The document discusses nanostructured ferritic alloys which are steels strengthened with nanoscale oxide precipitates. Density functional theory calculations were performed to determine the stable structures of Ti-O, Y-O, and Ti-Y-O clusters within the ferritic matrix. The calculations found that clusters resembling the structures of bulk metal oxides like TiO2 and Y2O3 were the most stable, with mixed termination and hyperstoichiometric compositions. The interfaces between oxide precipitates and the ferritic matrix were also examined using density functional theory, finding reconstructions occurred to accommodate lattice mismatches.
GENERAL CONDITIONS FOR CONTRACTS OF CIVIL ENGINEERING WORKS
Morgan tms ods 2015 02-29 v4.4 dist
1. 1
Structure and Thermokinetics of
Y-Ti-O Precipitates in Nanostructured
Ferritic Alloys
Dane Morgan
University of Wisconsin, Madison
Leland Barnard
Knolls Atomic Power Laboratory
Nicholas Cunningham, G.R. Odette
University of California, Santa Barbara
Samrat Choudhury, Blas Uberuaga
Los Alamos National Laboratory
March 18, 2015
TMS
Orlando, Florida
2. The Idea Behind Nanostructured Ferritic
Alloys
2
Steel (Fe, C, W, …)
Oxide (Y2O3, TiO2, …)
Mix+Consolidate
(Mechanical ball
milling, HIP)
Steel with fine grains, high density
of nanoscale (1-3nm) stable
precipitates
• Enhances mechanical properties
• Enhances radiation resistance
• Called Nanostructured Ferritic Alloys (NFAs) or Oxide Dispersion
Strengthened (ODS) Alloys
• Of interest for applications in next generation nuclear reactors which
include high temperature, high radiation dose conditions
• Practical and fundamental science issues related to nature and evolution of
nanoscale precipitates
3. Outline
• Introduction to Nanostructured Ferritic Alloys
• Precipitate “bulk” structure [1]
• Precipitate interfacial structure [2]
• Thermal Aging [3]
3
[1] L. Barnard, G. R. Odette, I. Szlufarska, and D. Morgan, An
ab initio study of Ti-Y-O nanocluster energetics in
nanostructured ferritic alloys, Acta Materialia 60, p. 935-947
(2012).
[2] S. Choudhury, D. Morgan, and B. P. Uberuaga, Massive
Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide
Interfaces, Scientific Reports 4, p. 8 (2014)
[3] L. Barnard, N. Cunningham, G. R. Odette, I. Szlufarska,
and D. Morgan, Thermodynamic and kinetic modeling of oxide
precipitation in nanostructured ferritic alloys, To be published
in Acta Materialia (2015).
4. Outline
• Introduction to Nanostructured Ferritic Alloys
• Precipitate “bulk” structure [1]
• Precipitate interfacial structure [2]
• Thermal Aging [3]
4
[1] L. Barnard, G. R. Odette, I. Szlufarska, and D. Morgan, An
ab initio study of Ti-Y-O nanocluster energetics in
nanostructured ferritic alloys, Acta Materialia 60, p. 935-947
(2012).
[2] S. Choudhury, D. Morgan, and B. P. Uberuaga, Massive
Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide
Interfaces, Scientific Reports 4, p. 8 (2014)
[3] L. Barnard, N. Cunningham, G. R. Odette, I. Szlufarska,
and D. Morgan, Thermodynamic and kinetic modeling of oxide
precipitation in nanostructured ferritic alloys, To be published
in Acta Materialia (2015).
5. Nanostructured Ferritic Alloy Mechanical
Properties
• Excellent
tensile, creep,
fatigue strength
• Good fracture
toughness
• Stable to high
temperatures
5
G.R. Odette, et al., Annu Rev Mater Res ‘08; G.R. Odette, JOM ‘14
6. Nanostructured Ferritic Alloy Mechanical
Properties
• Excellent
tensile, creep,
fatigue strength
• Good fracture
toughness
• Stable to high
temperatures
6
Klueh, et al., JNM, ‘02
800°C, 138 MPa
9. Open Questions about Nanostructured
Ferritic Alloys
• What alloying elements and heat treatments are needed
for optimum nanocluster density/size distribution?
• What is the thermal and radiation stability of nanoclusters?
