Computer modelling of materials: from nuclear fuels to nuclear clocks Rob Jackson 24 November 2010.

Computer modelling of materials: from nuclear fuels to nuclear clocks

Rob Jackson

24 November 2010

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A wide range of materials …

From:

To:

Keele Research Seminar, 24 November 2010

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Plan of talk

• Why do computer modelling of materials?• Types of problem• What techniques do we use?• Examples:

– Nuclear fuels– Optical materials– Geological materials– Materials for nuclear clock development


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Role of Computational Chemistry, and where Materials Modelling ‘sits’

Computational Chemistry

Fundamental calculations to:

Predict parameters often unavailable from experiment.

Elucidate ‘mechanistic’ information.

Materials Modelling can:

• Calculate material structures and properties.

•Help explain/rationalise experimental data.

•Predict material structures and properties.


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Types of problem

• Modelling the structures of nuclear fuels (UO2, PuO2, MOX)

• Modelling optical materials (YLiF4, BaMgF4)– Predicting the location of dopant ions– Calculating and predicting optical transitions

• Modelling geological materials (e.g. zircon, ZrSiO4 and related materials )– USiO4 → PbSiO4

• Nuclear clocks: 229Th doping in LiCaAlF6


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Techniques

• The main technique employed is atomistic modelling.

• The material structure (lattice parameters, ion positions) is provided, and interactions between ions are defined by interionic potentials:– These are simple mathematical functions that represent

the important interactions between atoms:• Van der Waals forces• Electron repulsion

• A well-known example is the Lennard-Jones potential.


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Sir John Lennard-Jones (1894-1954)

• Sir John Lennard-Jones was a mathematical physicist who became the first professor of theoretical chemistry in the UK, in Cambridge, where he worked from 1932-1953.

• He was born John Jones; Lennard was his wife’s surname.

• In 1953 he was appointed 2nd Principal of the University College of North Staffordshire, which later became Keele University.

http://www.quantum-chemistry-history.com/Le-Jo1Ue.htm#continue


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The Lennard-Jones potential

• Lennard-Jones developed his potential in 1931, 22 years before coming to Keele:V = Ar-12 – Cr-6

• The first term represents electron repulsion, and the second van der Waals attraction. A potential is thus defined for the interaction between each pair of atoms. How the parameters are obtained could fill another seminar!


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More on techniques used

• The basis of atomistic simulation is energy minimisation: structures are calculated corresponding to an energy minimum and properties are calculated for that structure.

• We are interested in defects; they destroy the periodicity of the unit cell, and need special treatment, and a method called the Mott-Littleton approximation is used.


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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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Modelling nuclear fuels

• Motivation: understanding the effect of the fission process on the structure and properties of UO2, PuO2 and other actinide oxides.

• This work forms part of a collaboration with AWE, and is the basis of Scott Walker’s PhD project.

• In addition, Gemma Turner (3rd year project student) is modelling MOX (mixed oxide fuel, UO2/PuO2).

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Why Study Uranium Dioxide?

Understanding Corrosion

[1] R. J. Pearce, I. Whittle, D. A. Hilton, The Oxidation of Uranium in Carbon Dioxide and Carbon Monoxide (A Review), J. Nucl. Mater. 33 (1969) 1-16.[2] J. R. Petherbridge, T. B. Scott, J. Glascott, C. Younes, G. C. Allen, I. Findlay, Characterisation of the surface over-layer of welded uranium by FIB, SIMS and

Auger electron spectroscopy, J. Alloys Compd. 476 (1-2) (2009) 543–549.[3] R. M. Harker, The influence of oxide thickness on the early stages of the massive uranium-hydrogen reaction, J. Alloys Compd. 426 (1-2) (2006) 106–117.

[1]

Understanding factors limiting or inducing uranium corrosion is of interest to a variety of industrial activities. [2]

Extreme affinity of pure uranium for oxygen is well documented. At least 16 oxides are known between UO2 and UO3 and are the principal products of uranium metal corrosion.

