metals
Article
Vitrification and Crystallization of Phase-Separated
Metallic Liquid
Yun Cheng, Wenchao Cui, Li Wang *, Chuanxiao Peng, Shenghai Wang and Yuyang Wang
School of Mechanical & Electrical and Information Engineering, Shandong University at Weihai, Weihai 264209,
China; [email protected] (Y.C.); [email protected] (W.C.); [email protected] (C.P.);
[email protected] (S.W.); [email protected] (Y.W.)
* Correspondence: [email protected]; Tel.: +86-631-5688224
Academic Editor: Jordi Sort Viñas
Received: 5 October 2016; Accepted: 17 February 2017; Published: 24 February 2017
Abstract: The liquid–liquid phase separation (LLPS) behavior of Fe50 Cu50 melt from 3500 K to
300 K with different rapid quenching is investigated by molecular dynamics (MD) simulation
based on the embedded atom method (EAM). The liquid undergoes metastable phase separation by
spinodal decomposition in the undercooled regime and subsequently solidifies into three different
Fe-rich microstructures: the interconnected-type structure is kept in the glass and crystal at a higher
cooling rate, while the Fe-rich droplets are found to crystalize at a lower cooling rate. During the
crystallization process, only Fe-rich clusters can act as the solid nuclei. The twinning planes can be
observed in the crystal and only the homogeneous atomic stacking shows mirror symmetry along the
twinning boundary. Our present work provides atomic-scale understanding of LLPS melt during the
cooling process.
Keywords: Fe50 Cu50 undercooled melt; phase separation; spinodal decomposition; twinning plane
1. Introduction
The typical microstructure of phase separation is classified into an interconnected structure or a
droplet-like structure by mechanisms such as spinodal decomposition and nucleation growth [1–3].
The liquid–liquid phase separation (LLPS) occurs first above the liquidus or in the undercooled liquid,
after which each liquid region undergoes a liquid-to-glass or liquid-to-crystal transition through a
combination of rapid quenching techniques and container-less undercooling, resulting in the formation
of a two-phase amorphous alloy, two-phase crystal or one-phase crystal, one-phase amorphous alloy.
Because the LLPS competes with crystallization, relatively, in metallic alloy, it is difficult to obtain
the interconnected structures by spinodal decomposition [4–6]. Thus, most of the microstructures
obtained by the phase separating alloy are the droplet structure, which is formed by nucleation and the
growth reaction. The successful fabrication of two-phase crystal makes it useful in various industrial
applications, such as bearing materials and electronic packaging materials. The bulk glass with a
nano-sized separated phase shows high strength and toughness [7–11] due to the enhancing overall
plastic deformability through the formation of a multiple-branched shear band [7,10,11]. The size,
shape and distribution of the second phase, controlled by the cooling rate, show great influence
on the final properties of glass or crystal after rapid solidification. However, the vitrification and
crystallization of phase-separated metallic liquid at atomic level is still unknown.
A metastable miscibility gap exists at higher temperatures [4] in the Fe–Cu phase diagram due
to its positive mixing enthalpy; while others think that Fe–Cu alloys are completely miscible in the
stable liquid state, the system shows a wide metastable miscibility gap at rather low undercooling
values [5]. Thus, the Fe–Cu system provides a model system to study LLPS. LLPS of the Fe–Cu
system is very difficult to observe because of its high temperature and opaque characteristics. In
Metals 2017, 7, 73; doi:10.3390/met7030073
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our earlier paper, the LLPS behavior of liquid Fe–Cu above the liquidus line has been studied by
molecular dynamics (MD) simulation [12]; in addition, MD simulation has also been performed to
explore the structural and dynamical heterogeneity of Fe75 Cu25 melts, which separate into Cu-rich
droplets surrounded by the Fe-rich matrix controlled by nucleation and the growth mechanism [13].
However, the separation process of Fe–Cu melts, especially the formation of metallic glass and crystal
after separation, is not involved in literature, although the liquid phase separation and metallic glass
formation in the Fe–Cu-based alloy has also been reported [14–17]. MD calculation, in combination
with a reasonable potential model, has been applied as a powerful tool to study the properties of liquid
alloy. The objective of the present work is to investigate the separation mechanism of Fe50 Cu50 melt as
well as the subsequent glass and crystal formation after separation during rapid cooling by computing
the structure, thermodynamics and dynamics parameters.
2. Simulation Details
In this study, calculations have been performed using the Fe–Cu potential according to G.
