A review of computer modelling of rare earth doped mixed metal fluoride materials Robert A Jackson Lennard-Jones Laboratories School of Physical and Geographical Sciences Keele University, Keele, Staffordshire ST5 5BG, UK With particular thanks to: Mario Valerio, Jomar Amaral, Marcos Rezende, Marcos Couto dos Santos, Jose de Lima (UFS); Elizabeth Maddock (Keele), David Plant (Keele/AWE)

2 TR2010, Aracaju, Brazil, April 2010 Plan of talk What materials are involved? What is the motivation? Methodologies employed Review of results Future work

3 TR2010, Aracaju, Brazil, 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 TR2010, Aracaju, Brazil, 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’

5 TR2010, Aracaju, Brazil, 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.

6 TR2010, Aracaju, Brazil, April 2010 Methodology Calculations are done 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.

7 TR2010, Aracaju, Brazil, April 2010 Derivation of interatomic potentials For the first stage of the calculation, interatomic potentials are required. These can be fitted empirically, transferred from other systems or calculated directly. Buckingham potentials plus electrostatic terms are normally employed: V(r) = A exp (-r/  ) - Cr -6 + q 1 q 2 /r A,  and C are parameters to be fitted

8 TR2010, Aracaju, Brazil, April 2010 Calculation of defect properties & solution energies Defect properties (incorporation of dopant ions) are modelled using the Mott- Littleton approximation. Here the dopant ion and surrounding ions are modelled explicitly, with more distant ions being treated as a dielectric continuum. The method is well-established for modelling defects in inorganic materials.

9 TR2010, Aracaju, Brazil, April 2010 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 TR2010, Aracaju, Brazil, April 2010 Solution energies Solution energies include all the energy terms involved in the doping process, including lattice energies and charge compensation terms:  e.g. in LiCaAlF 6, for substitution of M 3+ cations at the Al 3+ site, no charge compensation is needed  For substitution at other sites, there are a range of charge compensation schemes:

11 TR2010, Aracaju, Brazil, April 2010 Solution energy expressions M 3+ substitution at the Al 3+ site in LiCaAlF 6 MF 3 + Al Al → M Al + AlF 3  E sol = -E latt (MF 3 ) + E(M Al ) +E latt (AlF 3 ) M 3+ substitution at the Li + site in LiCaAlF 6 with Li + vacancy compensation: MF 3 + 3Li Li → M Li + 2V’ Li + 3LiF  E sol = -E latt (MF 3 ) + E(M Li ) + 2E(V’ Li ) +3E latt (LiF)

12 TR2010, Aracaju, Brazil, April 2010 Typical sequence of a modelling study 1.Derivation of an interatomic potential for each material, 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. *Example: ‘Computer modelling of BaY 2 F 8 : defect structure, rare earth doping and optical behaviour’ by Amaral et al, Applied Physics B 81 (2005)

13 TR2010, Aracaju, Brazil, April 2010 Review of materials Since 1995 (my first visit to Aracaju!), we have studied a range of rare-earth doped fluoride materials, particularly:  BaLiF 3  LiCaAlF 6 /LiSrAlF 6  BaY 2 F 8  ‘KYF’ (KYF 4, K 2 YF 5 and KY 3 F 10 ) And more recently, BaMgF 4 and YLiF 4

14 TR2010, Aracaju, Brazil, 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

15 TR2010, Aracaju, Brazil, 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 b/Åb/Å c/Åc/Å //

16 TR2010, Aracaju, Brazil, 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.

17 TR2010, Aracaju, Brazil, 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  7F D4  7F55D4  7F

18 TR2010, Aracaju, Brazil, April 2010 Summary of case study 1 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.

19 TR2010, Aracaju, Brazil, April 2010 Case study 2: rare earth doped BaLiF 3 * The study looked at the doping of BaLiF 3 with rare earth ions, with a view to identifying the substitution sites and charge compensation mechanisms. It was found that the RE ions divided into 4 groups with slightly differing behaviour. *Based on: ‘Computer modelling of rare-earth dopants in BaLiF 3 ’, by R A Jackson et al, J. Phys.: Condens. Matter 13 (2001) 2147–2154

20 TR2010, Aracaju, Brazil, April 2010 Case study 2 - continued The rare-earth ions can be classified into four groups according to the solution energies: Group I, La–Nd: substitution at the Ba site with Ba vacancy compensation Group II, Sm–Eu: The lowest-energy process is the same as for group I, but the second-lowest-energy process change Group III, Gd–Tb: The lowest-energy process is the same as for group I, but the second-lowest-energy process changes Group IV, Dy–Lu (except Ho): Substitution at the Li site becomes more favourable.

21 TR2010, Aracaju, Brazil, April 2010 Study 2 conclusions The main conclusions were the preferred substitution sites and the relative ease of doping, which was useful for the experimental work at the time.

22 TR2010, Aracaju, Brazil, April 2010 Case study 3: rare earth doped LiCaAlF 6 /LiSrAlF 6 * Both materials are used in optical applications. Considering RE doping, there are 3 cation sites! *Based on: ‘Computer modelling of defect structure and rare earth doping in LiCaAlF 6 and LiSrAlF 6 ’, by J B Amaral, D F Plant et al, J. Phys.: Condens. Matter 15 (2003) 2523–2533

23 TR2010, Aracaju, Brazil, April 2010 J B Amaral, D F Plant, M E G Valerio and R A Jackson, J. Phys.: Condens. Matter, 15 (2003) 2523 Solution energies for 4 rare earth dopants

24 TR2010, Aracaju, Brazil, April 2010 Case study 4: modelling rare earth doping in the KYF family KYF 4, K 2 YF 5 and KY 3 F 10 were considered RE ions substitute preferentially at the Y site in all cases. In KYF 4 a split between Y1 & Y2 sites is observed for some ions. KYF 4 a = b = Å c = Å K+K+ Y 3+ F-F-

RE 3+ KY 3 F 10 K 2 YF 5 KYF 4 (Y1 site)KYF 4 (Y2 site) La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

26 TR2010, Aracaju, Brazil, April 2010 Further work on the KYF materials In addition, surface energies were calculated, making it possible to: 1.Predict morphologies of the doped and undoped materials. 2.Study possible segregation of dopants from the bulk to the surface. This work will be presented at EURODIM2010 in Pécs, Hungary (

27 TR2010, Aracaju, Brazil, April 2010 Extra (non RE) case study: Th in LiCaAlF 6 /LiSrAlF 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!

28 TR2010, Aracaju, Brazil, April 2010 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)

29 TR2010, Aracaju, Brazil, 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

30 TR2010, Aracaju, Brazil, 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

31 TR2010, Aracaju, Brazil, April 2010 Future work: 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 concentration dependent solution energies up to a limit. These should overcome one problem with predictions based on solution energies, which are currently limited to isolated defects.

32 TR2010, Aracaju, Brazil, April 2010 Concentration dependent solution energies 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 + ( x) 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 )

33 TR2010, Aracaju, Brazil, April 2010 Acknowledgements Keele University Centre for the Environmental, Physical and Mathematical Sciences