Transcript The tatle of lecture - Warsaw University of Technology

Ionic Conductors: Characterisation of Defect
Structure
Lectures 9-10
Fast ion conduction in solids II
amorphous materials
Dr. I. Abrahams
Queen Mary University of London
Lectures co-financed by the European Union in scope of the European Social Fund
Oxide Glasses
Glasses are typically made up of polymeric frameworks which show no
long-range order. In inorganic oxide based glasses the framework
typically consists of corner sharing MO4 tetrahedra or MO3 trigonal
planes . Three types of oxides are of interest in glass chemistry:
(1) Network Formers
Oxides that readily form glasses when quenched from high
temperatures, e.g. SiO2, P2O5, B2O3 etc.
(2) Network Modifiers
Oxides that that can be mixed with network formers to yield glasses.
They are typically ionic and act by disrupting the network., e.g. Li2O,
Na2O, CaO etc.
(3) Network Intermediates
These oxide do not form glasses on their own, but when mixed with
glass formers may either act as network formers or network modifiers,
e.g. Al2O3, SnO2, TiO2 etc.
Lectures co-financed by the European Union in scope of the European Social Fund
Glass formation
Glasses are typically formed by rapid
cooling of melts and are thus
governed by kinetics, through the
control of the cooling rate.
In theory, every inorganic material,
within a certain compositional range,
can be transformed into a glass, if
extreme conditions of synthesis are
available
If the liquid cooling rate is sufficiently high, then instead of
crystallisation, the undercooled liquid is transformed into a supercooled
state. This state of the liquid is thermodynamically metastable, as it
possess a higher internal energy than the corresponding crystalline
state.
Lectures co-financed by the European Union in scope of the European Social Fund
A plot of entropy vs temperature
leads to the conclusion that a
glass, at 0K, would have a finite
amount of entropy known as the
zero-point entropy.
This is regarded as frozen-in
configurational entropy.
The described behaviour would be changed if the supercooled liquid
were cooled extremely slowly. In this case, the entropy of the
supercooled liquid would follow the dashed line and would be zero at a
positive temperature, T0.
Lectures co-financed by the European Union in scope of the European Social Fund
As a consequence, further cooling would result in a negative entropy of
the glass at 0 K.
Obviously, according to the third law of thermodynamics this hypothetical
behaviour is impossible and is known as the Kauzmann paradox.
This has been explained by considering that below T0 vibrational entropy
would still remain and this would be reduced to zero at 0 K in accordance
with the third law.
The major consequence of this is that glasses cannot be formed below
T0 (the Kauzmann temperature) and hence this temperature can be
identified as the ideal glass transition temperature.
Lectures co-financed by the European Union in scope of the European Social Fund
Thus glasses have a higher free energy than the corresponding crystal
and are considered metastable.
Lectures co-financed by the European Union in scope of the European Social Fund
Thermal Analysis of Glasses
When a glass is heated it exhibits characteristic thermal events, Tg the
glass transition temperature, Tc the crystallisation temperature and Tm
the melting temperature.
Lectures co-financed by the European Union in scope of the European Social Fund
DTA trace of 56Li2O:2ZrO2:40 P2O5
10
Tc
Heat Flow / microV
0
Tg
-10
-20
-30
-40
0
200
400
600
800
1000
o
Temerature / C
Lectures co-financed by the European Union in scope of the European Social Fund
Cation Conducting Glass Electrolytes
When oxides such as Li2O or Ag2O are used as a network modifiers,
the M+ ions are potentially mobile and can hop between available sites
in the glass.
Advantages over crystalline electrolytes:
While crystalline conductors show anisotropic conduction properties,
in glasses conduction is isotropic.
When used as real materials, crystalline electrolytes suffer from
grain boundary resistances which reduce their overall conductivity. In
monolithic glasses there are no grain boundaries.
Crystalline solid electrolytes generally have well defined composition
ranges. In glasses it is possible synthesize glasses with wide ranging
compositions and hence tailor specific properties such as conductivity,
air sensitivity and thermal stability.
Lectures co-financed by the European Union in scope of the European Social Fund
Monolithic Glass Batteries
Glass Electrodes
Substitution of the network forming oxide by suitable transition metal
oxides allows for the introduction of electronic conduction into the
system. This means that glasses can be synthesized which show
conductivities varying from pure ionic to pure electronic.