• What is the matrix-nanocluster interface structure and it
segregation tendencies (e.g. He trapping)?
• What are the nanocluster-dislocation interactions and their
effects on mechanical properties?
A detailed, atomistic-level understanding of the Y-Ti-O
precipitates and their energetics is a crucial step toward
addressing all of these concerns.
9
10. Todays Key Questions
• What “bulk” structures of oxide precipitates
form in Fe at ~1nm – coherent vs. incoherent?
• What interfacial structures occur at the oxide-
metal interface?
• What controls the thermal stability of the
precipitates?
10
11. Outline
• Introduction to Nanostructured Ferritic Alloys
• Precipitate “bulk’ structure [1]
• Precipitate interfacial structure [2]
• Thermal Aging [3]
11
[1] L. Barnard, G. R. Odette, I. Szlufarska, and D. Morgan, An
ab initio study of Ti-Y-O nanocluster energetics in
nanostructured ferritic alloys, Acta Materialia 60, p. 935-947
(2012).
[2] S. Choudhury, D. Morgan, and B. P. Uberuaga, Massive
Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide
Interfaces, Scientific Reports 4, p. 8 (2014)
[3] L. Barnard, N. Cunningham, G. R. Odette, I. Szlufarska,
and D. Morgan, Thermodynamic and kinetic modeling of oxide
precipitation in nanostructured ferritic alloys, To be published
in Acta Materialia (2015).
13. The Nature of the Nanoprecipitates
• Typical values: Number
density=1023-1024/m3,
Volume fraction=0.5-1%,
Diameter=1.5-3.0nm
• Explored with SANS/SAXS,
Atom Probe, TEM, Ab Initio
Tools
• Generally pyrochlore
Y2Ti2O7 (227) but significant
uncertainty due to
conditions and
interpretation challenges
(Y2TiO5, rocksalt,
amorphous)
13
TEM showing lattice spacings of Y2Ti2O7
J. Ribis, R. de Carlan , Acta Mat, ‘12
Fe–14Cr–1W–0.3Ti–0.3Y2O3 wt.%
14. The Nature of the Nanoprecipitates
• Typical values: Number
density=1023-1024/m3,
Volume fraction=0.5-1%,
Diameter=1.5-3.0nm
• Explored with SANS/SAXS,
Atom Probe, TEM, Ab Initio
Tools
• Generally pyrochlore
Y2Ti2O7 (227) but significant
uncertainty due to
conditions and
interpretation challenges
(Y2TiO5, rocksalt,
amorphous)
14
A. Hirata, Nat Mat, ‘11
14YWT (Fe-14Cr-3W-0.4Ti-0.25-Y2O3 wt.%)
Real space STEM showing NaCl structures
15. The Nature of the Nanoprecipitates
• Typical values: Number
density=1023-1024/m3,
Volume fraction=0.5-1%,
Diameter=1.5-3.0nm
• Explored with SANS/SAXS,
Atom Probe, TEM, Ab Initio
Tools
• Generally pyrochlore
Y2Ti2O7 (227) but significant
uncertainty due to
conditions and
interpretation challenges
(Y2TiO5, rocksalt,
amorphous)
15
G.R. Odette and D.T. Hoelzer, JOM ’10
G.R. Odette, JOM ‘14
Atom Probe: Ti/Y≈1.5-4, O/(Ti+Y)<1
Y2Ti2O7: Ti/Y=1, O/(Ti+Y)=7/4>1
MA957 (Fe–14Cr–0.3Mo–1Ti–0.3Y–0.2O–
0.03C wt.%)
Ti+Y >3% isocomposition contours
16. Atomistic models of coherent structures show
unusual chemistry – off stoichiometry, high
vacancy stability
The Nature of the Nanoprecipitates
• Typical values: Number
density=1023-1024/m3,
Volume fraction=0.5-1%,
Diameter=1.5-3.0nm
• Explored with SANS/SAXS,
Atom Probe, TEM, Ab Initio
Tools
• Generally pyrochlore
Y2Ti2O7 (227) but significant
uncertainty due to
conditions and
interpretation challenges
(Y2TiO5, rocksalt,
amorphous)
16
Posselt, et al. MSMSE ‘14
17. The Nature of the Nanoprecipitates
Why so much uncertainty?
