary Electron.

- 74 -


The images (a) and (d) in Figure 37 illustrate the equilibrium before the additional

treatment. Therefore the sample surface is smoother in comparison to the images (b) and

(e) where separate particles can be distinguished due to the previous powdering. The

black parts of the images are either holes in the sample surface or embedment resin. This

can be seen more clearly in the images (c) and (f) which are SE-images and thus depict

the topology of the specimen surface.

The sample SS07 annealed at 300°C should be located in the two phase field of Sb2Sn3

and SbSn according to Predel and Schwermann[132]

and Chen et al.[142]

. In contrast to this

the BSE-image of the sample (see Figure 37(d)) shows areas of quenched liquid in

equilibrium with SbSn of composition 44.56 at% Sb, which is a significantly higher

antimony content than 40 at% corresponding to Sb2Sn3.[132]

. Additionally, the powdered,

pressed and repeatedly annealed sample SS07 shown in Figure 37(e) and (f) appears a lot

more even than the accordingly treated sample SS02 located in the single phase field of

SbSn (Figure 37(b) and (c)). This is explained by the partial liquidity of sample SS07 at

300°C and the recombination of previously separated particles. The same observations

were made in the sample SS08 with a nominal composition of 40 at% Sb, which is

located at the proposed composition of the line compound Sb2Sn3. These results strongly

suggest that the reported compound does not exist in the given temperature range[132]

.

This is consistent with the previously discussed XRD-results.

- 75 -


5.1.3 DTA

The at lower temperatures annealed samples SS01 to SS08 (annealing temperatures, see

Table 2, page 44) were analyzed using the DTA Netzsch 404 S with zirconium as

reference material. The obtained DTA-curves were evaluated with the Calisto® software

provided by Setaram, which includes a peak deconvolution feature that allows the

separation of interfering peaks. For the reason that super-cooling is much more

pronounced than overheating the heating curves were used for the determination of the

characteristic temperatures. Figure 38(a) shows the measured DTA curves and a list of the

characteristic temperatures with the corresponding transformation reactions is given in

Table 13 and illustrated in Figure 38(b).

Table 13: Summary of the characteristic temperatures determined by DTA (first heating curves)

Transformation reaction Temperature [°C]

Lit. [132] Ø SS05 SS08 SS07 SS04 SS03 SS06 SS02 SS01

242 /250 244 244 244 243

324 324 325 325 324 323

Solidus temperature

331 355 379 400

425 423

425 423 422

Liquidus temperature 377 395 401 408 428 430 461 520

As can be seen from Figure 38(b) the obtained results are generally in good agreement

with the previously published phase diagrams[132, 142]

with some exceptions reported

below. The characteristic temperature of the peritectic reaction L + (Sb) SbSn(rhom)

was determined to be 424°C according to the heating curves of the first heating and

cooling cycle of the samples SS01, SS02 and SS06. This is in excellent agreement with

the values published in literature, 425°C[132]

and 424°C[142]

, and lies within the

experimental error of ± 1-2°C. However, one major difference was that only one

temperature effect at 244°C instead of two separated effects at 242 and 250°C was

observed. It is supposed that the Sb2Sn3 phase does not exist and the DTA-signal at 244°C

corresponds to the peritectic reaction L + (β-Sn) SbSn(rhom). As a consequence, the

temperature effect at 324°C cannot be caused by the peritectic formation of Sb2Sn3, but

has to have another origin.

- 76 -


Figure 38: (a) DTA- curves of the first heating of all samples (b) Characteristic temperatures evaluated

from (a) illustrated in the phase diagram assessed by Predel and Schwermann[132]

- 77 -


One possible explanation is a higher order transition between a low and high temperature

configuration of the phase SbSn within the homogeneity range. The result would be a

degenerated peritectic reaction L + SbSn(cub) SbSn(rhom) at 325°C. However, such a

higher order transition from rhombohedral to cubic SbSn within the homogeneity range

would cause only a very diffuse DTA-signal which usually disappears in the background.

Thus the detection of such a temperature effect can be very difficult, explaining the

missing effects in the DTA-curves of samples SS04, SS03, SS06, and SS02. However, the

DTA peaks corresponding to the L + SbSn(cub) two phase field can be clearly detected

after peak deconvolution.

Gallagher[122]

as well as Hansen and Anderko[183]

have already published phase diagrams,

that contain a high and low temperature configuration of SbSn (see β and γ in Figure 13,

page 32 and β and β’ in Figure 14, page 33 in section 3.2.1 Antimony-Tin (Sb-Sn)).

However, they reported a first order transition with a peritectic decomposition of the high

temperature phase, L + SbSn(HT) SbSn(LT), at low antimony content and a eutectic

decomposition, SbSn(HT) + Sb SbSn(LT), at high antimony content. In contrast to

their observations, a thermal effect corresponding to this eutectic reaction could not be

found in the samples SS01 and SS10, which are positioned in the two-phase field

SbSn + Sb. Gallagher also observed a lower temperature for the peritectic reaction

(319°C)[122]

, whereas the temperature reported by Hansen and Anderko, is in good

agreement with the results of this work: 325°C[183]

.

The characteristic temperature of the peritectic decomposition of rhombohedral SbSn:

L + SbSn(rhom) (β-Sn) (244°C) is in good agreement with most of the literature data.

Gallagher and Chen et al. reported a temperature of 243°C[122, 142]

, Predel and

Schwermann reported 242°C[132]

and Hansen and Anderko 246°C[183]

.

5.1.4 Conclusion

In the attempt to bring all obtained results of this work in accordance, a new phase

diagram was constructed which is shown in Figure 39. The figure shows the newly

assessed phase diagram in black and the previously assessed phase diagram by Predel and

Schwermann[132]

in gray and includes a summary of the obtained DTA, XRD and EPMA

results.

- 78 -


Fig

ure

39

: P

rop

ose

d p

ha

se d

iag

ram

wit

h a

ll d

ata

ob

tain

ed d

uri

ng

th

is w

ork

. T

he

ph

ase

dia

gra

m o

f P

red

el a

nd

Sch

wer

ma

nn

[132] is

sh

ow

n i

n g

ray.