This could allow for the construction of a monolithic glass battery with
anode, cathode and electrolyte regions.
Lectures co-financed by the European Union in scope of the European Social Fund
In such a system is that the network extends throughout the glass
monolith and components are air stable.
Advantages:
Problems associated with electrode/electrolyte interface are
diminished, while grain boundary resistances are removed
altogether.
Cheap construction
Potentially miniaturisable therefore suitable for miniature power
supplies e.g. on board and on chip power sources.
Lectures co-financed by the European Union in scope of the European Social Fund
Ionic Conduction in Glasses
There is no single theory of ion transport in glasses to explain high ionic
conductivity. The three most important models are:
(1) The strong electrolyte model (Anderson-Stuart)
This is based on the assumption that effective carrier density Ni is
independent of ion concentration and temperature and thus i the
mobility, of these species is a quantity that depends on both parameters,
(ion concentration and temperature).
(2) The weak-electrolyte model
According to this model i is independent of ion concentration and is
weakly dependent on temperature, while Ni depends on both parameters.
(3) The defect model
This is based on the same principles as those identified in crystalline ion
conductors.
Lectures co-financed by the European Union in scope of the European Social Fund
According to the strong electrolyte model
a cation hops from an occupied site near
a non-bridging oxygen (NBO) to a vacant
site which is close to another NBO.
In doing this, the conducting ion has to
overcome the energy barrier generated
by the bridging oxygen (BO).
At first the mobile ion needs to remove
itself from association with NBO (binding
energy, Eb,).
The energy that is associated with long
range motion, is strain energy, ES.
Thus, the total activation energy for this
process is given as a sum of these
energies.
E  Eb  ES
(a) strong-electrolyte model
and (b) weak- electrolyte
model
Lectures co-financed by the European Union in scope of the European Social Fund
After necessary approximations this equation can be written as
zz oe2
2
E 
 4GrD  r  rD 
  r  ro 
Where, zo and ro are the charge and radius of the O2- ion, respectively,
 is a non-periodic lattice parameter determined by the distance
between neighbouring sites, r is the cation radius rD is the bottleneck
radius in the glass, G is the elastic modulus and  is a covalency
parameter.
The weak electrolyte model assumes the existence of two sites and
that the conduction process is dominated by the ions, which are
thermally brought to higher energy sites.
Lectures co-financed by the European Union in scope of the European Social Fund
Structural Characterisation of Glasses
Because there is no long range order, the structure of glasses are not
easily accessible using standard characterisation techniques such as
X-ray diffraction.
Other techniques such as NMR, IR, EXAFS and neutron scattering,
can be employed to probe the local structure.
Most of these techniques are also suitable for crystalline materials
where diffraction methods can give a clear picture of the structure.
Therefore it is possible to compare results from the glasses with
crystalline compounds of similar composition in order to yield the
structure of the glass.
The preferred coordination environments of ions in oxides will be the
same whether in glass or crystalline forms.
Lectures co-financed by the European Union in scope of the European Social Fund
Glass Structure
Glass forming oxides
typically adopt
tetrahedral or trigonal
planar coordination
environments.
These can be classified
according to the Qn
nomenclature. Where n
represents the number
of bridging oxygens.
Lectures co-financed by the European Union in scope of the European Social Fund
Solid State NMR
NMR is a nucleus specific technique that can yield important
information on local structure.
Atomic nuclei are made up of protons and neutrons (except 1H).
The nuclear spin results from the coupling of these nucleons and is
characterised by the spin quantum number I
I can have integral, half integral or zero values. Nuclei with an odd
mass number have half-integral spins e.g.1H I = 1/2, 7Li I = 3/2
Nuclei with an even mass number and even charge number have zero
spin e.g. 12C and 16O I = 0
Nuclei with an even mass number, but with an odd charge number
have integral spins, e.g. 14N and 6Li I =1
Lectures co-financed by the European Union in scope of the European Social Fund
The motion of charged particles has an associated magnetic field. If a
nucleus possesses angular momentum then there is an associated
magnetic moment .