• Complex heterogeneous non-equilibrium system with many possible
behaviors (e.g., multiple phases can be present, coherent vs. incoherent)
• Systems may be quite different: stoichiometry, mixing, consolidation
differences
• Data interpretation challenging (e.g. atom probe stoichiometry)
• Sampling different precipitates (e.g., with TEM)
17
Need to guidance from Y-Ti-O precipitate structure-stability relationships
18. Density Functional Theory Calculation of
Y-Ti-O Clustering Energetics
18
•How do we search for stable clusters, considering
•Structure
•Coherence
•Stoichiometry
•Different approaches:
•Clusters based around strongly bound O-Vac pairs [1].
•Clusters that minimize interaction energies [2].
•Clusters that match bulk oxide stoichiometry [3].
•All assume clusters restricted to the Fe lattice.
•Here, we will investigate including some clusters not restricted to
the Fe lattice.
[1] C.L. Fu, M. Krcmar, G. S. Painter, and X. Q. Chen, Physical Review Letters 99 (2007).
[2] Y. Jiang, J. R. Smith, and G. R. Odette, Physical Review B 79 (2009); A. Gopejenko, Y. Zhukovskii, P. Vladimirov, E. Kotomin, A.
Moslang, and X. Q. Chen, Journal of Nuclear Materials 406 (2010); M Posselt, D Murali, and B K Panigrahi, MSMSE 22 (2014).
[3] C. Hin, B. D. Wirth, and J. B. Neaton, Physical review B 80 (2009).
19. Cluster Searching Methods
•On-lattice clusters:
•Clusters restricted to the bcc Fe lattice
•Structure matched clusters:
•Clusters guided by the structure of known bulk oxides (e.g,
rutile TiO2 and bixbyite Y2O3).
19
20. Methods: On Lattice Clusters
= Fe or Ti/Y
= O
20
• Metal atoms restricted
to bcc Fe lattice
• O atoms in interstitial
stites
[1] C.L. Fu, M. Krcmar, G. S. Painter, and X. Q. Chen, Physical Review Letters 99 (2007).
[2] Y. Jiang, J. R. Smith, and G. R. Odette, Physical Review B 79 (2009); A. Gopejenko, Y. Zhukovskii, P. Vladimirov, E. Kotomin, A.
Moslang, and X. Q. Chen, Journal of Nuclear Materials 406 (2010); M Posselt, D Murali, and B K Panigrahi, MSMSE 22 (2014)
[3] C. Hin, B. D. Wirth, and J. B. Neaton, Physical review B 80 (2009).
21. Methods: Structure Matched Clusters
• Some Ti, Y atoms mapped onto Fe lattice sites
• O atoms placed relative to Ti, Y atoms according to oxide structure.
• Fe atoms impinging closely upon Ti,Y,O atoms removed.
• Ti-O/Y-O matched to rutile TiO2 / bixbyite Y2O3 21
22. +z
Methods: Formation Energy Calculation
• Reference states:
• Pure Fe.
• Isolated Ti, Y on Fe substitutional site.
• Isolated O on octahedral Fe interstitial site.
• Calculations performed using Density Functional
Theory (VASP, PAW, GGA) according to methods
developed in [1].
[1] Y. Jiang, J. R. Smith, and G. R. Odette, Physical Review B 79 (2009).
x +y
-=
22
25. Ti-O Cluster Formation Energies
25
•Given a fixed number of Ti atoms but allowing any
number of O atoms, what sort of Ti-O cluster will be
most stable?
•Predicated on relative diffusivities:
•At 1150 oC:
•Fe: 1.1E-20 m2/sec
•Y: 1.5E-23 m2/sec
•Ti: 1.7E-20 m2/sec
•O: 1.0E-14 m2/sec
26. Ti-O Cluster Formation Energies
26
Hypostoichiometric
M Terminated
Stoichiometric
Mixed Termination
Hypertoichiometric
O Termination
27. Ti-O Cluster Formation Energies
27
Hypostoichiometric
Ti Terminated
Hypertoichiometric
O Termination
Stoichiometric
Mixed Termination
Increasing O
28. Y-O Cluster Formation Energies
28
Hypostoichiometric
Ti Terminated
Hypertoichiometric
O Termination
Stoichiometric
Mixed Termination
Increasing O
29. Y-Ti-O Clusters
•To assess whether these trends continue in the full Y-Ti-O
system, we will perform a much smaller suite of calculations
on Y-Ti-O on-lattice and structure matched clusters.