- 79 -


The biggest changes that had to be made were the abandonment of the binary line

compound Sb2Sn3 and the introduction of a cubic NaCl-type high temperature

configuration of the phase SbSn. Both changes go hand in hand with the observation that

a cubic structure, as proposed for the compound Sb2Sn3, could not be found in the

specially treated samples SS09 and SS04 located within the homogeneity range of SbSn

as well as in the sample SS07, which was located in the two phase field of SbSn and

Sb2Sn3 according to Predel and Schwermann[132]


. Additionally, the

samples SS07 and SS08 (40 at% Sb) always exhibited areas of quenched liquid in the

SEM micrographs contradicting the previously published phase diagrams and providing

further evidence against the existence of the compound Sb2Sn3.

The DTA results, however, showed a distinct temperature effect at 324°C, which at first

could not be explained without the existence of Sb2Sn3. The introduction of a higher order

phase transformation at higher temperatures solved this problem and the DTA-effect was

allocated to the transformation reaction: L + SbSn(cub) SbSn(rhom). The proposed

transformation of the rhombohedral Hg(LT)-type structure of SbSn to a cubic NaCl-type

structure within the homogeneity range of SbSn at elevated temperatures could not be

proved, see above. Nevertheless, the decreasing rhombohedral splitting of some

reflections in the XRD diffraction patterns towards lower Sb contents and the entropic

stabilisation of HT-phases supports the assumption of a seond order solid state

transformation.

In addition to this the DTA heating curves showed broad peaks in the temperature range

from 330 to 420°C corresponding to the solidus and liquidus temperatures of the

two-phase field L + SbSn(cub). The higher order transformation within the homogeneity

range occurs not at a specific temperature, but within a specific temperature range. This

and the fact that the transformation is based on such a small distortion of not even one

degree of the rhombohedral angle φ, explain that the corresponding temperature effect is

nearly impossible to detect by DTA. Furthermore, the degree of rhombohedral distortion

within Sb(1-x)Snx depends on the composition of the alloy: The less Sb-content the smaller

the distortion and thus the transformation energy. This is a further reason for the missing

DTA-effects as discussed above.

The other changes that were made in the phase diagram are small deviations of the phase

boundaries: at higher temperature (400°C) the composition of the phase SbSn shifts to

- 80 -


even higher antimony content than proposed by Predel and Schwermann[132]

. The phase

boundary on the antimony poor side of the phase SbSn up to the invariant reaction

temperature of 244°C is constant within the accuracy of the SEM-EDX analyses and was

set to 43.5 at% Sb. Between 244 and 324 °C the phase boundary bends towards the

Sb-rich side. The given phase diagram (Figure 39) is not the final but a preliminary

version. Details such as the existance of a SbSn-HT phase have to proved and thus further

experimental investigation is necessary.

- 81 -


5.2 Li-Sb-Sn

Before starting the discussion, it has to be mentioned that it is extremely difficult to get

homogeneous samples exactly at the nominal composition. There are several reasons for

this:

Li creeps up along the crucible walls and does not mix with the rest of the sample

Li can penetrate the crucible walls

Sb can react with the Ta-crucible

Very slow interdiffusion of Sb and Sn.

If, in the following section, it is referred to “inhomogeneous samples” or samples that

“have not reached equilibrium state” any of these reasons may apply.

5.2.1 XRD

In the ternary system Li-Sb-Sn 15 samples of different composition were prepared and

annealed at 300°C. The XRD-analysis of the samples was done consecutively and since

most of them had not reached full equilibrium state at the time when they were quenched,

three samples (LSS09, LSS11 and LSS12) were left in the furnace up to date. The

annealing durations of the other samples ranged between 22 and 40 days, as was listed in

Table 3 (page 45).

For the XRD measurements of the ternary samples the same Bruker D8 Powder

Diffractometer was used as for the binary samples. However, in order to prevent

oxidation of the lithium containing samples, the powders had to be mounted on special

specimen holders which were closed with a plastic dome under argon atmosphere. The

only drawback of these domes is that they generate a broad peak in the diffraction

patterns at low 2θ values. This peak was refined via insertion of a single peak phase in

addition to a higher number of background parameters.

Additionally to the disability of distinguishing between antimony and tin, lithium cannot

be detected in Powder-XRD patterns due to its low atomic scattering factor. The

composition of the samples and the allocation of atom sites to specific atom-types within

the structures, are therefore only approximations. Single crystal XRD will be necessary to

refine the Li-positions.

- 82 -


The first task of analysis in the ternary system was the determination of lithium solubility

in the binary phase SbSn. Table 14 lists the obtained XRD results of the samples LSS01,

LSS02 and LSS03, which were prepared for this purpose and Figure 40 shows a section

of their diffraction patterns. It can be seen that the content of additional phases together

with SbSn increases with increasing lithium content from LSS01 with 10at% Li, to

LSS02 with 20at% Li and LSS03 with 30at% Li.

Unfortunately, the sample LSS03 was comprised of four phases, which is against the

Gibbs phase rule of ternary phase diagrams and indicates that this sample did not reach

equilibrium state. However, the additional small amounts of Sn were neglected and the

solubility of lithium in the phase SbSn was determined accordingly. Starting at the binary

phase boundaries of the phase SbSn (44.56 to 61.19 at% Sb) the single phase field

narrows with increasing lithium content. The sample LSS01 with 10 at% Sb is perfectly

situated in the single phase field of SbSn, showing only very small reflections of

additional Sb. It is presumed that inhomogeneity rather than a stable equilibrium

Sb-phase is the reason for this and therefore the Sb-phase was neglected. LSS02 exhibited

already indisputable amounts of Sb and very small amounts of Li3Sb, which is why the

solubility limit of lithium in SbSn was set to ~20 at% Sb. The last sample LSS03 matched

this assumption with an even more increased content of Sb and Li3Sb.