Bonny [18]. The simulations are performed at zero external pressure in order to allow for a direct
comparison to experiments under ambient pressure. Systems of N = 25,600 atoms are put in a cubic
simulation box with periodic boundary conditions. To observe the structural change clearly, the box
size along the x y z direction are set to 40 L, 40 L and 4 L (L is the crystal lattice of the Fe) respectively.
The number ratio of Fe and Cu is 1:1. MD simulations in isothermal-isobaric (NPT) ensemble were
performed by the large-scale atomistic/molecular massively parallel simulator (LAMMPS, distributed
by Sandia National Laboratories, a US Department of Energy laboratory), and Newton’s equations
of motion are integrated with the velocity form of the Verlet algorithm using a time step of 1 fs.
The masses of Fe and Cu atoms are set to mFe = 58.587 amu and mCu = 63.546 amu. Firstly, the
system is fully equilibrated at 3500 K by performing runs: 2 × 105 time steps in NPT systems. To keep
temperature constant, we apply the Andersen thermostat where, after every 100 cycles, we have chosen
new velocities from a Maxwell–Boltzmann distribution in accordance with the temperature of the
system. Next, equilibrated configuration obtained from simulation is used as an initial configuration
for the following cooling process. The temperatures considered are from 3500 K to 300 K at a cooling
rate of 6.4 × 1012 K/s, 6.4 × 1011 K/s and 1.28 × 1011 K/s respectively, to examine the glass formation
and crystallization processes. The configurations are recorded every 200 K. The atom configurations
are reported every 10 K to explore the thermodynamics properties during phase transition.
3. Results and Discussion
Figure 1 shows the average energy of atoms versus the temperature. The curve is nearly straight
in the high and low temperature regime at the cooling rate of 6.4 × 1012 K/s. The changes in energy
are continuous. This is a typical feature of glass formation. The glass transition temperature Tg for
a model system is defined by the temperature at the intersection of the extrapolations of the liquid
and glassy plots. In Figure 1, Tg is estimated to be approximately 800 K at this cooling rate. The
energy–temperature curves decrease abruptly at low temperature, and the undercooled liquid becomes
crystal as the cooling rate is 6.4 × 1011 K/s and 1.28 × 1011 K/s; the higher the cooling rate, the lower
the crystallization temperature, as shown in Figure 1.
The Fe–Fe partial pair correlation functions (PPCF) in the liquid and glass state are shown in
Figure 2 to explore the structural difference between the liquid and undercooled liquid in the phase
separation system. The PPCFs during the crystallization process at the cooling rate of 6.4 × 1011 K/s
show the same tendency, except that the crystallization peak occurs at lower temperature. They are
not listed in the paper. The gFe-Fe (r) and gCu-Cu (r) show similar behavior, having almost the same
height of the first peak, much higher than that of gFe-Cu (r) in the undercooled liquid. It can be deduced
that there is a stronger interaction of homogeneous atom pairs than heterogeneous atom pairs in
Fe50 Cu50 melt. In particular, the height difference of the first peak between homogeneous atom pairs
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and heterogeneous atom pairs is more predominant at lower temperature, indicating that the stronger
Metals 2017,
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atom
pairs7, and
heterogeneous atom pairs is more predominant at lower temperature, indicating
LLPS happens in the glass rather than in the liquid.
that the stronger LLPS happens in the glass rather than in the liquid.
atom pairs and heterogeneous atom pairs is more predominant at lower temperature, indicating
that the stronger LLPS happens in the glass rather than in the liquid.
Figure 1. The average atom energy as a function of temperature.
Figure 1. The average atom energy as a function of temperature.
Figure 1. The average atom energy as a function of temperature.
Figure 2. Partial pair correlation functions (PPCFs) of Fe50Cu50 at 2500 K and 900 K respectively.
Figure
2. Partial
correlation
functions
(PPCFs)
at
2500
K and
900
KFerespectively.
Figure
2. Partial
pairpair
correlation
functions
(PPCFs)
of Fe
Fe5050Cu
Cu
at
2500
K and
KCu
respectively.
The
coordination
number
is also
calculated
to explore
its5050
local
packing
of900
50
50 during the
whole cooling process. Usually, the physical scene of short-range order can be observed from the
The coordination number is also calculated to explore its local packing of Fe50Cu50 during the
measured
curves ofnumber
the pair correlation
functionsto(PCF)
fromitswhich
coordination
may the
The
coordination
is also calculated
explore
localthe
packing
of Fe50number
Cu50
during
whole cooling process. Usually, the physical scene of short-range order can be observed
from the
be
obtained.
