Bergeon, N.

Ji, Kaihua

Karma, A.

Lyons, T.

Mota, F. L.

Pereda, J.

Song, Y.

Strutzenberg, L. L.

Trivedi, R.

English

NASA Technical Reports Server

1Comparison of three-dimensional in situ observations 
and phase-field simulations of microstructure 
formation during directional solidification of 
transparent alloys aboard the ISS
Kaihua Ji1, F.L. Mota2, Y. Song1, J. Pereda2, T. Lyons3, 
L.L. Strutzenberg4, R. Trivedi3, N. Bergeon2, A. Karma1
1Northeastern University
2IM2NP, Aix-Marseille Université
3Iowa State University
4Marshall Space Flight Center
https://ntrs.nasa.gov/search.jsp?R=20200001739 2020-03-28T19:09:41+00:00Z
2Losert, Shi, and Cummins (1998)
Solid
Liquid
Solute concentration C0
Growth velocity V
Temperature gradient 
G
Constitutional 
supercooling
• Microstructure formation under well-controlled growth conditions (G, V, C0)
The system – directional solidification
http://www.rksteel.com.pk/
David et al. Science (1992)
3Microgravity experiments – diffusive regime
Gravity-induced convection
Microstructure heterogeneities
Microgravity experiment
Two campaigns:
• Microgravity experiments 
from 2009-2011 dedicated 
to cellular regime.
• Microgravity experiments 
from 2017-2018 dedicated 
to dendritic regime.
4Polycrystalline solidification
SCN-0.24wt% Camphor, G = 19 K/cm, V = 2 μm/s
• Noticeable primary 
spacing evolution 
depending on sub-
grain.
• Cannot be attributed 
to the misorientation 
(1.4° < 𝜃𝜃𝑔𝑔 < 1.9°)
5• Initially: large spacing with 
homogeneous distribution.
• With time: global decrease of 
spacing except at a divergent 
sub-grain boundary.
Effects of sub-grain boundaries
6 6
Simulation geometry
Grid dimensions: 600×1586×306 ≈ 
300 million, over 4 million iterations!
Multi-GPU intra-node communicationSimulation of SCN-0.24wt% Camphor, G = 19 K/cm, V = 2 μm/s over 4 hours
3960 μm 760 μm
Phase-field simulation
7z
y
Regular hexagonal array Irregular hexagonal array
Divergent sub-grain boundary
z
y
• Peak of primary 
spacing at the 
divergent sub-grain 
boundary (same as 
experiments).
• A plateau with the 
increasing spacing 
(different from 
experiments). 
• A source on the left 
that produces larger 
cells.
8t=0.00 h
t=4.00 h
t=0.00 h
t=4.00 h
t=0.00 h
t=4.00 h
Microstructures
a)
b)
c)
Effect of a source
Spacing distribution Drifting velocity
9Master curve
• The ratio 𝜃𝜃𝑔𝑔/𝜃𝜃0 between the cell-
tilt angle and the misorientation 
angle is a function of the Péclet
number Pe (master curve).
• The master curve is independent 
of the misorientation angle 𝜃𝜃0.
• The master can be fitted by a 
phenomenological function with 
constants f an g.
z
y
x
y
Tilt angle 𝜃𝜃𝑔𝑔
Misorientation
angle 𝜃𝜃0
Deschamps, Georgelin and Pocheau, PRE (2008)Song el al. Phys Rev Mat (2018)
10
Effect of a divergent sub-grain boundary 
• The divergent sub-grain boundary can 
damp the drifting velocities of nearby cells in 
SG 3 (blue), which have large Pe and are 
placed below the master curve. 
• The divergent sub-grain boundary can boost 
the drifting velocities of nearby cells in SG 1 
(red), which have large Pe and are placed 
above the master curve. 
• The phase diffusion generically relaxes 
spatially modulated nonequilibrium patterns 
towards a spatially uniform spacing:
SG 1 SG 3
11
a)
b)
t=0.00 h
t=4.00 h
t=0.00 h
t=4.00 h
Spacing distribution Microstructures
• The primary spacing 
decreases about 60 
μm at a convergent 
sub-grain boundary 
in simulation, 
whereas 30 μm in 
experiments.
• Different stable 
spacing ranges.
• Different types of 
grain competition, 
elimination or 
invasion.
Effect of a convergent sub-grain boundary 
12
DSI-R: dedicated to the dendritic regime
• Increase the concentration from SCN-0.24wt% Camphor to SCN-0.46wt% Camphor. 
Dendrites form at lower pulling velocity.
• Study of the formation of well-developed dendritic array structures.
V = 1.5 μm/s, G = 12 K/cm V = 6 μm/s, G = 12 K/cm
13
Summary
• Both the divergent and convergent sub-grain boundaries can affect the microstructure 
evolution during directional solidification of binary alloys, including the primary spacing 
distribution and the drifting velocity profile.
• Phase-field simulations at experimentally relevant length and time scales show similar 
results as experiments for a divergent boundary, including the peak and distribution of 
primary spacing.
• The differences between simulations and experiments are because of a source of cells. 
In the simulation, a source can produce large cells and lead to an increasing plateau; in 
the experiment, the small cells are generated near the crucible boarder and leads to a 
decreasing plateau.
• Near a convergent sub-grain boundary, the differences between simulations and 
experiments stems from the difference in stable ranges of cell spacings, which leads to 
different types of grain competition (elimination versus invasion).
14
Outlook
• Investigate the pulling velocity jump and the history dependence of a dendritic pattern.
• Investigate the thermal diffusivity that varies with the distance from the crucible wall. 
The spatial dependent thermal diffusivity could affect primary spacing selection and the 
evolution of an interface curvature in the experiments.
• Experimental observations and phase-field simulations reveal that the selected pattern 
at a divergent sub-grain boundary is different from the initially selected pattern near the 
center region of the crucible. The pattern adjustment could come from the drifting 
dynamics of misoriented grains.
SCN-0.46wt% Camphor, 
G = 12 K/cm, V = 2 μm/s
15
This research is supported by NASA through
awards 80NSSC19K0135 and NNX16AL77G
and by CNES through the MISOL3D project
(Microstructures de SOLidification 3D).
Kaihua Ji, Y. Song*, A. Karma
Northeastern University
F.L. Mota, J. Pereda,
N. Bergeon
Aix-Marseillé Université
T. Lyons, R. Trivedi
Iowa state University
Acknowledgement
*Current address: Oak Ridge National Laboratory
L.L. Strutzenberg
Marshall Space Flight Center
16
Thank you
for your attention


Comparison of Three-Dimensional in Situ Observations and Phase-Field Simulations of Microstructure Formation During Directional Solidification of Transparent Alloys Aboard the ISS

Comparison of Three-Dimensional in Situ Observations and Phase-Field Simulations of Microstructure Formation During Directional Solidification of Transparent Alloys Aboard the ISS

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