Transcript Slide 1
Thermodynamics of oxygen defective TiO2-x :
The Magneli phases.
Leandro Liborio
Giuseppe Mallia
Nicholas Harrison
Computational Materials Science Group
Magneli Phases
Figure 1a
Figure 1b
TnO2n-1 composition, 4 n 9 .Oxygen defects in {121} planes.
Ti4O7 at T<154K insulator with 0.29eV band gap(1).
T4O7 Metal-insulator transition at 154K, with sharp decrease of
the magnetic susceptibility.
(1) K. Kobayashi et al., Europhysics Lett., Vol. 59, pp. 868-874, 2002.
( 2) W. Masayuki et al., J. of Luminiscence, Vol. 122-123, pp. 393-395, 2007.
(3) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.
Magneli Phases: T4O7 crystalline structure
Figure 3a
Rutile unit cell
Figure 3d
View of Hexagonal
oxygen network
Figure 3b
Figure 3c
View along the a
lattice parameter
View of Hexagonal
oxygen arrangement
Figure 3e
Metal nets in antiphase. (121)r
Cristallographic shear plane.
Technical details of the calculations
CASTEP
Local density functional: LDA
CRYSTAL
Ultrasoft pseudopotentials replacing core
electrons
Hybrid density functional: B3LYP,
GGA Exchange
GGA Correlation
20% Exact Exchange
Plane waves code
All electron code. No pseudopotentials
Supercell approach
Local basis functions: atom centred Gaussian
type functions.
Ti: 27 atomic orbitals, O: 18 atomic orbitals
Simulated systems: Oxygen point-defective
supercell, Magneli phases supercells,
Titanium bulk metal.
Supercell approach
Simulated systems: Oxygen point-defective
supercell, Magneli phases supercells, Oxygen
molecule.
Defect Formation Energies: Thermodynamical Formalism
Figure 5a
G Def
(T , pO2 )
f
Initial state
T, pO2
TiO2 bulk
nTiO2
1
nTiO2
G Def
(T , pO2 )
f
Phonon contribution
pV contribution
Final state
T, pO2
TiO2-x or TinO2n-
nDef oxygen atoms
sup cell
n
bulk
TiO
(T , pO )
TiO2
1
nTiO2
1
nTiO2
1
nTiO2
(T , pO2 ) nODef Oref (T , pO2 )
2
E
F
sup cell
2
sup cell
Vib
G Def
(T , pO2 )
f
1
nTiO2
(1)
bulk
(0 K ) nTiO2 ETiO
(0 K )
2
bulk
(T ) nTiO2 FVib
TiO2 (T )
Supcell
bulk
pO2 VVib
nTiO2VTiO
2
nODef ref
O (T , pO2 )
nTiO2 2
1
+
G
1
E
sup cell
(2)
bulk
(0 K ) nTiO2 ETiO
(0 K )
2
nODef ref
O (T , pO2 )
nTiO2
(3)
Defect Formation Energies: Oxygen chemical potential
G
Def
f
(T , pO2 )
1
nTiO2
E
sup cell
(0 K ) nTiO2 E
bulk
TiO2
nODef ref
(0 K )
O (T , pO2 )
nTiO2
(3)
Limits for the oxygen chemical potential:
E0
0
0
G Rutile
(
T
,
p
f
O2 )
2
Hard limit
O ( pO2 , T ) E0 (4)
Soft limit
Assuming the oxygen behaves as an ideal gas:
PO2
T 5k
T
O2 ( pO2 , T ) 2O ( pO2 , T ) E 0 ( E0 ) 0 T ln 0 kT ln 0
PO
T
2
T
2
0
O2
Oxygen molecule’s
total energy at 0K
Oxygen molecule’s
standard chemical
potential at T=298K
and pO2=1atm
(5)
Expression (5) allows the
calculation of 0O2(T,pO2) at any T
and pO2
Oxygen chemical potential
CASTEP
O0 ( p 0 , T 0 )
2
CRYSTAL
2 bulk
M xOy x Mbulk GM0 xOy ( p 0 , T 0 )
y
E0 and the 0K total energy of the oxygen
atom are calculated with CRYSTAL.
Exp.
