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Lecture Notes IIDefect Chemistry

Ole Toft Sørensen (Risoe National Laboratory)

Ceramic Materials ConsultantEmail:otsdk@yahoo.dk

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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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