Atomistic Scale Modelling of Phosphate Mineral Phases for Nuclear Waste Form Development

260 Pages·2012·43.88 MB·English

Atomistic Scale Modelling of Phosphate Mineral
Phases for Nuclear Waste Form Development
Submittedinpartfulfilmentoftherequirementsforthedegreeof
DoctorofPhilosophyinMaterialsScienceandEngineering
ofImperialCollegeLondon
andtheDiplomaofImperialCollegeLondon
by
Eleanor Elizabeth Jay
February 2012
DepartmentofMaterialsScienceandEngineering
ImperialCollegeLondon
Abstract
Phosphate minerals such as β-tricalcium phosphate and fluorapatite are abundant, exhibit a
large chemical variability and samples of both phases are often used for geochronometry; so
their stability over thousands of years is known. This makes them attractive as nuclear waste
formsastheyarestableoverextendedperiodsoftimeandareabletoaccommodatearangeof
wastespecies. Inparticular,duetothedifficultyofincorporatinghalidesinconventionalwaste
forms(inparticularglass),fluorapatitesareconsideredaspotentialhostsforradioactivewaste
streams containing both actinides and halides. β-tricalcium phosphate, a strucutre related to
fluorapatite, is not only used as a precursor for preparing apatites, but could itself be used as
a host for radioactive waste. To better understand the structure and stability of these phases,
atomicscalecomputersimulationhasbeenemployed(bothdynamicandstatic),usingclassical
pairpotentials.
Onesiteintheβ-tricalciumphosphatestructurehaspreviouslybeenassignedahalfoccupancy
from fitting to Rietveld power diffraction experimental data. The half occupancy gives rise to
anorderingeffectwheretheCa2+ ionsarearrangedoverthehalfoccupiedCa(4)sites,inmany
different configurations. A comparison of different cell sizes (and increasing configuration
number)isgivenandreportedintermsoflatticeenergyandstructuralparameters. Thelargest
cell size considered here generates the most stable structures, which have a symmetry group
related to the experimentally derived average primitive unit cell. Simulated X-ray diffraction
patternsindicateadifferenceinspectrafortheselowenergyconfigurations. However,experi-
mentalX-raydiffractionpatternsfailtodifferentiatebetweenlowenergystructures. Theresults
oftheexperimentandsmalldifferenceinlatticeenergyforthemoststablestructures,indicate
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Abstract Abstract
that domains containing different low energy structures are likely to exist. The configurations
describedherearealsodiscussedintermsofstatisticalanalysis.
Substitutionsofarangeofisovalentandtrivalentcationshavebeencarriedout(andcompared)
atCa2+sitesinbothfluorapatiteandβ-tricalciumphosphatestructures. Thedefectandsolution
energieswerecalculatedforbothstructuresandcompared, inordertopredictthepartitioning
across the two phases. For the isovalent defects investigated, the defects segregate to the β-
tricalcium phosphate lattice. The trivalent defects present a different trend such that defects
withasmallerionicradiithanCa2+ haveanenergypreferenceforβ-tricalciumphosphate,but
forthosewithatomicradiiclosertothatofthehostcationthepreferenceforeitherstructureis
indistinguishable. Theramificationsofcationpartitioningarediscussed.
Cation and anion migration in fluorapatite is considered, where the overriding feature of mi-
gration in this structure is that ionic transport (of either cations or anions) occurs preferably
alongthec-axis. Considerationoffluorinetransportyieldsamoresophisticatedmigrationme-
chanism than that reported previously. A “concerted mechanism” for fluorine ion transport in
thelatticeisdiscussedfullyanddescribedusingfluorinedensityplots,overarangeoftempe-
ratures.
Radiation damage effects in these minerals and their ability to recover and resist damage is a
crucialconsiderationwhendesigninganuclearwastehost. ThisthesiscomparestheKinchin-
Pease model of threshold displacement energies to full radiation cascades. Furthermore, the
effect of radiation damage on the lattice is considered by virtue of incident damage, defect
types, phosphate group response and recovery of the lattice. These results indicate that the
fluorapatite lattice is “relatively tolerant” to radiation damage, especially with regard to the
phosphate tetrahedra, but more cascades should be considered to obtain a more statistically
reliableprediction.
Finally,lossofmaterialfromthewasteformismostlikelytooccuratasurfaceandunderstan-
ding the processes by which this occurs is important. Therefore, it is necessary to first model
the surfaces, which involves static simulations of surfaces to predict surface formation ener-
gies. Theseenergiesareusedasthebasisforpredictionsofparticlemorphologyandtheeffect
ofisovalentdefectincorporationnearthesurfaceoffluorapatite.
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Dedication
ThisthesisisdedicatedtoMomsvilleandDadfordshire,thebestparentsagirlcouldeverwish
for. Wordssimplycannotexpressmygratitudetoyouboth.
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Acknowledgements
Iwouldliketothankallmyfriends,familyandeveryoneintheAtomisticSimulationGroupfor
alltheirsupport,coffeeinfusions,kindwordsandchairracesdownthecorridors. InparticularI
wouldliketoexpressmygratitudetoRobinforallhisadvice,supportandfantasticBlackadder
sketchesoverthelasteightyears,thankyou! IamalsoindebtedtoMichaelforhisassistance,
guidanceandproofreadingofthisthesis.