•We will restrict our search to clusters with Y:Ti ratio of 1:1,
matching the pyrochlore oxide Y2Ti2O7.
29
30. Ti-Y-O Cluster Formation Energies
Hypostoichiometric
M Terminated
Hypertoichiometric
O Termination
Stoichiometric
Mixed Termination
Increasing O
[1] Y. Jiang, J. R. Smith, and G. R. Odette, Physical Review B 79 (2009).
[2] D. Murali et al. Journal of Nuclear Materials 113 (2010). 30
•Again, most stable clusters are structure-matched, hyperstoichiometric
31. Conclusion - Clusters that Resemble Bulk
Oxide are Most Stable
31
Bulk oxide Embedded Cluster
Ti-O
(Rutile TiO2)
Y-O
(Bixbyite Y2O3)
Ti-Y-O
(Pyrochlore
Y2Ti2O7)
32. Outline
• Introduction to Nanostructured Ferritic Alloys
• Precipitate “bulk” structure [1]
• Precipitate interfacial structure [2]
• Thermal Aging [3]
32
[1] L. Barnard, G. R. Odette, I. Szlufarska, and D. Morgan, An
ab initio study of Ti-Y-O nanocluster energetics in
nanostructured ferritic alloys, Acta Materialia 60, p. 935-947
(2012).
[2] S. Choudhury, D. Morgan, and B. P. Uberuaga, Massive
Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide
Interfaces, Scientific Reports 4, p. 8 (2014)
[3] L. Barnard, N. Cunningham, G. R. Odette, I. Szlufarska,
and D. Morgan, Thermodynamic and kinetic modeling of oxide
precipitation in nanostructured ferritic alloys, To be published
in Acta Materialia (2015).
33. Atomic Structure of the Y2O3/Fe Interface
{010}FeAl|| {011}YO, <100>YO|| <001>FeAl
Inksonetal.MRSProc,1997
Relaxed Structure of the bi-layer of
metal and oxide
Iron Yttrium Oxygen
Fe
Y2O3
Orientation Relationship between Y2O3/Fe
Misfit dislocation at the
interface results in excessive
Fe/O ratio
Local structure of misfit
dislocation in metal/oxide is a
f (strain, chemistry)
Fe bcc {010} plane
Y2O3 {011} plane
34. Restoring Chemical Balance at Dislocation (Fe/O > 1)
Taking out Y
Interfacial Fe Vacancy
Taking out Fe
Fe ¯
O
Interfacial Y Vacancy
Inserting Oxygen
Oxygen in Interfacial Fe layer Fe
O -
Iron
Yttrium
Oxygen
Interstitial Oxygen
Reducing Conditions
Oxidizing Conditions
35. -8.0
-7.0
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
0 0.16 0.32 0.48
0.70.91.11.31.5
ChangeinEnergy(eV)
Vacancy Concentation in the Interfacial layer
Fe/O ratio at the Interface
Change in Energy of the System with Point Defects
Fe Vacancies
DE = EWith n Vacancies
Interface
+ n´ mFe
bulk
+ m´ mO - EWithout Vac
InterfaceMost of the vacancies/oxygen interstitials enter at the dislocation
Interstitial Oxygen
36. -8.0
-7.0
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
0 0.16 0.32 0.48
0.70.91.11.31.5
ChangeinEnergy(eV)
Vacancy Concentation in the Interfacial layer
Fe/O ratio at the Interface
Change in Energy of the System with Point Defects
Fe Vacancies
-14.0
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
0 0.1 0.2 0.3 0.4 0.5
0.480.640.80.96
ChangeinEnergy(eV)
Vacancy Concentation in the Interfacial layer
Fe/O ratio at the Interface
Interstitial Oxygen + Fe Vacancies
Under More Reducing Conditions: Fe vacancies
Under More Oxidizing Conditions (~Cr/Cr2O3): Interstitial Oxygen + Fe Vacancies
37. Conclusions - Fe/Y2O3 Interfaces are Highly
Defected
• Fe/Y2O3 semi-
coherent interface
shows highly defected
structure
• Undefected Fe/O=1.5,
Equilibrium Fe/O~0.5
(~50% Fe vac, ~50%
extra O interstitials at
PO2=Cr/Cr2O3)
• Will impact interface
segregation, stability.
