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Simple and Complex Defects
Nalini Vajeeston
Department of Chemistry University of Oslo FERMiO Gaustadalleen 21
NO-0349 Oslo Norway
Introduction
Kroumlger -Vink notations
Proton defects in oxides
Simple defect materials Acceptor doped-LaNbO4
Phosphates and pyrophosphates
Complex defect materials Ba2In2O5
Mayenite (Ca12Al14O33)
Ba3La(PO4)3
Summary
Outline
Introduction
Deviations from the ideal structures are present at any temperature and occur naturally in all crystalline compounds These deviations or imperfections are called defects
Defects in stoichiometric compounds(crystal composition is unchanged)
Schottky and Frenkel defects
bull Defect Structure
A complete description of the point and electronic defects in a compound and their concentrations as a function of the partial pressures of the constituents and the temperature is termed the defect structure of the compound
bull Defects
Defects in non-stoichiometric compounds (formed by introducing dopants or impurities) (composition is changed)
Cation vacancies interstitial anionsoxygen vacancies and electronic holes
Kroger-Vink notations for simple defects
Defect Type Notation Defect Type Notation
Non-metal vacancy at non-metal site
vX Impurity non-metal (Y) at non-metal site
YX
Metal vacancies at metal site vM Impurity metal (A) at metal site
AM
Neutral vacancies vXMvX
X Non-metal vacancies with positive effective charge
vbullX
Metal vacancies with negative effective charge
vM Interstitial metal Mi
Interstitial non-metal Xi Intertitial metal with positive effective charge
Mbulli
Interstitial non-metal with negative effective charge
Xi Free positive hole hbull
Free electron e Substitutional hydroxide OHbullO
The effective charge is the charge that the defect has with respect to the normal crystal lattice
bull The total effective charge is the same before and after the formation of the defects (The net charge on the left and right hand sides of a reaction equation must be the same)
Electroneutrality
Defect reactionsMass balance
bull The defect reaction must balance with respect to the massbull Vacancies which only represent empty sites have zero mass and do not countbull Electronic defects are not considered to count in the mass balance
Ratios of regular lattice sites
bull The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constantbull No sites are created in the formation of electronic defects
Hydrogen defects in metal oxides
When a metal oxide is equilibrated in gas mixtures with hydrogen containinggases eg H2O hydrogen will dissolve in the metal oxide The extent of the dissolution of hydrogen will depend on the defect structureof the oxide and the ambient oxygen and hydrogen activities
The dissolution of protons from water vapour may in these terms be written
g2
OxO2 O
2
12e2OH2OH
gO
OHO
oO
pO
pnOHK
2
2
2x
2
122
][
][
The concentration of protons in metal oxides is dependent on the partialpressures of both the ambient oxygen and water vapour as well as theconcentration of electronic defects
Defect equilibrium
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Introduction
Kroumlger -Vink notations
Proton defects in oxides
Simple defect materials Acceptor doped-LaNbO4
Phosphates and pyrophosphates
Complex defect materials Ba2In2O5
Mayenite (Ca12Al14O33)
Ba3La(PO4)3
Summary
Outline
Introduction
Deviations from the ideal structures are present at any temperature and occur naturally in all crystalline compounds These deviations or imperfections are called defects
Defects in stoichiometric compounds(crystal composition is unchanged)
Schottky and Frenkel defects
bull Defect Structure
A complete description of the point and electronic defects in a compound and their concentrations as a function of the partial pressures of the constituents and the temperature is termed the defect structure of the compound
bull Defects
Defects in non-stoichiometric compounds (formed by introducing dopants or impurities) (composition is changed)
Cation vacancies interstitial anionsoxygen vacancies and electronic holes
Kroger-Vink notations for simple defects
Defect Type Notation Defect Type Notation
Non-metal vacancy at non-metal site
vX Impurity non-metal (Y) at non-metal site
YX
Metal vacancies at metal site vM Impurity metal (A) at metal site
AM
Neutral vacancies vXMvX
X Non-metal vacancies with positive effective charge
vbullX
Metal vacancies with negative effective charge
vM Interstitial metal Mi
Interstitial non-metal Xi Intertitial metal with positive effective charge
Mbulli
Interstitial non-metal with negative effective charge
Xi Free positive hole hbull
Free electron e Substitutional hydroxide OHbullO
