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Lecture Notes II Defect Chemistry. Ole Toft Sørensen (Risoe National Laboratory) Ceramic Materials Consultant Email:[email protected] Electroceramics. Electrical properties determined by defects. Knowledge of defect chemistry necessary to understand Electroceramics!. What is a defect?.

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Lecture notes ii defect chemistry

Lecture Notes IIDefect Chemistry

Ole Toft Sørensen

(Risoe National Laboratory)

Ceramic Materials Consultant

Email:[email protected]


Electroceramics
Electroceramics

  • Electrical properties determined by defects

  • Knowledge of defect chemistry necessary to

  • understand Electroceramics!


What is a defect
What is a defect?

Fundamental definition:Any deviation from the perfect crystal is a defect!

- Macroscopic defects (porosities, cracks)

  • Atomic defects

  • Electronic defects


Atomic point defects in oxides
Atomic (point) defects in Oxides!

Missing ions:

- oxygen ions,

oxygen vacancies

- cations,

cation vacancies

Substituted ions

Interstitiel ions


Electronic defects in oxides
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


Defect notations
Defect notations

subscript

(Symbol for type)position

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


Charges of defects
Charges of defects

Relative chargeCharge 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


Charges of oxygen vacancies
Charges of oxygen vacancies

Formation 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

2

Oxygen vacancy – how many electrons left ?

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 !


Relative charges of interstitial ions
Relative charges of interstitial ions

-2

O2- ions,Oi ?

Cl-1 – ions, Cli, rel. charge = -1

Na+1 – ions, Nai , ?

+1

Zr4+ - ions, Zri, rel. charge = +4


Nomenclature relative charges
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″




Formation of defects
Formation of defects

Three typical areactions:

- ”high” temperatures, INTRINSIC DEFECTS

- reaction with surrounding atmosphere

- substitution


Intrinsic defects
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 !


Defects formed in an reaction with surronding atmosphere
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!


Defects formed in a reaction with a surrounding atmosphere 2
Defects formed in a reaction with a surrounding atmosphere - 2

Oxidation

MO + y/2O2 = M1-yO

Note – clusters !

Cations easily oxidized!


Formation of interstitial oxygen ions o i
Formation of interstitial 2oxygen ions- Oi

High oxygen pressures !

1/2 O2 + 2MMx = Oi″ + 2MM•

Oxides where cations are easily oxidized – FeO


Defects formed by substitution
Defects formed by substitution! 2

Substitution of cations !

Lower valency:

Higher valency:

ZrO2 doped with CaO:

Y2O3 doped with ZrO2:

CaO(ZrO2) = CaZr″ + VO•• + OOx

2ZrO2(Y2O3) =

2ZrY• + Oi″ + 3OO

Oxygen vacancies formed to

maintain electrical neutrality !

Same valency?


Practice formation of defects
Practice 2Formation of Defects


Answers practice formation of defects
Answers 2Practice – Formation of Defects


Dependence on oxygen pressure
Dependence on oxygen pressure 2

1

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.


Rules which must be obeyed
Rules which must be obeyed 2

  • ratio between cation and anion positions – Constant!

  • the total number of positions can be changed,

  • but not the ratio!

  • neutrality must be maintained



V o log p o2
[V 2O]  log pO2

1

2



Practise brouwer plots oxygen vacancies
Practise: 2Brouwer plots oxygen vacancies


Answers to practice brouwer plots oxygen vacancies
Answers to practice: 2Brouwer plots oxygen vacancies


V m log p o2
[V 2M]  log pO2

1

2

3

4

5



Practice formation of cation vacancies
Practice: 2Formation of cation vacancies


Answers to practice formation of cation vacancies
Answers to practice: 2Formation of cation vacancies



Brouwer plot many defects
Brouwer plot: 2many 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


Calculation of defect concentrations
Calculation of defect concentrations 2

  • Deviation from the stoichiometric composition.

  • Fraction of defects

  • Number of defects per cm3



Site fractions
Site Fractions 2

MO2-x

Fe1-yO

MO2+x



Practice calculation of defect concentrations
Practice 2Calculation of defect concentrations


Answers calculaion of defect concentrations
Answers 2Calculaion of defectconcentrations



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