Table 14: XRD results of the ternary samples LSS01, LSS02 and LSS03

ID Composition [at%]

Phase Fraction

[%] Space Group

Nr. Lattice Parameters [Å]

R-Bragg Li Sb Sn a c

LSS01 10 45 45 Sb 1,65 R -3mH 166 4.2476 (14) 12.0637 (81) 2.613

SbSn_rhom 98,35 R -3mH 166 4.32837 (10) 5.34417 (18) 1.553

LSS02 20 40 40

Sb 21,57 R -3mH 166 4.26506 (48) 11.4508 (24) 2.532

SbSn_rhom 77,07 R -3mH 166 4.33021 (90) 5.33871 (16) 1.319

Li3Sb 1,42 F m-3m 225 6.5979 (15)

2.881

Sb 21,62 R -3mH 166 4.26505 (48) 11.4509 (24) 2.534

SbSn_rhom 77,43 R -3mH 166 4.33021 (90) 5.33871 (16) 1.313

Li2+xSn1-xSb 1,04 F m-3m 225 6.5989 (10) 3.257

LSS03 30 35 35

Sb 43,16 R -3mH 166 4.26197 (21) 11.4468 (10) 2.770

SbSn_rhom 45,79 R -3mH 166 4.32866 (11) 5.33685 (20) 1.063

Li3Sb 8,57 F m-3m 225 6.59684 (19)

2.456

Sn 2,48 I 41/amdS 141 5.83926 (58) 3.18461 (47) 2.026

Sb 42,94 R -3mH 166 4.26213 (21) 11.4459 (11) 2.800

SbSn_rhom 45,72 R -3mH 166 4.32867 (11) 5.33682 (20) 1.050

Li2+xSn1-xSb 8,85 F m-3m 225 6.597 (21)

3.512

Sn 2,487 I 41/amdS 141 5.83987 (58) 3.18439 (47) 1.999

- 83 -


In literature there is a structural description of a ternary compound similar to Li3Sb and

SbSn. Rönnebro et al.[172]

investigated the lithiation of different ternary composite

compounds including Ag36.4Sb15.6Sn48 and suggested a lithium insertion mechanism for

the phase SbSn. They used high-energy synchrotron radiation for their XRD

measurements and thus were able to determine the atomic parameters and occupancy of

lithium in the compounds. However, they were not able to distinguish between antimony

and tin positions in the structures and proposed a statistical distribution of both forming a

rigid host structure enabling a facilitated diffusion of lithium and tin. Their mechanical

lithiation experiments yielded a compound Li2+xSn1-xSb, (see Figure 41) with an

estimated composition of Li2.78Sn0.22Sb.

Figure 41: Structural comparison of SbSn[140]

(space group R -3mR; the slight distortion of the cubic

structure cannot be perceived), Li2+xSn1-xSb[172]

(space group F m-3m) and Li3Sb[153]

(space group F m-3m).

Figure 40: Part of the diffraction patterns of the samples LSS01, LSS02 and LSS03.

- 84 -


If the structure model according to Li2.78Sn0.22Sb was used in the Rietveld refinement of

the samples LSS02 and LSS03 the R-Bragg values increased slightly (see Table 14).

Furthermore, refining the occupation of the atom position shared by lithium and tin led to

a complete absence of Sn. Since lithium cannot be located by this technique, these

observations indicate that the mixed position is supposedly not occupied by tin atoms.

Thus the equilibrium phase in samples LSS02 and LSS03 is rather Li3Sb than

Li2.78Sn0.22Sb. Accordingly for the isothermal section it was assumed that Li3Sb was in

equilibrium with SbSn and Sb in these samples.

The other samples were prepared in order to construct an isothermal section at the chosen

annealing temperature of 300°C. The results are presented in Table 15 and the first thing

to notice is that only a few samples had reached equilibrium state. As a consequence, it

was decided to leave the samples LSS09, LSS11 and LSS12 in the furnace for a longer

period of time and they have not yet been quenched when this master thesis was written.

The only samples that satisfied the Gibbs phase rule for ternary phase diagrams were

LSS04, LSS05 and LSS10. However, the preparation for XRD measurements of the latter

two presented some difficulties, because both samples were stuck in the tantalum crucible

and only very little powder could be extracted. Moreover, sample LSS10 was very ductile

and hard to grind to a reasonably fine powder. Thus the diffraction pattern exhibited a

poor signal to noise ratio, as can be seen in Figure 42. In contrast to the samples LSS02

and LSS03 the application of the Li2.78Sn0.22Sb structure model in sample LSS05 resulted

in a lower R-Bragg value compared to Li3Sb. Under consideration of these results a

ternary solubility of Sn in Li3Sb was assumed.

The two samples of high antimony content, LSS06 (76 at% Sb) and LSS07 (50 at% Sb)

gave rise to another problem: The refinement of both samples revealed that antimony had

reacted with the crucible material and formed different antimony-tantalum compounds

(Sb2Ta and Sb4Ta5). Therefore these samples had to be neglected completely for the

determination of phase relations. In order to solve this problem different crucible

materials need to be tested and investigations including boron nitride, aluminium oxide

and magnesium oxide crucibles are currently in progress.

- 85 -


R-B

ragg

2,1

72

2.1

03

1.7

26

5.3

59

2.8

6

2.3

16

2.2

28

3.4

44

3.7

79

2.5

40

1.6

09

1.7

08

3.7

78

4.7

54

2.2

66

1.6

02

7.1

02

2.7

64

Latt

ice

Par

ame

ters

[Å

]

β

(21

)

12

0.4

01

1

c

(90

)

(22

)

(17

)

(12

)

(16

)

(29

)

(12

)

(22

)

(23

)

(22

)

(30

)

(97

)

(73

)

(18

)

(11

)

(28

)

11

.43

55

7

5.3

58

81

5.3

38

74

3.1

82

29

11

.41

03

5.3

91

6

6.5

24

6

8.2

88

49

3.5

40

92

11

.27

15

5.3

61

65

6.5

20

88

3.5

42

95

2

11

.41

12

5.3

37

3

3.1

79

51

b

(87

)

3.6

41

68

1

a

(17

)

(99

)

(91

)

(13

)

(15

)

(32

)

(13

)

(80

)

(27

)

(47

)

(48

)

(14

)

(67

)

(14

)

(35

)

(50

)

(64

)

(34

)

4.2

57

36

4.3

17

19

4

4.3

25

51

0

6.5

88

68

5.8

39

67

4.2

65

79

4.3

11

3

7.9

33

19

10

.21

67

0

10

.24

25

5

4.3

03

30

4.3

20

30

7.9

37

49

10

.24

56

5

4.2

59

98

4.3

17

39

6,5

86

77

9

5.8

30

74

Nr.

