scientific presentation

1. Theoretical modelling of the
photoconversion and aggregation of
oxygen centres in calcium fluoride
A.S. Mysovsky, E.A. Radzhabov
Institute of Geochemistry SB RAS
1a Favorsky Street, 664033 Irkutsk, Russia
M. Reichling, J. Sils
Universität Osnabrück, Fachbereich Physik
Barbarastraße 7, D-49069 Osnabrück, Germany
A.L. Shluger, P.V. Sushko
University College London, Department of Physics &
Astronomy
Gower Street, London WC1E 6BT, UK

2. Outline
1. Calculation technique
2. Overview of possible defect species
3. F-centre
Ground state
Optical absorption
4. O ion
5. Oxygen-vacancy dipole
Optical absorption & luminescence
Reorientation
6. F- and F2A
+ centres perturbed with oxygen
7. Photodissociation and recombination mechanism
Conclusion

3. Calculation technique
GUESS calculations
(P.V. Sushko, A.L. Shluger and C.R.A. Catlow,
Surface Science 450, 153 (2000))
Quantum region (QM):
– modified B3LYP functional (40% HF
exchange + 60% Becke).
– Basis set: 6-31G + 2 additional d-functions
on calcium ions
– TD DFT for optical absorption calculations
Classical region: shell model & pair
potentials (A.M. Stoneham, Handbook of
interatomic potentials, AERE Harwell (1981))
Region of fixed point charges
Molecular dynamics (MD)
To study the reorientation of oxygen-vacancy dipoles we used
classical MD without shells.

4. Possible defects
VA F F
(VA)2 F2
+ F
+ e
+ VA
F
+ e
O O2
O VA O2 VA F O2 F O2
O VA)2 O2 VA)2 F2 O2 F2 O2 F2 O2
Not necessarily all these defects really exist, it's just a way to build all
possible species.
+ VA
+ VA
+ e

5. cluster Ca4F7 Ca16F33 Expt. *
F(100) || 89.29 88.15 79.07
59.5 64.5 58
F(110) || - 6.24 5.14
- 4.3 3.2
F(111) || - 9.63 9.75
- 5.9 6.5
F(11-1) || - 1.69 1.97
- 1.2 1.0
F(200) || - 2.04 1.68
- 1.1 0.91
*Hayes & Stott, Proc. Roy. Soc. A 301, 313 (1967)
F-centre hyperfine couplings (G)
F(100) F(110) F(111) F(11-1) F(200)
Theory* 87.6 3.87 7.61 1.33 1.16
Expt. 65.1 5.85 0.83 0.83 0.17
Another calculation (isotropic part of hyperfine tensor, G)
Stoneham, Hayes, Smith & Stott, Proc. Roy. Soc. A 306, 369 (1968)

6. Cluster Ca4F7 Ca4F27 Ca4F27 Ca16F33 Ca16F33 Expt.
Method MP2 HF MP2 B3LYP B3LYP
Basis set 6-311G 6-311G 6-311G LANL2 6-31G
F(100) || 77.6 96.7 73.2 113.3 88.15 79.07
51 71 51 87 64.5 58
F(110) || - 7.1 4.2 9.9 6.24 5.14
- 4 2.1 7.1 4.3 3.2
F(111) || - 1.4 3.4 4.1 9.63 9.75
- 0.4 1.8 2.1 5.9 6.5
F(11-1) || - 1 1.3 3.4 1.69 1.97
- -0.15 0.3 2.3 1.2 1.0
F(200) || - - - 2.6 2.04 1.68
- - - 1.5 1.1 0.91
F-centre hyperfine couplings (G) with different methods

7. F-centre optical absorption
Transition E, eV fosc IRREP
1s 2p 3.23 0.133 T2
1s 2s 3.48 A1
1s 3p 4.27 0.012 T2
1s 3d 4.74 E
1s ? 4.95 0.000 ?
1s 3d 5.02 T2
Delta-SCF (with symmetry constraint)
E(1s 2p) = 3.12 eV
Experimental absorption band at 3.3 eV

