1. Computer modelling of the concentration dependence of doping in solid state ionic materials Robert A Jackson School of Physical and Geographical Sciences, Keele University, Keele, Staffs ST5 5BG, UK Marcos V dos S Rezende, Mário E G Valerio Department of Physics, Federal University of Sergipe, 49.100-000 São Cristovão, Brazil

2. Plan for talk 1.Acknowledgements 2.Introduction: relevance of previous work 3.Motivation for developing a new approach 4.The method described 5.Latest results and their implications 6.Discussion and conclusions 2 SSI-18 (Warsaw): 3-8 July 2011

3. Acknowledgements 3 SSI-18 (Warsaw): 3-8 July 2011 Thanks to the organisers of SSI-18 for the invitation to take part in the workshop!

4. Relevance of recent research My recent research has concentrated on studying doping of oxides and fluorides for optical applications. However, the same approach is equally applicable, for example, to doping in solid state ionic materials for fuel cell or battery applications. –e.g. Doping ZrO 2 with CaO or Y 2 O 3 4 SSI-18 (Warsaw): 3-8 July 2011

5. Limitations of previous approach – (i) Take the material LiCaAlF 6 as an example. This is a laser host material, and laser properties are obtained by doping with trivalent rare earth ions, e.g. Nd 3+. Where does the Nd 3+ ion substitute, and if charge compensation is needed, what form does it take? 5 SSI-18 (Warsaw): 3-8 July 2011

6. Limitations of previous approach – (ii) Calculations (described later) show that the ion substitutes at the Ca 2+ site with charge compensation by creation of Li + vacancies, which is useful information for the crystal growers, but...... it assumes doping of a single ion in an otherwise perfect lattice, which is not realistic! 6 SSI-18 (Warsaw): 3-8 July 2011

7. Motivation for developing a new approach We would like to be able to understand how the doping process depends on the concentration of dopants. This will also enable solubility limits for dopants to be predicted. This is far more useful information to help in developing new materials for specific applications. 7 SSI-18 (Warsaw): 3-8 July 2011

8. Background to the method (i) Materials are modelled using interionic potentials. Potentials used are typically of the Buckingham form, parameterised empirically: V(r) =q 1 q 2 /r + A exp ( ‐ r/  ) – Cr ‐ 6 Structures and properties are calculated by lattice energy minimisation. 8 SSI-18 (Warsaw): 3-8 July 2011

9. Background to the method (ii) The Mott-Littleton approximation is used to model defects, assuming a 2- region strategy, with the region surrounding the defect being modelled explicitly. This enables the energies of formation of defects (vacancies, interstitials, substitutions) to be calculated. SSI-18 (Warsaw): 3-8 July 2011 9

10. Mott-Littleton approximation Region I Ions are strongly perturbed by the defect and are relaxed explicitly with respect to their Cartesian coordinates. Region II Ions are weakly perturbed and therefore their displacements, with the associated energy of relaxation, can be approximated. Region IIa Defect Region I © Mark Read (AWE) 10 SSI-18 (Warsaw): 3-8 July 2011

11. Solution energies for single ion doping – (i) In order to calculate the energy involved in doping a single ion into a lattice, the solution energy (E sol ) is calculated. It includes all terms involved doping. –For M 3+ substitution in LiCAF: MF 3 + Ca Ca →M Ca + V′ Li + LiF + CaF 2 E sol is the energy of this reaction SSI-18 (Warsaw): 3-8 July 2011 11

12. Solution energies for single ion doping – (ii) This solution energy can be used to 1.Predict dopant location 2.Predict the lowest energy form of charge compensation, if needed. It has been used widely in our papers on doped mixed metal fluorides and oxides. But it doesn’t include effect of finite defect concentration! SSI-18 (Warsaw): 3-8 July 2011 12

13. New method – application to M 3+ doped BaAl 2 O 4 To explain the new method, we move from fluorides to oxides, and consider the formation of M 3+ doped BaAl 2 O 4, which has applications as a phosphor material. Some of its applications will be shown on the next slide: SSI-18 (Warsaw): 3-8 July 2011 13

14.  BaAl 2 O 4 when doped with rare earth ions shows long lasting phosphorescence: BaAl 2 O 4 :Ce 3+, BaAl 2 O 4 :Ce 3+,Dy 3+, BaAl 2 O 4 :Eu 2+,Nd 3+, BaAl 2 O 4 :Eu 2+,Dy 3+. BaAl 2 O 4 :Eu 2+, BaAl 2 O 4 :Tb 3+, BaAl 2 O 4 :Tm 3+, BaAl 2 O 4 :Mn 2+,Ce 3+. 14

15. Basis of the new method Mimicking the crystal growth process, and assuming that the M 3+ ion dopes at an Al 3+ site*: 0.5x M 2 O 3 + BaO + (1-0.5x) Al 2 O 3  BaAl 2-x M x O 4 The procedure is now to calculate the solution energy as the energy of this reaction, which will now depend on x. –*It is repeated for different solution schemes SSI-18 (Warsaw): 3-8 July 2011 15

16. Concentration dependent solution energies The energy of the reaction is: E sol = E [BaAl 2-x M x O 4 ] - [0.5x E latt (M 2 O 3 ) + E latt (BaO) + (1-0.5x) E latt (Al 2 O 3 )] Where E [BaAl 2-x M x O 4 ] = (1-0.5x) E latt (BaAl 2 O 4 ) + x E (M Al ) Where the perfect and defective terms have been separated. SSI-18 (Warsaw): 3-8 July 2011 16

17. Some results! We can calculate solution energies for M 3+ ions in BaAl 2 O 4 as a function of x: –Energies in eV, T = 293 K SSI-18 (Warsaw): 3-8 July 2011 17 1% M 2 O 3 2% M 2 O 3 3% M 2 O 3 Max. x M 2 O 3 Ce-0.84661.09693.04041.4356 Pr-0.84261.10483.05221.4327 Nd-0.84161.10683.05521.4319 Sm-0.83941.11123.06181.4303

18. Interpretation of results Negative solution energies imply solution of the dopant in the crystal structure. The procedure is to increase the concentration, x, until the solution energy is zero, and this represents the solution limit. SSI-18 (Warsaw): 3-8 July 2011 18

19. Graphical summary SSI-18 (Warsaw): 3-8 July 2011 19

20. General discussion The method described can be applied to any combination of host lattice and dopant. Solution energies can be calculated as a function of concentration, and solubility limits for dopant ions obtained.  See Rezende et al, J. Sol. State Chem. (2011) http://dx.doi.org/10.1016/j.jssc.2011.05.053 http://dx.doi.org/10.1016/j.jssc.2011.05.053  Also, a proceedings paper will be submitted. SSI-18 (Warsaw): 3-8 July 2011 20

21. Conclusions The method presented should be useful in any application where doping is used to create or enhance a particular material property. Applications given have been to optical materials but it is not limited to these. And finally, looking back, now for something completely different! SSI-18 (Warsaw): 3-8 July 2011 21

22. SSI-18 (Warsaw): 3-8 July 2011 22 NATO SUMMER SCHOOL, CALABRIA 1985 ? ?

23. SSI-18 (Warsaw): 3-8 July 2011 23 Professor Alan Chadwick: a special mention