16

6

16

6

16

6

22

5

14

1

16

6

16

6

19

0

12

87

16

6

16

6

19

0

87

16

6

16

6

22

5

14

1

Spac

e

Gro

up

R -

3 m

H

R -

3 m

H

R -

3 m

H

F m

-3

m

I 41

/a m

d S

R -

3 m

H

R -

3 m

H

P -

6 2

c

C 1

2/m

1

I 4/m

R -

3 m

H

R -

3 m

H

P -

6 2

c

I 4/m

R -

3 m

H

R -

3 m

H

F m

-3

m

I 41

/a m

d S

Frac

tio

n

[%]

27

,85

72

,15

65

,79

21

,50

12

,71

20

,06

2,9

9

3,3

0

50

,68

22

,96

12

,30

47

,62

2,6

0

37

,48

47

,21

7,4

2

36

,38

8,9

8

Ph

ase

Sb

SbSn

_rh

om

SbSn

_rh

om

Li2+

xSn

1-xS

b

Sn

Sb

SbSn

_rh

om

Li2Sb

Sb2T

a

Sb4T

a 5

Sb

SbSn

_rh

om

Li2Sb

Sb4T

a 5

Sb

SbSn

_rh

om

Li3Sb

Sn

Co

mp

osi

tio

n [

at%

]

Sn

30

53

4

20

35

Sb

65

27

76

50

20

Li

5

20

20

30

45

ID

LSS0

4

LSS0

5

LSS0

6

LSS0

7

LSS0

8

Ta

ble

15:

XR

D r

esu

lts

of

the

tern

ary

sa

mp

les

- 86 -


R-B

ragg

5.3

09

2.0

23

1.7

03

2.1

46

1.5

83

3.4

59

2.9

67

3.0

7

5.1

41

2.8

12

4.3

57

1.7

75

2.9

62

2.7

49

3.6

92

2.0

54

4.0

32

4.2

65

Latt

ice

Par

ame

ters

[Å

]

β

(30

)

(63

)

(29

)

10

4.9

65

10

5.9

79

9

10

4.9

81

1

c

(51

)

(45

)

(13

)

(15

)

(35

)

(18

)

(26

)

(22

)

(55

)

(15

)

(56

)

(27

)

(24

)

(48

)

(42

)

5.3

29

57

3.1

78

05

5.3

18

3

3.1

27

9

3.1

72

98

3.0

95

73

7.7

85

0

3.1

78

64

8.3

17

58

5.3

37

8

9.4

57

17

7.7

60

01

3.0

99

42

8.3

30

52

3.1

82

15

b

(99

)

(25

)

(11

)

3.1

70

47

4.7

45

05

3.1

78

61

a

(23

)

(55

)

(59

)

(31

)

(90

)

(42

)

(36

)

(19

)

(27

)

(47

)

(16

)

(71

)

(58

)

(18

)

(47

)

(27

)

(16

)

(52

)

4.3

17

40

5.8

30

32

4.3

06

97

10

.27

11

6.5

75

54

5.8

15

79

10

.28

35

5.1

57

7

5.8

26

68

6.5

74

98

4.6

81

05

4.3

27

54

8.5

59

43

5.1

84

60

10

.26

20

0

6.5

78

00

4.6

91

01

5.8

35

37

Nr.

16

6

14

1

16

6

12

7

22

5

14

1

12

7

10

14

1

22

5

16

4

16

6

11

10

12

7

22

5

16

4

14

1

Spac

e

Gro

up

R -

3 m

H

I 41

/a m

d S

R -

3 m

H

P 4

/m b

m

F m

-3

m

I 41

/a m

d S

P 4

/m b

m

P 1

2/m

1

I 41

/a m

d S

F m

-3

m

P -

3 m

1

R -

3 m

H

P 1

21

/m 1

P 1

2/m

1

P 4

/m b

m

F m

-3

m

P -

3 m

1

I 41

/a m

d S

Frac

tio

n

[%]

68

,23

31

,77

9,2

5

5,8

7

11

,04

73

,84

45

,37

8,7

0

19

,77

6,2

1

19

,95

1,7

9

24

,20

37

,60

11

,49

7,1

2

14

,36

3,4

5

Ph

ase

SbSn

_rh

om

Sn

SbSn

_rh

om

Li2S

n5

Li3S

b

Sn

Li2S

n5

LiSn

_mo

no

Sn

Li3S

b

Li2S

b2S

n

SbSn

_rh

om

Li7S

n3

LiSn

_mo

no

Li2S

n5

Li3S

b

Li2S

b2S

n

Sn

Co

mp

osi

tio

n [

at%

]

Sn

70

75

50

35

Sb

20

5

5

5

Li

10

20

45

60

ID

LSS1

0

LSS1

3

LSS1

4

LSS1

5

Ta

ble

15:

XR

D r

esu

lts

of

the

tern

ary

sa

mp

les

(co

nti

nu

ed)

- 87 -


Similar to sample LSS10 the samples LSS08 and LSS13 were very hard to extract from

the crucible and difficult to grind, because of their ductility. Especially, the grinding of

sample LSS13 with a tin content of 75 at% presented a major obstacle. It is assumed that

liquid (Sn) could not crystallize properly during quenching which explains the ductility of

this sample. Finally, the alloy was cut into small pieces with a scissor, because grinding in

the DURIT mortar was not possible. As a consequence, the signal to noise ratio of the

diffraction pattern was even worse than in the diffraction pattern of sample LSS10 and the

reflections could not be allocated unambiguously. The presented phases in sample LSS13,

which are listed in Table 15 are only rough estimations.

