lattice defects in oxides. correlations between defects, properties and crystal structures
TRANSCRIPT
Lattice defects in oxides.
Correlations between defects, properties and
crystal structures
Defects in oxides
Lattice or point defects:
• Vacancies (oxygen, cation)• Interstitial ions• Foreign atoms at regular sites (doping/solid solutions)• Defect pairs and clusters• Electronic defects (free electrons and holes)
Defect chemistry. Lattice defect can be treated as chemical entities (energy of formation) using defect reactions (mass-action law, equilibrium constant).
Kroger-Vink notation for defects. Defect charge is referred to the perfect crystal.
Extended defects:
• Crystallographic shear• Dislocations• Grain boundaries
Cation vacancy Oxygen vacancy
Interstitial cation Interstitial oxygen
Foreign ion (donor) Foreign ion (acceptor)
Antisite defects
''ZnV
OV
iZn ''
iO
'ZnNa
ZnAl
Binary oxides (ZnO)
Ternary oxides (ZnAl2O4)
ZnAl '
AlZn
Defects in oxides
Rules for defect reactions:
• Site relation. The number of sites must be in the correct proportion (MaXb: M/X = a/b).• Sites can be created or destroyed taking into account the site relation.• Mass balance.• Electroneutrality condition.
surfsurfOMgMgO
OMg OMgVVOMg ''
OMgMgO VVzero ''
Schottky disorder
Frenkel disorder
'Agi
AgBriAg VAgVAg
1eV = 96.5 kJ/mol
vibrconfv SnSTHnGG 0
Defects and entropy
!!
!lnln
nN
nNkWkS BBconf
N atoms arranged at (N+n) sites with n vacancies
0;0;0 vibrconfv SSH
-
-
-
-
Thermodynamic probability for distinguishable particles
!!...!!
!
21 ro
o
nnnn
NW
N0: total number of atomsni: number of atoms on the i-th energy state
Oxygen nonstoichiometry (TiO2, CeO2, Nb2O5, V2O5)
Metal nonstoichiometry (FeO, NiO, MnO)
Defects and nonstoichiometry in binary oxides
Fe1-yO
22
12
'2 OCeVO CeO
CeOO
2'
2
122 OeVO O
CeOo 3' CeCeCe
FeFeOFeO FeVOO 2
2
1 ''2
hVOO FeOFeO 2
2
1 ''2
3FeFeFe
2'
2
122 OeVO O
CeOo
2/121 2
][ OO pnVK Equilibrium constant
OVn 2 Electroneutrality
2/132/13'1 22
][ OOO pxpVK
xVO 2
1 x: fraction of vacant sites in CeO2-x
6/1
2
Opx
nOpx /1
2
xnRTpRTG OOOO lnln2222
0
In general:
n = 6: doubly ionized vacanciesn = 4: singly ionized vacanciesn = 2: neutral vacancies
n ≤6 for isolated defects or defect complexes
Defects and nonstoichiometry in binary oxides
'en
Iso
late
d d
efec
ts
Def
ect
com
ple
xes
Def
ect
ord
erin
gF
orm
atio
n o
f su
bpha
ses
CeO2-x
n =
5
n =
4
n =
15-
18
-G
O2 (
kca
l/mol
)
- log x in CeO2-x
Defects and nonstoichiometry in binary oxides. Formation of shear planes
Ordering of defects and formation of superstructures is observed for large deviations from stoichiometry (TiO2-δ, Nb2O5-δ, WO3-δ, ReO3-δ, etc.). Elimination of oxygen vacancies by formation of metal-rich shear planes is a common mechanisms (crystallographic shear).
