Laurea Magistrale in Scienza dei Materiali
Materiali Inorganici Funzionali
Electrical conduction
in ceramics
Prof. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova
Conductivity in oxides
Defects
Defects and doping
Defects and oxygen
Defects in fluorite-type oxides
Conductivity in MO2-type oxides
Bibliography
1.
2.
P. J. van der Put: The inorganic chemistry of materials – How to
make things out of elements – Plenum Press 1998
N.Q. Minh, T. Takahashi: Science and technology of ceramic
fuel cells – Elsevier 1995
I siti difettuali sono responsabili del trasporto di materia e di carica:
1 Salto di uno ione da una posizione interstiziale ad un’altra
2 Salto di uno ione da una posizione reticolare ad una interstiziale
accompagnato dalla migrazione di un altro ione interstiziale nella
vacanza formatasi
3 Salto di uno ione da una posizione reticolare ad una vacanza
adiacente.
Il trasporto degli ioni avviene se:
1) la particella ha un difetto disponibile situato nei siti adiacenti
2) la particella ha energia sufficiente per attraversare la barriera di
potenziale che si oppone alla sua migrazione.
Defects
The properties of ceramics or crystalline solids depends on the
material lattice defects.
Stoichiometry
Stoichiometric defects: crystal composition is unchanged
Non-stoichiometric defects: crystal composition changes
Size and Shape
Point defects: interstitials or vacancies
Line defects: dislocations
Plane defects: the whole layer in a crystal structure is defective
Electrical conduction in ceramics or crystalline solids depends on
point defects.
Types of defects in solids
Defects and Kröger-Vink notation
Vacancies: V; in NiO: V’’Ni and V ¨O
Interstitials: subscript i; In AgBr: Ag˙i
Electrons or electron holes in the VB or CB: e’, h˙
Dopants: Y3+ ions in ZrO2: Y’Zr – Ti4+ in CeO2: TixCe
Defect concentrations are not independent of each other:
Electroneutrality
Mass balance
Site balance
Intrinsic defect concentrations:
< 10-4 ppm for an oxide with bandgap > 4 eV (impurity concentration:
10-100 ppm)
n Q exp (∆Hf/RT)
k = exp (∆Gf/RT)
Frenkel-type defects (1926): interstitials and vacancies
Frenkel defects move in the crystal
N = total number of ions; Ni = total number of interstitials;
k = Boltzmann constant, T = temperature, EF = formation
energy of the Frenkel defects)
the radii of ions of the crystal differ considerably
high van der Waals energy and dielectric constant
Schottky-type defects (1935): cation/anion vacancies
N = total number of ion pairs; Ni = total number of Schottky
defects; k = Boltzmann constant, T = temperature, ES =
formation energy of the Schottky defects)
Small differences between the radii of the cations and anions
Poor polarizability
Small van der Waals energy and dielectric constant
Extrinsic defect concentration: doped MO
Doping depends on solubility (phase diagrams)
MgO doped with Li2O
Mg2+ replaced by Li+
Li2O = 2 Li’Mg + OxO + V¨O
> Li > Oxygen vacancies
MgO doped with Sc2O3
Mg2+ replaced by Sc3+
Sc2O3 = 2 Sc˙Mg + 3 OxO + V’’Mg
> Sc > Mg vacancies
Doping with aliovalent species affects the concentration of the defects
that are formed thermally in the intrinsic equilibrium
The equilibrium constants: Ks and KF (if one defect is added by doping its
partner in the equilibrium decreases)
Phase diagram of a ZrO2-CaO system
Gas equilibria – Schottky type
½ O2 (g)
Adsorpion
= OxO + 2 h˙ + V’’M
Ka = [h˙]2[V’’M]p(O2)-1/2
> Oxygen partial pressure > p-type conductivity
OxO = ½ O2 (g)
Desorption
+ 2 e’ + V¨O
Kd = [e’]2[V¨O]p(O2)1/2
Oxides that prefer to desorb oxygen may more easily
accomodate electron than holes (n-type semiconductors) and
become less conducting with increasing oxygen partial pressure
Gas equilibria – Frenkel type
½ O2 (g)
Adsorpion
= O’’i + 2 h˙
Ka = [h˙]2[O’’i]p(O2)-1/2
> Oxygen partial pressure > p-type conductivity
MxM + OxO = ½ O2 (g)
