Development of an ENDF Thermal Library for SiO2 and Testing of ...

Thermal Neutron Scatteringand Energy TransferThe de Broglie wavelength (λ = h / p) of thermal neutrons (< ~ 1 eV) ison the order of the interatomic distances in crystalline solids.The energy of thermal neutrons is of the same order as the vibrationalexcitation modes (e.g., phonons) available in condensed matter.σ TOTAL =σ INEL + σ EL + σ ABS4Thermal Neutron Scattering

Total Cross Section (barns)Modifying the Free-AtomCross Section for SiO 21000.0Free Gas Library (300 K)Thermal Library (300 K)K03ats)arn(bnctioSesrolCtaTo100.010.01.01.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07Energy (eV)6

Calculating the InelasticScattering Cross SectionDouble-differential cross section can be written in terms of nuclearcross sections and a scattering law:Simplified NJOY form with S d (Q,ω) = 0:All that is required tosolve for σ inel is ρ(β)7

Calculating the ElasticScattering Cross SectionAll that is required tosolve for σ el is ρ(β)and f i8

Structure of α-Quartz and β-QuartzSilicons (yellow), Oxygens (red)11

Relative Density of States (1/eV)Relative Density of States (1/eV)Density of States3530252015Alpha PhaseBeta PhaseNatural Si in SiO 210500.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16Energy (eV)3530Alpha Phase252015105Beta PhaseO-16 in SiO 200.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16Energy (eV)12

VASP(DFT)PHONON(lattice dynamics)Hellmann-FeynmanForcesr(b) (DOS)LEAPR(NJOY)ACER (NJOY)(MCNP libraries)S ( ,b )Eel( E)THERMR(NJOY)Scattering Cross Sections inel (E ) and el (E )

Cross-Section (barns)SiO 2 Calculated Cross SectionsCompared to Experimental Values100.0293.6 K[1] J. J. BLOSTEIN and J. DAWIDOWSKI,“Experimental Neutron Data: Sigma(E)of Vitreous Silica (SiO2) Over theThermal Energy Range,” PrivateCommunication, Inst. Balseiro y CentroAtomico Bariloche, Argentina (1999).10.0[2] B. M. RUSTAD, et al., “Neutron CrystalSpectrometer with Range Extended toSubthermal Energies,” Review ofScientific Instruments, 36, 887 (1965).1.01.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00Neutron Energy (eV)14

ICSBEP HEU-MET-MIXED-005Benchmark15

BFS-79/3 Configuration16

Flux PercentageFlux PercentageThermal Neutron Flux inFuel Tube Silica Pellets10.0%8.0%Silica Pelletsw/ Fast Library293.6 K800 K6.0%4.0%2.0%0.0%1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01Upper Energy of Bin (eV)0.30%0.20%0.10%Thermal LibraryContribution inSilica Pellets293.6 K800 K0.00%-0.10%-0.20%-0.30%-0.40%1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01Upper Energy of Bin (eV)17

Flux PercentageFlux PercentageThermal Neutron Flux inFuel Tube HEU Pellets7.0%6.0%5.0%HEUw/ Fast Library293.6 K800 K4.0%3.0%2.0%1.0%0.0%1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01Upper Energy of Bin (eV)0.30%0.20%0.10%Thermal LibraryContribution inHEU293.6 K800 K0.00%-0.10%-0.20%-0.30%-0.40%1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01Upper Energy of Bin (eV)18

Differential Cross Section (b / eV)Secondary Neutron Energy DistributionDownscattering Example10.09.08.0E i = 0.112 eVPlots are normalized to 293.6 K (Phonons) such thatcross sections integrated over all energies are equal.293.6 K (Boltzmann)293.6 K (Phonons)800 K (Phonons)7.06.05.04.0293.6 K: 62.5% total downscatter37.5% total upscatter800 K: 50.3% total downscatter49.7% total upscatter3.02.01.00.00.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050Secondary Neutron Energy (eV)19

Thermal Contribution to Reactivity (pcm)Thermal Library Contribution to Reactivity(pcm)100274, +67293.6, +300200 300 400 500 600 700 800 900 1000 1100-100Benchmark Temperature (K)400, -149-200500, -234-300-400800, -3821000, -391-50022

Isotopics of Neutron Losses for SelectedFast and Thermal LibrariesAbsorptionsFissionTemperature / Library H U-235 Si U-238 Al Other U-235293.6 K / Fast 16.941% 8.807% 11.108% 5.494% 5.068% 11.743% 40.839%293.6 K / Alpha Thermal 16.962% 8.808% 11.089% 5.489% 5.063% 11.740% 40.849%800 K / Fast 16.529% 9.115% 10.345% 5.662% 4.764% 12.006% 41.579%800 K / Alpha Thermal 16.613% 9.092% 10.475% 5.626% 4.819% 11.955% 41.420%1000 K / Fast 16.457% 9.126% 10.161% 5.637% 4.696% 12.100% 41.823%1000 K / Beta Thermal 16.528% 9.094% 10.290% 5.627% 4.745% 12.066% 41.650%23

Summary / Conclusions The phonon DOS for SiO 2 generated through a first-principlesapproach with the VASP / PHONON sequence can produceaccurate thermal neutron scattering cross sections. The crystalstructure is the only fundamental input required. An ENDF-6 format thermal neutron scattering library for SiO 2was produced over a standard temperature grid (modelingα-quartz and β-quartz) that is ready for submission to NNDC. The impact on k eff of accurate thermal scattering treatment ofneutrons in SiO 2 in an ICSBEP benchmark is demonstrated. The use of a thermal neutron scattering library for SiO 2 maysignificantly impact criticality calculations for geologic systems,especially in loss of heat removal accident scenarios.24