In contrast to this, the allocation of reflections in the diffraction pattern of sample LSS08

was very clear. However, it contained a large amount of Sb which suggests a loss of

lithium and shift in composition to higher antimony content. Another explanation is that

due to the difficulty of extracting the powder from the crucible a non-representative part

of the sample was analyzed. In any case this sample could not be used for the

determination of phase relations at 300°C.

The last two samples that were analyzed after an annealing duration of 40 days were

LSS14 and LSS15. Despite the samples not being in equilibrium the diffraction patterns

Figure 42: Comparison of diffraction patterns of the samples LSS04 and LSS10, illustrating the poor signal

to noise ratio of the pattern of sample LSS10 in comparison to sample LSS04.

- 88 -


were refined and it turned out that some reflections could not be allocated to any known

phases. The software Topas3® provides the possibility of indexing unknown peaks,

calculates possible unit cells and lists them regarding to their “goodness of fit”. Through

this process a structure with trigonal space group was found. The ICSD database was

searched for suitable structures and after some “try and error”; one particular structure

yielded a reasonably good fit for the unknown reflections. Figure 43(a) illustrates the

refinement of the diffraction pattern of sample LSS14 with reflections of known phases

and the indexed unknown reflections. In Figure 43(b) the refinement of the diffraction

pattern including the new phase is shown.

Figure 43: Diffraction pattern of sample LSS14; (a) refined with known phases (b) refined with known

phases and the new phase Li2(Sb,Sn)3. The experimental diffraction pattern is shown in blue, the calculated

diffraction pattern in red, unknown reflections are indexed with violet lines and the calculated reflections of

the suggested structure correspond to the green lines.

- 89 -


The used structure model is based on a BaMg2Sb2 ternary compound[184]

and was adapted

for the ternary system Li-Sb-Sn as can be seen in Table 16 and Figure 44. The structure

exhibits a close resemblance to the binary phase SbSn with additional lithium atoms on

interstitial sites.

Table 16: Structural information about the new found ternary phase Li2(Sb,Sn)3 (declarations in

parentheses are from the original structure file[184]

)

Phase: Li2(Sb,Sn)3 (BaMg2Sb2)

Structure Type: La2O3

Space Group: P -3m1 (164)

Pearson Symbol: hP5

Lattice Parameters: a(Lit.)= 4,77 c(Lit.)= 8,1

a(exp.)= 4,68603 c(exp.)= 8,32405


Sb, Sn (Ba) 1 0 1a 0 0 0 0.5 / 0.5 (1)

Sb, Sn (Sb) 1 0 2d 0.33333 0.66667 0.26800 0.5 / 0.5 (1)

Li (Mg) 1 0 2d 0.33333 0.66667 0.62470 1 (1)

The usage of the structure Li2(Sb,Sn)3 in the refinement of the diffraction patterns of

samples LSS14 and LSS15 resulted in good agreement with the unknown reflections and

a decrease of the R-values. However, this alone is not evidence enough for the publication

of a new structure model. In order to get additional indication and to confirm the model,

single-crystal XRD measurements are needed. These will be subject of future

investigations and could not be included in this work. Nevertheless, the preliminary

structure Li2(Sb,Sn)3 was considered in the construction of an isothermal section at

300°C. The exact composition of the compound cannot be determined by XRD but was

roughly estimated based on the atom ratio in the unit cell.

Figure 44: Comparison of the binary phase SbSn[140]

(in hexagonal description), the ternary compound

BaMg2Sb2[184]

and the adapted new ternary compound Li2(Sb,Sn)3 (not yet confirmed).

- 90 -


5.2.2 Conclusion

With the combination of all obtained experimental data a first preliminary isothermal

section at 300°C was constructed (Figure 45). The binary information was taken from

phase diagrams assessed in this work (Sb-Sn), and assessments found in literature;

Li et al.[165]

(Li-Sn) and Sangster et al.[153]

(Li-Sb). Generally only the results of the

samples LSS01, LSS02, LSS03, LSS04, LSS05 and LSS10 could be used for the

estimation of phase relations at 300°C.

Sample LSS01 was located in the single phase field of LiySb1-xSnx, with negligible trace

amounts of Sb in the diffraction pattern. LSS02 and LSS03 were in good agreement with

each other and were situated in the three phase field of LiySb1-xSnx, Sb and Li3Sb. The

alloys that could have provided further evidence for the phase relations in the antimony

rich area of the phase diagram (LSS06 and LSS07) reacted with the crucible material and

could not be used for this purpose. Other samples with less tin and higher lithium content

(LSS11 and LSS12) were still in the furnace at the time when this master thesis was

written, but might confirm the statements above in close future.

The same also applies for the sample LSS09, which is still in the furnace for the

annealing purpose and could confirm the tie-triangle indicated by sample LSS05, where

LiySb1-xSnx, Sn, and Li(3-x)SnxSb are in equilibrium. The alloy LSS08, which should have

been located in the same three phase field, did not reach the equilibrium state and

therefore could not be used for drawing any conclusions.

Although the diffraction pattern of sample LSS10 exhibited a low signal to noise ratio the

results satisfied the Gibbs phase rule for ternary phase diagrams and confirmed the two

phase field of Sn and LiySb1-xSnx. Contrary to this, the sample LSS13 with a similar

Sn-content could not be powdered at all, making X-ray powder diffraction impossible and

preventing the deduction of phase relation information.

Despite not being in equilibrium, the samples LSS14 and LSS15 provided some

interesting results, because they both contained a to date unknown phase. During this

work it was not possible to characterize the new phase by single crystal XRD, but the

detailed evaluation of the powder diffraction patterns suggested a structure model similar

to the previously published phase BaMg2Sb2. Through adaption of this compound to the

requirements of the ternary system Li-Sb-Sn a provisional compound Li2(Sb,Sn)3 was

- 91 -


derived and used for the refinement of the two diffraction patterns. The composition of

Li2(Sb,Sn)3 was roughly estimated based on the atomic ratio in the unit cell. Since LSS05

and LSS08 did not show any indication of the new phase, its composition was set to

Li2+x(Sb,Sn)3-x with a rather small homogeneity range.