As
we
can
infer
from
the
Fe–Fe
pairs,
the
coordination
number
(CN)
at
the the
wholemeasured
cooling curves
process.
Usually,
the physical
scene(PCF)
of short-range
can be observed
from
of the
pair correlation
functions
from which order
the coordination
number may
temperature of 3500 K is 7.8, a little higher than that of the Cu–Cu pairs (7.3), and higher than that
measured
curves of
which the coordination
number
be obtained.
Asthe
wepair
can correlation
infer from functions
the Fe–Fe(PCF)
pairs, from
the coordination
number (CN)
at the may
of the Fe–Cu pairs (about 6.0). The changes of three partial CNs is slow as the temperature is higher
be obtained.
As we
can infer
from
the higher
Fe–Fe pairs,
theofcoordination
number
at thethan
temperature
temperature
of 3500
K is 7.8,
a little
than that
the Cu–Cu pairs
(7.3), (CN)
and higher
that
than 2000 K; after that, the strong increases of CN for Fe–Fe and Cu–Cu pairs is found and on the
of the
Fe–Cu
pairs
(about
6.0).
Thethat
changes
of Cu–Cu
three partial
CNs
is slow
as
the temperature
is higher
of 3500
K
is
7.8,
a
little
higher
than
of
the
pairs
(7.3),
and
higher
than
that
of
the
Fe–Cu
contrary, the sharp decreases for Fe–Cu pairs is also quite obvious. The number of Fe neighbors
than
2000
K; after
that,
the strong
increases
ofCNs
CN is
forslow
Fe–Fe
and
Cu–Cu
pairs isisfound
andthan
on the
pairsaround
(about
6.0).
The
changes
of
three
partial
as
the
temperature
higher
2000
K;
the Fe atom and the number of Cu atoms around the Cu atom are about 12 at the
contrary,
the
sharp
decreases
for
Fe–Cu
pairs
is
also
quite
obvious.
The
number
of
Fe
neighbors
after temperature
that, the strong
increases
of CN
and Cu–Cuatom
pairspairs,
is found
and on of
theCu
contrary,
of 700
K. Opposite
to for
thatFe–Fe
of homogeneous
the number
atoms the
around the Fe atom and the number of Cu atoms around the Cu atom are about 12 at the
sharparound
decreases
Fe–Cu
pairs
is 2also
quite
number
of Feobserved
neighbors
the Fe
the Fefor
atom
is only
about
at 700
K, inobvious.
agreementThe
with
the behavior
for around
PPCFs. Fe
temperature of 700 K. Opposite to that of homogeneous atom pairs, the number of Cu atoms
prefer
to accept
atom around
as their neighbor
and Cu
prefer
accept
the Cu atom
atomatoms
and the
number
of the
Cu Fe
atoms
the Cu atom
areatoms
about
12 attothe
temperature
ofas700 K.
around the Fe atom is only about 2 at 700 K, in agreement with the behavior observed for PPCFs. Fe
their neighbor.
the critical
temperature
of of
LLPS
determined
exactly
Opposite
to that ofAlthough
homogeneous
atom
pairs, the [19,20]
number
Cucannot
atomsbe
around
the Fe
atomby
is only
atoms prefer to accept the Fe atom as their neighbor and Cu atoms prefer to accept the Cu atom as
the
CN,
a
sudden
increase
of
homogeneous
pairs
and
decrease
of
heterogeneous
pairs
also
indicates
abouttheir
2 atneighbor.
700 K, inAlthough
agreement
with
the
behavior
observed
for
PPCFs.
Fe
atoms
prefer
to
accept
the critical temperature [19,20] of LLPS cannot be determined exactly by the
the occurrence of phase separation. The critical temperature is estimated roughly to be 2000 K, since
Fe atom
as their
neighbor
and
atoms prefer
accept
the of
Cuheterogeneous
atom as theirpairs
neighbor.
Although
the CN,
a sudden
increase
of Cu
homogeneous
pairstoand
decrease
also indicates
the obvious increase of CN for Cu–Cu and Fe–Fe pairs and the decrease for Cu–Fe pairs after 2000
the critical
temperature
[19,20]
of LLPS
determined
exactly by
the CN,
a 2000
sudden
increase
the occurrence
of phase
separation.