The effective charge is the charge that the defect has with respect to the normal crystal lattice
bull The total effective charge is the same before and after the formation of the defects (The net charge on the left and right hand sides of a reaction equation must be the same)
Electroneutrality
Defect reactionsMass balance
bull The defect reaction must balance with respect to the massbull Vacancies which only represent empty sites have zero mass and do not countbull Electronic defects are not considered to count in the mass balance
Ratios of regular lattice sites
bull The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constantbull No sites are created in the formation of electronic defects
Hydrogen defects in metal oxides
When a metal oxide is equilibrated in gas mixtures with hydrogen containinggases eg H2O hydrogen will dissolve in the metal oxide The extent of the dissolution of hydrogen will depend on the defect structureof the oxide and the ambient oxygen and hydrogen activities
The dissolution of protons from water vapour may in these terms be written
g2
OxO2 O
2
12e2OH2OH
gO
OHO
oO
pO
pnOHK
2
2
2x
2
122
][
][
The concentration of protons in metal oxides is dependent on the partialpressures of both the ambient oxygen and water vapour as well as theconcentration of electronic defects
Defect equilibrium
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Introduction
Deviations from the ideal structures are present at any temperature and occur naturally in all crystalline compounds These deviations or imperfections are called defects
Defects in stoichiometric compounds(crystal composition is unchanged)
Schottky and Frenkel defects
bull Defect Structure
A complete description of the point and electronic defects in a compound and their concentrations as a function of the partial pressures of the constituents and the temperature is termed the defect structure of the compound
bull Defects
Defects in non-stoichiometric compounds (formed by introducing dopants or impurities) (composition is changed)
Cation vacancies interstitial anionsoxygen vacancies and electronic holes
Kroger-Vink notations for simple defects
Defect Type Notation Defect Type Notation
Non-metal vacancy at non-metal site
vX Impurity non-metal (Y) at non-metal site
YX
Metal vacancies at metal site vM Impurity metal (A) at metal site
AM
Neutral vacancies vXMvX
X Non-metal vacancies with positive effective charge
vbullX
Metal vacancies with negative effective charge
vM Interstitial metal Mi
Interstitial non-metal Xi Intertitial metal with positive effective charge
Mbulli
Interstitial non-metal with negative effective charge
Xi Free positive hole hbull
Free electron e Substitutional hydroxide OHbullO
The effective charge is the charge that the defect has with respect to the normal crystal lattice
bull The total effective charge is the same before and after the formation of the defects (The net charge on the left and right hand sides of a reaction equation must be the same)
Electroneutrality
Defect reactionsMass balance
bull The defect reaction must balance with respect to the massbull Vacancies which only represent empty sites have zero mass and do not countbull Electronic defects are not considered to count in the mass balance
Ratios of regular lattice sites
bull The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constantbull No sites are created in the formation of electronic defects
Hydrogen defects in metal oxides
When a metal oxide is equilibrated in gas mixtures with hydrogen containinggases eg H2O hydrogen will dissolve in the metal oxide The extent of the dissolution of hydrogen will depend on the defect structureof the oxide and the ambient oxygen and hydrogen activities
The dissolution of protons from water vapour may in these terms be written
g2
OxO2 O
2
12e2OH2OH
gO
OHO
oO
pO
pnOHK
2
2
2x
2
122
][
][
The concentration of protons in metal oxides is dependent on the partialpressures of both the ambient oxygen and water vapour as well as theconcentration of electronic defects
Defect equilibrium
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Kroger-Vink notations for simple defects
Defect Type Notation Defect Type Notation
Non-metal vacancy at non-metal site
vX Impurity non-metal (Y) at non-metal site
YX
Metal vacancies at metal site vM Impurity metal (A) at metal site
AM
Neutral vacancies vXMvX
X Non-metal vacancies with positive effective charge
vbullX
Metal vacancies with negative effective charge
vM Interstitial metal Mi
Interstitial non-metal Xi Intertitial metal with positive effective charge
Mbulli
Interstitial non-metal with negative effective charge
Xi Free positive hole hbull
Free electron e Substitutional hydroxide OHbullO