Desorption
+ 2 e’ + M¨i
Kd = [e’]2[M¨i]p(O2)1/2
> metal-rich n-type semiconductors
Calculated equilibrium defect
diagrams for a binary oxide MO
with Schottky defect pairs
Ki « KS Oxides with a wide
bandgap: the oxide is a pure ionic
conductor under an oxygen
pressure at the middle region
Ki » KS Oxides with a narrow
bandgap: the oxide is a
semiconductor at all oxygen
pressures (low oxygen pressures =
n-type, high oxygen pressure = ptype)
TM oxides that can reach higher oxidation states
(MnO, FeO, CoO, NiO)
Oxygen uptake MO1+x (x > 1) to become p-type semiconductors
Aliovalent doping:
Li2O in NiO:
Li2O → 2 Li’Ni + OxO + V¨O
Vacancies may react with oxygen
½ O2 (g) + V¨O → OxO + 2 h˙
Li2O + ½ O2 (g) → 2 Li’Ni + 2 OxO + 2 h˙
Cr2O3 in NiO: n-type conductivity
Cr2O3 → 2 Cr˙Ni + 3 OxO + V’’Ni
Exceeding oxygen may be lost:
Cr2O3 → 2 Cr˙Ni + 2 OxO + 2 e’ + ½ O2 (g)
TM oxides that can not reach higher oxidation states
(Ta2O5, CeO2, ZnO)
Oxygen desorption MO1+x (x < 1) to become n-type semiconductors
Aliovalent doping:
Li2O in ZnO:
Li2O → 2 Li’Zn + OxO + V¨O
Vacancies may react with oxygen
Li2O + ½ O2 (g) + 2e’ → 2 Li’Zn + 2 OxO
Li doping oxidizes ZnO and lowers its n-type conductivity by consuming
the surplus electrons in the conduction band
Cr2O3 in ZnO: n-type conductivity
Cr2O3 → 2 Cr˙Zn + 2 OxO + 2e’ + ½ O2(g)
Doping ZnO with cromium oxide that has too many oxide ions for ZnO
evolves gaseous oxygen that leaves electrons behind; n-type character
of ZnO is increased
Defects in fluorite-type oxides
The fluorite (CaF2) structure is adopted by a number of oxides (MO2 with M
= large tetravalent cation), sulfides, hydrides, intermetallic compounds of
AX2 type
Unit cell (=M4O8 structure): each metal ion is
surrounded by eight oxygen ions forming a
body-centred cubic structure, and each oxygen
ion is surrounded by four metal ions forming a
tetrahedral arrangement.
The minimum
radius is 0.732
metal-ion
radius/oxygen-ion
At RT ZrO2 has not a fluorite structure (ionic radius ratio condition not satisfied);
fluorite structure is observed at T > 2370°C or when stabilized by aliovalent doping
(divalent or trivalent cations)
Defects in doped zirconia with fluorite structure:
1) oxygen-ion vacancies with the metal ions being fixed at their lattice points
2) cation interstitials with oxygen ions being fixed at their lattice sites
(Frenkel)
3) Schottky
Defect structure of doped MO2
Incorporation of AO into MO2:
Incorporation of oxygen from the
environment into MO2:
Equilibrium constant, K:
Intrinsic Schottky equilibrium:
Equilibrium constant, KS:
Intrinsic electronic equilibrium:
Equilibrium constant, Ki:
Electroneutrality condition:
Defect structure of doped MO2:
low oxygen partial pressure region
As the oxygen pressure decreases the concentration of oxygen-ion vacancy
increases (to maintain K); this increase causes the metal vacancy
concentration to decrease (to maintain KS); thus:
The concentration of oxygen-ion vacancy exceeds that of A’’M (fixed by the
dopant level); n must increase to maintain the electroneutrality condition
and p must decrease; electroneutrality reduces to:
Oxygen partial pressure dependence of
oxygen-ion vacancy:
Oxygen partial pressure dependence of the
metal vacancy concentration:
Oxygen partial pressure dependence of the
hole concentration:
Defect structure of doped MO2:
intermediate oxygen partial pressure region
Over the intermediate oxygen
pressure range, the concentration of
oxygen-ion
vacancies
is
not
dependent
on
oxygen
partial
pressure but fixed by the dopant
level:
As the oxygen partial pressure increases, the concentration of electrons
decreases and that of the holes increases; on the other hand the metalion vacancy concentration is independent of oxygen partial pressure and
determined solely the KS and the oxygen-ion vacancy concentration.