Thecannot
criticalbe
temperature
is estimated
roughly
to be
K, since
the obvious increase
of CN
for Cu–Cu
and Fe–Fe pairs pairs
and the
decrease
for Cu–Fe
pairs after 2000
of homogeneous
pairs and
decrease
of heterogeneous
also
indicates
the occurrence
of phase
separation. The critical temperature is estimated roughly to be 2000 K, since the obvious increase
Metals 2017, 7, 73
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Metals
7, 73 and Fe–Fe pairs and the decrease for Cu–Fe pairs after 2000 K can be observed
4 of 9
of CN
for2017,
Cu–Cu
from Figure 3. The total numbers around Cu neighbors, keeping almost unchanged during the whole
K can be observed from Figure 3. The total numbers around Cu neighbors, keeping almost
cooling process, is about 13.
unchanged during the whole cooling process, is about 13.
Metals 2017, 7, 73
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K can be observed from Figure 3. The total numbers around Cu neighbors, keeping almost
unchanged during the whole cooling process, is about 13.
Figure 3. Coordination number versus temperature at a cooling rate of 6.4 × 1012 K/s.
Figure 3. Coordination number versus temperature at a cooling rate of 6.4 × 1012 K/s.
The critical temperature is higher than the glass transition temperature of 800 K. It encourages
The
higher thanbetween
the glass
temperature
of 800 K.
It encourages
us tocritical
furthertemperature
explore the isrelationship
thetransition
phase separation
mechanism
and
the glass us
Figure 3. Coordination number versus temperature at a cooling rate of 6.4 × 1012 K/s.
to further
explore
relationship
between
phase undercooling.
separation mechanism
andit the
glass transition
transition
andthe
crystal
formation
under the
a certain
In addition,
is possible
to
investigate
the
effect
of
the
cooling
rate
on
the
formation
of
phase-separated
micro-structure.
The
and crystal
formation
under
a
certain
undercooling.
In
addition,
it
is
possible
to
investigate
the
The critical temperature is higher than the glass transition temperature of 800 K. It encourages effect
phase
separation
process
can be
explored
bythe
observing
the atommechanism
configuration
atthevarious
of theus
cooling
rateexplore
on the
formation
of phase-separated
micro-structure.
The
phase and
separation
process
to further
the relationship
between
phase
separation
glass
12 K/s, shown in Figure 4. For comparison, the atom
temperatures
at
the
cooling
rate
of
6.4
×
10
can be
explored
observing
the atom
at various In
temperatures
cooling
transition
andbycrystal
formation
underconfiguration
a certain undercooling.
addition, it at
is the
possible
to rate
11 K/s are also shown in Figures 5 and 6,
snapshot
theeffect
cooling
ratecooling
6.4 ×rate
1011 on
K/sthe
and
1.28 × 10of
investigate
the
of the
formation
phase-separated
micro-structure.
The rate
of 6.4
× 1012 atK/s,
shown
in of
Figure
4. For
comparison,
the
atom snapshot
at the cooling
respectively.
The configuration
seems
to be homogeneous
at 2800atom
K (Figure
4a), whileatit various
exhibits
11 K/s
process
be are
explored
by observing
configuration
of 6.4phase
× 1011separation
K/s and 1.28
× 10can
also shown
in Figuresthe
5 and 6, respectively.
The configuration
structural
heterogeneity
during
the
cooling
process
with
the
aggregation
of
Fe-rich
atom
12
temperatures
at the cooling
rateKof(Figure
6.4 × 10
K/s,
shown
in Figure
4. For comparison,
theclusters
atom the
seems
to be homogeneous
at 2800
4a),evident
while
ituntil
exhibits
structural
heterogeneity
during
among
the
Cu-rich
matrix.
The
LLPS
is
not
the
temperature
decreases
to
K,
snapshot at the cooling rate of 6.4 × 1011 K/s and 1.28 × 1011 K/s are also shown in Figures 51900
and 6,
cooling
process
with the
aggregation
of Fe-rich atom clusters
among
the Cu-rich
matrix.
The LLPS is not
shown
in
Figure
4c,
where
the
interconnected-type
structure
is
formed
by
spinodal
decomposition.
respectively. The configuration seems to be homogeneous at 2800 K (Figure 4a), while it exhibits
evident
until
the temperature
decreases
to 1900
K, shown
in Figure 4c,
wherethe
theinterfacial
interconnected-type
At the
primary
separation
period
during
theprocess
spinodal
decomposition
process,
energy
structural
heterogeneity
during
the
cooling
with
the aggregation
of Fe-rich
atom clusters
structure
is
formed
by
spinodal
decomposition.
