Scales by Coupling the Phase-Field Method to Spatially-Resolved Cluster Dynamics Dong-Uk Kim, Ali Muntaha, Michael R Tonks, University of Florida Sophie Blondel, Brian Wirth, University of Tennessee-Knoxville David Bernholdt, Phillip Roth, Oak Ridge National Laboratory David Andersson, Los Alamos National Laboratory Work is funded by Joint NE/SciDAC Project on the simulation of fission gas
n Grain boundary segregation n Grain growth with small precipitates There are various examples of where microstructural features of very different sizes impact material behavior Dendritic growth of precipitates in Ni- based super alloys Henry, M. F., Yoo, Y. S., Yoon, D. Y., & Choi, J. (1993). Metallurgical Transactions A, 24(8), 1733- 1743.
irradiated fuel occurs due to materials processes that occur across various length and time scales Kashibe, S., K. Une, and Kazuhiro Nogita. JNM 206, no. 1 (1993): 22-34. Rest, J., et al. JNM 513 (2019): 310-345.
44 nm n Interfacial width: 30 nm n Initial bubble radius: 1.5 nm n Interfacial width: 0.7 nm Intergranular bubble analysis Phase field simulations of fission gas bubbles currently target specific length scale of interest Intragranular bubble analysis L.K. Aagesen, D. Schwen, M.R. Tonks, Y. Zhang, Computational Materials Science. 161 (2019) 35–45. M.R. Tonks, et al., In proceedings M&C 2013, May 5 – 9, 2013, Sun Valley ID 20×20×20 nm 1.2×1.04×0.45 *m
hybrid model that uses cluster dynamics to model small bubbles and phase field for large Cluster Dynamics (Xolotl) Phase Field (MOOSE) Both codes are open source
!$ = ̇ '() + +) ,-.) − 0 .) , where n = 1, 2, …, >1000 n +) = 0 for n > 1 n Reactions are represented by 0 .) n 0 .) = 3) .) .4 − 3 )54 . )54 .4 + 3) 678$.) − 3 )94 678$ . )94 + 3) :6;<.) − 3 )94 :6;< . )94 n Include n Clustering: Xe1 + Xen → Xen+1 n Emission and resolution: Xen → Xe1 + Xen-1 The cluster dynamics model uses a series of coupled reaction diffusion equations to model Xe atom clusters + = …
equations using implicit finite difference n Nonlinear solves are carried out using PETSc n Scales well to 10,000’s of processors n GPU acceleration is underway Xolotl is an open source spatially-resolved cluster dynamics code developed at the University of Tennessee-Knoxville Limitations: • Cannot represent large bubbles due to high computational expense • Cannot represent interfacial motion such as grain boundary migration
and coalescence of fission gas bubbles and grain boundary migration n Grand potential model (Plapp) with multiphase field grain growth model n Xe atom and U vacancy chemical potentials (2 DOF). n Bubble order parameter (1 DOF). n Grain order parameters (1 – 20 DOF, reused for multiple grains). n The model uses 4 – 22 DOF per node. We are building our work on the most recent fission gas model in MOOSE/MARMOT (developed by Larry Aagesen) Aagesen et al. Computational Materials Science 161 (2019): 35-45.
gas model in MOOSE/MARMOT predicts bubble and grain boundary evolution 33 days 77 days 145 days Limitations: • Cannot represent bubbles that are much smaller than the grain size • Cannot directly represent bubble nucleation • Cannot directly represent re-solution
in the grains while MARMOT models grain boundary bubbles and migration Cluster Dynamics (Xolotl) • Xe production • Intragranular diffusion • Clustering • Resolution Phase Field (MARMOT) • Intergranular bubble growth and coalescence • Grain boundary migration Gas atom arrival rate at Interfaces Interface locations
coupled using the Multiapps and Transfers systems in the MOOSE framework MARMOT mesh MOOSE-Xolotl wrapper mesh Xolotl grid Interpolation transfer Direct copy Microstructure Gas source Interface coordinates Gas source
8 16 32 64 128 # of processors 0 1000 2000 3000 4000 5000 6000 Computation time (s) Data transfer MARMOT Xolotl Clu. & No Re-s. 4 8 16 32 64 128 # of processors 0 1000 2000 3000 4000 5000 6000 Computation time (s) Data transfer MARMOT Xolotl The computational cost of Xolotl and MARMOT are similar and cost of the data transfer is negligible No Clu. & No Re-s. 4 8 16 32 64 128 # of processors 0 1000 2000 3000 4000 5000 6000 Computation time (s) Data transfer MARMOT Xolotl
in Xolotl has a large impact on the overall fission gas behavior 20 µm 1800 K ̇ & = 1.09×10,- fissions/(m3s) Note: Initial intergranular bubbles are used to avoid the need to model nucleation in MARMOT
in Xolotl has a large impact on the overall fission gas behavior 20 µm 1800 K ̇ & = 1.09×10,- fissions/(m3s) Note: Initial intergranular bubbles are used to avoid the need to model nucleation in MARMOT
much as 70% of the fission gas being trapped within the grains 200 400 600 800 1000 1200 1400 Time (days) 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Intergranular bubble fraction No clustering & no re-solution Clustering & no re-solution Clustering & re-solution Effective diffusion 200 400 600 800 1000 1200 1400 Time (days) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Xe fraction in grains No clustering & no re-solution Clustering & no re-solution Clustering & re-solution 1800 K
less gas arriving at grain boundaries and less grain growth 1000 K, No re-solution 1000 K, Re-solution 1800 K, No re-solution 1800 K, Re-solution 20 µm ̇ & = 1.09×10,- fissions/(m3s)
with more grains, resulting in more sweeping up of gas by migrating grain boundaries 20 µm 1800 K, Clustering, Re-solution ̇ & = 1.09×10,- fissions/(m3s)
with more grains, resulting in more sweeping up of gas by migrating grain boundaries 20 µm 1800 K, Clustering, Re-solution ̇ & = 1.09×10,- fissions/(m3s)
field and cluster dynamics could be used to model other phenomena Cluster Dynamics • Diffusion and atom clustering • Nucleation and growth of small precipitates Phase Field • Large precipitate evolution • Interface evolution • Grain boundary evolution
wd15
olachinkei
genomethica
jagupath
xspa2012
.png){kind=avatar}
statditto
sshimizu2006
shunyanoda
gkazunii
tagtag
datascientistsociety
katiecoart
tammyeverts
csswizardry
minecr
bryan
lcolladotor
davidcarrasco
baasie
tanoku
jonoalderson
cassininazir
