1. CHE-30043 Materials Chemistry & Catalysis : Solid State Chemistry lecture 4
Rob Jackson
LJ1.16,
@robajackson

2. Plan of lecture Defects in crystalline materials
Classification of point defects
Intrinsic and extrinsic defects
Ionic conductivity in crystalline materials
Solid state electrolytes
Fast ion conductors
Lithium ion batteries
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3. Defects in crystalline materials
Crystalline materials are not perfect above 0K, since at finite temperatures atoms can move from their lattice positions.
Also, impurities are nearly always introduced during crystal growth (intentionally or not!)
We will be concentrating on point defects, which affect isolated atom sites, and have a significant effect on the chemistry of the crystal.
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4. Classification of point defects
First, distinguish between intrinsic and extrinsic defects.
Intrinsic defects do not affect the chemical composition of the crystal, and include:
vacancies – atoms missing from the lattice
interstitials – atoms at non-lattice positions
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5. Classification of intrinsic defects
Frenkel defects occur when an atom moves from a lattice site to an interstitial site.
(this will be illustrated)
Schottky defects occur when a formula unit of vacancies is created. Note that this is still a neutral defect since both cation and anion vacancies are created (e.g. Na+ and Cl- vacancies in NaCl).
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6. Which intrinsic defects form? - 1
Frenkel defects occur on one or other sublattice in the crystal (i.e. in MX, either the M+ or X- ions are involved).
A Frenkel defect is called a ‘Frenkel pair’ – it is the combination of a vacancy and an interstitial.
Frenkel pair formation depends on the availability of space in the lattice for interstitial formation.
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7. Which intrinsic defects form? - 2
Schottky defects will normally form when there is insufficient space in the lattice for interstitials.
e.g. the rock salt structure – very little space, so Schottky defects predominate.
However, in the fluorite structure there are alternate unoccupied cube centres and Frenkel defects can form.
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8. Extrinsic defects
Impurity atoms present in crystals are called extrinsic defects.
They may be there deliberately, or as a consequence of the preparation process.
Examples are K+ ions in NaCl
Charge must always be balanced – e.g. if Ca2+ substitutes for Na+ in NaCl, a Na+ vacancy or Cl- interstitial must be formed.
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9. Ionic Conduction Mechanisms
The presence of point defects makes it possible for ions to move through a structure.
There are two common mechanisms that are adopted, the vacancy mechanism and the interstitial mechanism.
These mechanisms will be illustrated – but see the diagrams in Smart and Moore for an alternative view!
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10. How is ionic conductivity defined?
Ionic conductivity () is defined as follows:
 = n Ze 
where n is the number of charge carriers (defects per unit volume), Ze is their charge (e is the electron charge), and  is the mobility of the ions – a measure of the speed with which they move through the lattice.
So  depends on (i) the number of available defects (ii) the charge of the defect species, and (iii) how easily the ion can move through the lattice.
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11. Some conductivity values
conduction type material conductivity
(ohm -1 m -1)
ionic conductors ionic crystals – 10-3
solid electrolytes – 103
liquid electrolytes – 103
electronic conductors
metals – 107
semiconductors – insulators < 10-10
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12. Solid Electrolytes
Solid electrolytes are ionic crystals with a sufficient volume of defects to be able to act like a liquid electrolyte.
Example – LiI (rock salt structure, Schottky defects) has sufficient vacancies in its crystal structure to enable Li+ ions to move freely.
It was one of the first solid electrolytes to be used in the design of lithium batteries.
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13. Lithium batteries: how they work - 1
Lithium batteries are made up of:
a lithium anode, ‘iodine’ cathode (iodine embedded in a polymer, poly-2-vinyl-pyridine).
a lithium iodide electrolyte.
Li+ ions can pass through the electrolyte by the vacancy mechanism, and the valence electrons go round the external circuit.
A diagram will be drawn in the lecture.
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14. Lithium batteries: how they work - 2
The following cell reaction occurs:
anode: 2Li(s)  2Li+ + 2e-
cathode: I2(s) + 2e-  2I-
overall: 2Li(s) + I2(s)  2LiI(s)
Note – the same principal applies to different Li salts (e.g. Li2CO3).
Lithium batteries have been replaced by lithium ion batteries, considered later.