Iron Yttrium Oxygen
Fe
Y2O3
-14.0
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
0 0.1 0.2 0.3 0.4 0.5
0.480.640.80.96
ChangeinEnergy(eV)
Vacancy Concentation in the Interfacial layer
Fe/O ratio at the Interface
38. Outline
• Introduction to Nanostructured Ferritic Alloys
• Precipitate “bulk” structure [1]
• Precipitate interfacial structure [2]
• Thermal Aging [3]
38
[1] L. Barnard, G. R. Odette, I. Szlufarska, and D. Morgan, An
ab initio study of Ti-Y-O nanocluster energetics in
nanostructured ferritic alloys, Acta Materialia 60, p. 935-947
(2012).
[2] S. Choudhury, D. Morgan, and B. P. Uberuaga, Massive
Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide
Interfaces, Scientific Reports 4, p. 8 (2014)
[3] L. Barnard, N. Cunningham, G. R. Odette, I. Szlufarska,
and D. Morgan, Thermodynamic and kinetic modeling of oxide
precipitation in nanostructured ferritic alloys, To be published
in Acta Materialia (2015).
39. Thermal Aging Nanostructured Ferritic
Alloy
• Long-term stability of nanoprecipitates at
elevated temperature (potentially under
irradiation) is critical for sustained
performance.
• Thermal aging experiments show excellent
stability.
• Goal is to model these experiments to develop
molecular scale understanding of mechanisms
controlling stability of nanoprecipitates.
39
40. Experimental Thermal Aging Data from Odette Group (UCSB)
MA957 (Fe–14Cr–0.3Mo–1Ti–0.3Y–0.2O–0.03C wt.%)
40
M. Alinger, PhD Thesis, University of California Santa Barbara, 2004.
N. Cunningham, et al, Mat Sci & Eng A (2014)
N. Cunningham, et al., Fusion Materials Report June 30, 2012, DOE/ER-0313/52
1
2
3
4
5
-4 -2 0 2 4 6
MeanRadius(nm)
LOG Aging Time (hr)
1223K Cunningham
1273K Cunningham
1423K Alinger
1473K Alinger
1523K Alinger
1573K Alinger
Fits to classical
coarsening models
suggest pipe
diffusion
41. Chemical rate theory/mass action kinetics
Method – Cluster Dynamics (CD)
• Cluster growth/shrink rates determined from diffusion coefficients,
thermodynamics, and interfacial energy.
• Solve coupled ODEs to obtain the number of clusters at each size.
Generalized for standard and pipe diffusion.
Time evolution
V. Slezov, Kinetics of First-Order Phase Transitions, 1st ed., Wiley-VCH, 2009.
42. Parameterizing Cluster Dynamics Model
• Fe-Y-Ti-O Thermodynamics
– Y-Ti-O Bulk + Impurity (CALPHAD)
– Interfacial (Fitting)
– PO2 (Fitting)
– Y–dislocation binding (ab initio)
• Fe-Y-Ti-O Kinetics
– Bulk impurity diffusion (experiments, ab initio (Y in
Fe))
– Dislocation impurity diffusion (empirical correlation)
42
44. Parameterizing Cluster Dynamics Model:
Interfacial Energy
44
TiAx 00
Simple model to
get one fitting
parameter 0. Set by bare (TiO2)-(Y2O3)
0.0
1.0
2.0
3.0
0.00 0.33 0.67 1.00
InterfacialEnergy(J/m2)
Ti fraction of metal atoms in oxide
Y2O3 Surface Energy
TiO2 Surface Energy
TiO2/liquid Fe Interface Energy
Pipe Diffusion Model Best Fit
Standard Model Best Fit
Close agreement with
bare and liquid Fe
interfacial energies
validates approach
45. Parameterizing Cluster Dynamics Model:
PO2
45
PO2 fit to give best agreement
to coarsening data
-30
-25
-20
-15
-10
1200 1300 1400 1500 1600
LOGPO2
Temperature (K)
Pipe Diffusion Best Fit
Standard Model Best Fit
Cr/Cr2O3 Equillibrium
Ti/TiO2 Equilibrium
• Close agreement with Cr/Cr2O3
equilibrium validates approach
• Suggests no exception PO2 in
NFA steels
46. Parameterizing Cluster Dynamics Model:
Y–dislocation binding (ab initio)
46
Calculate dislocation
binding energy for
multiple elements
• Good agreement with experiment,
elasticity for C, N, O
• Y exceptionally stable – drives Y
solubility for pipe diffusion!