Once formed as a layer on the surface of metallic uranium, the oxides act as a passive barrier to further corrosion. [2,3]

Thus it is the generally accepted view that the reactivity of uranium towards various gases is primarily affected by the properties of its native oxide layer. For example, in the case of uranium–hydrogen systems, the surface oxide layer prevents rapid concentration of hydrogen at the metal surface and, as a result, provides a limiting influence on the onset of the gas–solid reaction that forms pyrophoric uranium hydride (UH3). [3]


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Simulation of Uranium Dioxide

Simulation of the bulk lattice →

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Experimental Data for Empirical Fitting

S. A. Barrett, A. J. Jacobson, B. C. Tofield, B. E. F. Fender, The Preparation and Structure of Barium Uranium Oxide BaUO3+x, ActaCryst. 38 (Nov) (1982) 2775–2781.

Elastic Constants / GPa

Reference C11 C12 C44

Dolling et al. [1] 401 ± 9 108 ± 20 67 ± 6

Wachtman et al. [2] 396 ± 1.8 121 ± 1.9 64.1 ± 0.17

Fritz [3] 389.3 ± 1.7 118.7 ± 1.7 59.7 ± 0.3

Dielectric Constants / GPa

ReferenceStatic

e0

High Frequency

e∞

Dolling et al. [1] 24 5.3

[1] G. Dolling, R. A. Cowley, A. D. B.Woods, Crystal Dynamics of Uranium Dioxide, Canad. J. Phys. 43 (8) (1965) 1397–1413.

[2] J. B. Wachtman, M. L. Wheat, H. J. Anderson, J. L. Bates, Elastic Constants of Single Crystal UO2 at 25°C, J. Nucl. Mater. 16 (1) (1965) 39–41.[3] I. J. Fritz, Elastic Properties of UO2 at High-Pressure,

J. Appl. Phys. 47 (10) (1976) 4353–4358.


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How good is the fit?

Comparison of Model with Experiment

Parameter Calc. Obs. D% Parameter Calc. Obs. D%

Lattice Constant [Å] 5.4682 5.4682 0.0 C11 [GPa] 391.4 389.3 0.5

U4+ – U4+

Separation [Å] 3.8666 3.8666 0.0 C12 [GPa] 116.7 118.7 -1.7

U4+ – O2-

Separation [Å] 2.3678 2.3678 0.0 C44 [GPa] 58.1 59.7 -2.7

O2- – O2-

Separation [Å] 2.7341 2.7341 0.0 Bulk Modulus [GPa] 208.3 204.0 2.1

Static Dielectric Constant 24.8 24.0 3.3 High Frequency

Dielectric Constant 5.0 5.3 -5.7

See: M S D Read, R A Jackson, Journal of Nuclear Materials, 406 (2010) 293–303


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Some results from UO2 modelling

• Formation energies for defects (vacancies, dopants) in the structure can be obtained.

• Location of dopant ions in the structure, and atoms formed from fission processes (e.g. Xe) can be predicted.

• Surface energies can be calculated and crystal morphology predicted:


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Surface Simulations

Morphology

111111If UO2 crystallites attain thermodynamic equilibrium, the morphology will be dominated by the (111) surfaces, forming an octahedron


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Modelling optical materials

• Motivation: we are interested in helping to develop new materials for optical applications, including solid state lasers and scintillators for detection of ionising radiation.

• Interesting (and useful) optical properties can be added to metal fluorides and metal oxides by doping, usually with lanthanide elements.

• This topic is the theme of Tom Littleford’s PhD project (also funded by AWE).


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Blue John: CaF2 with F-centres• The picture shows a

sample of Blue John, CaF2 coloured by the presence of F-centres (electrons trapped at vacant F- sites in the crystal).

• There is a Blue John mine at Castleton in Derbyshire.


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Amethyst: SiO2 with Fe3+ impurities

• The picture shows a sample of amethyst, which is quartz, SiO2 doped with Fe3+ ions from Fe2O3.

• The value of the quartz is drastically increased by the presence of a relative small number* of Fe3+ ions!

*’As much iron as would fit on the head of a pin can colour one cubic foot of quartz’

http://www.gemstone.org/gem-by-gem/english/amethyst.html


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More on amethyst

• The colour is due to the Fe3+ ions occupying the Si4+ sites, so a charged [FeO4]4- centre results.

• The amount of iron present is very small, about 40 parts per million!

