The document discusses how phase field simulations can assist with materials science experiments. It provides 4 examples of how the author's research group has used phase field modeling to help design experiments, interpret experimental data, and determine material properties that are difficult to measure experimentally. The phase field simulations allowed the group to optimize bicrystal geometries for measuring grain boundary mobility, determine the effects of bubble pinning on grain growth in nanocrystalline iron, extract kinetic parameters and grain boundary properties of uranium silicide from annealing experiments, and reanalyze diffusion couple and reactor data to understand species redistribution in uranium-zirconium nuclear fuels.

1. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Using phase field simulations to assist with
experiments and experimental data
Michael R Tonks
Materials Science and Engineering, University of Florida
Amani Cheniour, Jacob Hirshchhorn

2. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
n M.R. Tonks, L.K. Aagesen, The Phase Field Method: Mesoscale Simulation
Aiding Material Discovery, Annual Review of Materials Research. 49 (2019)
Most applications of the phase field method for scientific
discovery involve a close connection with experiments
# 1st Author Year Quantitative? Experiments? New
model?
Discr. Integr.
1 Carmack 2015-18 No No Yes FDM Explicit
2 Zhang 2018 Partially Yes No FDM Explicit
3 Damodaran 2017 Yes Yes No SM Explicit
4 Gránásy 2004 Partially Inspired No FDM Explicit
5 Wheeler 2010 No Inspired No FVM Implicit
6 Mitchell 2017 No Yes No FEM Implicit
7 Huang 2014 Yes Yes Yes SM Explicit

3. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Both advanced modeling and experiments have strengths
and weaknesses
Strengths
§ It’s the real thing
§ Everything is included
Weaknesses
§ There will be some error in data
collection
§ Experiments and characterization
can be expensive
§ Repeated experiments keep being
expensive
§ They can require specialized
facilities
§ Separating effects requires
designing specialized experiments
Strengths
§ Separate effects can be easily
investigated
§ Cheaper and faster
Weaknesses
§ Various sources of error decrease
accuracy
§ Some mechanisms might be missing
§ Must be verified and validated before
they can be trusted
§ Can require large computational
facilities (supercomputers)
Experiments Simulation

4. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Coupled simulations and experiments allow us to take
advantage of the strengths of each approach
Strengths
§ It’s the real thing
§ Everything is included
Strengths
§ Separate effects can be easily
investigated
§ Cheaper and faster
Experiments Simulation

5. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
There are various interactions that can take place
between modeling and experiments
Experimental data
Simulations
Mechanism identification
Calibration
Validation
Simulations
Experimental data
Experiment design
Experiment analysis

6. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
I am going to give four examples of how we have used the
phase field method with experiments

7. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
n However, these samples are difficult to create so it is expensive to try to
experimentally optimize the geometry.
Bicrystal experiments can be designed to measure the
grain boundary mobility of a single grain boundary
Molodov, D. A., Barrales-Mora, L. A., & Brandenburg, J. E. (2015). In IOP Conference Series: Materials
Science and Engineering (Vol. 89, No. 1, p. 012008). IOP Publishing.

8. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
We have used multi-phase field grain growth simulations
to help in the design of the bicrystal geometry

9. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Simulations were used to determine the notch angle that
would minimize the time before data could be collected
0 1 2 3
10
15
20
25
30
(1) (2)
M* = 2.14e−09 m2
/s
Time (ms)
Grainvolume(µm3
)
PF Data
Fit
0 1 2
4
5
6
7
8
9
10
(1) (2)
Time (ms)
y−posofGBincenter(µm)
PF Data
Fit
Simulations found that a
notch angle of 60°
minimized the time
required for release.
Tonks et al., Acta Materialia, 61 (2013) 1373–1382.
0 1 2
0
5
10
15
20
25
Time (ms)
Grainarea(µm2
)
30°
40°
50°
60°
65°
30 40 50 60 70
0.5
1
1.5
2
2.5
Notch angle θ (°)
Time(ms)
Release
Steady−state

10. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Measuring the average grain boundary mobility typically
requires samples with many grains

11. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
In Situ TEM of nanocrystalline FE samples indicated
significant bubble pinning of GB motion
TEM video of in-situ annealing of a Fe
nanocrystalline thin film sample (10x speed)
from Professor Mitra Taheri’s group at Drexel
University. Experiment performed by Greg
Vetterick.
Vetterick, G. A., et al. Journal of Nuclear Materials 481 (2016): 62-65.

12. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Phase field grain growth simulations were used to
determine the pinned and unpinned GB mobilities
Vetterick, G. A., et al. Journal of Nuclear Materials 481 (2016): 62-65.
Mobility at 900 ºC
with voids
2.0×10−18 m4J/s
Mobility at 900 ºC
without voids
1.0×10−14m4J/s

13. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
n U3Si2 is being considered as an alternative to UO2 as a reactor fuel
n One critical property that is unknown is the grain boundary mobility
Many of the properties of uranium silicide (U3Si2) are not
well understood

14. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
n 𝐷" − 𝐷$
"
= 𝐾𝑡, where 𝐾 = 2𝛼𝛾+, 𝑀+,
n 𝐾 = 𝐾$ 𝑒
/
0
123
Our collaborators used polycrystal grain growth anneal to
determine the kinetic parameter 𝐾 and MD for 𝛾+,
(A)
0.5 1
Q (eV)
0
2
4
6
8
10
PDF
0
5
10
15
20
25
Error(nm)
500 1000 1500
T (K)
0.2
0.4
0.6
0.8
1
GBenergy(J/m2
)
MD values
Fit
(C)
0 5000
K0
(nm2
/min)
0
0.5
1
PDF
10-3

15. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
n The shape parameter is the relationship between the average GB curvature
and the average grain size.
n We also compared the value from grain surfaces to grain volumes
We used phase field simulations to determine the shape
parameter 𝛼
(B)
0 0.5 1
M (m4
/(Js))
10-18
0
5
10
PDF
1018
T = 1000 K
T = 1100 K
T = 1200 K
T = 1300 K

16. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
There is not enough data to define the diffusion and
behavior in UZr reactor fuel
Species redistribution in reactorDiffusion couple data
Petri, M. C., and M. A. Dayananda. J. Nucl.
Mater. 240, no. 2 (1997): 131-143.
Hofman, G. L., S. L. Hayes, and M. C. Petri. J. Nucl.
Mater. 227, no. 3 (1996): 277-286.

17. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
We are modeling the UZr behavior using 1 concentration
and two order parameters with the KKS model
Hirschhorn, J., Tonks, M., Aitkaliyeva, A. and Adkins, C., 2019. Journal of Nuclear Materials.

18. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
We used phase field simulations to reanalyze the diffusion
couple data at T = 750℃

19. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
We also determined which parameters should be
investigated further, using Monte Carlo simulations

20. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
We also reanalyzed the reactor data
Originalresult
Optimized result Validation result

21. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
We conducted sensitivity analyses for the diffusion couple
as well

22. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
n Phase field simulations can be used to help design or interpret experimental
data
Conclusions

23. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Tonks Research Group