The effective charge is the charge that the defect has with respect to the normal crystal lattice
bull The total effective charge is the same before and after the formation of the defects (The net charge on the left and right hand sides of a reaction equation must be the same)
Electroneutrality
Defect reactionsMass balance
bull The defect reaction must balance with respect to the massbull Vacancies which only represent empty sites have zero mass and do not countbull Electronic defects are not considered to count in the mass balance
Ratios of regular lattice sites
bull The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constantbull No sites are created in the formation of electronic defects
Hydrogen defects in metal oxides
When a metal oxide is equilibrated in gas mixtures with hydrogen containinggases eg H2O hydrogen will dissolve in the metal oxide The extent of the dissolution of hydrogen will depend on the defect structureof the oxide and the ambient oxygen and hydrogen activities
The dissolution of protons from water vapour may in these terms be written
g2
OxO2 O
2
12e2OH2OH
gO
OHO
oO
pO
pnOHK
2
2
2x
2
122
][
][
The concentration of protons in metal oxides is dependent on the partialpressures of both the ambient oxygen and water vapour as well as theconcentration of electronic defects
Defect equilibrium
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
bull The total effective charge is the same before and after the formation of the defects (The net charge on the left and right hand sides of a reaction equation must be the same)
Electroneutrality
Defect reactionsMass balance
bull The defect reaction must balance with respect to the massbull Vacancies which only represent empty sites have zero mass and do not countbull Electronic defects are not considered to count in the mass balance
Ratios of regular lattice sites
bull The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constantbull No sites are created in the formation of electronic defects
Hydrogen defects in metal oxides
When a metal oxide is equilibrated in gas mixtures with hydrogen containinggases eg H2O hydrogen will dissolve in the metal oxide The extent of the dissolution of hydrogen will depend on the defect structureof the oxide and the ambient oxygen and hydrogen activities
The dissolution of protons from water vapour may in these terms be written
g2
OxO2 O
2
12e2OH2OH
gO
OHO
oO
pO
pnOHK
2
2
2x
2
122
][
][
The concentration of protons in metal oxides is dependent on the partialpressures of both the ambient oxygen and water vapour as well as theconcentration of electronic defects
Defect equilibrium
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Hydrogen defects in metal oxides
When a metal oxide is equilibrated in gas mixtures with hydrogen containinggases eg H2O hydrogen will dissolve in the metal oxide The extent of the dissolution of hydrogen will depend on the defect structureof the oxide and the ambient oxygen and hydrogen activities
The dissolution of protons from water vapour may in these terms be written
g2
OxO2 O
2
12e2OH2OH
gO
OHO
oO
pO
pnOHK
2
2
2x
2
122
][
][
The concentration of protons in metal oxides is dependent on the partialpressures of both the ambient oxygen and water vapour as well as theconcentration of electronic defects
Defect equilibrium
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Effect of water vapour on oxygen-deficient M2O3
Undoped oxygen-deficient oxide
The predominant defects electrons and oxygen vacancies
Electroneutrality condition in dry environments
In wet environments
The predominant defects protons
Electroneutrality condition
612
313131 ][2][2
OX
OO pOKVnOV
][2 OVn
812
412
41][ OOHO ppKOHn
][ OOHn
Brouwer plot of effects of water vapour on defect concentrations in oxygen deficient M2O3-d
PO2 = constant PH2O = varied
Proton concentration is propotional to 212OHp
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
OxOO2 2OHOvOH
constant][A][OH]2[v OO
OHOO
O
pOv
OH
RT
ΔH
R
ΔS K
2]][[
][expexp
x
200
2
][OH-][A][v O
O
4
]Kp[O
]8[A11[O]Kp
][OHOH
xO
OH
O
2
2
Effect of water vapour on acceptor-doped M2O3
Hydration reaction Equilibrium constant
Electroneutrality
Concentration of protons
Brouwer plot of the effect of water vapour (at constant oxygen pressure) on defect concentrations in acceptor-dopedoxygen deficient M2O3
Oxygen vacancies and protons compensate the acceptor doping
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
4
272722 )(frac12frac12 POLn OPMOPM
44 242272 )()(frac12)(frac12 POPO HPOgOHOP
Proton defects in Phosphates (Sr-doped LaPO4)
Substitution of divalent metals for rare earth metalsleads to condensation of orthophosphate ions ie formation of pyrophosphate ions as oxygen deficits
