Modelling the concentration dependence of doping in

optical materials

Robert A JacksonSchool of Physical and Geographical

Sciences, Keele University, Keele, Staffs ST5 5BG, UK

Mário E G ValerioDepartment of Physics, Federal University of

Sergipe, 49.100-000 São Cristóvão, Brazil

Contributed to the session in honour ofProfessor Patrick Jacobs

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Plan for talk

1. Introduction

2. Previous work – setting the scene

3. Methodology and results 1. Rare earth ions in YLiF4

2. Thorium in LiCaAlF6, CaF2

4. Future work

5. Patrick’s influence: research & conferences

6. General acknowledgements

Introduction

• Motivation – for optical materials, dopants are responsible for most of their important properties.

• We can predict where they substitute in the lattice, and what form of charge compensation will be preferred.

• We can predict morphologies for the perfect and doped materials.

• A range of materials have been modelled in this way, including BaMgF4 and YLiF4.

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From EURODIM 2010 proceedings

YLF Morphology

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T E Littleford, R A Jackson, M S D Read: ‘An atomistic simulation study of the effects of dopants on the morphology of YLiF4’, Phys. Stat. Sol. C 10 (2), 156-159 (2013) (ICDIM 2012 paper)

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YLF morphology as affected by Ce dopants

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Ce-YLF

Surface energy approach

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.

Predicting maximum dopant concentration – (i)

• As well as knowing where and how the dopants are incorporated, how many are involved?– Consider doping YLiF4 (YLF) with M3+ dopants:

(1-x) YF3 + x MF3 + LiF → Y1-xMxLiF4

– The procedure is to calculate the energy of this reaction (Esol) as a function of the dopant concentration x:

Esol = E (Y1-xMxLiF4) - [(1-x) Elatt(YF3) + x Elatt(MF3) + Elatt(LiF)]

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Predicting maximum dopant concentration – (ii)

• Calculating the first term (in red) has involved much thought!– The term is calculated using this expression:

ED(x) = x EDML + Ep(1)

– This splits the energy into defective and perfect terms (& assumes they don’t interact).

– The final expression is then:

Esol = E (x EDML + Elatt(YLiF4)) - [(1-x) Elatt(YF3) + x Elatt(MF3) +

Elatt(LiF)]

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Results for M3+ dopants in YLF*

REMax

mol % MF3

REMax

mol % MF3

La 0.69 Tb 1.41

Ce 0.76 Dy 1.28

Pr 0.85 Ho 1.40

Nd 0.93 Er 1.52

Sm 1.23 Tm 1.33

Eu 1.15 Yb 1.51

Gd 1.22 Lu 1.49

• Supercell methods can also be used to calculate the RHS term (and include all interactions).

• Experimental data to test these results are needed!

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* T E Littleford, PhD thesis 2014

The nuclear clocks story

• 229Th 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.

• These promise up to 6 orders of magnitude improvement in precision over next generation atomic clocks, as well as enhanced stability.

• Eric Hudson’s plenary lecture at EURODIM 2010 introduced the general field.

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Previous work

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Two previous papers (below, PDFs available) have modelled Th4+ in these materials, and established the energetically favoured dopant sites and charge compensation mechanism (Ca2+ site with 2 F- interstitials).

Th4+ has to be doped into a suitable crystal; CaF2 and LiCaAlF6/LiSrAlF6 are being investigated.

Solution schemes for Th4+ incorporation

• LiCaAlF6

x ThF4 + (1-x) CaF2 + LiF + AlF3 LiThxCa1-xAlF6+2x

• CaF2

x ThF4 + (1-x) CaF2 Ca1-xThxF2+2x

(Assuming Th4+ substitutes at the Ca2+ site with compensation by 2 F- interstitials)

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How much Th4+ can be doped into these materials?

• Applying the method to LiCaAlF6 and CaF2 gives interesting contrasting results.

• For LiCaAlF6 we calculate a maximum Th4+ concentration of ~ 5 mol %. Experimental values are eagerly anticipated!

• For CaF2, we observe a linear relationship between solution energy and Th4+ concentration. Recent experimental concentrations are between 0.4-0.7 mol%, corresponding to solution energies in the range 2.3 – 3.5 eV.

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Conclusions & Future Work

• The method we have developed gives results that agree with existing experimental data, but more is needed to test it and develop it further.

• We would welcome collaboration with groups who have data on doping particular materials.

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A tribute to Patrick

• I have much to be grateful to Patrick for. Early in my career he gave me this advice:

• (Your research plan) must be realistic, but should bring out the fact that you have plenty of ideas and will be able to develop an active research programme which will involve not only yourself but future graduate students.

• This was very useful to me as I began my career, and I have tried to continue to follow it ever since.

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Early research influence: Keele, August 1986

• In 1986 the development of photographic film was still a topic of commercial importance, and Patrick, Sean Corish, along with Roger Baetzold and Yen Tan from Kodak, visited Keele to try to improve the existing potentials for the silver halides.

• My small part in this story was showing Patrick how to use CASCADE (based on HADES, and which preceded GULP).

• This visit ultimately led to the following paper:EURODIM2014: 14-18 July 2014

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Three body interactions in silver halides

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Meetings in Oxford and London, Ontario

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‘Retirement’ meeting (London, Ontario, September 1989

ICDIM 1992 (Nordkirchen)

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EURODIM 1998 (Keele)(The last EURODIM/ICDIM

conference attended by Patrick)

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Some more photos …

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19811988

19981999

Final conclusions

• Patrick’s influence on the EURODIM-ICDIM series of conferences has been considerable.

• More generally, his influence on the field of solid state chemistry was significant and wide ranging, as is shown by the diversity of topics presented in this session.

• He was always generous in his encouragement and enthusiasm, which is much appreciated by those who knew him.

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Acknowledgements

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Tom Littleford (Keele, UK)Jomar Amaral (UFS, Brazil)

Thorsten Schumm (TU-Wien, Austria)Eric Hudson (UCLA, USA)