AWE Presentation: 29 April 2013
R A Jackson
School of Physical & Geographical Sciences
Keele University
r.a.jackson@keele.ac.uk
http://www.keele.ac.uk/chemistry/staff/rjackson/
Plan of presentation
• Tom Littleford’s
highlights:
project:
summary
and
– Materials studied
– Methodology
– Results
• Publications and conference presentations
from both projects.
Computer modelling of optical materials
for laser applications: rare earth doping
in YLiF4 and BaMgF4
• The project was concerned with the
development of new materials for optical
applications (e.g. solid state lasers).
• Two mixed metal fluorides were modelled,
both of which have potential optical
applications when doped with rare earth ions.
Research aims
• To determine the optimum location of rare
earth dopants in these materials by modelling
the energetics of the solution process.
• To calculate the morphology of the undoped
materials and to see how this is affected by
the presence of dopants.
More about the materials
The materials used need to be transparent in the laser
range and to easily accept optical doping cations.
YLiF4 (YLF)
BaMgF4 (BMF)
Summary of computational methods used - 1
• Interactions between ions are described by
potentials, empirically fitted to structures and
properties, giving the following expression for
the lattice energy:
• The potential parameters A,  and C are
specified for each interaction.
Summary of computational methods used - 2
• Structures and properties are determined by
energy minimisation:
– Predict the structure corresponding to an energy
minimum.
– Calculate lattice properties (elastic constants,
dielectric constants, phonon frequencies etc.) at
this structure.
• Reproduction of experimental values gives
confidence in further use of the potential.
Summary of computational methods used - 3
• Defects in materials are modelled by the
Mott-Littleton approximation, which places
the defect at the centre of a region of the
lattice where interactions are considered
explicitly, surrounded by regions where
approximations are applied.
• Details of the method are on the next slide:
Lattice defects: Mott-Littleton approximation*
The Mott-Littleton approximation is a two
region approach:
Region I
Ions are strongly perturbed by the defect and
are relaxed explicitly. This region typically
contains ions ~600 ions.
Region IIa
Ions are weakly perturbed and therefore
relaxation energy is approximated. This region
typically contains ~1300 ions.
* N F Mott, M J Littleton:
Trans. Faraday Soc. , 1938, 4, 485
Substitution and solution energies
• Substitution energies are the energies
involved in substituting an ion into the
material, but they do not take into account all
the energetic terms involved in the solution
process.
• Solution energies include all these terms, so
they can be used to determine where the ion
will substitute, and what form of charge
compensation will occur (if it is needed).
Summary of computational methods used - 4
• Surfaces are of interest in this project because
if surface energies can be calculated,
morphologies can be predicted.
• For device construction, morphology is
important:
– If a material is doped with a particular ion, does
this result in a change in its morphology?
• Details of the method are on the next slide:
Surface Simulation
The method uses the same interatomic
potentials as before but we create a surface
region and an bulk region.
Block I
Region I
Ions in region I are allowed to fully relax after
the cutting.
Unit Cell
Block I
Ions in region II are fixed at their equilibrium
bulk coordinates.
Region II
Surface
Block II
Region I
Cuts are performed for all low Miller Indices.
The energy of the stable surfaces are then
calculated.
Regions I and II are shown on the next slide.
Block II
Region II
Region I and II in surface simulations
Prediction of morphology from surface energies
The procedure is to calculate all low
index surface energies.
Low surface energy 
stable surface 
surface appears in morphology
The method then allows the affect of
dopants on morphology to be predicted,
since their presence will affect surface
energies.
Diagram is based on a Wulff
construction, which relates morphology
to surface energy.
Results highlights: bulk properties*
• The structures and properties of the ‘perfect’
materials have been modelled successfully.
• For YLiF4, rare earth (lanthanide) dopants
substitute preferentially at the Y3+ site as
expected.
• For BaMgF4, charge compensation is needed (3+
ions at 2+ sites), and there are a variety of
possibilities involving either Ba or Mg vacancies.
* R A Jackson, T E Littleford, G E Newby, D F Plant, ‘Computer modelling of rare
earth doping in BMF & YLF’, IOP Conf. Series: Mat. Sci. & Eng. 15 012048 (2010)
YLF: perfect and defective morphology
calculations*
For YLF, the morphology has been calculated for the perfect crystal and in the
presence of La3+ doping. The main difference is the replacement of the (111)
surface by the (110) surface.
* 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)
BMF perfect morphology calculations*
• Defect
morphology
calculations on BMF are
still in progress, but the
perfect morphology is
given.
Key: front face (001), top face (010),
upper side face (110)
* T E Littleford, R A Jackson, M S D Read, ‘Modelling rare-earth doped BaMgF4:
a potential laser material’, Phys. Stat. Sol. C 10 (2) 153-155 (2013)
Summary
• Rare-earth doping in YLF and BMF has been
modelled:
– Location of dopants (and charge compensation
schemes) has been established
– Perfect lattice morphologies have been calculated
– Dopant morphologies have been obtained for YLF and
are being obtained for BMF
• Future work includes use of ab initio methods to
calculate optical transition energies – software
dependent!
• AWE funding is gratefully acknowledged.
Publications from the projects
R A Jackson, T E Littleford, G E Newby, D F Plant, ‘Computer modelling of rare
earth doping in BMF and YLF’, IOP Conf. Series: Materials Science and
Engineering 15 012048 (2010)
T E Littleford, R A Jackson, M S D Read, ‘An atomistic surface simulation study
predicting morphologies and segregation in yttrium lithium fluoride’, Surface
Science 606 1550–1555 (2012)
T E Littleford, R A Jackson, M S D Read, ‘Modelling rare-earth doped BaMgF4:
a potential laser material’, Phys. Stat. Sol. C 10 (2) 153-155 (2013)
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) 156159 (2013)
S R Walker, R A Jackson, M S D Read, ‘Atomistic modelling of actinide oxides
for nuclear fuel applications’, Phys. Stat. Sol. C 10 (2) 197-201 (2013)
Major conference presentations
• Tom Littleford
EURODIM2010, Pécs, Hungary, July 2010
ICDIM2012, Santa Fe, USA, June 2012
• Scott Walker
MMSNF, Aix en Provence, France, Sept 2011
ICDIM2012, Santa Fe, USA, June 2012
(Plus RSC Solid State Group meetings)