Protons dissolve into phosphates forming hydrogen phosphate groups through the equilibrium betweenthe condensed phosphate ions and water vapor inambient atmosphere
The electroneutrality condition of an acceptor-doped phosphateswith oxygen vacancies and protons
constantMOPHPO LnPOPO
44 2724 )(2)(
Monoclinic monazite type structure
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
727272 OPOPg
xOP OHPOPOHOP )(2)()(3 72
82)(272
7272 OPOP OHPAOP )()(2 72
82
RT
H
R
S
OpHOP
OHPOPK hydrhydr
OP
OPOP
72
7272
expexp)(
)()(
23x
72
2
72
82
0)(2)()(3
7222
723
72 xOPOPOP 727272
OPOKpHOHPAOHP
3
1
3
1
3
72233
7223
7223
3
1
3
72233
7223
7223
23
1
72
32
)(2274)(233)(2272
)(2274)(233)(22723
2
3)(
xOP
xOP
xOP
xOP
xOP
xOP
OP
727272
727272
72
OPOKpHAOPOKpHOPOKpHA
OPOKpHAOPOKpHOPOKpHA
AAOHP
Proton defects in PyrophosphatesHydration reaction
Equilibrium constant
Electroneutrality
TiP2O7
Cubic superstructure
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Acceptor doped LaNbO4
LaNbO4 exists in two different polymorphs
Low temperature phase Monoclinic-Fergusonite-type structure
High temperature phase Tetragonal-Scheelite structure
Monoclinic Tetragonal
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
OOO2 OH2OVO(g)H
Condensation occurs when oxygen vacancy is formed in phosphate
Based on this oxygen vacancy in phosphate can be expressed as
42PO72OP
Same condensation can occur in LaNbO4
Oxygen vacancy in LaNbO4 can be written as
more complicated than phosphate
43NbO113ONb
The condensed coordinationpolyhedra of Nb3O11 found by theoretical calculation
LaNbO4 may have a tendency to dissolve ptotons by interacting with ambient water vapor
Electroneutrality condition constant][A][OH]2[v OO
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Ba2In2O5 (or BaInO25)
Ba2In2O5 is an oxygen deficient perovskite ordered into the brownmillerite-structureat low temperatures
Around 930 degC it disorders into the perovskite
The oxygen vacancy conductivity jumps two orders of magnitude
The disordered phase has 5 oxide ions and 1 oxide ion vacancy sharing the same perovskite site
Ov
what is the compensating negative effective charge
Defects
Perovskite
Brownmillerite-structure
The disordering can be seen as a anion-Frenkel-disorder (the formation of oxide ion vacancies and interstitials) Acceptor New nomenclature
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
][][ 35
65
31
65 3
5
31 OO vO 6][][ 3
5
65
31
65
OO
vO
Ba2In2O5 (or BaInO25)- new nomenclature
Disordered Ba2In2O5 oxide ions and vacancies on the oxide ion sublattice
The perfect oxide ion site is statistically occupied 56 with an oxide ion and 16 with a vacancy O6
5
Each oxide ion occupying the site to a degree of 56 has a formal charge -2
the site statistically has a charge of -2 56 = -53
Real charge of oxide ion = -2 Real charge of vacancy = 0Its effective charge = ‑2 ‑ (‑53) = -13 Effective charge = 0-(-53) = +53
The oxide ion is denoted in the expanded Kroumlger-Vink nomenclature as
31
65 O
O
Electroneutrality condition Site occupancy sum interms of mole fraction
5][ 31
65 O
O 1][ 35
65
Ovand
Oxide ion vacancy 3
5
65Ov
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
)(2 221
35
65
31
65 gOevO
OO
][
]][e[
2
31
65
21
2
35
65
O
OO
RO
pvK
][][e][ 35
65
31
65 3
5
31
OOvO ][][ 3
5
65
31
65 3
5
31
OOvO
5
][e
]5[
]][e[ 21
2
35
65
21
2
35
65
22
O
O
OO
R
p
v
pvK
41
2
21
)5(][e OR pK
hOvgOOO
2)( 22
1 31
65
35
65
he 220 he0
Defect chemical reactions with Ba2In2O5
Electroneutrality
Equilibrium coefficient
Electrons minority defects
Equilibrium coefficient
Solve this with respect to theconcentration of electrons and obtain
Reduction and oxidation
The corresponding oxidation reaction is
sum of the reduction and oxidation reactions yields the intrinsic ionisation of electrons
or
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
OxOO OHOvgOH 2)(2
32
65
31
65
35
65 2)(
2 OOOOHOvgOH
OHOO
O
HpOv
K2
31
65
35
65
32
65
]][[
][OH
2
][][OH
31
32 3
1
65
32
65 OO
O
Hydration reaction
Hydration reaction for disordered Ba2In2O5
Equilibrium coefficient
Hydroxide defects lt two native defects are dominatingand constantThe concentration of hydroxide defects takes on a dependency
21
2OHp
To increase the water vapour partial pressurethe hydroxide defects become dominating
Electroneutrality
The 6 oxygen sites are disorderly filled with 4 oxide ions and 2 hydroxide ions overall formula Ba2In2O4(OH)2 or BaInO2(OH)
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
2
31
653OIn
xBa OZrBaZrOBaO
][][ 35
65
31
65 3
5
31
OInOvZrO
Zr Doping
The electroneutrality becomes
