1. Computer modelling of defects and dopants in LiNbO 3, with a look ahead to LiTaO 3, and Li(Nb, Ta)O 3 solid solutions 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 @robajackson http://www.slideshare.net/robajackson

2. Acknowledgements Mário Valerio, Romel Araujo (Aracaju, Brazil) László Kovács, Krisztián Lengyel (Budapest, Hungary) Bud Bridges (Santa Cruz, USA) Günter Borchardt, Peter Fielitz (Clausthal, Germany) Günter Borchardt, Holger Fritze, Klaus Dieter Becker … for the invitation! 2 Clausthal Seminar: 3 June 2015

3. Relevant publications [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) [4] R M Araujo, M E G Valerio, R A Jackson ‘Computer simulation of metal co-doping in lithium niobate’ Proc. R. Soc. A 470, 20140406 (2014) [5] R M Araujo, M E G Valerio, R A Jackson ‘Computer modelling of hafnium doping in lithium niobate’ (http://arxiv.org/abs/1505.01661) 3 Clausthal Seminar: 3 June 2015

4. Plan of talk Summary of our previous work on LiNbO 3 – Background – Structural agreement – Intrinsic defects – Dopants Modelling LiTaO 3 – Potential and structural agreement – Li(Nb, Ta)O 3 solid solutions 4 Clausthal Seminar: 3 June 2015

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 Clausthal Seminar: 3 June 2015

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 Clausthal Seminar: 3 June 2015

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 Clausthal Seminar: 3 June 2015

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 Clausthal Seminar: 3 June 2015

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. Clausthal Seminar: 3 June 2015 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 Clausthal Seminar: 3 June 2015

12. Formation energies for basic defects (in stoichiometric LiNbO 3 ) Clausthal Seminar: 3 June 201512 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) Clausthal Seminar: 3 June 201513 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 observed 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. Clausthal Seminar: 3 June 2015 14

15. Clausthal Seminar: 3 June 2015 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. Clausthal Seminar: 3 June 2015 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. Clausthal Seminar: 3 June 2015 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. Clausthal Seminar: 3 June 2015 18 Divalent and trivalent dopants The incorporation of a range of dopant ions in LiNbO 3 was modelled. Divalent, trivalent and tetravalent 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. References [4] and [5] consider co-doping and Hf doping respectively. [2] Journal of Physics: Condensed Matter, 19, 046211 (2007) [3] Journal of Physics: Condensed Matter, 20, 035201 (2008) [4] Proc. R. Soc. A 470, 20140406 (2014) [5] http://arxiv.org/abs/1505.01661 Clausthal Seminar: 3 June 2015 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: Clausthal Seminar: 3 June 2015 20

21. Solution energies Assuming M 2+ substitution at the Li + site, a possible scheme could be ( using Kröger-Vink notation ): 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. Clausthal Seminar: 3 June 2015 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. Clausthal Seminar: 3 June 2015 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. Clausthal Seminar: 3 June 2015 23

24. 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. Clausthal Seminar: 3 June 2015 24

25. ‘EXAFS evidence for a primary Zn Li dopant in LiNbO 3 ’ (F Bridges et al, Phys. Rev. B 85 064107 (2012)) Doesn’t find Zn at the Nb site, but may not be directly comparable with the calculations (concentration effects, stoichiometry of sample?) – Measurements on a ‘stoichiometric’ sample give same result. – EXAFS measurements on In have also been performed, and preliminary results suggest In Li dopants. Clausthal Seminar: 3 June 2015 25

26. General comments on comparison with experimental data The calculation results reported are at infinite dilution, so no concentration effects are considered. – Now 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’?) – But recently EXAFS was done on a stoichiometric sample and we are comparing results. Clausthal Seminar: 3 June 2015 26

27. Hf 4+ doping The lowest energy scheme again involves self- compensation: 4HfO 2 + Li Li + 3Nb Nb → Hf Li  + 3Hf Nb ’ + ½ Li 2 O + 3/2 Nb 2 O 5 These results are supported by experimental studies: Marques J G, Kling A, de Jesus C M, Soares J C, da Silva M F, Dieguez E and Agulló-Lopez F 1998 Nuclear Instruments and Methods in Physics Research B 141 326-331 Li S, Liu S, Kong Y, Deng D, Gao G, Li Y, Gao H, Zhang L, Hang Z, Chen S and Xu J 2006 J. Phys.: Condens. Matter 18 3527–3534 Clausthal Seminar: 3 June 2015 27

28. Co-doping by transition metal ions TM co-doped LiNbO 3 finds applications in holographic recording devices. We have modelled co-doping by Fe 3+ Cu +, Ce 3+ Cu +, Ce 4+ Mn 2+, Rh 3+ Fe 3+ and Ru 4+ Fe 3+. In most cases the solution energy is reduced compared to doping with single ions. – Has implications for device development. Clausthal Seminar: 3 June 2015 28

29. Modelling LiTaO 3 : obtaining an (initial) Ta-O potential Structure from: Abrahams & Bernstein, J. Phys. Chem. Sol. 28 (1967) 1685-1692 Structure after refitting of Ta-O potential. Based on Ta-O potential from KTaO 3 paper (Exner) Phys. Rev. B 52(6) (1995) 3930-3940 Exp.Calc.% a=b5.154285.180920.52 c13.783513.78520.01 =β=β90  0  120  0 Clausthal Seminar: 3 June 201529

30. Modelling Li(Nb, Ta)O 3 solid solutions Two approaches: – Mean field calculation: take LiNbO 3 and treat the Nb site as an averaged (Nb, Ta) site. With good potentials, can predict structure-composition relationship. – Supercell calculation: model a supercell of LiNbO 3 with Ta substituted for the Nb as required. Takes more time, but gives more detailed results. Clausthal Seminar: 3 June 2015 30

31. Photos from my last visit to Clausthal (August 2001) Clausthal Seminar: 3 June 201531

32. Thank you! 32Clausthal Seminar: 3 June 2015