Additionally,IacknowledgeAWEfortheircontinuedfinancialassistanceandinterestingwork
discussions. In particular Brian, Philip and Shirley for providing additional assistance over
the course of this challenging project. Lastly, thanks to Brian-the-Skunk for keeping an ever
watchfuleyeovermydesk.
iv
Thecopyrightofthisthesisrestswiththeauthorandnoquotationsfromitorinformation
derivedfromitmaybepublishedwithoutthepriorwrittenconsentoftheauthor.
(cid:13)c E.E.Jay2012
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Contents
Acronyms xxix
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 RadioactivityandTypesofRadioactiveWaste . . . . . . . . . . . . . . . . . . 5
1.2.1 WasteClassifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 ReactorWastevs. DefenceWastes . . . . . . . . . . . . . . . . . . . . 11
1.3 WasteHostMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1 ImmobilisationofRadioactiveWastesinGlass . . . . . . . . . . . . . 15
1.3.2 EncapsulationofRadioactiveWastesinCement . . . . . . . . . . . . . 16
1.3.3 ImmobilisationofRadioactiveWastesinCrystallineWasteForms . . . 17
1.3.3.1 Synroc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.3.2 Zircon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
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Contents Contents
1.3.4 Pyrochlores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.5 PhosphateCeramics . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4 Fluorapatite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 CrystallographyofFluorapatite . . . . . . . . . . . . . . . . . . . . . 24
1.4.2 CationSubstitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5 β-TricalciumPhosphate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5.1 Crystallographyofβ-TricalciumPhosphate . . . . . . . . . . . . . . . 29
1.5.2 HalfOccupancyofβ-TricalciumPhosphate . . . . . . . . . . . . . . . 33
1.5.3 RelationshipBetweentheβ-TricalciumPhosphateandFluorapatiteStruc-
tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.6 LatticeDefectsandNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.6.1 PointDefects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.6.2 Kro¨ger-VinkNotation . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.6.2.1 SchottkyDefects . . . . . . . . . . . . . . . . . . . . . . . . 36
1.6.2.2 FrenkelDefects . . . . . . . . . . . . . . . . . . . . . . . . 37
1.7 ComputationalModelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.8 ThesisSummaryandStructure . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2 Methodology 41
2.1 IntroductiontoAtomicPhysics . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 ClassicalPotentialSimulations . . . . . . . . . . . . . . . . . . . . . . . . . . 42
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Contents Contents
2.2.1 LongRangeIonicInteractions . . . . . . . . . . . . . . . . . . . . . . 43
2.2.2 ShortRangeIonicInteractions . . . . . . . . . . . . . . . . . . . . . . 45
2.2.3 PotentialDerivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3 Potentialsforβ-TricalciumPhosphateandFluorapatite . . . . . . . . . . . . . 52
2.4 ElectronicPolarisabilty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.5 PartialCharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.6 StaticEnergyMinimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.7 Mott-LittletonMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.8 NudgedElasticBand;TransitionStateSearchMethodology . . . . . . . . . . 60
2.9 MolecularDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.9.1 PotentialsforMolecularDynamics . . . . . . . . . . . . . . . . . . . 67
2.9.1.1 Ziegler,BiersackandLittmark(ZBL)Potentials . . . . . . . 68
2.10 Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.10.1 TypesofSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.10.2 ModellingSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.10.3 CrystalMorphologies . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.10.3.1 ConstructingaWulffDiagram. . . . . . . . . . . . . . . . . 79
3 HalfOccupancyofβ-TricalciumPhosphate 82
3.1 Structureofβ-TricalciumPhosphate . . . . . . . . . . . . . . . . . . . . . . . 82
3.2 β-TricalciumPhosphateCells . . . . . . . . . . . . . . . . . . . . . . . . . . 83
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Contents Contents
3.2.1 (1×1×1)UnitCell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.2.2 (2×1×1)Supercell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.2.3 (3 ×1×1)Supercell . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
h
3.3 AtomicScaleSimulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.1 ConfigurationalAveraging . . . . . . . . . . . . . . . . . . . . . . . . 89
3.4 SimulatedConfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4.1 (1×1×1)UnitCell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4.2 (3 ×1×1)Supercell . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
h
3.5 X-RayDiffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.5.1 SimulatedX-RayDiffraction . . . . . . . . . . . . . . . . . . . . . . . 94
3.5.2 ExperimentalX-RayDiffraction . . . . . . . . . . . . . . . . . . . . . 97
3.6 StatisticalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4 CationSubstitutionandPartitioningofFluorapatiteandβ-TricalciumPhosphate105
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1.1 CationSitesinFluorapatite . . . . . . . . . . . . . . . . . . . . . . . . 106
4.1.1.1 CationSitesinβ-TricalciumPhosphate . . . . . . . . . . . . 108
4.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 DivalentSubstitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.1 DivalentSubstitutionintoβ-TricalciumPhosphate . . . . . . . . . . . 109
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