-3
-2
-1
0
C N O Y
BindingEnergy(eV)
Elasticity Theory
Ab Initio
Experiment
5
[100]
[010]
2
1
3
4
47. Cluster Dynamics Modeling of Thermal
Aging
47
1
2
3
4
5
-4 -2 0 2 4 6
MeanRadius(nm)
LOG Aging Time (hr)
1223K Cunningham
1273K Cunningham
1423K Alinger
1473K Alinger
1523K Alinger
1573K Alinger
Pipe Model
Standard Model
48. 0.0
0.5
1.0
1.5
2.0
2.5
1000 1100 1200 1300 1400
Changeinmeanradius
(nm)
Temperature (K)
50 years
80 years
Predictions of Coarsening Over Reactor
Lifetimes
Excellent stability up to over 1,100K
49. Conclusions – Successful Y-Ti-O Nanocluster
Coarsening
• Confirms results of reduced
order fitting from Odette et al
that process is pipe diffusion
• Predicts long term stability of
>100 years at >1,100K.
• Suggests PO2 may be
controlled by Cr/Cr2O3 in
Nanostructured Ferritic Alloys
with Cr
• Provides useful molecular
scale parameters (interfacial
energies, Y diffusivity, …) for
models of processing and
thermal/irradiation stability
49
1
2
3
4
5
-4 -2 0 2 4 6
MeanRadius(nm)
LOG Aging Time (hr)
1223K Cunningham
1273K Cunningham
1423K Alinger
1473K Alinger
1523K Alinger
1573K Alinger
Pipe Model
Standard Model
1
2
3
4
5
-4 -2 0 2 4 6
MeanRadius(nm)
LOG Aging Time (hr)
1223K Cunningham 1273K Cunningham
1423K Alinger 1473K Alinger
1523K Alinger 1573K Alinger
Pipe Model Standard Model
50. Summary Conclusions on Y-Ti-O Precipitates in
Nanostructured Ferritic Alloys
• Nanoprecipitates are bulk-like
structures down to very small sizes –
remaining on bcc lattice is higher in
energy
• Larger particle semi-coherent
interfaces create complex defect
structure to maintain Fe/O balance
• Molecular understanding of
coarsening is available
– Confirms pipe diffusion
– Shows exceptional stability (>100
years at >1100K)
– Foundation for composition,
processing, irradiation modeling
50
1
2
3
4
5
-4 -2 0 2 4 6
MeanRadius(nm)
LOG Aging Time (hr)
1223K Cunningham
1273K Cunningham
1423K Alinger
1473K Alinger
1523K Alinger
1573K Alinger
Pipe Model
Standard Model
Iron Yttrium Oxygen
Fe
Y2O3
51. 51
http://matmodel.engr.wisc.edu/
COMPUTATIONAL MATERIALS GROUP
Faculty
* Izabela Szlufarska * Dane Morgan
Postdocs
* Guangfu Luo * Georgios Bokas
* Henry Wu * Jia-Hong Ke
* Mahmood Mamivand * Min Yu
* Wei Xie * Yueh-Lin Lee
Graduate Students
* Amy Kaczmarowski * Ao Li
* Austin Way * Benjamin Afflerbach
* Cheng Liu * Chaiyapat Tangpatjaroen
* Franklin Hobbs * Hao Jiang
* Huibin Ke * Hyunseok Ko
* James Gilbert * Jie Feng
* Kai Huang * Kumaresh Murugan
* Lei Zhao * Mehrdad Arjmand
* Ryan Jacobs * Shenzen Xu
* Tam Mayeshiba * Xing Wang
* Yipeng Cao * Zhewen Song
* Zhizhang Shen
Acknowledgements
52. U.S. DEPARTMENT OF ENERGY
Rickover Fellowship Program
In Nuclear Engineering
DMR MMN
(110564)
10-888
Computing time provided by NSF TG-
DMR110074 and NSF TG-
DMR090023, NSF grant number
OCI-1053575
Funding/Resources Acknowledgements