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15. Fast ion conductors
Fast ion conductors are particular examples of solid electrolytes.
We will consider some examples and show how they work.
There are two mechanisms:
(i) structures which have unoccupied lattice sites without defects being present.
(ii) structures whose conductivity occurs because of defects.
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16. Example 1 - -AgI - 1
The structure of -AgI is such that there are more possible sites for the Ag+ ions than needed (see Smart and Moore for diagrams). Structure is BCC with I- anions at the BCC sites.
Conductivity occurs because the Ag+ ions can easily move through the lattice via unoccupied lattice sites.
Conductivity is 131 ohm-1 m-1 (high).
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17. Example 1 - -AgI - 2
We can relate the high conductivity to properties of the structure:
Low charge on the Ag+ ions
Low coordination of the Ag+ ions
Many vacant Ag+ ion sites
However the -phase of AgI only exists above 146C, limiting its use.
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18. More examples of fast ion conductors
-AgI can be modified to lower the temperature at which fast ion conduction occurs.
Partial replacement of Ag by Rb results in RbAg4I5, which has an ionic conductivity of 25 ohm-1 m-1 at room temperature.
Materials with the fluorite structure should have good potential as fast ion conductors, since there are many interstitial sites.
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19. Zirconia and stabilised zirconia
Zirconia, ZrO2 exists naturally as the mineral baddeleyite, with a monoclinic structure.
On heating, the structure transforms first to a tetragonal phase, and then, at 1600 C, to a cubic fluorite phase, where it would be expected to have good ionic conduction properties.
It is possible to stabilise the structure in the cubic phase at room temperature by adding, e.g. 15 mol % CaO.
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20. Stabilised zirconia
Addition of CaO (or other oxides, including Y2O3), produces a cubic fluorite phase.
The structure is a good ion conductor because of the interstitial sites, but addition of the stabiliser ions improves this further.
If Ca2+ is substituted for Zr4+, the charge has to be compensated.
This can be achieved by creating O2- vacancies – so oxygen ion conduction can occur. Stabilised zirconia is widely used in fuel cells.
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21. Oxygen ion conduction in CaO stabilised zirconia - summary
The CaO can be added up to 28 mol%.
Addition of the CaO stabilises the structure in the cubic phase at room temperature.
The interstitial sites mean oxygen ion conduction will be possible via the interstitial mechanism.
Further oxygen vacancy sites are created to compensate for the charge imbalance caused by Ca2+ substituting for Zr4+. This enhances conduction further.
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22. Lithium ion batteries
Lithium batteries were not always ideal to work with, mainly because of the reactivity of the lithium metal!
Lithium ion batteries were developed in the 1990s, mainly by Sony, to provide reliable rechargeable batteries. They are now used routinely in laptop computers, mobile phones, mp3 players etc.
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23. How lithium ion batteries work – (i)
Their design is based on intercalation compounds (compounds formed by the reversible addition of ‘guest’ ions to a host lattice).
The electrolyte is a conducting polymer such as polyacetylene:
n (H-CC-H)
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24. How lithium ion batteries work – (ii)
The anode is composed of Li embedded in graphitic carbon, forming LixC6.
The cathode is made from Li combined in an intercalation compound with a transition metal oxide like CoO2, forming LixCoO2.
The electrolyte is a conducting polymer.
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25. How lithium ion batteries work – (iii)
The Li+ ions move between the two intercalation compounds.
At the anode, LixC6 = xLi+ + 6C + xe-
At the cathode:
xLi+ + CoO2(S) + xe- = LixCoO2
The Li+ ions move through the electrolyte while the electrons go around the external circuit.
The process is reversed on charging.
See diagram on the next slide.
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26. Lithium ion battery diagram
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27. Improvements to the lithium ion battery
There is much current research on improving the performance of lithium batteries.
These have focussed on using nanostructured materials for the cathode and anode.
The rationale is that the ‘hopping distance’ for the Li+ ions is reduced.
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28. Improvements to anode materials
Journal of New Materials for Electrochemical Systems, 15(4) 2012,
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29. Nanoporous cathode materials
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30. Summary of lecture
Defects in solids have been introduced and classified
Ion migration mechanism have been discussed.
Applications to fast ion conductors and battery materials have been described.
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