The preliminarily constructed isothermal section shown in Figure 45 is based on very few

experimental data and a lot more samples need to be prepared and analyzed in order to

confirm it.

Figure 45: Tentative ternary phase diagram for the system Li-Sb-Sn. The samples LSS09, LSS11 and LSS12

(in parenthesis) are not yet analyzed, LSS06 and LSS07 contained Sb-Ta phases, and LSS08, LSS13, LSS14

and LSS15 (pink) did not reach the equilibrium state. The three phase fields (tie-triangles) are shown in

light blue, two phase fields are white and single-phase fields are shown in gray.

- 92 -


6. SUMMARY

6.1 English

Li-ion batteries are important energy storage components for smart-grids of the future. To

enable the development of a secure, long lasting power supply for high energy

applications, the life time, energy density and operation safety of Li-ion batteries need to

be improved. Intermetallic alloys which are able to reversibly uptake lithium are

considered as promising anode materials which could enhance the energy densities.

However, lack of knowledge about phase relations and basic thermodynamic properties of

suitable materials systems hinder a systematic development of new Li-ion anodes.

Within the scope of this master thesis the binary system Sb-Sn was newly investigated,

due to many discrepancies within literature data. This was done by means of X-ray

powder diffraction (XRD), difference thermal analysis (DTA) and electron probe micro-

analysis (EPMA). It was possible to prove that the binary line compound Sb2Sn3, reported

by Predel and Schwermann[132]


does not exist in the given temperature

range. Furthermore, a higher order transformation within the homogeneity range of the

binary phase Sb1-xSnx at elevated temperatures was proposed based on XRD and DTA

results. This non-invariant transformation is based on the distortion of the cubic NaCl-

type structure of Sb(1-x)Snx at higher temperature to the rhombohedral Hg-type structure of

Sb(1-x)Snx at lower temperatures. Validation of this assumption was not possible with the

given samples and analysis techniques and further investigations are necessary to provide

final confirmation. At last, a newly assessed phase diagram based on experimental data of

this work and previously published phase diagrams was constructed.

Another task was the initial investigation of phase relations in the ternary system

Li-Sb-Sn at 300°C. The XRD-analysis demonstrated that the preparation of equilibrium

samples located at the nominal composition is very difficult. Nevertheless, results of

phase relations, the solubility of lithium in the binary phase Sb(1-x)Snx and an up to date

unknown ternary compound Li2+x(Sb,Sn)3-x were obtained and summarized in a tentative

isothermal section at 300°C. Regardless of this, investigations with extended scope and

depth need to be carried out to confirm the reported observations.

- 93 -


6.2 Deutsch

Li-Ionen Batterien sind aufgrund ihrer hohen Energiedichte wichtige

Energiespeichermedien für die Entwicklung von Stromspeichermedien (Smart-Grids) der

Zukunft. Allerdings müssen für den Einsatz in Hochenergieapplikationen die

Lebensdauer, Energiedichte und Betriebssicherheit solcher Batterien verbessert werden.

Intermetallische Legierungen, welche Lithium reversibel aufnehmen können, sind

vielversprechende Anodenmaterialien mit erhöhten Ladungsdichten. Einer

systematischen Entwicklung von Anodenmaterialien für Li-Ionen Batterien steht zurzeit

aber noch das teilweise dürftige Wissen über Phasengleichgewichte und

thermodynamischen Eigenschaften der Phasen in geeigneten intermetallischen Systemen

entgegen.

Im Zuge dieser Master Arbeit wurde das binäre System Antimon-Zinn (Sb-Sn), aufgrund

bestehender Widersprüche in der Literatur neuerlich untersucht. Dies geschah mittels

folgender Methoden: Röntgen-Kristallstrukturanalyse (X-ray diffraction, XRD),

Differenz-Thermoanalyse (DTA), sowie Elektronen-Mikrostrahl Analyse (electron probe

micro-analysis, EPMA). Auf diese Weise konnte die Existenz der binären

stöchiometrischen Phase Sb2Sn3, welche in den Phasendiagrammen von Predel und

Schwermann[132]

sowie Chen et al. [142]

publiziert wurde, widerlegt werden. Weiters wurde

ein Übergang höherer Ordnung im Homogenitätsgebiet der binären Phase Sb(1-x)Snx bei

höheren Temperaturen vorgeschlagen. Diese nicht-invariante Reaktion basiert auf einer

Verzerrung der kubischen Struktur von Sb(1-x)Snx (NaCl-Typ) bei höheren Temperaturen

zur rhomboedrischen Struktur von Sb(1-x)Snx (Hg(LT)-Typ) bei niedrigeren

Temperaturen. Ein sicherer Beweis für diese Vermutung konnte mit den bereiteten

Proben und oben genannten Methoden allerdings nicht erbracht werden, weshalb weitere

Untersuchungen zur Absicherung notwendig sind. Schlussendlich wurde aus den im Zuge

dieser Arbeit gewonnenen experimentellen Daten, sowie bereits in der Literatur

veröffentlichten Daten ein neues Phasendiagramm des Systems Sb-Sn erstellt.

Eine weitere Zielsetzung dieser Master Arbeit war die Durchführung erster

Untersuchungen im ternären System Lithium-Antimon-Zinn (Li-Sb-Sn), um Erkenntnisse

über die Phasengleichgewichte bei 300°C zu gewinnen. Die Ergebnisse der

Röntgenbeugungsanalyse zeigten rasch, dass die Präparation von Proben, welche sich am

Ort ihrer nominellen Zusammensetzung im Gleichgewicht befinden, sehr schwierig ist.

- 94 -


Gründe dafür sind die Fähigkeit des Lithiums an den Tiegelwänden hochzukriechen,

durch die Tiegelwände zu diffundieren, aber auch die langsame Interdiffusion von

Antimon und Zinn. Nichtsdestotrotz konnten erste Schlüsse aus den Resultaten gezogen

werden. Diese beinhalten Abschätzungen der Phasengleichgewichte, der Löslichkeit von

Lithium in der binären Phase Sb(1-x)Snx, sowie die Existenz einer bisher unbekannten

ternären Phase Li2+x(Sb,Sn)3-x. Diese Ergebnisse wurden in einem vorläufigen isothermen

Schnitt bei 300°C zusammengefasst. Da es sich hierbei allerdings nur um grobe

Abschätzungen handelt, sind umfangreiche und tiefer gehende Untersuchungen zusätzlich

notwendig.

