Ionic conductors
Ionic solids contain defects that allow the migration of
ions in an electric field
Some solid materials have very high ionic
conductivities at reasonable temperatures
– useful in solid state devices
mobile vacancy
mobile interstitial
Applications of solid ionic conductors
Membranes in separation processes
Electrolytes in sensors
Electrolytes in fuel cells and batteries
– should be a poor electronic conductor
Electrode materials in solid state batteries
– should be a good electronic and ionic
conductor
Factors effecting the conductivity
σ=nZeµ
Conductivity is influenced by 1)the carrier concentration n,
2) the carrier mobility µ
Usually, defects act as the charge carriers
– not many defects in most ionic solids
– mobility is usually low at room temperature
Material
Conductivity (S m-1)
Ionic crystals
< 10-16 – 10-2
Solid Electrolytes
10-1-103
Liquid electrolytes
10-1-103
Metals
103-107
Semiconductors
10-3-104
Insulators
< 10-10
Ionic conductors
Electronic conductors
Ionic conductivity in NaCl
NaCl is a poor ionic
conductor
Conduction involves
migration of cation
vacancies
Cation vacancies are
present due to
– doping - extrinsic defects
– Schottky defects - intrinsic
defects
Conduction is an activated process
µ = µ0 exp (-Ea/kT) - Arrhenius equation
Temperature dependence of conductivity
σ = (σ0/T) exp(-Ea/kT)
– Contribution from mobility and defect formation
Idealized conductivity for NaCl
At low T conductivity is
dominated by mobility of
extrinsic defects
At High T, conductivity is
due to thermally formed
(intrinsic) defects
Intrinsic versus extrinsic conductivity
Extrinsic conductivity
– σ = (σ0/T) exp(-Ea/kT)
– carrier concentration is fixed by doping
Intrinsic conductivity
– carrier concentration varies with temperature
– σ = (σ’0/T) exp(-Ea/kT) exp(-∆HS/2kT)
– slope of plot gives Ea + ∆HS/2
Cation vacancy migration mechanism
Cations can not hop from site to site via a
direct route
– not enough space
Cations migrate via an interstitial site
– this is a tight squeeze and requires energy
Experimental conductivity of NaCl
Broadly
as expected
– Get deviation at low T due
to vacancy pairing
– Get deviation at high T due
to screening of mobile
defects by defects of
opposite charge
» Debye-Huckle type model
Energetics of ionic conduction in NaCl
Process
Activation energy (eV)
Migrationof Na+, Em
0.65-0.85
Migration of Cl-
0.90-1.10
Formation of Schottky pair
2.18-2.38
Dissociation of vacancy pair
~1.3
Dissociation of vacancy –
Mn2+ pair
0.27-0.50
AgCl
The predominant defect in AgCl is cation
Frenkel
Cation interstitials are more mobile than cation
vacancies
Cation interstitials can migrate by one of two
mechanisms
– direct movement
– indirect movement
Migration mechanism in AgCl
Two possible pathways for interstitial migration:
1) move directly from interstitial to interstitial
2) interstitial displaces regular cation onto
interstitial position
Migration actually occurs by second pathway
Evidence for the indirect mechanism
Both charge and mass transport through a crystal
can be measures
– conductivity gives charge mobility
– diffusion measurements using radiolabelled Ag+ gives
mobility of Ag+
Charge is transported twice as fast as Ag+ ions
suggesting the indirect mechanism is correct
Doping in AgCl
Doping AgCl with a divalent impurity like Cd2+
reduces the ionic conductivity of the specimen
There is an equilibrium between cation vacancies
and Ag+ interstitials
– doping increases vacancy concentration
– doping decreases interstitial concentration
Cd2+ doped AgCl
Schematic showing effect of Cd2+ impurity
on conductivity – Presence of Cd2+ reduces
number of Ag+ interstitials and hence
lowers conductivity
Get minimum in conductivity
curve when doped – at high
impurity concentrations
