Thermodynamic treatment of defects and conduction mechanisms

How does semiC occur in oxides

presence of impurities and non-stoichiometry

How does conductivity vary in a p type SCO

σ~pO2 ^1/6 for 2 holes per O; ^1/4 for 1 hole per O; exponent is positive for a p type

How does defect association change with temp and pO2

trapping of charge carriers is more dominant at lower T and higher pO2

Where do the holes go

oxidation of Ni2+ to 3+; oxidation of O2- to O-; covalency of bonds suggests some on each

How do n type SCO behave

σ ~ -1/6 or -1/4; higher pO2 makes it harder to lose O so decreases conductivity

Limitations of this approach

ignores defect interactions (eg clusters and extended defects); charge carriers must interact through long range Coulombic forces so need to consider activity coefficient instead of concentration

Why is it suggested that titanium dioxide should be written as Ti O2+-x

as in n type we have TiO2-x; p type has TiO2+x; in between at minimum conductivity we have TiO2 (very hard to get stoichiometric TiO2)

What are the five main defect equations that can dominate the defect chemistry in TiO2

1) conventional oxygen loss Ti4+ reduced to 3+ (-1/6 slope);

2) interstitial Ti4+ ions with oxygen loss causing partial reduction of the lattice Ti to Ti3+ (-1/5 slope)

3) Interstitial Ti3+ ions with oxygen loss causing further reduction of lattice Ti to Ti3+ (-1/4 slope)

4) Intrinsic charge carrier generation: no change in oxygen content

5) Oxygen gain on surface creating metal vacancies with partial oxidation of lattice O2- to O- (slope +1/5) (Ti can’t be oxidised further so must oxidise O2-)

Summary of predominant effects at elevated T

x<0: oxygen loss, Ti interstitials, e- (n type); x=0: intrinsic; x>0 oxygen gain, Ti vacancies, holes (p type)

BaTiO3

expect n type via oxygen loss and reduction of Ti4+ to 3+; p type not expected as can’t oxidise Ba2+ or Ti4+; get n type region at low pO2: oxygen loss; also get p type region at high pO2: oxygen gain

Where do the oxygen vacancies come from in BT as B and T can’t be oxidised?

inevitable impurities of Fe3+ and Al3+ can occupy tetrahedral sites (in place of Ti4+); they act as acceptor impurities in BT creating oxygen vacancies