- 95 -


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8. APPENDICES

8.1 List of Figures

Figure 1: Comparison of gravimetric and volumetric energy density of various

rechargeable battery systems. (adapted from Scrosati et al.[9]

) ................................... - 9 -

Figure 2: Operating principle of Li-ion batteries (adapted from Yoshino[17]

) .......................... - 10 -

Figure 3: Battery and electrode structure proposed by Yoshino[17]

......................................... - 11 -

Figure 4: Electrochemical Cell (adapted from Besenhard[22]

) .................................................. - 12 -

Figure 5: (a) Comparison of specific conductivities of different materials and

(b) electrolytes used in LIBs (c) Electrochemical series of different

metal/metal-ion couples (adapted from Besenhard[22]

and Scrosati et al.[9]

). ........... - 13 -

Figure 6: Charge and discharge curves of LiNi0.5Mn1.5O4 at different C rates[24]

..................... - 16 -

Figure 7: Structure of a lithium-ion battery[25]

......................................................................... - 18 -

Figure 8: Schematic open-circuit diagram adapted from Goodenough et al.[26]

. ΦA and ΦC are

the anode and cathode work functions. Eg is the window of the electrolyte for

thermodynamic stability. A μA>LUMO and/or a μC<HOMO requires kinetic

stabilisation by the formation of a SEI layer. ........................................................... - 19 -

Figure 9: (a) Schematic diagram of corresponding energy vs. density of states, showing the

relative positions of the Fermi energy in an itinerant electron band for different

electrode materials (b) Discharge characteristics of different electrode materials

vs. Li/Li+. (taken from Goodenough et al.

[26]) .......................................................... - 21 -

Figure 10: Comparison of theoretical capacity (mAhg-1

), volume change (%) and potential

vs. Li (~V) of different anode materials (data taken from Zhang et al.[66]

) ............ - 23 -


) vs. cycle number of different

Sn-based composite anode materials (taken from Kamali et al. [67]

) ...................... - 24 -


) of different Sn-based intermetallic

and/or composite materials (taken from Kamali et al. [67]

) ..................................... - 25 -

Figure 13: Phase diagram by Gallagher[122]

.............................................................................. - 32 -

Figure 14: Phase diagram by Hansen, based on work of Iwase et al.[129]

................................. - 33 -

Figure 15: Phase diagram by Predel and Schwermann[132]

in Massalski's compilation

for binary alloys ...................................................................................................... - 34 -

Figure 16: Phase diagram by Vassiliev et al.[138]

...................................................................... - 35 -

Figure 17: Phase diagram by Chen et al.[142]

............................................................................ - 36 -

- 102 -


Figure 18: XRD patterns of Sb-Sn intermetallic alloys with (a) 30 at% Sb at 280 °C (b) 30 at%

Sb at 210 °C and (c) 70 at% Sb at 300 °C. (taken from Chen et al.[142]

) .................. - 37 -

Figure 19: Phase diagram of Li-Sb from Massalski's Binary Alloy Phase Diagrams[131]

(assessed by Sangster et al.[153]

) .............................................................................. - 39 -

Figure 20: Phase diagram of Li-Sn by Li et al.[165]

................................................................... - 40 -

Figure 21: Graphical representation of the binary Sb-Sn samples and their annealing

temperatures (phase diagram taken from Predel and Schwermann[132]

) .................. - 42 -

Figure 22: Graphical representation of the compositions of the ternary Li-Sb-Sn sample;

the binary phase diagram data were taken from Predel and Schwermann[132]

(Sb-Sn),

Li et al.[165]

(Li-Sn) and Sangster et al.[153]

(Li-Sb). ................................................. - 46 -

Figure 23: Schematic diagram of an X-ray tube (adapted from Suryanarayana[178]

) ................ - 48 -

Figure 24: (a) characteristic X-ray spectrum and (b) possible electron transitions based on

Bohr’s model (adapted from Suryanarayana[178]

) .................................................... - 49 -

Figure 25: Diffraction of X-rays by a crystal (adapted from Suryanarayana[178]

) ..................... - 51 -

Figure 26: (a) Geometry of an X-ray diffractometer and (b) arrangement of slits in an X-ray

diffractometer (adapted from Suryanarayana[178]

) ................................................... - 52 -

Figure 27: Schematic diagram of a differential thermal analyzer (adapted from Speyer [181]

) . - 55 -

Figure 28: Temperature program for the DTA ......................................................................... - 56 -

Figure 29: EPMA - instrumental setup (taken from lecture material of K. Richter[180]

) ........... - 57 -

Figure 30: Production and path of backscattered and secondary electrons in the specimen

(taken from lecture material of K. Richter[180]

) ........................................................ - 58 -

Figure 31: Scanning electron microscope Zeiss Supra 55 VP (taken from Faculty Centre for

Nano Structure Research[182]

) ................................................................................... - 59 -

Figure 32: Part section of the diffraction patterns of the binary Samples SS01, SS03 and SS07

(annealed at 300 °C), depicting the splitting of reflexes that occurs upon distortion

of the cubic to the rhombohedral structure of SbSn. ............................................... - 64 -

Figure 33: Scheme for the sequence of distortion and loss of order in the phase SbSn to get

from the not distorted, ordered structure (NaCl-type) to the distorted and disordered

structure (Hg(LT)-type). Literature data of the lattice parameters was taken from

Noren et al.[140]

. ....................................................................................................... - 65 -

Figure 34: Cubic (left) and rhombohedral structure (right) of SbSn with the respective

hexagonal cell inscribed. Sb = blue, Sn = orange, hexagonal unit cell = pink. ...... - 66 -

Figure 35: Diffraction patterns before (black) and after (blue) the additional treatments of

different samples ordered from low antimony content (top) to high antimony

content (bottom). ..................................................................................................... - 67 -

