Using computer modelling to help design materials for optical applications Robert A Jackson Chemical & Forensic Sciences School of Physical & Geographical Sciences Keele

Emerging Analytical Professionals Conference, 8-10 May Plan for talk 1.A (short) introduction to materials modelling 2.Optical materials and their applications 3.How computer modelling is applied to optical materials 4.Two recent applications 5.Conclusions and ongoing work See

Examples of materials of interest Emerging Analytical Professionals Conference, 8-10 May UO 2 – nuclear fuel LiNbO 3 – many optical applications YAG– example of laser material

Computational Chemistry and Materials Modelling Computational Chemistry Calculate material structures and properties. Help explain and rationalise experimental data. Predict material structures and properties. 4 Emerging Analytical Professionals Conference, 8-10 May 2015

Introduction to materials modelling The modelling being described here is at the atomic level (quantum mechanics is not involved). – Materials are described in terms of the positions (coordinates) of their atoms, and the forces acting between them. – Interatomic forces are described using interatomic potentials. Emerging Analytical Professionals Conference, 8-10 May

Generating a starting model The fundamental principle of atomistic simulation is to describe the forces acting between the ions and to minimise this energy through shifting atomic coordinates. 1)Input the unit cell information: unit cell size, atomic coordinates, space group. 2)Place charges on the ions and define interatomic potentials acting between them. 3)Interatomic potentials typically represent electron repulsion/van der Waals attraction. Emerging Analytical Professionals Conference, 8-10 May

Energy minimisation Given the unit cell of the structure, we can generate the crystal structure using space group symmetry. – We can then calculate the lattice energy by summing the interatomic interactions. The structure is then adjusted systematically to get the lowest possible energy (structure prediction). – Lattice properties like dielectric constants can be calculated. – The method can be adapted for defects and dopants in the crystal. Emerging Analytical Professionals Conference, 8-10 May

8 Model the LiNbO 3 structure using energy minimisation. Calculate the energy involved in co-doping the crystal with pairs of ions (e.g. Fe 3+, Cu + ) at different sites, so the optimum sites can be determined. The resulting information is useful for designing new doped forms of LiNbO 3 for specific applications. Example of materials modelling:

Optical materials Materials that have interesting/useful properties in the solid state: Emerging Analytical Professionals Conference, 8-10 May e.g. YLF (Yttrium Lithium Fluoride, YLiF 4 ), which behaves as a solid state laser when doped with rare earth ions, e.g. Nd 3+ ( at %)

YLF in more detail The rare earth ions (e.g. Nd 3+ ) substitute at the Y sites, so there is no need for charge compensation. For Nd-YLF, laser frequency is 1047 or 1053 nm depending on crystal morphology. Emerging Analytical Professionals Conference, 8-10 May Figure taken from T E Littleford, PhD thesis (Keele University, 2014)

What information can computer modelling provide? If optical properties depend on dopants, where do they substitute in the lattice? – Not always obvious, e.g. M 3+ ions in LiCaAlF 6, where there are 3 different cation sites. How is the crystal morphology (shape) changed? – Important if the crystals are used in devices. Can optical properties (e.g. transitions) be predicted? Emerging Analytical Professionals Conference, 8-10 May

Example of an application BaY 2 F 8 can be used as a scintillator for detecting radiation when doped with rare earth ions, specifically Nd and Tb. In the diagram, the Ba 2+ ions are green, and the Y 3+ ions are orange. Emerging Analytical Professionals Conference, 8-10 May

Emerging Analytical Professionals Conference, 8-10 May

Details of the paper Experimental: samples were grown & characterised using XRD, photoluminescence (PL) and radioluminescence (RL). – PL measurements allowed identification of the main optical active transitions of the RE dopant. – RL measurements proved that the material is a promising material for scintillation detectors. Modelling: confirmed the dopants substitute at the Y 3+ site, and identified the optical transitions observed. Emerging Analytical Professionals Conference, 8-10 May

Emerging Analytical Professionals Conference, 8-10 May 2015 Crystal field calculation of the optical transitions 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. 15

16 Emerging Analytical Professionals Conference, 8-10 May 2015 How good is the method? In the 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

Conclusions on this work Computer modelling, used in conjunction with experimental methods, can help characterise optical materials and suggest ones. – e.g. by calculating transitions with different dopants before the sample preparation is carried out. Crystal field calculations are still ‘classical’, and ultimately we would like to use quantum methods. But usable software is still not available. Emerging Analytical Professionals Conference, 8-10 May

How is the shape of crystals affected by doping? YLF (YLiF 4 ) has already been considered, and it was mentioned that laser frequency depends on crystal morphology. We have used modelling to predict changes in the morphology when YLF crystals are doped. – This can be done by calculating surface energies, and predicting morphology from the most stable surfaces. Emerging Analytical Professionals Conference, 8-10 May

YLF Morphology Emerging Analytical Professionals Conference, 8-10 May 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), (2013)

YLF morphology as affected by Ce dopants Emerging Analytical Professionals Conference, 8-10 May Ce-YLF Surface energy approach 021 face appears, 111 disappears

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. Emerging Analytical Professionals Conference, 8-10 May

Conclusions on morphology study Changes in morphology can be predicted, and comparison with experimental results made where these are available. The next step is to look at how the optical behaviour of the dopant ions depend on location in the bulk or surface of the crystal. – This might explain dependence of laser frequency on morphology. Emerging Analytical Professionals Conference, 8-10 May

Conclusions I have shown how computer modelling can be used to: – (i) interpret optical behaviour of materials, and potentially help to design new ones. – (ii) predict the effect on crystal morphology of dopants, with a view to extending this to looking at the effect on optical behaviour as well. Emerging Analytical Professionals Conference, 8-10 May

Acknowledgements 24 Emerging Analytical Professionals Conference, 8-10 May 2015 Tom Littleford (PhD, Keele, 2014) Mark Read (AWE, then Birmingham) Mário Valerio, Jomar Amaral (UFS, Brazil)