My talk given at the EURODIM 2014 conference at the University of Kent, July 2014, including a tribute to Professor Patrick Jacobs.

1. Modelling the concentration
dependence of doping in optical
materials
Contributed to the session in honour of
Professor Patrick Jacobs
Robert A Jackson
School of Physical and Geographical
Sciences, Keele University, Keele, Staffs
ST5 5BG, UK
Mário E G Valerio
Department of Physics, Federal University of
Sergipe, 49.100-000 São Cristóvão, Brazil

2. EURODIM2014: 14-18 July 2014
Canterbury, UK
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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

3. 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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4. EURODIM2014: 14-18 July 2014
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From EURODIM 2010 proceedings

5. 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)

6. YLF morphology as affected
by Ce dopants
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Ce-YLF
Surface energy approach

7. 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.

8. 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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9. Predicting maximum
dopant concentration – (ii)
• Calculating the first term (in red) has involved
much thought!
– The term is calculated using this expression:
ML + Ep(1)
ED(x) = x ED
– This splits the energy into defective and perfect terms
(& assumes they don’t interact).
– The final expression is then:
ML + Elatt(YLiF4)) - [(1-x) Elatt(YF3) + x Elatt(MF3)
Esol = E (x ED
+ Elatt(LiF)]
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10. 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 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

11. 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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12. Previous work
Th4+ has to be doped into a suitable crystal; CaF2 and LiCaAlF6/LiSrAlF6 are being
investigated.
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).
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13. 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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14. 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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15. 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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16. 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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17. 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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18. Three body interactions in
silver halides
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19. Meetings in Oxford and
London, Ontario
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‘Retirement’ meeting
(London, Ontario, September 1989

20. ICDIM 1992 (Nordkirchen)
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21. EURODIM 1998 (Keele)
(The last EURODIM/ICDIM
conference attended by Patrick)
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22. Some more photos …
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1981
1988 
1998
1999 

23. 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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24. Acknowledgements
Tom Littleford (Keele, UK)
Jomar Amaral (UFS, Brazil)
Thorsten Schumm (TU-Wien, Austria)
Eric Hudson (UCLA, USA)
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