PW-GGA (4)
CRYSTAL
Binding energy [eV]
2.56
3.6
2.53
Bond length [ang]
1.21
1.22
1.23
MxOy: ZnO, Anatase, Rutile, Ti4O7, Ti3O5
0O2(T0, p0O2)= mean +/-
Now 0O2 has to be calculated
Now E0 has to be calculated
1
2
1
6
O ( pO0 , T ) A(T T ln(T )) BT 2 - CT 3 2
2
1
E
DT 4 F - GT (6)
12
2T
PO2
T 5k
T
O2 ( pO2 , T ) E 0 ( E0 ) 0 T ln 0 kT ln 0
PO
T
2
T
2
0
O2
(4) W. Li et al., PRB, Vol. 65, pp. 075407-075419, 2002.
(5)
T>298K and
pO2=1atm
T>0K and any pO2
Results for the Magneli phases
Figure 8a
Isolated defects
G
Def
f isolat .
nODef
nTiO
2
1
T4O7 4
GDef
Ti
like Ti 4 O7
O
Figure 8b
nODef
bulk
(T , pO2 )
E sup cell (0 K ) nTiO2 ETiO
(0 K ) Oref (T , pO2 )
2
nTiO2
(T , pO2 )
1 Supcell
bulk
E
(0K ) 27ETiO
(0K ) Oref (T , pO2 )
2
4
Magneli phases
G
Def
f
nODef
nTiO
2
(T , pO2 )
1
nTiO2
E
sup cell
(0 K ) nTiO2 E
bulk
TiO2
nODef ref
(0 K )
O (T , pO2 )
nTiO2
1
T4O7 4
GTiDef4O7 (T , pO2 )
1 Ti 4O7
1 ref
bulk
E
(0 K ) 8ETiO
(
0
K
)
O (T , pO2 )
2
16
4
Results for the Magneli phases
Equilibrium point 1:
GTiDef4O7 (O ) GTiDef5O9 (O ) Tieq4O7 Ti5O9
1
Equilibrium point 2:
GTiDef4O7 (O ) GTiDef3O5 (O ) Tieq4O7 Ti3O5
2
T
0
4 7
5 9
2
T
PO2
5k
T
T ln 0 kT ln 0
PO
2
T
2
Tieq O Ti O E 0 ( O0 E0 )
GTiDef3O5 ( O ) KTi 3O5
GTiDef4O7 ( O ) KTi 4O7
GTiDef5O9 ( O ) KTi 5O9
O
3
O
4
O
5
Relationship between pO2
and T in the phase
equilibrium.
Results for the Magneli phases
Figure 10a
1
Ti3O5
2
3
Ti4O7
Ti5O9
Figure 10b
3
2
1
Forbidden region
log10 pO2
KTieq4O7 Ti5O9
T
T
K1 ln 0 K 2
T
(1) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.
CASTEP Results for the Magneli phases
Figure 10a
Forbidden
region
Figure 10b
Figure 10c
Forbidden
region
(1) P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.
Figure 10d
CRYSTAL Results for the Magneli phases
Figure 12a
Figure 12b
P. Waldner and G. Eriksson, Calphad Vol. 23, No. 2, pp. 189-218, 1999.
Figure 12c
Formation mechanism for an oxygen-defective plane
Cation + anion (100) layer
Ti
bulk
TiO
Tisup ercell 2Oref ( pO , T )
2
L. Bursill and B. Hyde, Prog. Sol. State Chem. Vol. 7, pp. 177, 1972.
S. Andersson and A. D. Waldsey, Nature Vol. 211, pp. 581, 1966.
2
Formation mechanism for an oxygen-defective plane
Final stages
a)
e)
f)
b)
•Antiphase boundaries (dislocation) acts
as high conductivity paths for titanium.
c)
•Dislocations are needed
•No long-range diffusion
•Formation of Ti interstitials.
d)
Conclusions
•The thermodynamics of rutile’s higher oxides has been investigated by first principles
calculations.
•First principles thermodynamics reproduce the experimental observations reasonably
well.
•Spin does not affect the thermodynamics.
•At a high concentration of oxygen defects and low oxygen chemical potential, oxygen
defects prefer to form Magneli phases.
•But, at low concentration of oxygen defects and low oxygen chemical potential, titanium
interstitials proved to be the stable point defects.
•These results support the mechanism proposed by Andersson and Waldsey for the
production the crystalline shear planes in rutile.
Acknowledgements
•Prof. Nic Harrison
•Dr. Giuseppe Mallia
•Dr. Barbara Montanari
•Dr Keith Refson