At
the
primary
separation
period
during
the
spinodal
differences
between
two
liquids
are
quite
small
due
to
their
similar
initial
compositions,
and
among the Cu-rich matrix. The LLPS is not evident until the temperature decreases to 1900 the
K,
interconnected-type
structure
without
an
obvious
interface
can
be
formed
through
atom
diffusion.
decomposition
process,
the
interfacial
energy
differences
between
two
liquids
are
quite
small
shown in Figure 4c, where the interconnected-type structure is formed by spinodal decomposition.due to
After
the liquid
phase
withand
aduring
small
volume
fraction
will be
transformed
to ainterfacial
spherical
droplet
theirAt
similar
initial
compositions,
the interconnected-type
structure
without
an obvious
interface
the that,
primary
separation
period
the
spinodal
decomposition
process,
the
energy
because
of
the
increasing
composition
difference
between
two
liquids
[3].
The
interconnected-type
can be
formed through
diffusion.
Aftersmall
that,due
the to
liquid
a small
volume and
fraction
differences
between atom
two liquids
are quite
their phase
similarwith
initial
compositions,
the will
structure formed in structure
our simulation
system
is hardly
transformed
toformed
a spherical
droplet
due
to such
interconnected-type
without
an
obvious
interface
can
be
through
atom
diffusion.
be transformed to a spherical droplet because of the increasing composition difference between two
a highthat,
cooling liquid
rate, thus
it iswith
keptain
the glass
at low
temperature,
as shown in to
Figure 4d.
After
phase
small
volume
fraction
willsimulation
be transformed
droplet
liquids
[3]. Thethe
interconnected-type
structure
formed
in our
systemaisspherical
hardly transformed
because
of
the
increasing
composition
difference
between
two
liquids
[3].
The
interconnected-type
to a spherical droplet due to such a high cooling rate, thus it is kept in the glass at low temperature, as
structure formed in our simulation system is hardly transformed to a spherical droplet due to such
shown
in Figure 4d.
a high cooling rate, thus it is kept in the glass at low temperature, as shown in Figure 4d.
(a)
(b)
(c)
(d)
Figure 4. Atom snapshot of Fe50Cu50 at different temperatures at the cooling rate of 6.4 × 1012 K/s.
(a–d) correspond to the atomic configuration at temperature of 2800 K, 2200 K, 1900 K, 800 K,
(a)
(b)
(c)
(d)
respectively.
Figure 4. Atom snapshot of Fe50Cu50 at different temperatures at the cooling rate of 6.4 × 1012 K/s.
Figure 4. Atom snapshot of Fe50 Cu50 at different temperatures at the cooling rate of 6.4 × 1012 K/s.
(a–d) correspond to the atomic configuration at temperature of 2800 K, 2200 K, 1900 K, 800 K,
(a–d) correspond to the atomic configuration at temperature of 2800 K, 2200 K, 1900 K,
respectively.
800 K, respectively.
In contrast to the configuration at the cooling rate of 6.4 × 1012 K/s, the interconnected-type structure
is more pronounced. The crystallization temperature is about 1170 K at the cooling rate and the
interconnected-type structure is kept in the crystal, although some small Fe-rich droplets occur in
both liquid and solid. Generally speaking, the spherical droplet is still not totally formed due to the
relatively
higher cooling rate. However, what would happen if the cooling rate were further
Metals 2017, 7, 73
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decreased?
(a)
(b)
(c)
Metals 2017, 7, 73
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cooling rates mean higher glass transition temperature or lower crystallization temperature. The
diffusion of the homogeneous atom is too slow to form the droplet-like structure as it reaches the
glass transition temperature or crystallization temperature. Fe50Cu50 melt undergoes phase
separation by spinodal decomposition at three cooling rates. The droplet-type structure will be
formed as the cooling rate is relatively low; it cannot be formed finally as the cooling rate is
(d) Sohn [21] reported the LLPS
(e) process of Gd-Zr-Al-Ni melts
(f)
relatively large.
by spinodal
decomposition
when
the
degree
of
undercooling
is
relatively
large,
and
by
nucleation
and the
11 K/s.
Figure
5. Atom
Atom snapshot
snapshot of
of Fe
Fe50Cu
50 at different temperatures at the cooling rate of 6.4 × 1011
Figure 5.
50 Cu50 at different temperatures at the cooling rate of 6.4 × 10 K/s.
growth
mechanism
when
the degree
of undercooling
is relatively
low.
InK,our
opinion,
the1200
spinodal
(a–f)
correspond to
to
the atomic
atomic
configuration
temperature
2000K,K,
1800K,
1600
1400
(a–f) correspond
the
configuration
atattemperature
ofof2000
1800
1600
K,K,
1400
K,K,
1200 K,
decomposition
reaction
happens
in
Fe
50
Cu
50
melts
whether
at
the
higher
or
lower
cooling
rate,
K,
1000
K, respectively.
