1. Modelling mixed metal fluorides for optical applications Robert A Jackson Lennard-Jones Laboratories School of Physical and Geographical Sciences Keele University, Keele, Staffs ST5 5BG, UK Thanks especially to: Elizabeth Maddock, Thomas Littleford (Keele) Mark Read (AWE), Dave Plant (AWE/.../Keele) Mario Valerio, Jomar Amaral, Marcos Rezende (UFS) Sonia Baldochi (IPEN) Eric Hudson (UCLA), David deMille (Yale)

2. 2 RSC SSCG conference, April 2010 Plan of talk What materials are involved? What is the motivation? Methodologies employed. Case studies. Future work.

3. 3 RSC SSCG conference, April 2010 What materials? Mainly mixed metal fluorides and oxides They do not have to have complex structures – e.g. BaLiF 3 : For optical applications, doping is usually necessary. Rare earth (RE) ions are typically used, as their emission wavelengths are suitable for optical applications (in the  m range). inverted perovskite structure

4. 4 RSC SSCG conference, April 2010 How important is doping to enhance optical properties? The picture shows a sample of amethyst, which is quartz, SiO 2 doped with Fe 3+ ions from Fe 2 O 3. The value of the quartz is drastically increased by the presence of a relative small number* of Fe 3+ ions! *’As much iron as would fit on the head of a pin can colour one cubic foot of quartz’ http://www.gemstone.org/gem-by-gem/english/amethyst.html

5. 5 RSC SSCG conference, April 2010 Blue John: CaF 2 with F- centres The picture shows a sample of Blue John, CaF 2 coloured by the presence of F-centres (electrons trapped at vacant F - sites in the crystal). Blue John is mined in a relatively few locations, including Castleton in Derbyshire.

6. 6 RSC SSCG conference, April 2010 Optical Materials: motivation We are interested in understanding the behaviour and properties of materials with applications in a range of devices: Solid state lasers, where the laser frequency can be ‘tuned’ by changing the dopant. Scintillator devices for detecting electromagnetic or particle radiation. Nonlinear optical devices, frequency doublers and optical waveguides.

7. 7 RSC SSCG conference, April 2010 Methodology The calculations are carried out in 2 stages: 1.Standard energy minimisation/Mott-Littleton calculations to establish location of dopants and charge compensation mechanisms, involving calculation of solution energies.* 2.Crystal field (or QM) calculations to access electronic properties and optical transitions. * Some new developments will be mentioned later.

8. 8 RSC SSCG conference, April 2010 Case study 1: Nd- and Tb- doped BaY 2 F 8 * BaY 2 F 8, when doped with RE ions, in this case Nd 3+ and Tb 3+, has applications as a scintillator for radiation detection. This material has been the focus of a joint experimental and modelling study. Modelling can (i) predict location of dopant ions, and (ii) predict optical properties. * Based on: ‘Structural and optical properties of Nd- and Tb-doped BaY 2 F 8 ’ by Valerio et al, Optical Materials 30 (2007) 184–187

9. 9 RSC SSCG conference, April 2010 Sequence of the modelling study 1.Derivation of an interatomic potential for BaY 2 F 8, and for the RE-lattice interactions. 2.Calculation of intrinsic defect properties of the material to allow prediction of intrinsic disorder. 3.Calculation of solution energies, used to predict the location of the RE dopants. 4.Calculation of optical properties using crystal field methods. *Details in: ‘Computer modelling of BaY 2 F 8 : defect structure, rare earth doping and optical behaviour’ by Amaral et al, Applied Physics B 81 (2005) 841- 846

10. 10 RSC SSCG conference, April 2010 Potential fitting and solution energy calculations M 3+ doping at the Y 3+ site in BaY 2 F 8 MF 3 + Y Y → M Y + YF 3 E sol = -E latt (MF 3 )+ E(M Y )+ E latt (YF 3 ) Calculated values for Nd, Tb are: 0.64 eV, 0.32 eV expcalc% diff a/Åa/Å 6.986.96-0.44 b/Åb/Å 10.5210.671.42 c/Åc/Å 4.264.20-1.61 // 99.798.4-1.31

11. 11 RSC SSCG conference, April 2010 Crystal field calculations The RE ions are predicted to substitute at the Y sites, and relaxed coordinates of the RE ion and the nearest neighbour F ions are used as input for a crystal field calculation. Crystal field parameters B k q are calculated, which can then be used in two ways – (i) assignment of transitions in measured optical spectra, and (ii) direct calculation of predicted transitions.