8. O ion
Affinity with respect to CB
EA=3.86 eV
Hyperfine couplings of O
This work Expt.*
atom A, G axis A, G axis
O (0 0 0) -116.43 <0 0 1> 97.8 <0 0 1>
7.68 9 6
F (0 0 1) 63.79 <0 0 1> 63.6 <0 0 1>
20.69 <1 1 0> 15.4 0.5
20.39 <1 -1 0> 15.4 0.5
F (1 0 0) -3.98 <1 0 0> 3.6 0.5 <1 0 0>
-2.24 <0, 0.87, -0.49> 3.4 0.5 <0 0 1>
-2.04 <0, 0.49, 0.87> 1.2 0.8 <0 1 0>
*Bill & Silsbee, PRB 10, 2697 (1974)

9. Optical absorption of O ion
Hole transition to other to 2p-states of
oxygen
E=0.4 eV
Hole transition to VB
E=7.06 eV, f=0.076
Experimental evidence of O- ion absorption is absent at present
moment. It can be done if it will be possible to establish correlation
between EPR signal of O- ion and some absorption band in VUV

10. Calcium below the plane
Calcium above the plane
Vacancy
O - ion
Energy, eV
1 – luminescence
2 – excitation of the luminescence
3 – absorption
4 – creation
5 – absorption of pure crystal
6 – photodissociation spectra
Two distinct absorption bands at 6.7 and
8.5 eV
The luminescence band at 2.6 eV.
E. Radzhabov, P. Figura, pss(b) 136, K55
(1986); E. Radzhabov, pss(b)136, K149
(1986)
Oxygen-vacancy dipole

11. 2px-y(O) 2pz(O)2px+y(O)
1(V)=1s(V)
2(V)
Optical absorption of the dipole
(V)
Transition E, eV fosc
2px-y(O) 1s(V) 6.38 0.019
2px+y(O) 1s(V) 6.48
2pz(O) 1s(V) 6.63 0.084
2px-y(O) 2(V) 8.10
2px+y(O) 2(V) 8.22 0.018
2pz(O) 2(V) 8.22
2pz(O) (V) 8.38 0.006
2px-y(O) (V) 8.38 0.007
8.66 0.029
8.69 0.005
8.71 0.005
8.76 0.019
8.81 0.015
One-electron
interpretation
impossible
9.00 0.021

12. Luminescence of the dipole
Triplet absorption
ESCF = 6.23 eV
Triplet luminescence
ESCF = 1.71 eV
TDDFT in the geometry of relaxed triplet
1.99 eV f=0.0014
2.23 eV f=0.0012
3.00 eV f=0.1162
?
1 – luminescence
2 – excitation of the
luminescence
3 – absorption
nonradiative
transition

13. Reorientation/migration of the dipole
Example of
<100>→<110> →
<010>
reorientation
Simultaneous jump
of two fluorines
<100> → <200> →
<100> process
Barrier for reorientation
EB(<100> <110>)=0.64 eV
Barrier for oxygen jump
ED(O2--VA)=1.61 eV

14. FA(O2-)-centre
Transition E, eV fosc
1s(V) 2px+y (V) 3.16 0.086
1s(V) 2pz(V) 3.43 0.150
1s(V) 2px-y (V) 3.46
EA=-0.49 eV
EI=4.69 eV
FA (O2-)-centre
Transition E, eV fosc
1s(V) 2px+y (V) 2.84 0.226
1s(V) 2pz(V) 2.93 0.116
1s(V) 2px-y (V) 3.06
EI=1.74 eV

15. Absorption of F2A
+-centres at
4 – 130 K;
1,5 – 230 K;
6 – 260 K;
7 – 295 K;
2,3 – after heating to 295 K
Temperature dependence of F2A
+ absorption
band (3.4 eV) created by photodissociation
Photodissociation under irradiation in 2nd
band leads to the creation of FA and F2A
+-
centres.
Absorption of F2A
+ – 2.3-2.4 and 3.4 eV
Absorption of FA – 2.8 and 3.2 eV