At 50 substitution one oxygen vacancy and eleven oxide ions out of twelve positions Ba4In2Zr2O11At high doping levels it gets the same whether one considers it to be Zr-doped Ba2In2O5 or In-doped BaZrO3
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Mayenite Ca12Al14O33
Unit cell (Ca24Al28O64)4+ middot 2O2-
lattice framework with 12 nano-cages extra-framework oxide ions are randomlydistributed in the nano-cages and can bereplaced by F-Cl-OH- and H- ions
Each nano-cage contains two crystallographicpositions for the oxide ion
It is reasonable to assume that only one oxideion can be fitted in a cage at any time and thatthe energy barrier between the two positions is small enough that the oxide ion is effectively delocalized over the two positions at elevated temperatures
In this way each oxide ion occupies one out of 6 available cages
J Medvedeva
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Effective charge of O2- (-2) ndash (-13) = -53 Effective charge of cage (0) ndash (-13) = +13 Effective charge of OH- -1 ndash (-13) = -23
The real charge of the speciesminus the real charge of the perfect reference lattice
3
1
6
13
5
6
13
2
6
1O
O
OvOOH
The defect situation in mayenite can be described as onewith an inherently deficient sublattice (the oxide ions in the extra-framework nanocages) The site is denoted as 16 occupancy of oxide ions as the perfect state consequently with a charge of -26 = -13
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
3
1
6
1
3
5
6
15OO
vO
3
2
6
13
1
6
1
3
5
6
12 2)(OOO
OHvOgOH 1
1
3
1
6
1
1
3
5
6
1
2
3
2
6
1 2
OH
OOOpvOOHK
The electroneutrality in the pure dry material then reads
Mayenite has a strong tendency to become hydrated by replacing the oxide ions with hydroxide ions
Hydration reaction Equilibrium constant
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
OH
OHOHOH
O Kp
KpKpKpOH
2
222
4
5)(46 2
3
2
6
1
63
1
6
1
3
5
6
1
3
2
6
1
OOOvOOH
3
1
6
1
3
5
6
1
3
2
6
1 52OOO
vOOH
The new electroneutrality
Site limitation
The site sum of 6 enforces concentrations to refer to fractions of one formula unit mayenite Ca12Al14O33 or molar fraction of the same
The concentration of hydroxide ions as a function of watervapour partial pressure and temperature
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Ba3La(PO4)3
Eulytite structure
The four cations (three divalent Ba2+ and one trivalent La3+) disorderly occupies the same site
The site is statistically occupied by (3middot2 + 1middot3)4 = 94 = 2frac14 positive charges
New nomenclature
Site or or
Ba2+ or La3+ ion would be denoted or
49
4
13 LaBa 49
43LaBa
49
4143 LaBa
4
1341
LaBaBa
43
4
13 LaBaLa
Systems with disordered occupancy by several cccupants
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
4
43
41
)( 443
41
POMM HPOLaBa
43
41
43
41
MM LaBa
The electroneutrality reads
An abbreviation for the complex site expression can be useful in such cases
Thus defining allows to denote
Ba2+
La3+
49
49
4
13 LaBaM
41
MBa
43
MLa
Acceptor doping with an excess of Ba2+ to dissolve protons in phosphates represented as hydrogen phosphate defects on phosphate sites The new electroneutrality reading
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
61
22 Oi pOp
Assume the compound is perfectly stoichiometric
we consider a minor concentration of additional defects formed by oxidation
(oxygen interstitials and electron holes)
Since the two defects of disordered Ba2+ and La3+ are dominating in numbersthe holes end up as minor defects with the familiar
dependency they attain when ionic defects rule
41
2Opp
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
Summary
The new extension of the Kroumlger-Vink nomenclature and defects present in the disordered Ba2In2O5 have been discussed
Defect structures of Mayenite (Ca12Al14O33) and Ba3La(PO4)3 are derived
Proton defects in oxides phosphates and pyrophosphates are explained
Defect chemistry of acceptor doped-LaNbO4 was discussed
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
References
A Kroumlger-Vink-compatible notation for defects in inherently defective sublattices Truls Norby - to be submitted
High temperature hydration and conductivity of mayenite Ca12Al14O33
Ragnar Strandbakke Camilla Kongshaug Reidar Haugsrud Truls Norby - to be submitted
Local condensation of oxygen vacancies in t-LaNbO4 from first principle calculations Akihide Kuwabara Reidar Haugsrud Svein StoslashlenTruls Norby ndashsubmitted
Defects and transport in crystalline solids Per Kofstad and Truls Norby
High-temperature protonic conduction in TiP2O7 and Al-doped TiP2O7
Nalini Vajeeston Reidar Haugsrud Helmer Fjellvaringg Truls Norby - to be submitted
High-temperature protonic conduction in acceptor doped-LaPO4
K Amezawa S Kjelstrup T Norby and Y Ito Electrochem Soc 145 (1999) 3313