Brazilian amethyst, value $94.50(June 2007)

http://www.mineralminers.com/html/ameminfo.htm#items


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Doping for technological applications

• For most applications, doping with rare earth cations is carried out:

http://perso.univ-rennes1.fr/martinus.werts/lanthanides/ln_descr.html

The rare earth elements are chosen because of their emission wavelengths as dopants (in the m range).


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KYF4

Hexagonal (P31)

a = b = 14.060 Åc = 10.103 Å

KY3F10

Cubic (Fm3m)

a = b = c = 11.543 ÅK2YF5

Orthorhombic (Pna21)

a = 10.791 Åb = 6.607 Åc = 7.263 Å

Host Materials: mixed metal fluorides

Plus K3YF6

Monoclinic (P21/n)

E M Maddock, PhD thesis (2010)

Keele Research Seminar, 24 November 2010 24

Structural modelling studies of KYF materials (E M Maddock, PhD thesis 2010)

• A common set of interatomic potentials was fitted to all 4 materials, giving reasonable agreement with structures to within a few % (better than 1% for KYF4

shown below).

KYF4

Exp (Å) Calc (Å) % Diffa=b 14.060 13.953 -0.76c 10.103 10.185 0.81


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Solution energies for RE doping

• Solution energies give the total energy needed for doping to take place.

• Potentially 2 sites are available, Y and K.• Solution energies were calculated for doping

at the Y3+ site (and the K+ site with various forms of charge compensation).

• As expected the lowest energy site is the Y3+ site (no charge compensation needed).


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Crystal morphology and RE doping

• We are interested in the answers to 2 questions here:

1. What is the crystal morphology of the pure materials and how is it affected by doping?

2. Do the dopants have a tendency to segregate to the crystal surface?

• In both cases there are implications for the use of doped materials in devices.

Keele Research Seminar, 24 November 2010 27

Morphology: Wulff plots

• Wulff plots can be constructed to give morphologies based on surface energies, & also issues like low indices & interplanar spacing.

• An example is shown for KY3F10:

Miller index Esurface/Jm-2

1 -1 1 0.8764

2 0 0 1.9114

2 0 -2 1.1617


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Surface segregation of dopants

• If a material is doped, it is important to know if the dopant ion remains in the bulk or moves to the surface.

• The segregation energy (Eseg) of a dopant is defined as the difference between the energy to substitute it at the surface and in the bulk: Eseg = E (dopant, surface) – E (dopant, bulk)

• A negative value of the segregation energy indicates that there will be a tendency for surface segregation to occur for a particular dopant.


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Segregation energies to dominant surfaces in KY3F10 / eV

dopant 1 -1 1 2 0 0 2 0 -2

La -2.97 -2.11 -2.86

Ce -2.52 -1.58 -2.32

Pr -2.05 -1.75 -1.79

Nd -1.65 -0.98 -1.80

Sm -1.13 -0.60 -0.90

Eu -0.25 0.03 -0.52

Gd - 0.29 0.03

dopant 1 -1 1 2 0 0 2 0 -2

Tb 0.01 0.29 0.11

Dy 0.54 0.89 0.63

Ho 0.73 1.42 1.178

Er 1.05 1.54 1.30

Tm 1.11 1.64 1.35

Yb 1.37 2.01 1.23

Lu 1.80 2.156 1.87


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Modelling optical properties

• As well as understanding what happens to the structure and morphology, we are interested in trying to predict the optical transitions of dopant ions.

• This can be done in 2 ways:– Crystal field calculations– Quantum mechanics (embedded clusters)

• Some results from crystal field calculations will be shown:

Keele Seminar - 13 June 2007 (KPA) 31

Calculation of energy levels for LaF3: Ce3+

Exp. [11] Calculated Term symbol

0 0 151 428 2F5/2 280 567

Exp. [11] Calculated Term

symbol

2160 2212 2240 2555 2F7/2 2635 2891 2845 2973

[11] R A Buchanan, H E Rast, H H Caspers, J. Chem. Phys. 44 4063 (1966)

Poor agreement for low energy transitions

Much better agreement (within10% or better) for higher energytransitions

R A Jackson, M E G Valerio, J B Amaral, M A Couto dos Santos and E M MaddockPhys. Stat. Sol. (c) 4(3) 1185-88 (2007)

Energy levels in cm-1


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Modelling geological materials: Zircon and coffinite

• Zircon readily accommodates U at the Zr site, and the fully substituted compound, USiO4, is the mineral coffinite.

