Defects, non-stoichiometry, solid solutions and ionic conductivity in ...

Defects, non-stoichiometry, solidsolutions and ionic conductivity inthe solid stateNot based on Atkins and Shriver,although the solid state section doescover some of this material

Defects in crystals• It is not possible to make crystals that are perfect inevery respect– some are more perfect than others• It takes energy to create defects in crystals• The presence of defects increases the entropy of thecrystal– above absolute zero always expect some intrinsic defects

Non-stoichiometric compoundsTiO x “TiO” 0.65 < x < 1.25“TiO 2 ” 1.998 < x < 2.000VO x “VO” 0.79 < x < 1.29Mn x O “MnO” 0.848 < x< 1.000Ni x O “NiO” 0.999 < x < 1.000Li x V 2 O 5 0.2 < x < 0.33

The thermodynamics of defect formation All macroscopic samples of materials contain somedefects as defect formation is entropically favored– when defect formation is enthalpically very unfavorable theremay be very small numbers of defects

Types of defect• Defects may occur in isolation due to the increase inentropy of the crystal– intrinsic point defects• May occur in isolation to balance the presence of animpurity– extrinsic point defect• Defect may occur throughout the crystal– extended defect

Intrinsic point defects• Two common types of intrinsic point defect– Schottky and Frenkel• A Schottky defect consists of charge balancing cationand anion vacancies– Found in NaCl• A Frenkel defect is a charge balancing interstitial andvacancy– can have cation or anion Frenkel defects

Schottky and Frenkel defectsShottky defect in NaCl- both cation and anion are missing fromtheir regular lattice sites-at room temp on 1 in 10 15 sites are vacant in NaCl-200 kJmol -1 creation energyCation Frenkel defect in AgCl-cation is displaced from regular latticesite onto interstitial site- 130 kJ mol -1 creation energy

Frenkel defects• Frenkel defects may occur on either the anionor cation sublattice• Cation Frenkel defects are more common thananion defects– cations are smaller than anions and hence easier toaccommodate in interstitial positions• Fluorite structures (CaF 2 , SrF 2 , ZrO 2 , UO 2 ) aregood at accommodating anion Frenkel defects

∆H f for defects

Imaging plates• Color centers are useful in medical X-raysusing BaFBr:Eu 2+ phosphors

BaFBr:Eu 2+ phosphors

Extrinsic point defects• If cationic impurities are introduced into a solid and thedopant does not have the same valence as the cation it isreplacing extrinsic defects will be introduced–Fe 1-x O has cation vacancies–Ca 2+ in ZrO 2 - anion vacancies–Y 3+ in ZrO 2 - anion vacancies–Ca 2+ or Cd 2+ in NaCl- cation vacancies• Real crystals contain both intrinsic and extrinsic defects– the dominant defect type depends upon temperature anddoping/nonstoichiometry level

Nonstoichiometric 3d oxides

FeO• Wustite is a very well studied example of anonstoichiometric compound• The compound “FeO” is not stable• The stoichiometry is always Fe 1-x O

The iron oxygen phase diagram

The nature of the defects in “FeO”• Density measurements confirm that thenonstoichiometry is incorporated by having vacantiron sites• There is Fe(III) present to charge compensate thesystem

The defect structure of “FeO”• The defect structure is more complicated thanrandom iron vacancies and Fe(III)

Koch clusters in Fe 1-x O

The Fluorite structure

Defect clusters in UO 2+x Excess oxygen isincorporated in interstitialsites– This leads to displacementof oxygens from normalsites– Arrangement of defects issimilar to structure of U 4 O 9» Can view defects as formingclusters of U 4 O 9 in UO 2matrix

Substitutional solid solutions In many compounds it is possible to replace a metalatom or ion with another element that has similar sizeand bonding requirements– In metal alloy can replace metal atom with another elementthat is within 15% size– Can get complete solid solution formation between Al 2 O 3and Cr 2 O 3 –Al 2-x Cr x O 3– Extensive solid solution formation is favored by hightemperatures due to the disorder associated with the solidsolution

Criteria for solid solution formation Typically, for an ionic solid the ion size differenceshould be less than 15-20% to get complete solidsolution formation– > 30% size difference usually precludes solid solutionformation End member of solid solution should have samestructure if complete solid solutions is to form–Zn 2 SiO 4 and Mg 2 SiO 4 have different metal coordination»So Zn 2-x Mg x SiO 4 and Mg 2-x Zn x SiO 4 have different structures

Interstitial solid solutionsSome solid solutions involve inserting atomsinto interstitial sites in a parent structure–PdH x 0 < x < 0.7 - hydrogen occupies interstitialsites in fcc Pd– Carbon in interstitial sites of fcc Fe

Aliovalent substitution If you replace an ion by one with a different oxidationstate (aliovalent substitution) there has to be a chargecompensation mechanism Cation vacancies– Dope calcium into NaCl – Na 1-2x Ca x V x Cl– Replacement of Mg 2+ by Al 3+ in spinel»[Mg 1-3x V x Al 2x ] tet [Al 2 ] oct O 4– Oxidation of NiO»Ni 2+ 1-3xV x Ni 3+ 2xO

Aliovalent substitution Interstitial anions– Not common due to limited size of interstitial sites butoccurs for fluorite structure»Ca 1-x Y x F 2+x»U 4+ 1-xU 6+ xO 2+x Anion vacancies– Important in ionic conductors»Zr 1-x Ca x O 2-x 0.1 < x < 0.2 Interstitial cations–Li x (Si 1-x Al x )O 2 stuffed quartz structure (0 < x < 0.5)

