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Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids
journal homepage: www.elsevier.com/locate/jnoncrysol
Effect of pressure on the structure of Ti75Al25 alloy during rapid-quenching
process
X.Y. Wanga, S.L. Zhanga, S.D. Fengb, L. Qib, R.P. Liub,
a
b
⁎
Key Laboratory for Microstructural Material Physics of Hebei Province, Yanshan University, Qinhuangdao 066004, PR China
State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords:
Ti75Al25 alloy
High pressure
Molecular dynamics simulation
H-A indices
Amorphous phase
The structures of the Ti75Al25 alloy during rapid-quenching with and without external pressure are investigated
by using molecular dynamic techniques. The amorphous phase can be obtained at the cooling rate 10.0 K/ps
without pressure. The alloy is composed of crystal and amorphous phase at the cooling rate 0.1 and 1.0 K/ps
without pressure, but the pure amorphous phase can be formed when the pressure exceeds the critical value. The
critical pressure is about 20 and 30 GPa when the cooling rate is 0.1 and 1.0 K/ps, respectively. H-A indices
analysis indicates that high pressure favors the formation of the ideal icosahedral structures in the amorphous
Ti75Al25 alloy, and the content of 1551 bond-type can reach near to 50% when the pressure is 30 GPa. The
amorphous state can be maintained if the external pressure is removed from the alloy step-by-step. The content
of 1551 bond-type decreases with the deceasing of the pressure, but the 1541 and 1431 bond-types increase in
this process.
1. Introduction
Bulk metallic glasses (BMGs) have a series of superior mechanical
properties compared to their crystalline counterpart, including: high
strength, high hardness and high corrosion resistance [1–3]. Most of
BMGs are obtained by rapid-quenching technology at very high cooling
rates [4–6]. Especially for binary alloy, only limited alloy systems, such
as CueZr [7–9], NbeSi [10] and PdeSi [11, 12] can be experimentally
formed into BMGs. How can obtain BMGs at relative low cooling rates,
particularly for the alloy systems with very weaker amorphous formation ability? Besides alloy compositions and cooling rates, the microstructures of the alloy during the rapid solidification process are also
affected by the external hydrostatic pressure. It is an important parameter for controlling and affecting vitrification and crystal nucleation
during the quenching process [13–15]. Qu et al. investigated the solidification mechanism of the alloy under high pressure and found that
the high-pressure can promote nucleation, decrease the diffusion coefficient and inhibit the growth of grains [16]. However, it is difficult to
study the pressure effect on glass transition experimentally. In recent
years, some scholars use molecular dynamics simulation to study this
problem [17, 18]. Kazanc et al. studied the rapid solidification of liquid
CuNi alloys by using the molecular dynamic simulation method [19].
Their results indicated that high pressure can favor glass formation and
different pressure values can led to different glass transition
⁎
temperatures. Researches on pure zirconium also show that appropriate
pressure can promote the formation of amorphous phases [20].
TieAl alloys are of both technical and theoretical interest because
their excellent mechanical properties [21, 22]. However, there has few
report on how the pressure affects the solidification process of the
TieAl binary alloys. Thus, in this work, we utilized MD simulations to
study the microstructure evolution of Ti75Al25 alloy during rapid solidification under different pressure.
2. Method
The simulations were performed using large-scale atomic/molecular
massively parallel simulator (LAMMPS) [23, 24]. The initial random
model contained 10,000 atoms, and the ratio of Ti and Al atoms was
3:1. The embedded-atom model (EAM) was developed for the TieAl
alloys to describe the interatomic interactions in a many-body framework [25]. Fifteen independent simulations were performed for each
state point for the ensemble average. Firstly, we equilibrated the model
with 3D periodic boundary conditions (PBC) for 500 ps at 2600 K,
which is above the melting point of the alloy. Secondly, the model was
cooled from 2600 K to 300 K at MD cooling rates 0.1, 1.0 and 10.0 K/ps,
respectively. These processes were carried out for different pressure
values (0, 5, 10, 15, 20, 25, 30 GPa), respectively. The NPT ensemble
(constant number, constant pressure, and constant temperature) was
Corresponding author.