Let us represent the magnetic moment by a vector
No Applied field
Random orientation
Applied field
Parallel or antiparallel to
applied field direction
Lectures co-financed by the European Union in scope of the European Social Fund
mI = -1/2
mI = 1/2
In an applied field the
energy of the nucleus is
dependent on the magnetic
quantum number mI
Energy
This interaction of the magnetic moment with the applied static magnetic
field is known as the Zeeman interaction.
Lectures co-financed by the European Union in scope of the European Social Fund
In order to obtain an NMR spectrum
we need to excite nuclei. This is
achieved using a radio frequency
pulse.
rf
Energy
The resulting NMR spectrum
shows an absorption of the rf
frequency. The resonance
frequency is proportional to the
strength of the applied field.
Lectures co-financed by the European Union in scope of the European Social Fund
Chemical shift
One of the most important features of NMR is the chemical shift. This is
caused by nuclei with differing degrees of shielding. This means that
they absorb at different applied field strengths.
Electrons surrounding each nucleus interact with the magnetic field
causing a circulation of the electronic charge around the nucleus. This
results in a secondary magnetic field at the nucleus that is opposed to
the applied field.
Thus the circulating electrons
shield the nucleus from the full
extent of the applied field.
Lectures co-financed by the European Union in scope of the European Social Fund
Electron withdrawal causes a de-shielding effect, while electron donation
causes a shielding effect. The degree of shielding is dictated by the
chemical environment, i.e. the neighbouring atoms/ions and the nature of
the bonding.
The resulting chemical shift of the resonance is therefore characteristic
of particular chemical environments.
Chemical shifts are recorded with respect to a standard reference
Chemical shift ( ppm) =
(observed resonance frequency – resonance frequency of standard)
____________________________________________________
operating frequency
Lectures co-financed by the European Union in scope of the European Social Fund
Dipolar interactions between spins can occur. In the case of
interaction between like spins, for a single nucleus the spectrum would
consist of two lines with peak separation given by:
3  2 2
2
V 
1

3
cos

3
2 r


Where
 is the gyromagnetic ratio for a particular nucleus
 is the angle between the internuclear vector and the magnetic field
r is the distance between nuclei.
A similar equation can be written for interactions between unlike spins.
Lectures co-financed by the European Union in scope of the European Social Fund
This interaction occurs between a nucleus and all of its neighbours. In
addition in a randomly orientated polycrystalline solid this interaction is
averaged over all values of . This leads to severe broadening of spectra
compared to solution state NMR.
The peculiar line shape of
solid state spectra is due
to directionally dependent
differences in shielding.
This is known as
chemical shift
anisotropy.
Lectures co-financed by the European Union in scope of the European Social Fund
The solid state line shape can be described by the chemical shift
tensor which has three principal components which are ordered
according to the Haeberlen convention
|33- iso| > |11-iso| > |22-iso|
Isotropic Chemical Shift
iso = (11 + 22 + 33)/3
Chemical Shift Anisotropy
 = 33 - (11 + 22)/2
Asymmetry
h = (22 - 11)/(33 - iso)
Lectures co-financed by the European Union in scope of the European Social Fund
In order to narrow the line width and minimise the effects of chemical
shift anisotropy, the sample can be spun in the magnet.
If the spinning sample is orientated at the so called magic angle of 54
44’ to the applied field then the term (1- 3cos2) = 0 and the spectrum
simplifies.
In order to reduce the spectrum to a single line, the sample must be spun
at frequency greater than or equal to the spread of frequency
corresponding to the anisotropy. At lower spinning speeds the spectrum
appears as a central isotropic peak flanked by spinning sidebands.
Lectures co-financed by the European Union in scope of the European Social Fund
31P
NMR spectra of lithium aluminium
titanium phosphate (LATP) glasses
(NMR-sp.)exp.
NMR-sp.)fit
difference
x
4.5
Intensity (a.u.)
3.5
3.0
1.5
1.25
Q1Li
Q1Ti/Al
0.5
-200
-100
0
100
200
Chemical shift (ppm)
Lectures co-financed by the European Union in scope of the European Social Fund
Q2
Derived NMR parameters for 31P spectrum of
LTP glass.
iso
ppm

ppm
h
Area
(%)
Q1Li
-3.2
136
0.0
12.8
Q1Ti
-10.4
119
1.0
41.5
-19
-158
0.6
45.7
Qn
Q 02
Lectures co-financed by the European Union in scope of the European Social Fund
The area of each peak (and its associated spinning sidebands) is
proportional to the number of phosphate atoms in a particular
environment. This means that the spectrum contains quantitative
information.