1000
K, respectively.
which only determine the final micro-morphology in crystal.
For comparison, we depict the atom configuration at various temperatures at the cooling rate of
1.28 × 1011 K/s in our simulation system, shown in Figure 6. The crystallization temperature that we
determined from the energy–temperature curve is about 1200 K. Despite the crystal formation at low
temperature, the atom configuration is quite different from that obtained at a higher cooling rate of
6.4 × 1011 K/s. The interconnected-type structure is the most pronounced among the three atom
snapshots. In contrast to the former two groups of configurations, the interconnected-type structure
disappears gradually, and a Fe-rich spherical droplet is formed, as shown in Figure 6a–f, although
the spheroidizing process is not completely finished. The crystallization process starts at
temperature of 1200 K. The final configuration is a mixture of all kinds of droplets with different
(a)
(b)
(c)
(d)
shapes. To summarize, Fe50Cu50 melt separates into Fe-rich liquid and Cu-rich liquid controlled by
the spinodal decomposition mechanism at a temperature of about 2000 K; the selection of
interconnected or droplet-type structure of the separated glass phases or crystal phases depends on
the cooling rate. Once the interconnected-type structure is formed, it cannot be broken easily
because of the limited atom diffusion under a certain undercooling at a higher cooling rate; high
(e)
(f)
(g)
(h)
11 K/s.
Figure6.6.Atom
Atomsnapshot
snapshotofofFeFe50Cu
Cu50at
atdifferent
differenttemperatures
temperaturesatatthe
thecooling
coolingrate
rateofof
1.28
11 K/s.
Figure
1.28
× ×1010
50
50
(a–h)correspond
correspondtotothe
theatomic
atomicconfiguration
configuration
temperature
2000
1800
1600K,K,1400
1400K,K,1200
1200K,
K,
(a–h)
at at
temperature
of of
2000
K,K,
1800
K,K,
1600
1100K,
K,1000
1000 K,
K, 800
1100
800 K,
K,respectively.
respectively.
We depict the atom configuration at various temperatures during the crystallization process at
We depict the atom configuration at various temperatures at the cooling rate of 6.4 × 1011
the cooling rate of 6.4 × 1011 K/s, shown in Figure 7. The system is still in a liquid state at the
K/s in our simulation system, shown in Figure 5. Although the spinodal decomposition reaction
temperature of 1180 K, and no solid nucleus can be found in Figure 7a. While a small nucleus with
Fe-rich composition can be observed in Figure 7b, the grain begins to grow around the nucleus along
the [110] crystal direction. The new nucleus forms at the temperature of 1150 K, shown in Figure 7d.
The number of nuclei is almost unchanged until the temperature is decreased to 1110 K. Only Fe-rich
clusters can act as the solid nuclei due to the higher melting point of Fe than that of Cu. The grain N1
Metals 2017, 7, 73
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happens at about 2000 K, no obvious sudden change in structure can be observed; the LLPS is
a continuous process. The homogeneous atom pairs begin to aggregate and the Fe-rich phase
precipitates in the liquid. The domain size of the new liquid phase becomes bigger and bigger
by spontaneous concentration fluctuation with decreasing temperature, as shown in Figure 5b–e.
In contrast to the configuration at the cooling rate of 6.4 × 1012 K/s, the interconnected-type structure
is more pronounced. The crystallization temperature is about 1170 K at the cooling rate and the
interconnected-type structure is kept in the crystal, although some small Fe-rich droplets occur in
both liquid and solid. Generally speaking, the spherical droplet is still not totally formed due to the
relatively higher cooling rate. However, what would happen if the cooling rate were further decreased?
For comparison, we depict the atom configuration at various temperatures at the cooling rate
of 1.28 × 1011 K/s in our simulation system, shown in Figure 6. The crystallization temperature that
we determined from the energy–temperature curve is about 1200 K. Despite the crystal formation
at low temperature, the atom configuration is quite different from that obtained at a higher cooling
rate of 6.4 × 1011 K/s. The interconnected-type structure is the most pronounced among the three
atom snapshots. In contrast to the former two groups of configurations, the interconnected-type
structure disappears gradually, and a Fe-rich spherical droplet is formed, as shown in Figure 6a–f,
although the spheroidizing process is not completely finished. The crystallization process starts at
temperature of 1200 K. The final configuration is a mixture of all kinds of droplets with different
shapes. To summarize, Fe50 Cu50 melt separates into Fe-rich liquid and Cu-rich liquid controlled by the
spinodal decomposition mechanism at a temperature of about 2000 K; the selection of interconnected
or droplet-type structure of the separated glass phases or crystal phases depends on the cooling rate.