12. 12 RSC SSCG conference, April 2010 How good is the method? In the OM paper, measured and calculated transitions were compared, and a typical agreement of between 3-5% was observed: transitionExp. /cm -1 Calc. /cm -1 5D4  7F45D4  7F4 1718117724 1803718041 5D4  7F55D4  7F5 1811619111 1990019364

13. 13 RSC SSCG conference, April 2010 Summary of case study and other applications The method described has been shown to be able to calculate optical transitions for RE dopant ions in BaY 2 F 8, and reasonable agreement has been obtained with experimental data, implying that it can be used predictively. It has been applied to several other fluoride and oxide materials, including LiNbO 3.

14. 14 RSC SSCG conference, April 2010 Alternative approaches In future we intend to used embedded QM methods (e.g. ChemShell) to model these systems in more detail. The overall aim is to be able to tailor combinations of host crystal and dopant for given optical applications. This work forms part of our new collaboration with AWE.

15. 15 RSC SSCG conference, April 2010 Case study 2: Th in LiCaAlF 6 /LiSrAlF 6 229 Th is being investigated for use in ‘nuclear clocks’; its first nuclear excited state is (unusually) only ~ 8 eV above the ground state, and can be probed by VUV radiation. Nuclear clocks promise up to 6 orders of magnitude improvement in precision over next generation atomic clocks!

16. 16 RSC SSCG conference, April 2010 Case Study 2: practical considerations The 229 Th nucleus needs to be embedded in a VUV-transparent crystal for use in devices. Metal fluorides, e.g. LiCaAlF 6 /LiSrAlF 6 have been identified as being suitable. A modelling study was therefore carried out.* *Details in ‘Computer modelling of thorium doping in LiCaAlF 6 and LiSrAlF 6 : application to the development of solid state optical frequency devices’ by Jackson et al, Journal of Physics: Condensed Matter 21 (2009) 325403

17. 17 RSC SSCG conference, April 2010 Modelling Th in LiCaAlF 6 /LiSrAlF 6 – (i) In previous work potentials were fitted to the host lattices, and defect properties obtained, including the location of RE dopants (more of a challenge than in BaY 2 F 8 !)* The challenge was to determine the optimal location of a Th 4+ ion in the material. Charge compensation will be needed wherever substitution occurs, and resulting defects might affect optical properties. * See ‘Computer modelling of defect structure and rare earth doping in LiCaAlF 6 and LiSrAlF 6 ’ by Amaral, Plant, et al, J. Phys.: Condensed Matter 15 (2003) 2523–2533

18. 18 RSC SSCG conference, April 2010 Modelling Th in LiCaAlF 6 /LiSrAlF 6 – (ii) Having fitted a Th 4+ - F - potential to the ThF 4 structure, solution energies were calculated for doping at the Li (+1), Ca/Sr (+2) and Al (+3) sites, with a range of charge compensation mechanisms. The lowest energy scheme was found to correspond to location at a Ca 2+ /Sr 2+ site with charge compensation by F - interstitials. Crystal growth studies are in progress, but delayed by scarcity/cost* of 229 Th, and politics! *$50k/mg

19. 19 RSC SSCG conference, April 2010 Future work (i): concentration dependent solution energies In modelling the doping of materials, we make extensive use of the concept of solution energies to determine location of dopants, charge compensation mechanisms etc. We are developing new methods which enable us to calculate solution energies as a function of dopant concentration. These should overcome the major problem with predictions based on solution energies, which are currently limited to isolated defects.

20. 20 RSC SSCG conference, April 2010 Concentration dependent solution energies (i) The basis of the technique is to model, directly, the process for preparing the doped materials: e.g. producing doped BaAl 2 O 4 : 0.5x M 2 O 3 + BaO + (1 - 0.5x) Al 2 O 3  BaAl 2-x M x O 4 We calculate the solution energy of the process by calculating the energy of the reaction directly. The left hand side is straightforward; for the right hand side we assume (for solution at the Al site): E [BaAl 2-x M x O 4 ]= (1–0.5x) E latt (BaAl 2 O 4 ) + x E(M Al )

21. 21 RSC SSCG conference, April 2010 Concentration dependent solution energies (ii) The result of these calculations is that we can obtain solution energies as a function of dopant concentration, up to the limit of non-interacting defects. The method is still being developed, but results are promising, and publications have been submitted!

22. 22 RSC SSCG conference, April 2010 Future work (ii): reappraisal of modelling of UO 2 We are looking at UO 2 again, 23 years after our last paper on this subject*! The focus will be on modelling hydrogen gas incorporation and diffusion. A summary of the literature has been carried out with a view to deciding which potential to use, etc. * 'The Calculation of Basic Defect Parameters in UO 2 ’ by Jackson et al, Phil. Mag. A, 53, 27-50 (1986)

23. 23 RSC SSCG conference, April 2010 Acknowledgements Keele University Centre for the Environmental, Physical and Mathematical Sciences