Non-stoichiometric compounds
- Compounds with non-integer values of the atomic composition
- Large change of the properties depending on the non-stoichiometric
character.
Example:
Stoichiometric
ZnO
Transparent
Insulator
NiO
Green
semiconductor
Non-stoichiometric
Zn1.000033O
Orange
n-type semiconductor
Ni0.9999O
Black
p-type hopping semiconductor
Origin of non-stoichiometry:
- Impurities. Example: NaCl heated in Na vapor→Na1+xCl
- Variable valence of metal ions. Example: Transition metal compounds
COMPOUND
FexO
TiOx
TiOx
NixO
ZnxO
COMPOSITION RANGE
0.833 < x < 0.957
0.65 < x < 1.25
1.998 < x < 2.00
0.95 < x 1.000
1.000 < x 1.033
Structure of Wustite
Wustite FeO: rock salt structure. Always non-stoichiometric.
FeO stoichiometric phase is
never stable
FeO always defective in Fe:
Fe1-xO or FeO1+x?→ Fe1-xO
lattice parameter varies
following Vegard’s law
Electronic structure:
Electrical neutrality: 1 Fe2+ vacancy→2 Fe2+ in the lattice
oxidazed to Fe3+
General feature of non-stoichiometric compounds:
defect, vacancy creation →change in the oxidation state of
neighboring atoms to preserve electrical neutrality.
Crystalline structure of Wustite
FeO: ccp array of O2- anions, Fe2+ occupying all octahedral sites
Fe3+ are incorporated in tetrahedral sites
Defects form clusters: ordered structure
Koch-Cohen cluster in Wustite
Atomic content and charge distribution in a cluster:
- 32 O2- anions (front and back faces not shown)
- 13 Fe vacancies→32-13=19 Fe ions in octahedral holes
- 4 Fe3+ in tetrahedral holes →19+4=23 Fe ions
- So, formula of the cluster: Fe23O32 →almost Fe3O4
- Charge balance: x Fe2+ and y Fe3+ in octahedral holes
x + y=19
2x + 3y=52
- Solving: 5 Fe2+ and 14 Fe3+ in octahedral positions in the cluster
Electronic properties of non-stoichiometric
compounds
Type A: anion vacancies: 1 O2- vacancy → 2 M2+ reduced to M+
MO1-x
2 e-
Type B: interstitial metal atom: interstitial Mi → 2M2+ reduces to M+ at
lattice sites + Mi2+
M1+xO
Type C:
interstitial anion: 2 M2+ → 2 M+
Type D:
cation vacancies: 1 M2+ vacancy →
2 M2+ at lattice sites oxidized to M3+
MO1+x
M1-xO
M2+
M
M3+
M+
O2-
Stoichiometric transition metal monoxides
TiO
E
ZnO
NiO
Ti 4s
E
eg
4N states
available
Ni 4s
E
Eg
Zn 4s
Eg
t2g
6N states
available
O 2p
n(E)
Metal
Ti 4s2 3d2
Low effective nuclear
charge
Expanded d orbitals
Delocalized d bands
2 d electrons
Partly filled d bands
→ metal
low DOS at EF
O 2p
O 2p
n(E)
n(E)
Semiconductor
Insulator
Ni 4s2 3d8
Zn 4s2 3d10
Higher effective nuclear
Large effective nuclear
charge
charge
More contracted d orbitals
Very contracted d
orbitals
More localized d bands
Very localized d bands
8 d electrons
Partly filled but very
narrow d
bands→semiconductor
High DOS at EF
10 d electrons
Completely filled
bands
Structure and electronic properies of NS-Nickel
oxide: Ni1-xO
Structure
hopping
hole h+
NiO: rock-salt structure.
Ni1-xO: Metal deficiency,
creation of metal vacancies
by heating in O2 vapor. Some
N2+ oxidazed to N3+ to keep
electrical neutrality.
Conduction due to hopping of
holes from N3+ to N2+ sites.
Ni2+
O2Ni3+
Electrical conductivity
There is no migration of Ni3+. Charge carriers are holes.
Ni1-xO is a p-type hopping semiconductor, with activated diffusion of
holes.
h+
t=t0
h+
t>t0
Ni3+ O2- Ni2+ O2- Ni2+ O2- Ni2+ O2- Ni2+ O2- Ni3+ O2- Ni2+ O2- Ni2+ O2Migration of holes by activated hopping process→origin of Ea
E
− a
k BT
σ increases with T
σ = Neµ
σ = C⋅e
[
σ ∝ Ni3+
]
n independent of T
Structure and electronic properies of NS-Zinc
oxide: Zn1+xO
Structure
ZnO: zinc blende structure.
Zn1+xO: Metal excess, creation
of metal Frenkel-like defects
by adding Zn atoms that are
incorporated in interstitial sites.
Zni oxidazed to Zni2+ and Zn2+
in lattice sites reduced to Zn+.
Zn2+
O2Zn
Zn+
Electronic structure and electrical conductivity
Zn1+xO
E
Zn 4s
Eg=3.2 eV
Zn 3d eg
n(E)
e- given by the impurity are
weakly bound to the Zn+ atom.
Zn impurities behave as n-type
dopant.
Zn1+xO: n-type semiconductor.
Valence induction: increasing the σ of Ni1-xO by
controlled doping
Li2O doped NiO→LixNi1-xO
Number of Ni3+ increases as we introduce Li+: charge balance
Structure
hopping
hole h+
LixNi1-xO
Ni2+
O2Ni3+
Li+
x/2Li2O + (1-x)NiO + x/4O2 → LixNi1-xO What is LixNi1-xO? Li+x Ni2+1-2x Ni3+x O2Electroneutrality check: x + 2 - 4x + 3x - 2 = 0
r(Ni2+) = 0.69 Å ~ r(Li+) = 0.60 Å → Easy replacement of Ni2+ by Li+ without
appreciable lattice distortion
Valence induction→ Every Li+ gives one Ni3+
Electrical conductivity
Conductivity increases with [Li+] levels
σ can be as high as that of a metal but increasing with T as in a SC!!!
Hole p-type migration
Activated hopping escaping Li+ neighboring sites
Hopping motion Ea ~ 0.15 eV
Stoichiometric Ti monoxide
TiO, rock salt structure
Equal numbers of vacancies in the Ti and O sub-lattices
One sixth of the Ti and O are vacant!!
Every alternate atom is missing along every third (110) diagonal plane
New unit cell is monoclinic, ordered defects at RT, random at 900°C.
Vacant sites allow good averlap of d bands.
Rock salt structure model
TiO model
z=0
Oxygen
z=0
Titanium
TiO model
TiO
E
Ti 4s
z=1/2
O 2p
n(E)
Non-stoichiometric Ti monoxide: Ti0.8O
z=0
z=1/2
Ti0.8O, rock salt, stable 900-1400oC
Different defect structure than TiO: all O present
Pattern of Ti vacancies in the rock salt lattice.
every fifth Ti is missing giving Non Stoichiometry: Ti0.8O
Defect ordering produces a superlattice structure