Once the interconnected-type structure is formed, it cannot be broken easily because of the limited
atom diffusion under a certain undercooling at a higher cooling rate; high cooling rates mean higher
glass transition temperature or lower crystallization temperature. The diffusion of the homogeneous
atom is too slow to form the droplet-like structure as it reaches the glass transition temperature or
crystallization temperature. Fe50 Cu50 melt undergoes phase separation by spinodal decomposition at
three cooling rates. The droplet-type structure will be formed as the cooling rate is relatively low; it
cannot be formed finally as the cooling rate is relatively large. Sohn [21] reported the LLPS process of
Gd-Zr-Al-Ni melts by spinodal decomposition when the degree of undercooling is relatively large, and
by nucleation and the growth mechanism when the degree of undercooling is relatively low. In our
opinion, the spinodal decomposition reaction happens in Fe50 Cu50 melts whether at the higher or
lower cooling rate, which only determine the final micro-morphology in crystal.
We depict the atom configuration at various temperatures during the crystallization process
at the cooling rate of 6.4 × 1011 K/s, shown in Figure 7. The system is still in a liquid state at the
temperature of 1180 K, and no solid nucleus can be found in Figure 7a. While a small nucleus with
Fe-rich composition can be observed in Figure 7b, the grain begins to grow around the nucleus along
the [110] crystal direction. The new nucleus forms at the temperature of 1150 K, shown in Figure 7d.
The number of nuclei is almost unchanged until the temperature is decreased to 1110 K. Only Fe-rich
clusters can act as the solid nuclei due to the higher melting point of Fe than that of Cu. The grain N1
becomes the biggest one among all the grains. The solute redistribution at the liquid–solid interface
is restricted because of the high cooling rate. The solid morphology is quite similar to that of liquid,
as shown in Figure 7a–i.
Metals 2017, 7, 73
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Metals 2017, 7, 73
7 of 9
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 7. Atom snapshot of Fe50Cu50 during the crystallization process at the cooling rate of 6.4 × 1011 K/s.
Figure 7. Atom snapshot of Fe50 Cu50 during the crystallization process at the cooling rate of
(a–i) correspond to the atomic configuration at temperature of 1180 K, 1170 K, 1160 K, 1150 K, 1140 K,
6.4 × 1011 K/s. (a–i) correspond to the atomic configuration at temperature of 1180 K, 1170 K, 1160 K,
1110 K, 1100 K, 1090 K, 1060 K, respectively.
1150 K, 1140 K, 1110 K, 1100 K, 1090 K, 1060 K, respectively.
In addition, there are many twinning planes in the crystal as shown in Figure 7i. The interfaces
addition,
many
twinning
planesN1
in the
crystal as
shown
in Figure
The
interfaces
I1, I2,InI3,
I5 and there
I7 areare
the
boundary
of grain
connected
with
other
grains.7i.
The
nucleus
N1 I1,
is
I2,
I3,
I5
and
I7
are
the
boundary
of
grain
N1
connected
with
other
grains.
The
nucleus
N1
is
formed
formed at the temperature of 1170 K, a little higher than that of the other four grains at a temperature
at
temperature
of 1170the
K, ahomogeneous
little higher than
that
the other on
fourboth
grains
at aoftemperature
of
of the
1110
K. Surprisingly,
atoms
areof arranged
sides
the twinning
1110
K.
Surprisingly,
the
homogeneous
atoms
are
arranged
on
both
sides
of
the
twinning
boundary.
boundary. As we can see along the interface I1, the atomic stacking of Cu shows mirror symmetry
As
werespect
can seetoalong
the interface
I1,along
the atomic
stackingI2,
ofthe
Cu Fe
shows
mirror
symmetry
with respect
with
the adjacent
grains;
the interface
atoms
are arranged
symmetrically
to
the
adjacent
grains;
along
the
interface
I2,
the
Fe
atoms
are
arranged
symmetrically
both its
on both its sides. The grains N1, N2 and N3 are connected to each other, and three-foldon
symmetry
sides.
The
grains
N1,
N2
and
N3
are
connected
to
each
other,
and
three-fold
symmetry
twinning
twinning planes are formed, as shown in Figure 7i. The nuclei of grain N2 and N3 are formed at
planes
as shown inshown
Figurein7i.(f).
The
nuclei
of grain
N2 twinning
and N3 are
formed
almost the
almost are
the formed,
same temperature,
The
existence
of the
plane
mayatdecrease
the
same
temperature,
shown
in
(f).
