Neutron Displacement Cross-Sections for Materials from Be to U Calculated Using the Arc-dpa Concept
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1 Neutron Displacement Cross-Sections for Materials from Be to U Calculated Using the Arc-dpa Concept A.Yu. Konobeyev, U. Fischer, S.P. Simakov INSTITUTE for NEUTRON PHYSICS and REACTOR TECHNOLOGY (INR) KIT The Research University in the Helmholtz Association
2 Objective o preparation of the data set for improved estimation of the number of defects produced in materials from Be to U o calculation of atomic displacement cross-sections for neutron incident energies to 200 MeV using data from actual versions of ENDF/B, JEFF, JENDL, and TENDL 2
3 Atomic displacement cross-section max Ti d (E p,z T,A T,Z,A) i i (E ) N (T,Z,A,Z,A )dt dt d p d i T T i i i i E i d dσ/dt : recoil energy distribution N d : number of stable displacements produced by PKA 0.8 N d(t) (T) T dam(t) 2E Robinson formula (NJOY, MCNP, SPECTER) T dam (T) d T 1 k(z,a,z,a )g(z,a,z,a ) PKA PKA T T PKA PKA T T NRT : reference model (poor agreement with experiments and MD) (T ) 1 dam 3
4 4 Athermal recombination-corrected dpa (arc-dpa) concept* *K.Nordlund et al, NEA/NSC/DOC(2015)9 damdddamddamdarcdpadamdamddamd0whenten(t)1whenet2e/0.80.8(t)twhen2e/0.8t2e barcdpaarcdpaarcdpaarcdpadamdamarcdpabd1c(t)tc2e/0.8w arc-dpa: Fe, Ni, Cu, Pd, Ag, W, Pt, Au
5 Estimation of parameters of arc-dpa equations I. Parameter c arcdpa : asymptotic value of defect generation efficiency EdrcdpaaEdef: the effective threshold cedeff displacement energy <> = 1 for neutron irradiation in reactors E d : the averaged displacement threshold energy max Ti d (E p,z T,A T,Z,A) i i d(e p) N d(t,z i T,A T,Z,A i i)dti dt i E i d E dmin : the minimum displacement threshold energy 5
6 The first systematics (1983) E deff = C 1 E dmin (P.Jung) and E d = C 2 T melt (Yu.Konobeev,Yu.Korovin) Blind search for correlation for E dmin E dmin data: Jung, Eckstein compilations (45 materials) Quantity Correlation coefficient Z T melt 0.70 T melt 0.83 ( T melt ) 1/ E coh * 0.78 E coh /T melt E coh 0.85 *cohesive energy: difference between the energy of free atoms and the energy of atoms in solid 6
7 Example E dmin = a ( T melt ) 1/2 +β 7
8 Estimated E dmin values 8
9 Search for correlation for E d E d : Jung, Broeders compilations (24 materials) Quantity Correlation coefficient E dmin 0.77 Z T melt 0.89 T 3/2 melt 0.90 E coh 0.86 E 2 coh 0.90 E coh T melt
10 Estimated E d values 9 Be: systematics: 31 ± 6 ev MD DFT*: ev (unknown before analysis) * Vladimirov, Borodin (KIT), NIMB (2017) 10
11 Search for correlation for E deff E deff : Broeders compilations (21 materials) Quantity Correlation coefficient E dmin 0.47 E d 0.58 Z T melt 0.50 E coh
12 Estimated values of c arcdpa 12
13 ,arcdpa((e)()dee)()dii. Parameter b arcdpa : the rate of (T dam ) decrease d d,nrte E Ebarcdpa value: from -1.5 to -0.2 S.P.Simakov 22 neutron irradiation spectra Nordlund b arcdpa data Fe, Ni, Cu, Pd, Ag, W, Pt, Au 13
14 14
15 Averaged efficiency values <> for tungsten (b arcdpa, c arcdpa : Nordlund) Irradiation ENDF/B-VIII.b4 JEFF-3.3T3 JENDL-4.0 TENDL-2015 APWR KWO PWR TRIGA/TRADE TTB, FRM Fission MeV neutrons (d,be) 40 MeV deuterons HFIR PWR Robinson Typical LWR EPRI, BWR 1/4T EPRI, BWR 3/4T EPRI, PWR 1/4T EPRI, PWR 3/4T LWR Kori Omega West Reactor EBR-II expr breeder reactor Bor RTNS-II Fusion simulation ITER, first wall DEMO IFMIF
16 183 DMaterial axmin e44mhg ENDF/B-VIII.b4 JEFF-3.3T3 JENDL-4 TENDL-2015 Co < <20 Cu* Rh <20 <20 43 <20 Pd* 20 <20 <20 <20 Ag* 30 <20 <20 <20 Cd In Sm Eu Gd Dy Er 29 <20 29 <20 Lu 32 <20 <20 Hf <20 <20 32 <20 W* Pt* Au* % av* b arcdpa : Nordlund, b arcdpa = 0.8 in other cases 16
17 Li to U : 70 materials Fe, Ni, Cu, Pd, Ag, W, Pt, Au: Nordlund data or c arcdpa, b arcdpa obtained Co, Cd, In, Sm, Eu, Gd, Dy, Hg: c arcdpa obtained, b arcdpa is very approximate other materials: c arcdpa, b arcdpa obtained Example MD: Borodin, Vladimirov (KIT), Nucl. Mat. Energy (2016) 17
18 Calculation of displacement cross-sections ENDF/B-VIII.beta4, JEFF-3.3T3, JENDL-4.0, TENDL
19 Extension of the data up to 200 MeV Examples 19
20 Atomic displacement cross-sections for materials from Be to U Neutron incident energy: from to 200 MeV Format: ENDF-6 and ACE arc-dpa (MT=900) and NRT model (MT=901) ENDF/B-VIII.beta4: JENDL-4.0: TENDL-2015: 20
21 Conclusion Atomic displacement cross-sections were calculated for materials from Be to U at neutron energies up to 200 MeV using arc-dpa model 21
22 22
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