- 103 -


Figure 36: Change of lattice parameters ah and ch as well as ratio ch/ah over a certain

composition range. ................................................................................................. - 68 -

Figure 37: Different micrographs of the binary Sb-Sn samples SS02(a-c) and SS07(d-f);

BSE = Back Scattered Electron; SE = Secondary Electron. ................................... - 73 -

Figure 38: (a) DTA- curves of the first heating of all samples (b) Characteristic temperatures

evaluated from (a) illustrated in the phase diagram assessed by Predel and

Schwermann[132]

...................................................................................................... - 76 -

Figure 39: Proposed phase diagram with all data obtained during this work. The phase diagram

of Predel and Schwermann[132]

is shown in gray. .................................................... - 78 -

Figure 40: Part of the diffraction patterns of the samples LSS01, LSS02 and LSS03. ............ - 83 -

Figure 41: Structural comparison of SbSn[140]

(space group R -3mR; the slight distortion

of the cubic structure cannot be perceived), Li2+xSn1-xSb[172]

(space group F m-3m)

and Li3Sb[153]

(space group F m-3m). .................................................................... - 83 -

Figure 42: Comparison of diffraction patterns of the samples LSS04 and LSS10, illustrating

the poor signal to noise ratio of the pattern of sample LSS10 in comparison

to sample LSS04. .................................................................................................... - 87 -

Figure 43: Diffraction pattern of sample LSS14; (a) refined with known phases (b) refined

with known phases and the new phase Li2(Sb,Sn)3. The experimental diffraction

pattern is shown in blue, the calculated diffraction pattern in red, unknown reflections

are indexed with violet lines and the calculated reflections of the suggested structure

correspond to the green lines. ................................................................................. - 88 -

Figure 44: Comparison of the binary phase SbSn[140]

(in hexagonal description), the ternary

compound BaMg2Sb2[184]

and the adapted new ternary compound Li2(Sb,Sn)3

(not yet confirmed). ................................................................................................ - 89 -

Figure 45: Tentative ternary phase diagram for the system Li-Sb-Sn. The samples LSS09,

LSS11 and LSS12 (in parenthesis) are not yet analyzed, LSS06 and LSS07 contained

Sb-Ta phases, and LSS08, LSS13, LSS14 and LSS15 (pink) did not reach the

equilibrium state. The three phase fields (tie-triangles) are shown in light blue,

two phase fields are white and single-phase fields are shown in gray. .................. - 91 -

- 104 -


8.2 List of Tables

Table 1: Sample compositions of binary Sb-Sn samples .......................................................... - 41 -

Table 2: SbSn samples - annealing temperature and applied analysis ...................................... - 44 -

Table 3: Sample composition of ternary Li-Sb-Sn samples ...................................................... - 45 -

Table 4: Commonly used X-ray wavelengths of different metals[178]

....................................... - 50 -

Table 5: Derivation of Miller indices[22]

.................................................................................... - 51 -

Table 6 : XRD results of the binary Sb-Sn samples ordered from lowest to highest

antimony-fraction ........................................................................................................ - 61 -

Table 7: XRD results of the additionally powdered. pressed and repeatedly annealed

binary Sb-Sn samples ordered from lowest to highest antimony-fraction .................. - 63 -

Table 8: Structural details for the cubic phase SbSn ................................................................. - 65 -

Table 9: Structural details for the small simple-cubic (Po-type) and large rhombohedral

(GeTe-type) structures of the phase SbSn .................................................................... - 65 -

Table 10: Structural details for the disordered rhombohedral phase SbSn ............................... - 65 -

Table 11: EPMA results of the binary Sb-Sn samples ordered from lowest to highest

antimony-fraction ....................................................................................................... - 70 -

Table 12: Summary of the determined phase boundaries in the binary system Sb-Sn ............. - 72 -

Table 13: Summary of the characteristic temperatures determined by DTA ........................... - 75 -

Table 14: XRD results of the ternary samples LSS01, LSS02 and LSS03 ............................... - 82 -

Table 15: XRD results of the ternary samples .......................................................................... - 85 -

Table 16: Structural information about the new found ternary phase Li2(Sb,Sn)3 .................... - 89 -

- 105 -


8.3 Curriculum Vitae et Studiorum

PERSONAL INFORMATION

Name: Julia Polt, BSc

Date of Birth: 06.02.1989

Nationality: Austrian

Home Adress: Fellinggraben 3, 3021 Wolfsgraben

Contact: +43 (0)664 5990098

[email protected]

EDUCATION AND TRAINING

WORK EXPERIENCE

ADDITIONAL INFORMATION

March 2012 to date

Master of Chemistry (MSc) University of Vienna, Vienna (Austria)

Thesis Title: “ Phase Equilibria in the Intermetallic Systems Sb-Sn and Li-Sb-Sn”

January 2013 to June 2013

ERASMUS exchange program University of Warwick, Coventry (UK)

Oct. 2008 to Feb. 2012

Bachelor of Chemistry (BSc) University of Vienna, Vienna (Austria)

Thesis Title: “Untersuchungen in für Li-Ionen Batterien relevanten Phasendiagrammen”

2007-2008 Foundation Course

New Design University, St. Pölten (Austria)

2003-2007 General qualification for University entrance

Academic secondary school, Purkersdorf (Austria)

1999-2003 Sacré Coeur Academic secondary school, Pressbaum (Austria)

April 2014 to June 2014

Laboratory Tutor University of Vienna, Vienna (Austria)

Oct. 2009 to Feb. 2012

Mathematic Tutor University of Vienna, Vienna (Austria)

Academic secondary school, Purkersdorf (Austria)

Publications: Zeiringer, P. Rogl, A. Grytsiv, J. Polt, E. Bauer, and G. Giester; Crystal Structure

of W1-xB3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B; Journal of Phase Equilibria and Diffusion; 2014 (accepted)

T.R. Congdon, C. Wilmet, R. Williams, J. Polt, M. Lilliman and M.I. Gibson; European Polymer Journal; 2014 (submitted)

- 106 -


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