Formation of shear planes in ReO3 (left) and WO3 (right) by elimination of oxygen vacancies
Lattice defects and nonstoichiometry in perovskites
Partial Schottky disorder (BaO-rich side)
Full Schottky disorder
Oxygen nonstoichiometry
Partial Schottky disorder (TiO2–rich side)
BaTiO3
1eV = 96.5 kJ/mol
Lattice defects and nonstoichiometry in perovskites
BaTiO3
Ti-rich
Ba-
rich
Lattice defects, nonstoichiometry and phase transitions in perovskites
Cubic (paraelectric) – tetragonal (ferroelectric) phase transition in BaTiO3
1200°C
Ti-rich
Ba-rich
Enthalpy of transition
1320°C
Transition temperature
Ti-rich
Ba-rich
Lattice defects and electrical conductivity in perovskites
Electrical conductivity iii cez Z: numero di cariche; e: carica dell’elettrone; : mobilitàc: concentrazione
'2 2
2
1eVOO OO
(1) At low p(O2) << p0(O2)
6/12/121 22
2 OOOO pnVnpnVK
(2a) At intermediate p(O2) and R = Ba/Ti < 1
4/1''
2
OOBa pnaRVV
(2b) At intermediate p(O2) with R = 1 and acceptor impurities
4/1
22 OO pnVA
(3) At high p(O2) p(O2) > p0(O2)
hOVO OO 22
12
4/12/1122 22
OOOO pVppVpKReduction (1): H2-3 eVOxidation (3): H1 eV
hpen ;'
n-type p-type
(1)m = -1/6
(2)m = -1/4
BaTiO3
p0(O2)n = p
Doping of perovskites: controlling defect nature and concentration
Acceptor doping: the substitutional impurity has a lower charge than the regular and bring less oxygen into the lattice
OOTiBaBaTiO OVFeBaBaOOFe 5222 '
323
OOTiBaBaTiO OVTiNaTiOONa 5222 '
223
OTiBaBaTiO OhFeBaBaOOFeO 62222
2
1 '322
3
Donor doping: the substitutional impurity has a higher charge than the regular and bring more oxygen into the lattice
OTiBaBaTiO OeTiLaOTiOOLa 6222
2
12 '
22323
OTiBaBaBaTiO OTiVLaTiOOLa 9223 ''
2323
OBaTiBaTiO OeBaNbOBaOONb 6222
2
12 '
2523
OBaBaTiBaTiO OBaVNbBaOONb 62 ''
523
Doping of perovskites: influence of doping on electron conductivity
Donor doped compounds:• Black colour;• Good conductivity (>10-2 S/cm) even at RT;• Some show metallic conduction (103 S/cm, La:SrTiO3);
OTiBaBaBaTiO OTiVLaTiOOLa 9223 ''
2323
1200°CLa:BaTiO3
OTiBaBaTiO OeTiLaOTiOOLa 6222
2
12 '
22323
'2 2
2
1eVOO OO
p0(O2)
Acceptor doped compounds• Light colour;• Good conductivity at high temperature• Many are insulators at RT;• Can be fired in reduced atmosphere retaining their dielectric properties.
Doping of perovskites: influence of doping on electron conductivity
p0(O2)
OOTiBaBaTiO OVMnBaBaOOMn 5222 '
323
OTiBaBaTiO OhMnBaBaOOMnO 62222
2
1 '322
3
Doping of perovskites: from isolated defect to oxygen vacancy ordering and formation of layered structures
Due to the high dielectric constant (20-1000) and structural stability, perovskites can accomodate a large concentration of foreign aliovalent impurities (good solvent) and related charge compensating defects (cation or oxygen vacancies). The simple model of randomly distributed isolated defects (no association) holds up to high dopant concentration (few at.% for acceptors, 10 at.% for donors). At higher dopant concentration, ordering of defects, formation of shear planes and layered structures is observed.
OOTiSrSrTiO OVFeSrSrOOFe 5222 '
323
OTixxx VFeOTiSrFe 2; '
2/31
x = 0: SrTiO3; x = 1: Sr2Fe2O5
At T < 700°C, oxygen vacancy ordering occurs in Sr2Fe2O5 (brownmillerite structure).For intermediate compositions, intergrowth of perovskite blocks and brownmillerite layer with general formula AnBnO3n-1.Perovskites doped with high concentration of acceptor impurities (10-20 at.%) shows high ionic (oxygen) and electronic (holes related to transition metals Ti, Fe, Co, Nb) conductivity. Application as mixed conductors in electrochemical devices.
A4B4O11Sr2Fe2O5
ABO3 A2B2O5
Doping of perovskites: from isolated defect to oxygen vacancy ordering and formation of layered structures
La1-xSrxFeO3 with 0 < x <0.25 can be accurately described as an acceptor-doped perovskite with randomly distributed defects
At low p(O2): OOFeLaLaFeO OVFeSrOFeSrO 52222 '
323
'2 2
2
1eVOO OO
n-typeFe2+
hOVO OO 22
12 Fe4+ p-typeAt high p(O2)
n-type
p-type
La4Srn-4TinO3n+2
31
232 )1(2
TiOSrLa
TiOSrOxOLax
xx
δ = x/2
231
232
2
)1(2
Ox
TiOSrLa
TiOSrOxOLax
xx
cubic distortedorthorhombic
SrTiO3 La2Ti2O7
x = 0, δ = 0 : SrTiO3
x = 1, δ = 0.5 : La2Ti2O7
Doping of perovskites: excess oxygen, shear planes and layered structures
Reducing atmosphere, black conducting ceramics (up to 103 Scm-1) , random distribution of defects, x up to 0.3
Oxidizing atmosphere, less conducting, O excess accomodated by formation of shear planes when x > 0.17, by small isolated defects when x<0.17
The structure can be described as the intergrowth of perovskite layers (SrTiO3) and La2Ti2O7 layers. A layered perovskite with general formula:
Layered perovskites
A typical example: Ruddlesden-Popper phases SrO(SrTiO3)n or Srn+1TinO3n+1
Sr3Ti2O7
(n = 2)
SrO
SrO
P
P
P
Sr3Ti2O7
SrTiO3+Sr3Ti2O7
Aurivillius compounds: ((Bi2O2)2+(Bim-1TimO3m+1)2-) Ferroelectric & piezoelectric materials with high TC