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 interstitialmobile vacancy

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 = n Z e µ� 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

< 10-10Insulators

10-3-104Semiconductors

103-107MetalsElectronic conductors10-1-103Liquid electrolytes10-1-103Solid Electrolytes

< 10-16 – 10-2Ionic crystalsIonic conductorsConductivity (S m-1)Material

Ionic conductivity in NaCl

� NaCl is a poor ionic conductor

� Conduction involves migration of cationvacancies

� 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 defectsAt High T, conductivity isdue 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

0.27-0.50Dissociation of vacancy –Mn2+ pair

~1.3Dissociation of vacancy pair

2.18-2.38Formation of Schottky pair

0.90-1.10Migration of Cl-

0.65-0.85Migrationof Na+, Em

Activation energy (eV)Process

AgCl

� The predominant defect in AgCl is cation Frenkel

� Cation interstitials are more mobile than cationvacancies

� 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 interstitial2) 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+ impurityon conductivity – Presence of Cd2+ reducesnumber 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+ + 2e-

� 2Na+ + 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