1. Modelling the concentration dependence of doping in optical materials Robert A Jackson School of Physical and Geographical Sciences, Keele University, Keele, Staffs ST5 5BG, UK Mário E G Valerio Department of Physics, Federal University of Sergipe, 49.100-000 São Cristóvão, Brazil Contributed to the session in honour of Professor Patrick Jacobs

2. EURODIM2014: 14-18 July 2014 Canterbury, UK 2 Plan for talk 1.Introduction 2.Previous work – setting the scene 3.Methodology and results 1.Rare earth ions in YLiF 4 2.Thorium in LiCaAlF 6, CaF 2 4.Future work 5.Patrick’s influence: research & conferences 6.General acknowledgements

3. Introduction Motivation – for optical materials, dopants are responsible for most of their important properties. We can predict where they substitute in the lattice, and what form of charge compensation will be preferred. We can predict morphologies for the perfect and doped materials. A range of materials have been modelled in this way, including BaMgF 4 and YLiF 4. EURODIM2014: 14-18 July 2014 Canterbury, UK 3

4. 4 From EURODIM 2010 proceedings

5. YLF Morphology EURODIM2014: 14-18 July 2014 Canterbury, UK 5 T E Littleford, R A Jackson, M S D Read: ‘An atomistic simulation study of the effects of dopants on the morphology of YLiF 4 ’, Phys. Stat. Sol. C 10 (2), 156-159 (2013) (ICDIM 2012 paper)

6. YLF morphology as affected by Ce dopants EURODIM2014: 14-18 July 2014 Canterbury, UK 6 Ce-YLF Surface energy approach

7. Relative effect on surfaces The (011) surface becomes less prominent with the (111) surface disappearing. The 021 surface is stabilised by Ce dopants and appears in the defective morphology.

8. Predicting maximum dopant concentration – (i) As well as knowing where and how the dopants are incorporated, how many are involved? –Consider doping YLiF 4 (YLF) with M 3+ dopants: (1-x) YF 3 + x MF 3 + LiF → Y 1-x M x LiF 4 –The procedure is to calculate the energy of this reaction (E sol ) as a function of the dopant concentration x: E sol = E (Y 1-x M x LiF 4 ) - [(1-x) E latt (YF 3 ) + x E latt (MF 3 ) + E latt (LiF)] EURODIM2014: 14-18 July 2014 Canterbury, UK 8

9. Predicting maximum dopant concentration – (ii) Calculating the first term (in red) has involved much thought! –The term is calculated using this expression: E D (x) = x E D ML + E p (1) –This splits the energy into defective and perfect terms (& assumes they don’t interact). –The final expression is then: E sol = E (x E D ML + E latt (YLiF 4 )) - [(1-x) E latt (YF 3 ) + x E latt (MF 3 ) + E latt (LiF)] EURODIM2014: 14-18 July 2014 Canterbury, UK 9

10. Results for M 3+ dopants in YLF* RE Max mol % MF 3 RE Max mol % MF 3 La 0.69 Tb 1.41 Ce 0.76 Dy 1.28 Pr 0.85 Ho 1.40 Nd 0.93 Er 1.52 Sm 1.23 Tm 1.33 Eu 1.15 Yb 1.51 Gd 1.22 Lu 1.49 Supercell methods can also be used to calculate the RHS term (and include all interactions). Experimental data to test these results are needed! EURODIM2014: 14-18 July 2014 Canterbury, UK 10 * T E Littleford, PhD thesis 2014

11. The nuclear clocks story 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. These promise up to 6 orders of magnitude improvement in precision over next generation atomic clocks, as well as enhanced stability. Eric Hudson’s plenary lecture at EURODIM 2010 introduced the general field. EURODIM2014: 14-18 July 2014 Canterbury, UK 11

12. Previous work EURODIM2014: 14-18 July 2014 Canterbury, UK 12 Two previous papers (below, PDFs available) have modelled Th 4+ in these materials, and established the energetically favoured dopant sites and charge compensation mechanism (Ca 2+ site with 2 F - interstitials). Th 4+ has to be doped into a suitable crystal; CaF 2 and LiCaAlF 6 /LiSrAlF 6 are being investigated.

13. Solution schemes for Th 4+ incorporation LiCaAlF 6 x ThF 4 + (1-x) CaF 2 + LiF + AlF 3  LiTh x Ca 1-x AlF 6+2x CaF 2 x ThF 4 + (1-x) CaF 2  Ca 1-x Th x F 2+2x (Assuming Th 4+ substitutes at the Ca 2+ site with compensation by 2 F - interstitials) EURODIM2014: 14-18 July 2014 Canterbury, UK 13

14. How much Th 4+ can be doped into these materials? Applying the method to LiCaAlF 6 and CaF 2 gives interesting contrasting results. For LiCaAlF 6 we calculate a maximum Th 4+ concentration of ~ 5 mol %. Experimental values are eagerly anticipated! For CaF 2, we observe a linear relationship between solution energy and Th 4+ concentration. Recent experimental concentrations are between 0.4-0.7 mol%, corresponding to solution energies in the range 2.3 – 3.5 eV. EURODIM2014: 14-18 July 2014 Canterbury, UK 14

15. Conclusions & Future Work The method we have developed gives results that agree with existing experimental data, but more is needed to test it and develop it further. We would welcome collaboration with groups who have data on doping particular materials. EURODIM2014: 14-18 July 2014 Canterbury, UK 15

16. A tribute to Patrick I have much to be grateful to Patrick for. Early in my career he gave me this advice: (Your research plan) must be realistic, but should bring out the fact that you have plenty of ideas and will be able to develop an active research programme which will involve not only yourself but future graduate students. This was very useful to me as I began my career, and I have tried to continue to follow it ever since. EURODIM2014: 14-18 July 2014 Canterbury, UK 16

17. Early research influence: Keele, August 1986 In 1986 the development of photographic film was still a topic of commercial importance, and Patrick, Sean Corish, along with Roger Baetzold and Yen Tan from Kodak, visited Keele to try to improve the existing potentials for the silver halides. My small part in this story was showing Patrick how to use CASCADE (based on HADES, and which preceded GULP). This visit ultimately led to the following paper: EURODIM2014: 14-18 July 2014 Canterbury, UK 17

18. Three body interactions in silver halides EURODIM2014: 14-18 July 2014 Canterbury, UK 18

19. Meetings in Oxford and London, Ontario EURODIM2014: 14-18 July 2014 Canterbury, UK 19 ‘Retirement’ meeting (London, Ontario, September 1989

20. ICDIM 1992 (Nordkirchen) EURODIM2014: 14-18 July 2014 Canterbury, UK 20

21. EURODIM 1998 (Keele) (The last EURODIM/ICDIM conference attended by Patrick) EURODIM2014: 14-18 July 2014 Canterbury, UK 21

22. Some more photos … EURODIM2014: 14-18 July 2014 Canterbury, UK 22  1981 1988   1998 1999 

23. Final conclusions Patrick’s influence on the EURODIM-ICDIM series of conferences has been considerable. More generally, his influence on the field of solid state chemistry was significant and wide ranging, as is shown by the diversity of topics presented in this session. He was always generous in his encouragement and enthusiasm, which is much appreciated by those who knew him. EURODIM2014: 14-18 July 2014 Canterbury, UK 23

24. Acknowledgements 24 EURODIM2014: 14-18 July 2014 Canterbury, UK Tom Littleford (Keele, UK) Jomar Amaral (UFS, Brazil) Thorsten Schumm (TU-Wien, Austria) Eric Hudson (UCLA, USA)