E-mail address: wangxiaoying@ysu.edu.cn (R.P. Liu).
https://doi.org/10.1016/j.jnoncrysol.2018.08.001
Received 19 April 2018; Received in revised form 27 July 2018; Accepted 2 August 2018
0022-3093/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Wang, X.Y., Journal of Non-Crystalline Solids (2018), https://doi.org/10.1016/j.jnoncrysol.2018.08.001
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
X.Y. Wang et al.
energy changes continuously with temperature when the cooling rate is
10 K/ps, representing the typical character of a liquid-glass transition
[21]. The glass transition temperature (Tg) can be defined by extrapolating and intersecting two linear parts in the potential energy versus
temperature curve. The inset in Fig. 1 shows Tg of the Ti75Al25 MG is
about 840 K at the cooling rate of 10 K/ps. When the cooling rate is
1.0 K/ps, the feature of the cooling curve was between the former two.
It indicates that the final solids maybe composed of amorphous and
crystalline phases.
Fig. 2(a–c) demonstrate the g(r) curves of the alloy with decreasing
temperature from 1700 K to 300 K under different cooling rates, and it
is obviously that the structure of the alloy is in liquid phase at 1700 K.
For all cooling rates, with decreasing temperature, the first peak gradually becomes higher and sharper, and the bottom between the first
and the second peak of the g(r) becomes deeper. As can be seen from
Fig. 2(a) and (b), the g(r) curve shows typical crystal structure when the
temperature decreased to 300 K. When the cooling rate is 10 K/ps, the
very slightly split in the second peak can be observed when the temperature is 900 K, and the bottom between the separated peaks becomes
deeper with the decrease of temperature. After the simulated system
was quenched into the glass state, splitting of the second peak is finally
turns into two subpeaks. This result shows that the final structure of the
alloy is amorphous phase.
RDF only reflects the statistical average distributions of atoms on
the one-dimensional scale and cannot reflect local atomic configurations on the three dimensional space. So, we adopt the H-A band-type
indices method to describe and analyze the microstructure transitions
of the alloy. Fig. 3 illustrates the variation of relative numbers of main
bond-types during the cooling process with the temperature changing
from 1700 K to 300 K under the cooling rate 0.1, 1.0 and 10.0 K/ps,
respectively. In Fig. 3(a) and (b), the 1421 bond-type increases suddenly at the temperature 900 K and 700 K, respectively. This result
suggests that the alloy began to crystallize at this temperature. The total
content of the 1421 and 1422 bond-types reaches 83% at 300 K when
cooling rate is 0.1 K/ps, while it is only 52% when the cooling rate is
1 K/ps. At the cooling rate 10.0 K/ps, the 1551 and 1541 bond-types
increase with the decreasing of the temperature, but the 1431 bondtype shows barely change. The total content of 1551, 1541, and 1431
bond-types at 300 K showed in Fig. 3(c) is about 63%, and it suggest
that the solid is amorphous phase.
used for quenching. The temperature is controlled using a Nose–Hoover
thermostat [26]. The Andersen method is applied to control pressure in
every direction [27]. The velocity–Verlet algorithm was used to integrate the motion equation with a time step of 1.0 fs. During the rapid
solidification, atomic positions and other relevant data in the system
were recorded with an interval of 100 K. Finally, the effect of pressure
on the glass formation and crystallization of Ti75Al25 alloy was obtained
by radial distribution function (RDF) and H-A bond-type indices
methods.
The RDF has been widely used to describe the structure characterization of liquid and amorphous phases. It is defined as
g (r ) =
V
N2
∑i ni (r )
4πr 2Δr
(1)
here r is the radial distance, ni(r) is the coordination number of atom i
separated with r within Δr interval, and brackets denote the time
average [19].
