1. Optical Engineering of Metal Oxides
Jessica Bristow
Department of Chemistry
University of Bath
Supervisors: Dr Aron Walsh, Professor Chris Bowen, Professor Frank Marken

2. Oxides are stable, abundant materials:
A Band Gap
Conduction band
Band gap e-
Valence band
Oxides are stable, abundant materials:
ZnO (3.4 eV) , Al2O3 (9.25 eV), MgO (7.8 eV)

3. Light Absorption and Emission
(Pixomar image)
Light emitting diodes (LED)
“electricity to light”
Photovoltaics (PV)
“light to electricity”
AIM: Control λ to tune optical properties

4. Maximum theoretical efficiency
Shockley–Queisser limit for solar cells under AM1.5 illumination
Most metal oxides
Peter L M, Phil. Trans. R. Soc. A 2011; 369 :

5. Sensitise with 3d Metals
Band gap engineering
Conduction band
Applications:
LED Phosphors
Intermediate band PV
Transition
metal impurities
Tuning optical
Properties by doping λ1 λ2 λ3
Valence band
Predicted maximum PV efficiency
for intermediate gap device: 63%
Luque, A. and Marti, A., Phys. Rev. Lett. 1997, 78, 5014–5017.

6. (Source: Unithaigems)
Al2O3
Fe + Ti
impurities
(Source: Unithaigems)
Sapphire (α-Al2O3 + Fe,Ti)
Corundum (α-Al2O3)
WHY?

7. Materials modelling
The principle is to model materials and resolve their properties:
INPUT OUTPUT
Methods employed:
Ionic potentials
Electronic structure techniques
Atom coordinates and identities
Electronic and material properties

8. Born-ionic potential results
Blue Sapphire
Mechanism of colour:
TiIII + FeIII  TiIV + FeII
III/III cations are the ground state configuration
II/IV configuration represents a meta-stable state
Only stable Tri-cluster in sapphire:
TiIII-(TiIV-FeII)
Jessica K. Bristow, Stephen C. Parker, C. Richard A. Catlow, Scott M. Woodley and Aron Walsh, Chem Commun., 2013, 49, 5259.

9. Electronic structure results
Density Functional Theory (with hybrid exchange-correlation)
Theory
Input  Output
Relative Energy (eV)
Spin density
HSE 06
TiIV + FeII  TiIII + FeIII
0.00
TiIII + FeIII  TiIII + FeIII
0.82
Within the level of theory box it is written HSE06, a Hybrid DFT functional that has continuously shown to be an accurate level of theory to use when modelling inorganic structures such as Al2O3. Within DFT to calculate the total energy of a system the energy is segegrated via the Born Oppenheimer approximation into both electron and nuclear contributions. In total there are six energy terms, which when summed will give the total energy of the system. Two of these terms in DFT require an approximation via an exchange and correlation functional. I wont go any deeper but within DFT the correlation energy term is approximated and in HF its is not and purely the exchange is considered. There are others but this is the principle difference. Hybrid DFT is a combination of the two theories and in this example 25% of the calculation is conducted at the HF level of theory and 75% at the DFT level.
The spin density confirms the self-consistent solution to the III/III ground state, even when starting from a IV/II initial configuration.
The III/III configuration is shown to be the ground state with spherical (d5) spin density on Fe and a single electron (d1) on Ti.
J. K. Bristow et al, Defect theory of Ti and Fe impurities and aggregates in alpha-Al2O3, To be submitted.

10. Computational Requirements
Interatomic potential calculations
4 cores on local iMac
Primary code: GULP (General Utility Lattice Program)
Electronic structure calculations
64 and 128 core jobs (for defective supercells) on Aquila
12 – 96 hours (dependent on level of theory and optimisation)
Primary code: VASP (Vienna ab-initio Simulation Package)
k-point parallelised version available: potential 256 and 512 core jobs on HECToR
Future codes: FHI-AIMS and GPU accelerated Quantum Espresso
G. Kresse and J. Hafner., Phys. Rev. B, 1994, 49:14251.

11. Conclusion
From this work we propose: A new ground state for neighbouring Fe/Ti pairs (III/III) The FeII/TiIV pairs represent a metastable state with a limited life time The tri-cluster [TiIII-(TiIV-FeII)] may be present in sapphire and aid the stability of the FeII/TiIV pairs

12. Electronic structure results
Ti Homo-nuclear system
Theory
Input  Output
Spin density
HSE 06
TiIII + TiIV  Ti Ti3.5+
ELF
(Electron Localised Function)
So Far I have introduced Hybrid DFT and in doing so have described the priciple difference between DFT and Hybrid DFT calculations. Ti homonuclear systems were modelled:
A further method was employed to analysed the extent of delocalisation that may be occurring in this homonuclear system. The ELF is a function considered to be independent to the level of theory employed during a calculation. The principle behind this is to calculate the probability of finding an electron at a given point in space (x,y,z) and localizing this density at this point.
Delocalisation – a true effect or due to an inherent problem with DFT?
Heyd, Jochen, and Gustavo E. Scuseria, J. Chem. Phys., 2004, 121, 1187.
Becke, Axel D., and Kenneth E. Edgecombe, J. Chem. Phys., 1990, 92, 5397.

13. Acknowledgements EPSRC (CSCT DTC) University's HPC service (Aquila)
MCC HPC service (HECToR)
Supervisor: Dr Aron Walsh
Dr Davide Tiana & Walsh Group
Professor Steve Parker
Additional supervisors: Professors Frank Marken and Professor Chris Bowen (Mech Eng)