Characterizing solid solutionsCan determine if solid solution forms bymeasuring lattice constants of material usingx-ray diffraction– Lattice constants typically vary linearly with solidsolution composition» Vegard’s lawCan work our mechanism of solid solutionformation with the aid of densitydetermination

Ionic conductors• Ionic solids contain defects that allow the migration ofions in an electric field• Some solid materials have very high ionicconductivities at reasonable temperatures– useful in solid state devicesmobile vacancymobile 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 ionicconductor

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 temperatureIonic conductorsElectronic conductorsMaterialIonic crystalsSolid ElectrolytesLiquid electrolytesMetalsSemiconductorsInsulatorsConductivity (S m -1 )< 10 -16 –10 -210 -1 -10 310 -1 -10 310 3 -10 710 -3 -10 4< 10 -10

Ionic conductivity in NaCl• NaCl is a poor ionicconductor• Conduction involvesmigration of cationvacancies• Cation vacancies arepresent due to– doping - extrinsic defects– Schottky defects - intrinsicdefects

Conduction is an activated process• µ = µ 0 exp (-Ea/kT) - Arrhenius equation

Temperature dependence of conductivity• σ = (σ 0 /T) exp(-Ea/kT)– Contribution from mobility and defect formation

Idealized conductivity for NaClAt low T, conductivity isdominated by mobility ofextrinsic defectsAt High T, conductivity isdue to thermally formed(intrinsic) defects

Intrinsic versus extrinsic conductivity• Extrinsic conductivity– σ = (σ 0 /T) exp(-E a /kT)– carrier concentration is fixed by doping• Intrinsic conductivity– carrier concentration varies with temperature– σ = (σ’ 0 /T) exp(-E a /kT) exp(-∆H S /2kT)– slope of plot gives E a + ∆H S /2

Experimental conductivity of NaClBroadly as expected– Get deviation at low T dueto vacancy pairing– Get deviation at high T dueto screening of mobiledefects by defects ofopposite charge» Debye-Huckle type model

Energetics of ionic conduction in NaClProcessActivation energy (eV)Migrationof Na + , E m0.65-0.85Migration of Cl - 0.90-1.10Formation of Schottky pairDissociation of vacancy pairDissociation of vacancy –Mn 2+ pair2.18-2.38~1.30.27-0.50

AgCl• The predominant defect in AgCl is cationFrenkel• Cation interstitials are more mobile than cationvacancies• Cation interstitials can migrate by one of twomechanisms– direct movement– indirect movement

Migration mechanism in AgClTwo possible pathways for interstitial migration:1) move directly from interstitial to interstitial2) interstitial displaces regular cation ontointerstitial positionMigration actually occurs by second pathway

Evidence for the indirect mechanism• Both charge and mass transport through a crystalcan be measured– conductivity gives charge mobility– diffusion measurements using radiolabelled Ag + givesmobility of Ag +• Charge is transported twice as fast as Ag + ionssuggesting the indirect mechanism is correct

Solid electrolytes• There is a technological need for solids that havevery high ionic conductivities• Such materials are referred to as FAST IONCONDUCTORS• They include:– α AgI–Na β alumina– NASICON, Na 1+x Zr 2 [(PO 4 ) 3-x (SiO 4 ) x ]– Stabilized zirconias

Ionic conductivity of some good solid electrolytes

β - alumina• Na 1+x Al 11 O 17+x/2 (β) and Na 1+x Mg x Al 11-x O 17 (β”) aregood sodium ion conductors at moderate temperatures• Na ions have high mobility and can be ion exchangedwith a wide variety of other cations• M 2 O.x Al 2 O 3 x = 5 - 11– M = Alkali + , Cu + , Ag + , Ga + , In + , Tl + , NH 4+– x = 5-7 usually produces β” material– x = 8 - 11 gives β material– β” material usually stabilized by addition of Li + or Mg 2+

The structures of β and β” alumina

The sodium sulfur cell• Sodium sulfur cells have ahigh energy density– useful for electric vehicles• There are safety concerns– molten sodium• 2Na (l) 2Na + + 2e -• 2Na + + 5S (l) + 2e - Na 2 S 5(l)

Silver iodide• At low temperatures AgI adopts either a Wurtzite orzinc blende structure–Ag + fills half of the tetrahedral holes in a close packed I -array• Above 146 o C it transforms to a BCC structure withthe Ag + filling a small fraction of the availabletetrahedral 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

RbAg 4 I 5• AgI is polymorphic. The hightemperature α phase has ahigh ionic conductivityassociated with a melted Ag +sublattice• At low T ionic conductivitydrops• RbAg 4 I 5 discovered whiletrying to find materials that stillhad α – AgI structure at low T

RbAg 4 I 5 Highest room temperature ionic conductivity ofany crystalline solid, 0.25 S cm -1– Not stable < ~25 °C

Stabilized zirconias• Y 2 O 3 and CaO can bedissolved in ZrO 2– creates a lot of oxygenvacancies• At high temperaturesthe 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 O 2 inexhaust gases, molten metals …– fuel cell membranes• ZrO 2 is only usable at high temperatures

An oxygen sensor• An O 2 concentration cell can be built• E = [2.303RT/4F] log(p’/p ref )

Fuel cellsFuel cells aredevices for thedirect conversionof fuels such asCH 3 OH, H 2 , CO toelectrical energy

Solid oxide fuel cells• Fuel cells offer anefficient and cleanway of using fossilfuels, but– high cost– thermal cyclingproblems

Electrochromic devicesColor changes suchas those needed insmart windows canbe achieved bymoving ions into asuitable solid

Lithium batteriesBatteries based onlithium are attractiveas they can be light ahave a very highvoltage output– Considerable currentresearch on cathodesand electrolytes forthese devices