Defect structure of doped MO2:
high oxygen partial pressure region
Electroneutrality condition con be approximated as:
Oxygen partial pressure dependence
of the anion and cation vacancies:
Electron concentration is given
by:
Electron concentration is constant in this oxygen partial pressure region.
Defect structure of doped MO2:
very high oxygen partial pressure region
The concentration of metal-ion vacancy becomes very large:
Electroneutrality condition con be approximated as:
Oxygen partial pressure dependence of
defect concentration:
Defect structure of AO and B2O3 doped MO2
Variation of defect
concentration as a function of
oxygen partial pressure for a
MO2-AO system
Variation of defect
concentration as a
function of oxygen partial
pressure for a MO2-B2O3
system
Conductivities of oxygen ions, electrons,
and electron holes
The total electrical conductivity, σ, of a fluorite-type oxide is given as:
µ = mobilities; i, n, p = ions, electrons, electron holes;
the ionic conductivity due to the migration of cations of the dopants and
the host is neglected because the mobilities of the cations have been shown
by diffusivity measurements to be several order of magnitude lower than
the mobility of oxygen-ion vacancy.
Conductivities of MO2-B2O3 systems
Since the mobility of oxygen-ion vacancy is generally much lower than
that of electrons and electron holes, B2O3-doped MO2 can only exhibit an
appreciable ionic conductivity over a wide range oxygen partial pressures
when the concentration of oxygen-ion vacancy is considerably larger than n
and p.
Conductivity is at the maximum when σn = σp
Variation of
electrical
conductivity as a
function of
oxygen partial
pressure for a
MO2-B2O3 system
Defect domains in Patterson type maps
Electrolytic domain
boundaries = oxygen
partial pressure
where σi = 100σp and
σi = 100 σn
Electronic, ionic, and electrolytic domains of a MO2-B2O3 system
Defect association and clusters
At low temperature oppositely charged oxygen-ion vacancies and dopant
cations may associate to form randomly distributed pairs; the concentration
of free oxygen-ion vacancy is determined by the association equilibriums:
Break temperature = temperature for the break of the associated vacancy
behaviour
Defect association and clusters
1. The formation of defect association and clusters and trapped vacancies
causes the decrease of conductivity: trapped vacancies are not immobile but
must overcome an energy barrier to move (dissociation or rearrangement of
clusters), this barrier is higher than that present in systems having only
single vacancies.
Calculated break
temperature between
associated and free
vacancies in CaO-doped
CeO2 for various association
energies.
Conductivity data of CaO-doped ThO2 indicate the association of vacancies and does
not show break temperature as ceria does: the association energies (1.16 to 1.42 eV
or 111.9 to 137.0 kJ/mol) of CaO/ThO2 (dopant 1 to 7 mol%) are much higher than
those (0.20 to 0.50 eV or 19.3 to 48.2 kJ/mol) of CaO/CeO2
2. At high defect concentration a random distribution of defects and
defect pairs may be converted into an ordered two- or three-dimensional
defect structure