conductivity is dominated by
cation vacancy migration, at
low concentrations interstitial
migration dominates
Solid electrolytes
There is a technological need for solids that have
very high ionic conductivities
Such materials are referred to as FAST ION
CONDUCTORS
They include:
–
–
–
–
α AgI
Na β alumina
NASICON, Na1+xZr2[(PO4)3-x(SiO4)x]
Stabilized zirconias
Ionic conductivity of some good solid electrolytes
β=- alumina
Na1+xAl11O17+x/2 (β) and Na1+xMgxAl11-xO17 (β”) are
good sodium ion conductors at moderate temperatures
Na ions have high mobility and can be ion exchanged
with a wide variety of other cations
M2O.x Al2O3 x = 5 - 11
–
–
–
–
M = Alkali+, Cu+, Ag+, Ga+, In+, Tl+, NH4+
x = 5-7 usually produces β” material
x = 8 - 11 gives β material
β” material usually stabilized by addition of Li+ or Mg2+
The structures of β and β” alumina
The structure of β - alumina
Conduction plane of β alumina
The sodium sulfur cell
Sodium sulfur cells have a
high energy density
– useful for electric vehicles
There are safety concerns
– molten sodium
2Na(l) --> 2Na+ + 2e2Na+ + 5S(l) + 2e- ---->
Na2S5(l)
Sodium sulfur phase diagram
Need to operate at high temperatures
Can not fully discharge cell (solidifies)
Silver iodide
At low temperatures AgI adopts either a Wurtzite
or zinc blende structure
– Ag+ fills half of the tetrahedral holes in a close packed
I- array
Above 146o C it transforms to a BCC structure
with the Ag+ filling a small fraction of the
available tetrahedral sites
– the cation sublattice “melts”
σ ~ 130 Sm-1
The structure of α - AgI
Cation sites in α=- AgI
Ionic conduction in α=- AgI
There are many possible sites for Ag+
– 12 tetrahedral
– 24 trigonal
– 6 octahedral
There are only 2 Ag+ ions per unit cell!
– these ions are found disordered on the tetrahedral sites
Motion between sites is facile
– ~0.05 eV activation barrier
RbAg4I5
AgI is polymorphic. The high
temperature α phase has a
high ionic conductivity
associated with a melted Ag+
sublattice
At low T ionic conductivity
drops
RbAg4I5 discovered while
trying to find materials that still
had α – AgI structure at low T
RbAg4I5
Highest
room temperature ionic conductivity of
any crystalline solid, 0.25 S cm-1
– Not stable < ~25 °C
Cu2HgI4
Material shows an order disorder phase
transition similar to AgI
– color change at phase transition
– marked increase in ionic conductivity at phase
transition
Structure has FCC array of I- with cations
filling tetrahedral holes
– at low T cations are ordered
– at high T they are disordered over all sites
The structure of Cu2HgI4 at low T
Stabilized zirconias
Y2O3 and CaO can be
dissolved in ZrO2
– creates a lot of oxygen
vacancies
At high temperatures
the defects are mobile
– oxide ion conductor
Applications of stabilized zirconia
Oxide conductors are of use for
– oxygen sensors
» based on concentration cell, can be used to measure O2 in
exhaust gases, molten metals …
– fuel cell membranes
ZrO2 is only usable at high temperatures
An oxygen sensor
An O2 concentration cell can be built
E = [2.303RT/4F] log(p’/pref)
Fuel cells
Fuel
cells are
devices for the
direct conversion
of fuels such as
CH3OH, H2, CO to
electrical energy
Solid oxide fuel cells
Fuel cells offer an
efficient and clean
way of using fossil
fuels, but
– high cost
– thermal cycling
problems
Solid oxide fuel cell performance
from a paper by S.C. Singhal in Proceedings of the Fourth International Symposium on Solid Oxide Fuel Cells, 1995
Electrochromic devices
Color
changes such
as those needed in
smart windows can
be achieved by
moving ions into a
suitable solid
Lithium batteries
Batteries
based on
lithium are attractive
as they can be light a
have a very high
voltage output
– Considerable current
research on cathodes
and electrolytes for
these devices