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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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
(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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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]
- 17 -
Master Thesis, Julia Polt, University of Vienna (2014)
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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Master Thesis, Julia Polt, University of Vienna (2014)
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]
- 19 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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
Figure 12: Comparison of reversible capacities (mAhg-1
) of different Sn-based intermetallic and/or
composite materials (taken from Kamali et al. [67]
; references correspond to Kamali et al. [67]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
.
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Master Thesis, Julia Polt, University of Vienna (2014)
3.1.2 Antimony
Greek anti + monos = not alone
Chemical symbol Sb: latin stibium = german Grau/Spießglanz
Chemical symbol: Sb
Atomic number: 51
Relative atomic mass:
(C12
=12.0000) 121.75
Radii /pm: Sb5+
62; Sb3+
89; atomic 182;
covalent 141
Electronegativity: 2.05 (Pauling)
Electron configuration: [Kr] 4d10
5s2 5p
3
Oxidation states: SbIII
, SbV
Melting point /°C: 630.89
Boiling point /°C: 1587
Density /g·cm-3
: 6.691 [20 °C]
Photo taken from periodictable.com with permission of Theodore Gray
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,
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Master Thesis, Julia Polt, University of Vienna (2014)
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
Relative atomic mass:
(C12
=12.0000) 118.710
Radii /pm: Sn2+
93; Sn4+
74; atomic 140.5;
covalent 140
Electronegativity: 1.96 (Pauling)
Electron configuration: [Kr] 4d10
5s2 5p
2
Oxidation states: SnII , Sn
IV
Melting point /°C: 232.118
Boiling point /°C: 2270
Density /g·cm-3
: 7.310 [20 °C]
Photo taken from periodictable.com with permission of Theodore Gray
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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)).
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
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Master Thesis, Julia Polt, University of Vienna (2014)
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,
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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).
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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)
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
4.2.2 Difference Thermal Analysis (DTA)
4.2.2.1 Basic principles
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]
)
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
4.2.3 Scanning Electron Microscopy (SEM) and Electron Probe
Microanalysis (EPMA)
4.2.3.1 Basic principles
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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
Atom Nr OX Site x y z SOF
c(Lit.)= 10.6752
Sn 1 0 1a 0 0 0 0.5
Sb 1 0 1a 0 0 0 0.5
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 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
Atom Nr OX Site x y z SOF
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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).
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
(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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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]
and Chen et al.[142]
. 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
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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
Atom Nr OX Site x y z SOF
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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]
and Chen et al.[142]
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 -
Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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.
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Master Thesis, Julia Polt, University of Vienna (2014)
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[183] Hansen, M.; Anderko, K., Constitution of binary alloys. [Hauptbd], McGraw-Hill: New
York, (1958).
[184] Deller, K.; Eisenmann, B., Zeitschrift für Naturforschung - Teil B, (1977) 32, 612.
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Master Thesis, Julia Polt, University of Vienna (2014)
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 -
Figure 11: Comparison of reversible capacities (mAhg-1
) vs. cycle number of different
Sn-based composite anode materials (taken from Kamali et al. [67]
) ...................... - 24 -
Figure 12: Comparison of reversible capacities (mAhg-1
) 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 -
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Master Thesis, Julia Polt, University of Vienna (2014)
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 -
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Master Thesis, Julia Polt, University of Vienna (2014)
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 -
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Master Thesis, Julia Polt, University of Vienna (2014)
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 -
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Master Thesis, Julia Polt, University of Vienna (2014)
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
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)
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Master Thesis, Julia Polt, University of Vienna (2014)