Transcript Lecture Notes III Defect Chemistry

Lecture Notes II
Defect Chemistry
Ole Toft Sørensen
(Risoe National Laboratory)
Ceramic Materials Consultant
Email:[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
Substituted ions
Interstitiel 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 charge
Charge relative to the charge normally
present in the position of the defect
Examples:
ZrZr – relative charge = zero,
but
YZr - relative charge = -1
FeO:
Fe2+ vacancy – rel. ch. = ?
-2 of course!
ZrY ?
Rel. ch.+1
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Charges of oxygen vacancies
Formation of oxygen vacancies:
Oxygen atoms are removed from the crystal
Oxygen ions – how many electron in outer orbital ?
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Oxygen atoms – how many electrons in outer orbital ? 6
Oxygen vacancy – how many electrons left ?
Rel. Charge ?
2
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 charges
Relative charges are indicated
by a superscript:
• neutral - x
• positive charges – black dots
• negative charges - apostrophes
Examples:
Neutral: VOx
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 defects
Three typical areactions:
- ”high” temperatures, INTRINSIC DEFECTS
- reaction with surrounding atmosphere
- substitution
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Intrinsic defects
Pair 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 + MMx = VO•• + VM″
M2O3: 3OOx + 2MMx = 3VO•• + 2VM″′
Stoichiomtry must be maintained !
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Defects formed in an reaction
with surronding atmosphere.
Reduction
MO2 = MO2-x+ x/2 O2
OOx + 2MMx = VO•• + 2MM′ + 1/2O2
Oxides with cations
easily reduced!
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Defects formed in a reaction with
a surrounding atmosphere - 2
Oxidation
MO + y/2O2 = M1-yO
Note – clusters !
Cations easily oxidized!
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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:
ZrO2 doped with CaO:
CaO(ZrO2) = CaZr″ + VO•• + OOx
Oxygen vacancies formed to
maintain electrical neutrality !
Same valency?
Y2O3 doped with ZrO2:
2ZrO2(Y2O3) =
2ZrY• + Oi″ + 3OO
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Practice
Formation of Defects
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Answers
Practice – Formation of Defects
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Dependence on oxygen
pressure
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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
Law of mass action can be used.
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Rules which must be obeyed
• ratio between cation and anion positions – Constant!
• the total number of positions can be changed,
but not the ratio!
• neutrality must be maintained
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Formation of oxygen
vacancies
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[VO]  log pO2
1
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
1
2
3
4
5
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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
1
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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Practice
Calculation of defect
concentrations
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Answers
Calculaion of defect
concentrations
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Content
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