The
existence
of
the
twinning
plane
may
decrease
the
interface energy, especially the coherent twinning interface. The different grains have interface
random
energy,
especiallyorientations,
the coherentseparated
twinning interface.
The different
grains have
crystallographic
by high-angle
grain boundaries.
Asrandom
shown crystallographic
in Figure 7i, the
orientations,
separated
by
high-angle
grain
boundaries.
As
shown
in
Figure
7i,
theand
orientation
angle
orientation angle between {110} planes of the adjacent grains marked with I1, I2
I3 is 155°,
65°,
◦ , 65◦ , and 92◦ respectively.
between
{110}
planes
of
the
adjacent
grains
marked
with
I1,
I2
and
I3
is
155
and 92° respectively. The three dihedral angles in our simulation system are 126°, 122°, and 112°; the
◦
◦ ; the deviation between the
The
three dihedral
in our simulation
system areangle
126◦ ,is122
deviation
betweenangles
the maximum
and the minimum
14°., and
This112
is due
to the high cooling rate;
there is not enough time and driving force for the grains to adjust their crystal orientations and
merge with each other.
Metals 2017, 7, 73
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maximum and the minimum angle is 14◦ . This is due to the high cooling rate; there is not enough time
and driving force for the grains to adjust their crystal orientations and merge with each other.
In summary, the crystallization process can be roughly divided into two stages. In the first state
(1110 K < T < 1180 K), a few nuclei emerge in the liquid matrix, and the size is quite small, and then it
grows quickly by consuming liquid atoms. Furthermore, the total energy decreases sharply. In the
following stage II (1110 K < T < 1060 K), a large number of nuclei emerge in the liquid matrix and the
total energy successively falls off; the total number of grains keeps unchanged at this stage. During
the rapid solidification process of LLPS melts, the twin crystal can be formed in two ways: the first
is that the two solid nuclei form at different temperatures—the one formed at higher temperature
grows quickly along a certain crystal direction, and becomes a bigger grain, the others formed at lower
temperature grow slowly and the grain size is smaller. There is a coherent interface between the edge
of the bigger one and the smaller ones, as shown in Figure 7i. The interfaces I1, I2, I3, I5 and I7 are the
twinning boundary formed by the grain N1 with another five smaller grains; the second is that the
two nuclei form at the same temperature and grow at almost the same rate. The two grains meet at the
grain boundary and form the coherent twining boundary, as shown in Figure 7i. The interface I6 is the
twinning boundary formed by the grain N2 and N3.
4. Conclusions
The liquid PCFs and CN, as well as the atom snapshot as a function of temperature during the
rapid solidification, are calculated by molecular dynamics simulation to explore the LLPS behavior
of Fe50 Cu50 melt from 3500 K to 300 K. Fe50 Cu50 melt undergoes LLPS in the undercooled regime by
spinodal decomposition and subsequently solidifies into three different morphologies at three different
cooling rates. At the cooling rate of 6.4 × 1012 K/s, the interconnected-type structure is kept in the
glass; at the cooling rate of 6.4 × 1011 K/s, the interconnected-type structure is more pronounced and
kept in the crystal, although some small Fe-rich droplets occur in both liquid and solid; at the cooling
rate of 1.28 × 1011 K/s, the droplet-type structure is formed in the crystal.
Only Fe-rich clusters can act as the solid nucleus; it emerges in the liquid matrix at the temperature
of 1170 K, and grows up quickly by consuming liquid atoms. A large number of nuclei emerge in the
liquid matrix at the temperature of 1110 K, and the total number of grains keeps unchanged during
the following crystallization process. We also find the twinning plane in the final crystal, and only
the homogeneous atoms are arranged along the twinning boundary, which is the typical feature of
phase separation crystal. The different grains have random crystallographic orientations, separated by
high-angle grain boundaries. There is not enough time and driving force for the grains to adjust their
crystal orientations and merge with each other. The solute redistribution at the liquid–solid interface is
restricted because of the high cooling rate.
Acknowledgments: The authors thank National Science Foundation of China (No. 51371108) for financial support.
The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing
Center, Shandong University, Weihai.
Author Contributions: Yun Cheng and Li Wang conceived and designed the experiments; Wenchao Cui,
Yuyang Wang and Yuncheng performed the experiments and analyzed the data; Chuanxiao Peng, Yun Cheng,
and Shenghai Wang contributed reagents/materials/analysis tools; Yun Cheng wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the
decision to publish the results.
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