1 Lecture Notes II Defect Chemistry Ole Toft Sørensen (Risoe National Laboratory) Ceramic Materials Consultant Email:[email protected]
Jan 20, 2016
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Lecture Notes IIDefect Chemistry
Ole Toft Sørensen (Risoe National Laboratory)
Ceramic Materials ConsultantEmail:[email protected]
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Electroceramics
• Electrical properties determined by defects
• Knowledge of defect chemistry necessary to understand Electroceramics!
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What is a defect?
Fundamental definition:Any deviation from the perfect crystal is a defect!
- Macroscopic defects (porosities, cracks)
- Atomic defects
- Electronic defects
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Atomic (point) defects in Oxides!
Missing ions:
- oxygen ions,
oxygen vacancies
- cations,
cation vacancies
Interstitiel ionsSubstituted ions
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Electronic defects in oxides
•Atomic (point) defects – type, properties depend on position !
•Electronic defects – type, properties depend on energy levels available for the electrons
• electrons• positive holes
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Defect notations
(Symbol for type)position
subscript
VO = vacancy on oxygen position
VM = vacancy on metal position, VFe
Oi = interstitial oxygen ion
Mi = interstitial cation
YZr = Y-ion on Zr-ion position
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Charges of defects
Relative chargeCharge relative to the charge normally present in the position of the defect
Examples:ZrZr – relative charge = zero,butYZr - relative charge = -1
ZrY ? Rel. ch.+1
FeO:Fe2+ vacancy – rel. ch. = ?
-2 of course!
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Charges of oxygen vacanciesFormation of oxygen vacancies:Oxygen atoms are removed from the crystal
Oxygen ions – how many electron in outer orbital ? 8
Oxygen atoms – how many electrons in outer orbital ? 6
Oxygen vacancy – how many electrons left ? 2
Rel. Charge ? Zero!
But these electrons can easily migrate to neighbouring ions forming vacancies with one or zero electrons present. Thus VO with rel. charges of zero, +1 and +2 can be formed !
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Relative charges of interstitial ions
O2- ions,Oi ? -2
Cl-1 – ions, Cli, rel. charge = -1
Na+1 – ions, Nai , ? +1
Zr4+ - ions, Zri, rel. charge = +4
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Nomenclature: relative chargesRelative charges are indicated by a superscript:• neutral - x• positive charges – black dots• negative charges - apostrophes
Examples:Neutral: VO
x
Positive charges: VO•, VO
••
Negative charges: VFe″
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Practise: Nomenclature
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Answers to practise
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Formation of defectsThree typical areactions:
- ”high” temperatures, INTRINSIC DEFECTS
- reaction with surrounding atmosphere
- substitution
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Intrinsic defectsPair of defects:
-Frenkel defect: cation vacancy and interstitial cation
-Anti-Frenkel defect: oxygen vacancy and interstitial oxygen ion
-Schottky defect: oxygen vacancy and cation vacancy
MO: OOx + MM
x = VO•• + VM
″
M2O3: 3OOx + 2MM
x = 3VO•• + 2VM
″′
Stoichiomtry must be maintained !
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Defects formed in an reaction with surronding atmosphere. Reduction
Oxides with cationsOxides with cationseasily reduced!easily reduced!
MO2 = MO2-x+ x/2 O2
OOx + 2MM
x = VO•• + 2MM
′ + 1/2O2
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Defects formed in a reaction with a surrounding atmosphere - 2 Oxidation
Cations easily oxidized!
Note – clusters !
MO + y/2O2 = M1-yO
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Formation of interstitial oxygen ions- Oi
High oxygen pressures !
1/2 O2 + 2MMx = Oi
″ + 2MM•
Oxides where cations are easily oxidized – FeO
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Defects formed by substitution!
Substitution of cations !
Lower valency: Higher valency:
Same valency?
ZrO2 doped with CaO:
CaO(ZrO2) = CaZr″ + VO
•• + OOx
Oxygen vacancies formed to maintain electrical neutrality !
Y2O3 doped with ZrO2:
2ZrO2(Y2O3) =2ZrY
• + Oi″ + 3OO
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PracticeFormation of Defects
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AnswersPractice – Formation of Defects
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Dependence on oxygen pressure
Law of mass action can be used.
Can defects in a solid be considered as ions in a solution?
Yes if these conditions are fulfilled:- random distribution of defects- no interactions- high mobility
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Rules which must be obeyed
• the total number of positions can be changed, but not the ratio!
• neutrality must be maintained
• ratio between cation and anion positions – Constant!
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Formation of oxygen vacancies
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[VO] log pO2
2
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Brouwer plots - VO
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Practise:Brouwer plots oxygen vacancies
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Answers to practice:Brouwer plots oxygen vacancies
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[VM] log pO2
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2
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4
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Brouwer plots - VM
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Practice:Formation of cation vacancies
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Answers to practice:Formation of cation vacancies
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Brouwer plot for Oi
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2
3
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Brouwer plot:many defects
Construction:
- Log Conc. defect vs log(pO2)- 3 p(O2) regions;
- one type of defect dominates in each region
- sharp transition between regions, approximation
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Calculation of defect concentrations
• Deviation from the stoichiometric composition.
• Fraction of defects
• Number of defects per cm3
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Deviation from stoichiometric composition
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Site Fractions
MO2-x
Fe1-yO
MO2+x
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Number of defects per cm3
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PracticeCalculation of defect
concentrations
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AnswersCalculaion of defect
concentrations
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