By taking the ratios of the different phosphate species present and with a
knowledge of the composition of the glass it is possible to calculate how
much oxygen is not associated with the phosphate network and therefore
bonded exclusively to Ti.
Since the number of Q1Ti species is known we can also calculate the
number of phosphate groups that are linked to Ti (i.e. coordination
number).
Hence it is possible from this simple 1-dimensional spectrum to derive a
structural formula for LTP glass.
Lectures co-financed by the European Union in scope of the European Social Fund
Structure of LTP glass
Ions
Network
Li+10Ti4+0.17(TiOO4/2)2-0.83 (PO2O2/2)-6.98(PO3O1/2)2-1.03
5-CN Ti
Q2 P
Q1 P
Lectures co-financed by the European Union in scope of the European Social Fund
27Al
NMR spectra of LATP glasses
[Al(OP)5]
[Al(OP)6]
[Al(OP)4]
x
intensity (a.u.)
4.50
2.50
0.50
300
200
100
0
-100
chemical shift (ppm)
-200
-300
Lectures co-financed by the European Union in scope of the European Social Fund
Compositional Variation of Al species in LATP
glasses
90
80
70
Al(OP)6
Al(OP)5
Intensity (%)
60
Al(OP)4
50
40
30
20
10
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Mol % Al2O3
Lectures co-financed by the European Union in scope of the European Social Fund
Electrode Glasses
Electrode glasses, show mixed ionic/electronic conduction.
e.g. in lithium manganese phosphate the Mn2+ ion is strongly
paramagnetic causing severe line broadening in NMR. However at low
concentrations it is possible to obtain spectra.
LMnP
(60-x)Li2O : (10-x)MnO : 40P2O5
Lectures co-financed by the European Union in scope of the European Social Fund
At x = 5, both Q1 and Q2 groups
are visible in the 31P spectrum
At x = 10, both sites are still
visible. However the relative
intensity of the Q1 resonance is
greatly reduced. This suggests
that Mn2+ is preferentially
located near Q1 sites.
Lectures co-financed by the European Union in scope of the European Social Fund
Trends in isotropic chemical shift (iso)
Trends in (iso) with composition can yield
important structural information.
For example in the glass system
(0.55-x)Na2O: xSrO:0.45P2O5 (0  x  0.55)
The glass network is a mixture of Q1
and Q2 phosphate groups
R. Pires, I. Abrahams, T.G. Nunes and G.E. Hawkes,
J. Non-Cryst. Solids. 337, 2004, 1.
Lectures co-financed by the European Union in scope of the European Social Fund
The trend observed iso, appears
to indicate a preferential
substitution of Na+ ions by Sr2+
associated with the Q1 phosphate
species and subsequent
substitution of the Q2 associated
cations.
This suggests that the distribution
of cations is non-random. At the
critical composition (x  0.20)
Sr2+ is predominantly associated
with Q1 phosphate groups, while
Na+ is predominantly associated
with Q2.
Lectures co-financed by the European Union in scope of the European Social Fund
EXAFS
Extended X-ray Absorption Fine Structure (EXAFS) is a useful technique
for examining the local environment around an atom. It is element specific
and so is useful for distinguishing different species in mixed systems. It is
useful in both crystalline and amorphous solids.
The EXAFS phenomenon is weak and requires a high intensity X-ray beam
as obtained at a synchrotron source.
If a sample is irradiated with X-rays of a small range of energies then when
the energy of an X-ray matches the binding energy of a core electron in a
specific element, absorption occurs and the electron is either promoted to a
higher energy level or ejected.
By measuring the X-ray absorption coefficient  as a function of photon
energy an X-ray absorption spectrum is obtained. resulting transmitted (or
reflected) intensity an X-ray absorption spectrum is obtained.
 Im 
  ln 
 I0 
where Im is the measured intensity
(transmitted) and I0 is the incident
intensity.