16. F2A
+(O2-)-centre
Two configurations denoted <100> and <110>
In <110> spin density is completely localised on one vacancy
In <100> distributed over both vacancies.
<100> configuration is energetically favourable, but not much
E=0.06 eV
e
e
<110> conf.
EA= 0.85 eV
EI = 5.98 eV
<110><100>
<100> conf.
EA= 1.45 eV
EI = 6.47 eV

17. 2.76
6.05
vertical
vertical
thermal
0.86
3.38
5.31
2.03
1s(F )1s(VA)
Energy levels
1s(F)
EA = Etot(defect) – Etot(defect + e ) – A(cryst.) (vertical affinity)
EI = Etot(defect – e ) – Etot(defect) – A(cryst.) (vertical ionization)
EI (thermal)= Etot(defect – e relax.) – Etot(defect) – A(cryst.)
A(cryst.) = Etot(cryst.) – Etot(cryst. + e ) (affinity of the crystal CB)
3.86
6.16
8.36
2p(O ) 2p(O2 )

18. 10.24
4.69
-0.49
1.92
O2--VA dipole
0.69
2p(O2-)
1s(VA)
FA(O2-)
1s(VA)
1.34
0.70
1s(VA)
FA (O2-)
8.17
3.15
F2
+
6.47
1.45
F2A
+(O2-)
Energy levels (continued)

19. The photodissociation and “recombination”
The dissociation stage
The “recombination” stage
The photodissociation of dipoles is more
or less clear. It occurs:
1) under irradiation in 8.4 or 9.2 eV
bands
2) with higer energies (which leads to
the creation of electron-hole pairs)
3) under X-irradiation
The puzzling stage is «recombination».

20. Photodissociation occurs during irradiation in 2nd (8.4 eV) or 3rd (9.2 eV)
OA bands.
The mechanism includes following steps:
1. Excitation from O2- to excited states of vacancy;
2. Thermoionisation of electron;
3. Dissociation of remaining O–VA centre;
4. The electron (from step 2) is trapped on other O2--VA dipole;
5. Finally the free vacancy (from step 3) is also trapped there.
Photodissociation mechanism

21. Conclusion
List of possible recombination channels.
1. FA (O2-) ==> FA(O2-) + e thermoionization ( Ethermal = 0.70 eV)
2. Tunnelling recharging
a) FA(O2-) O ==> O2 VA + O2-
Evertical= -0.83 eV; Ethermal = 4.24 eV
b) FA(O2-) F2A
+(O2-) ==> O2 VA + F2A(O2-)
Evertical= -3.51 eV; Ethermal > -0.47 eV
c) FA(O2-) F2
+ ==> O2 VA + F2
Evertical= -1.81 eV; Ethermal > 1.23 eV
d) F2A
+(O2-) O ==> O2 VA)2 + O2-
Evertical= -2.12 eV; Ethermal > 0.18 eV
e) F2A
+(O2-) F2
+ ==> O2 VA)2 + F2
3. Separation of vacancy from F2A
+(O2-) ?
4. Migration of F2A
+(O2-) ?

22. Conclusion
1. Correct description of the F-centre excited and even ground states requires electronic
correlation to be taken into account as well as tails of F-centre electronic density on the
distances of several lattice constants from the defect. Using of B3LYP functional, all-
electron basis set and relatively large quantum clusters allows to achieve qualitative and
reasonable quantitative (with the relative error not more than 15% for hyperfine
couplings).
2. TD DFT allows to calculate optical absorption energies with a precision of 0.1 eV (in
the case of F-centre and oxygen-vacancy dipole). Such a good agreement with
experiment is even suspicious, especially if we take into account that there is some
controversy about TD DFT among theoreticians. However, we believe such a good
precision can not be just a coincidence.
3. O ion should have an optical absorption band in VUV region about 7 eV.
4. Possible channels of oxygen-vacancy dipoles recombination are discussed.