Computer modelling of the concentration dependence of doping

in solid state ionic materials

Robert A JacksonSchool of Physical and Geographical Sciences, Keele

University, Keele, Staffs ST5 5BG, UK

Marcos V dos S Rezende, Mário E G ValerioDepartment of Physics, Federal University of Sergipe,

49.100-000 São Cristovão, Brazil

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Plan for talk

1. Acknowledgements

2. Introduction: relevance of previous work

3. Motivation for developing a new approach

4. The method described

5. Latest results and their implications

6. Discussion and conclusions

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Acknowledgements

Thanks to the organisers of SSI-18 for the invitation to take part in the workshop!

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Relevance of recent research

• My recent research has concentrated on studying doping of oxides and fluorides for optical applications.

• However, the same approach is equally applicable, for example, to doping in solid state ionic materials for fuel cell or battery applications.– e.g. Doping ZrO2 with CaO or Y2O3

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Limitations of previous approach – (i)

• Take the material LiCaAlF6 as an example.

• This is a laser host material, and laser properties are obtained by doping with trivalent rare earth ions, e.g. Nd3+.

• Where does the Nd3+ ion substitute, and if charge compensation is needed, what form does it take?

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Limitations of previous approach – (ii)

• Calculations (described later) show that the ion substitutes at the Ca2+ site with charge compensation by creation of Li+ vacancies, which is useful information for the crystal growers, but ...

• ... it assumes doping of a single ion in an otherwise perfect lattice, which is not realistic!

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Motivation for developing a new approach

• We would like to be able to understand how the doping process depends on the concentration of dopants.

• This will also enable solubility limits for dopants to be predicted.

• This is far more useful information to help in developing new materials for specific applications.

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Background to the method(i)

• Materials are modelled using interionic potentials.

• Potentials used are typically of the Buckingham form, parameterised empirically:

V(r) =q1q2/r + A exp (‐r/) – Cr‐6

• Structures and properties are calculated by lattice energy minimisation.

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Background to the method(ii)

• The Mott-Littleton approximation is used to model defects, assuming a 2-region strategy, with the region surrounding the defect being modelled explicitly.

• This enables the energies of formation of defects (vacancies, interstitials, substitutions) to be calculated.

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Mott-Littleton approximation

Region IIons are strongly perturbed by the defect and are relaxed explicitly with respect to their Cartesian coordinates.

Region IIIons are weakly perturbed and therefore their displacements, with the associated energy of relaxation, can be approximated.

Region IIa

Defect

Region I

© Mark Read (AWE)

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Solution energies for single ion doping – (i)

• In order to calculate the energy involved in doping a single ion into a lattice, the solution energy (Esol) is calculated.

• It includes all terms involved doping.– For M3+ substitution in LiCAF:

MF3 + CaCa→M•Ca + V′Li + LiF + CaF2

• Esol is the energy of this reaction

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Solution energies for single ion doping – (ii)

• This solution energy can be used to

1. Predict dopant location

2. Predict the lowest energy form of charge compensation, if needed.

• It has been used widely in our papers on doped mixed metal fluorides and oxides.

• But it doesn’t include effect of finite defect concentration!

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New method – application to M3+ doped BaAl2O4

• To explain the new method, we move from fluorides to oxides, and consider the formation of M3+ doped BaAl2O4, which has applications as a phosphor material.

• Some of its applications will be shown on the next slide:

14

BaAl2O4 when doped with rare earth ions shows long lasting phosphorescence:

BaAl2O4:Ce3+,

BaAl2O4:Ce3+,Dy3+,

BaAl2O4:Eu2+,Nd3+,

BaAl2O4:Eu2+,Dy3+.

BaAl2O4:Eu2+,

BaAl2O4:Tb3+,

BaAl2O4:Tm3+,

BaAl2O4:Mn2+,Ce3+.

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Basis of the new method

• Mimicking the crystal growth process, and assuming that the M3+ ion dopes at an Al3+ site*:0.5x M2O3 + BaO + (1-0.5x) Al2O3 BaAl2-xMxO4

• The procedure is now to calculate the solution energy as the energy of this reaction, which will now depend on x.– *It is repeated for different solution schemes

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Concentration dependent solution energies

• The energy of the reaction is:

Esol = E [BaAl2-xMxO4] - [0.5x Elatt (M2O3)

+ Elatt (BaO) + (1-0.5x) Elatt (Al2O3)]

• Where

E [BaAl2-xMxO4] = (1-0.5x) Elatt (BaAl2O4)

+ x E (MAl)• Where the perfect and defective terms have been

separated.

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Some results!

• We can calculate solution energies for M3+ ions in BaAl2O4 as a function of x:– Energies in eV, T = 293 K

1% M2O3 2% M2O3 3% M2O3

Max. x M2O3

Ce -0.8466 1.0969 3.0404 1.4356

Pr -0.8426 1.1048 3.0522 1.4327

Nd -0.8416 1.1068 3.0552 1.4319

Sm -0.8394 1.1112 3.0618 1.4303

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Interpretation of results

• Negative solution energies imply solution of the dopant in the crystal structure.

• The procedure is to increase the concentration, x, until the solution energy is zero, and this represents the solution limit.

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Graphical summary

0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02-0.86

-0.85

-0.84

-0.83

-0.82

-0.81

-0.80

Solu

tion e

nerg

y(e

V)

Ionic radii- 6 fold coordination

MAl

2M.Ba

-V,,

Ba

M.Ba

-Ba,

Al

2M.Ba

-O,,

i

3M.Ba

-V,,,

Al

CePrNd

SmEuGd

Ho TbDyYb ErTmLu

293K

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General discussion

• The method described can be applied to any combination of host lattice and dopant.

• Solution energies can be calculated as a function of concentration, and solubility limits for dopant ions obtained.

See Rezende et al, J. Sol. State Chem. (2011) http://dx.doi.org/10.1016/j.jssc.2011.05.053 Also, a proceedings paper will be submitted.

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Conclusions

• The method presented should be useful in any application where doping is used to create or enhance a particular material property.

• Applications given have been to optical materials but it is not limited to these.

• And finally, looking back, now for something completely different!

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NATO SUMMER SCHOOL, CALABRIA 1985

?

?

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Professor Alan Chadwick: a special mention