Lectures co-financed by the European Union in scope of the European Social Fund
The region just before and after the edge is known as the X-ray Absorption
Near Edge Structure. While the EXAFS is present as small post edge
oscillations.
Lectures co-financed by the European Union in scope of the European Social Fund
The XANES region can be analysed for information on the oxidation state
of metals.
Structural information is obtained from the EXAFS part of the spectrum
which is typically in the rage 400 to 1000 eV above the absorption edge.
The energy in this range is much higher than the binding energy of the
electron and so the excited electron has a high kinetic energy and is
ejected.
On leaving the atom the electron wave undergoes interference with
electrons in neighbouring atoms. The resulting constructive and
destructive interference gives rise to oscillations in the absorption cross
section  seen in the EXFAS region of the XAS spectrum.
The outgoing electron wave will be backscattered by its neighbours.
Therefore the pattern is a complex mixture of scattered and backscattered
waves.
Lectures co-financed by the European Union in scope of the European Social Fund
The energy data (E) in eV are usually transformed to wave vector to
wave vector k for analysis.
 2m  E  E  
k e 2 0 



1
2
where E0 is the absorption edge energy, me is the mass of an electron
and  is h/2.
The amplitude of each EXAFS wave depends on the number of
surrounding atoms and their backscattering power (i.e. their atomic
number) and the distance between the excited atom and the
backscattering atom. One can define the total EXAFS spectrum (k)
as the sum of individual EXAFS contributions in a multi-component
system.
 k    i k 
i
Lectures co-financed by the European Union in scope of the European Social Fund
i(k) can be defined as:
N S S02 AS k 
  2Ras 
2 2
i k  
exp  2k  as exp
 sin 2kRas  as k 
2
kRas
  


Where Ns is the number of backscattering atoms at distance Ras from the
absorbing atom, As is the backscattering strength of the backscattering
atom, S0 is a passive electron reduction factor in the interaction,  2 is
the Debye-Waller factor,  is the mean free path of the electron and as
is the phase shift of the wave.
Analysis of the EXAFS spectrum yields Ns, Ras and  2as
There are a number of theoretical approaches to modelling EXAFS data.
We will not discuss these here.
Lectures co-financed by the European Union in scope of the European Social Fund
NaCaP3O9 glass
Na spectrum
Observed
Calculated
3
Observed
Calculated
10
2
I[FT(k . (k)]
8
3
6
3
k . (k)
1
0
4
-1
2
-2
0
2
3
4
5
6
7
8
0
2
-1
k (Å )
4
6
r (Å)
R1 = 2.317(7) Å
22 = 0.034(2) Å2
N1 = 6
R2 = 3.16(8) Å
22 = 0.07(2) Å2
N2 = 6
Lectures co-financed by the European Union in scope of the European Social Fund
8
10
Diffraction by glasses
In diffraction experiments amorphous materials show no Bragg peaks, but
they do exhibit scattering that can be analysed.
For analysis of glass diffraction data we transform the data to Q space
where:
4
2
Q
sin  

d
 = Bragg angle,  = wavelength and d = d-spacing.
Lectures co-financed by the European Union in scope of the European Social Fund
In order to get good radial distribution function data. the range of Q should
be large. Typically neutron data allows Q ranges up to ca. 50 Å-1 while in
X-ray data the maximum useable Q value is close to 20 Å-1
For laboratory X-ray data, Cu tubes have maximum Q value around 8 Å-1.
Ag tubes increase the Q-max to ca. 20 Å-1
Synchrotron radiation is commonly used for X-ray experiments. The total
interference function F(Q) is given by
F Q    c c b b S Q   1
n
 ,
Where c represents the fraction of a chemical species, b is the mean
scattering length and S is the partial structure factor. The total pair
correlation function G(r) is obtained by Fourier transfor of F(Q), while
individual pair correlations gi,j(r) are obtained by Fourier transform of
the partial structure factors.
Lectures co-financed by the European Union in scope of the European Social Fund
b
Neutron diffraction correlation functions for lithium borate glasses
Swenson et al. Phys Rev. B. 52 (1995) 9310
For more detail see Lecture 15 January lectures.
Lectures co-financed by the European Union in scope of the European Social Fund