1. Computer modelling of structural and defect properties of stoichiometric lithium niobate Robert A Jackson School of Physical & Geographical Sciences Keele University Keele, Staffordshire ST5 5BG, UK r.a.jackson@keele.ac.uk http://www.robajackson.com 1

2. Acknowledgements Mário Valerio, Romel Araujo (Aracaju, Brazil) László Kovács, Krisztián Lengyel (Budapest, Hungary) Günter Borchardt, Peter Fielitz (Clausthal, Germany) Bud Bridges (Santa Cruz, USA) … and the workshop organisers for the invitation! 2 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

3. Relevant publications (some hard copies available) [1] R A Jackson, M E G Valerio ‘A new interatomic potential for the ferroelectric and paraelectric phases of LiNbO 3 ’ Journal of Physics: Condensed Matter, 17, 837-843 (2005) [2] R M Araujo, K Lengyel, R A Jackson, L Kovács, M E G Valerio ‘A computational study of intrinsic and extrinsic defects in LiNbO 3 ’ Journal of Physics: Condensed Matter, 19, 046211 (2007) [3] R M Araujo, M E G Valerio, R A Jackson ‘Computer modelling of trivalent metal dopants in lithium niobate’ Journal of Physics: Condensed Matter, 20, 035201 (2008) 3 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

4. Plan of talk Motivation & background Brief introduction to methodology Potential derivation & structural properties Defect properties Ongoing & future work 4 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

5. Motivation & background The interatomic potential published by Donnerberg and co- workers in 1989-90 was widely used. However: (i) advances in computational software and (ii) the continued interest in the material and the availability of new experimental data prompted us to revisit and re-derive the potential (published in 2005). 5 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

6. Potential derivation The potential was fitted to simultaneously reproduce the structures of LiNbO 3 a, Li 2 O and Nb 2 O 5 to allow consistency in later defect calculations. The GULP code b was used, employing the free energy option (allowing temperature dependence of the structure to be treated). a S C Abrahams, P Marsh, Acta Cryst., B 42, 61 (1986) b J Gale, see: http://projects.ivec.org/gulp/ 6 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

7. Brief details of the potential* Full ionic charges on Li, Nb and O. Buckingham potentials describe the interactions between Li-O, Nb-O & O-O. A shell model is employed for O. A 3-body bond bending potential describes the O- Nb-O interactions. * R A Jackson, M E G Valerio, J Phys.: Condensed Matter, 17, 837 (2005) 7 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

8. 8 Ferroelectric phase Exp. [1] This workDonnerberg potential 0 K295 K0 K295 K a=b5.14745.15595.18685.22715.2631 c13.856113.683413.710314.273014.2167 Paraelectric phase Exp. [2] This workDonnerberg potential 0 K293 K0 K293 K a=b5.29245.15305.09192.30302.3042 c13.846213.841813.21115.64125.6402 [1] S C Abrahams, P Marsh, Acta Cryst. B, 42, 61 (1986) [2] H Boysen, F Altorfer, Acta Cryst. B, 50, 405 (1994) Structural agreement International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

9. 9 Lattice parameter as a function of temperature T/Ka exp (Å)a calc (Å)  a (  ) c exp (Å)c calc (Å)  c (  ) 0-5.1559--13.6834- 10-5.1745--13.7035- 2955.14745.18680.7713.856113.7103-1.06 2975.14835.18640.7413.863113.7101-1.10 5235.17005.21330.8413.870013.7200-1.08

10. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 10 Modelling defect properties Using the Mott-Littleton method, energies of formation of the intrinsic defects in LiNbO 3 were calculated. These allow predictions to be made about the defect chemistry of the material. (See Araujo et al: Journal of Physics: Condensed Matter, 19, 046211 (2007))

11. 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. © Mark Read 11 International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

12. Formation energies for basic defects (in stoichiometric LiNbO 3 ) International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 201312 Defect0 K293 K *[1] model II V Li ’ 9.819.719.8 V Nb ’’’’’ 127.56127.45117.3 V O  18.9818.9119.5 Li i  -7.08-7.12-8.87** Nb i  -104.12-104.25-110.68** O i ’’ -9.47-9.64-16.08** Nb L i  -98.37-98.49-99.5 Li Nb ’’’’ -113.99 [1] Donnerberg et al, Phys. Rev. B., 40, 11909 (1989) * Temperature taken into account via lattice expansion. ** Deduced values since paper does not report these values.

13. Frenkel, Schottky and pseudo-Schottky energies* (per defect) International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 201313 Defect0 K293 K *[1] Li Frenkel1.371.300.93 Nb Frenkel11.7211.606.26 O Frenkel4.764.643.42 Schottky LiNbO 3 3.953.853.91 Pseudo- Schottky Li 2 O 1.811.801.94 Pseudo- Schottky Nb 2 O 5 5.095.072.85 *Calculated for information only since defects are more complex. Expected trends in values are observed.

