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 of

Professor 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)

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*

RE

Max

mol %

MF3

RE

Max

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 canalso be used tocalculate the RHS term(and include allinteractions).

• Experimental data totest these results areneeded!

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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, butshould bring out the fact that you have plentyof ideas and will be able to develop an activeresearch programme which will involve notonly yourself but future graduate students.

• This was very useful to me as I began mycareer, and I have tried to continue to follow itever 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:

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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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1981

1988

1998

1999

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)