• Starting with zircon and progressively substituting U at the Zr site allows the structure of coffinite to be predicted, and the result can be compared with the experimental structure:

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Coffinite

• The structure is predicted to better than -2%

• Structures for the full range of solid solutions can be calculated.

Predicted coffinite structure

Exp (Å) Calc (Å) %

a=b 6.995 6.874 -1.8

c 6.262 6.371 -1.7

Black, interstitial coffinite cementing a sub-angular quartzose sandstone. Schumacher Coll.(Temple Mountain, San Rafael District (San Rafael Swell), Emery Co., Utah, USA)


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Coffinite and radioactive decay• U decays radioactively,

eventually to Pb.• Due to the long t1/2 of U,

the oldest samples of coffinite found have around 3% Pb.

• The structure of the end member, PbSiO4, can be predicted, as can the full Pb-U solid solution.

PbSiO4

Exp (Å) Calc (Å) %a=b ? 6.489

c ? 6.102

Attempted synthesis of PbSiO4 (Keelite) is in progress!

Older samples of coffinite arebeing searched for.


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Development of nuclear clocks

• 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.

• Nuclear clocks promise up to 6 orders of magnitude improvement in precision over next generation atomic clocks!

• They also have advantages of improved stability over existing atomic clocks.


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Practical considerations

• The 229Th nucleus needs to be embedded in a VUV-transparent crystal for use in devices.

• Metal fluorides, e.g. LiCaAlF6/LiSrAlF6 have been identified as being suitable.

• A modelling study was therefore carried out, to find where the Th ions substitute in the lattice.*

* Details in ‘Computer modelling of thorium doping in LiCaAlF6 and LiSrAlF6: application to the development of solid state optical frequency devices’ by Jackson et al, Journal of Physics: Condensed Matter 21 (2009) 325403


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Results of modelling study and planned experimental study

• The modelling showed that the Th4+ ions preferentially substitute at the Ca2+ site, with charge compensation by F- interstitial ions.

• Crystal growth experiments are in progress, but hindered by the difficulties of growing fluoride systems, plus the cost (and location) of 229Th ($50k/mg!).

• This is a collaboration with UCLA and LANL.

BiIII2ZrIV

2O7

BiIII2TiIV

2O7 BiIII2HfIV

2O7

Pyrochlores and Defect Fluorite Materials (with Richard Darton)

Defect Fluorite

Pyrochlore Pyrochlore


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Bi2Zr2O7 : where modelling can help

• Can Bi2Zr2O7 exist as a pyrochlore phase ?• Can we predict intermediate structures ?

• Can the structure be doped with +2, +3 and +4 cations ?• e.g. SrTiZr2O7

• (Doping will change structure and therefore properties)• e.g. dielectrics, nuclear waste storage materials

• Can we predict new materials ?

BiIII2ZrIV

2O7

BiIII2TiIV

2O7 BiIII2HfIV

2O7


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Plan for pyrochlores project

• Model Bi2Ti2O7 (known structure, but …).• Substitute Zr for Ti and calculate the energy

minimised structure.• Compare with the structure synthesised by

Luke Daniels (predict powder pattern and compare with experimental pattern).

• We can then model intermediate structures and doped materials.


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Summary

• The technique of materials modelling has been introduced and set in the overall context of computational chemistry.

• Some current examples have been considered, both of complete and ongoing projects.

• I have (hopefully) given you an idea of the scope of the technique, and what can be achieved.


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Acknowledgements

Keele University Centre for the Environmental, Physical and Mathematical Sciences (iEPSAM)

Liz Maddock, Tom Littleford, Scott Walker, Michael Montenari, Richard Darton (Keele)

Mark Read, Dave Plant (AWE)Mário Valerio, Jomar Amaral, Marcos Rezende (UFS)

Eric Hudson (UCLA)

Computer modelling of materials: from nuclear fuels to nuclear clocks Rob Jackson 24 November 2010.

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