14. Models to explain the observed experimental data The simple Frenkel and Schottky models do not explain the observed behaviour in LiNbO 3. For example, the Nb Li  + 4V Li ’ defect cluster has a formation energy of –63.61 eV. We needed to consider possible reactions that give rise to such defects. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 14

15. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 15 Explaining the observed non- stoichiometry Following the work of Kovács and Polgár*, we considered models based on antisite or interstitial Nb compensated by Li or Nb vacancies. 3 possible reactions were considered (see next slide): * L Kovács and K Polgár, Crystal Research and Technology, 21, K101 (1986)

16. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 16 Possible defect reactions that give rise to Li deficiency Antisite Nb compensated by Li vacancies 5Li Li + ½Nb 2 O 5  4V’ Li + Nb Li  + 5/2Li 2 O  E(reaction) = -0.98 (-2.52*) eV per Li 2 O formula unit Antisite Nb compensated by Nb vacancies 5Li Li + 4Nb Nb + ½Nb 2 O 5  5Nb Li  + 4V Nb ’’’’’ + 5/2Li 2 O  E(reaction) = 29.8 eV per Li 2 O formula unit Interstitial Nb compensated by Li vacancies 5Li Li + ½Nb 2 O 5  5V Li ’ + Nb i  + 5/2Li 2 O  E(reaction) = 0.49 eV per Li 2 O formula unit * ‘Bound’ defect configuration

17. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 17 Conclusions from the reactions If the reaction energies are calculated, using the basic defect energies already obtained, we concluded that: – only the antisite Nb/Li vacancy model is energetically favourable. – of the other two mechanisms, the interstitial Nb/Li vacancy model is more favourable than the antisite Nb/Nb vacancy model.

18. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 18 Divalent and trivalent dopants The incorporation of a range of dopant ions in LiNbO 3 was modelled. Divalent and trivalent ion substitution was considered. Charge compensation is needed for substitution at either the Li + or Nb 5+ site.

19. Dopant ions considered Reference [2]: M 2+ dopants Mg, Mn, Fe, Co, Ni, Zn, Sr, Cd, Ba & Pb, and M 3+ lanthanide dopants Ce-Lu. Reference [3] focused on M 3+ dopants: Sc, Cr, Fe and In. [2] Journal of Physics: Condensed Matter, 19, 046211 (2007) [3] Journal of Physics: Condensed Matter, 20, 035201 (2008) International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 19

20. Summary of modelling procedure The GULP code is used to calculate the substitution energies, e.g. M 2+ at the Li + site, denoted by M Li  in Kroger-Vink notation. The substitution energies are then converted into solution energies, which give the total energy involved in the process: International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 20

21. Solution energies Assuming M 2+ substitution at the Li + site, a possible scheme could be: MO + 2 Li Li → M Li  + V Li ’ + Li 2 O This assumes charge compensation by Li vacancies, but other possibilities are considered. The same idea is applied to M 3+ dopants. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 21

22. Predicted doping schemes: M 2+ ions From the calculations, the following predictions are made based on lowest energies: Co-doping at both Li + and Nb 5+ sites, except for Fe 2+ and Cd 2+ for which substitution at the Nb 5+ site with charge compensation by Nb - Li anti- site substitution is preferred. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 22

23. Predicted doping schemes: M 3+ ions The predicted scheme for all the lanthanide ions and Sc, Cr and Fe is self-compensation: M 2 O 3 + Li Li + Nb Nb → M Li  + M Nb ’’ + LiNbO 3 For In, the preferred scheme involves doping at the Nb 5+ site with charge compensation by Nb-Li anti-sites. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 23

24. Further calculations – M 4+ & co-doping Calculations have also been performed on Hf 4+ doping, and a range of pairs of co-doped ions. These results will be submitted for publication, possibly in the ‘Lithium Niobate: Properties and Applications’ special journal issue being planned. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 24

25. Some relevant experimental data Studies of M 2+ & M 3+ dopants in LiNbO 3 have included: Mn 2+ - LiNbO 3 : Darwish et al, NIMB, 141, 679-683 (1998)  Supports the idea of Mn 2+ self compensation; does not give dopant concentration. Mg 2+ - LiNbO 3 : González-Martínez et al, Opt. Comm., 282, 1212-1219 (2009)  Dopant concentration 0.0714-0.2422 mol%; suggests that self compensation occurs ‘after a certain dopant concentration level’. Er 3+, Cr 3+ - LiNbO 3 : Dierolf & Sandmann, J. Lum., 125, 67-79 (2007)  Mainly assumes Li site occupancy, but dopant concentration is unclear as several samples have been used. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 25

26. Comparison with recent experimental data Bud Bridges recently published a paper: ‘EXAFS evidence for a primary Zn Li dopant in LiNbO 3 ’ (F Bridges et al, Phys. Rev. B 85 064107 (2012)) This doesn’t find any Zn at the Nb site, but may not be directly comparable with the calculations (concentration effects, stoichiometry of sample?) EXAFS measurements on In have also been performed. International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 26

27. General comments on comparison with experimental data The calculation results reported are at infinite dilution, so no concentration effects are considered. In recent work we are looking at finite dopant concentrations in other materials, and this could be done for dopants in LiNbO 3 (needs persons and €€€). There may be issues with the stoichiometry of the older crystal samples (i.e. are we comparing ‘like with like’?) International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 27

28. Ongoing and future work Results on tetravalent dopants and co-doping is still to be published. Bud Bridges has detailed EXAFS data on Zn & In doped LiNbO 3, which we are hoping to reproduce. We are in discussions with Peter Fielitz and Günter Borchardt about modelling defects using some different reaction schemes (talk at 12:00 tomorrow). International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013 28

29. Thank you! 29International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013

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