The H-A band-type indices method is widely used to describe and
analyze the microstructure transitions of liquid and amorphous alloys
[21]. In the pair analysis technique, two atoms are regarded as a bondpair if their distance is less than the cut-off radius. A sequence of four
integers (i j k l) is designed to describe the different microstructures: (i)
the first integer i indicates the root pair; (ii) the second integer j denotes
the number of near-neighbors shared by the root pair; (iii) the third
integer k represents the number of the nearest-neighbor bonds among
the shared neighbors; and (iv) the fourth integer l is used to distinguish
configurations with the same first three indices but with different
geometries. Different structures have different H-A indices, and the
general observations are as follows: 1551 bond-type gives a measure of
the degree of ideal icosahedral structure. 1541 and 1431 bond-types are
relative to the defective icosahedral structures. 1421 and 1422 are
characteristic bond-types of fcc and hcp crystal structures, respectively.
1661 and 1441 are characteristic bond-types of bcc crytstal structure.
3. Results and discussion
3.1. The case without pressure
The solidification process of the Ti75Al25 alloy without pressure was
analyzed firstly. The temperature dependence of the average atomic
potential energy during the quenching of Ti75Al25 liquids under different cooling rates is displayed in Fig. 1. The sudden drop of the potential energy can be seen when the cooling rate is 0.1 K/ps, which
corresponds to a liquid-crystal transition. However, the potential
3.2. The case with pressure
As described above, Ti75Al25 alloy forms amorphous phase at
cooling rate 10.0 K/ps under 0 GPa, but crystal phase is formed at the
cooling rates 0.1 and 1.0 K/ps. As all know, the structures of the alloy
during cooling process are highly affected by pressure. So, we want to
know if the amorphous structure can be formed at a low cooling rate by
adding pressure on the sample during cooling process? Fig. 4(a) and (b)
show the average atomic potential energy during the quenching of
Ti75Al25 liquids with different pressure at cooling rates 0.1 and 1 K/ps,
respectively. It can be seen from Fig. 4(a) that the crystallization temperature increases with the increasing of the pressure when the pressure
is less than 20 GPa. When the pressure is greater than 20 GPa, the
crystallization temperature decreases with the increasing of the pressure. However, the sudden drop of the cooling curve disappears when
the pressure reaches 30 GPa. It suggests the final structure of solid is
amorphous phase, and Tg is about 1260 K determined by the method
described in the part 3.1. In other words, the critical pressure for
amorphous transformation of the Ti75Al25 alloy at the cooling rate
0.1 K/ps is about 30 GPa. Compared with Fig. 4(a), (b) shows the different result. The amorphous transformation occurs when the pressure
reaches 20 GPa. It indicates that the critical pressure for amorphous
transformation decrease with the increasing of the cooling rate. The
glass transition temperature (Tg) is about 1086, 1194 and 1309 K when
the pressure is 20, 25 and 30 GPa, respectively. It is clearly that Tg
Fig. 1. Potential energy vs temperature at different cooling rate without pressure.
2
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
X.Y. Wang et al.
Fig. 2. RDF of Ti75Al25 alloy under different cooling rate without pressure: (a) 0.1 K/ps; (b) 1.0 K/ps; (c) 10 K/ps.
pressure on the sample during cooling process. How to explain this
phenomenon from physics perspective? Usually, the applied pressure
on the alloy has three effects. The first is densification, and it can favor
the crystallization process because the crystallization of the alloy involves densification. The second effect is to reduce atomic mobility,
which constrains atomic diffusion in the alloy. This will strongly affect
the crystallization process of the alloy. The last effect is that the pressure can change the Gibbs free energy of the amorphous and crystalline
phases. This could change the relative number of crystalline phases in
the alloy. Yang et al. gave a formula to describe the effect of the
pressure on the crystallization process of the alloy [29]:
increases with the increasing of the pressure under a certain cooling
rate.
Fig. 5 compares the g(r) curves of the alloy at 300 K with different
pressure values. With increasing pressure, the positions of the maximum are shifted to lower values. Splitting of the second peak which
represents the formation of amorphous can be found in Fig. 5(a) when
the pressure is 30 GPa, and it happens at 20, 25 and 30 GPa in Fig. 5(b).
Meanwhile, all the other g(r) curves show that the system contains
crystal phases. According to the above results, the amorphous phase can
be formed at a relative low cooling rate by increasing the pressure
during cooling process.
In order to determine the structure characteristics of the alloy
formed under different pressure, we analyzed the content of the main
bond-types of the alloy (shown in Fig. 6). It can be seen that the content
of the 1421 bond-type reaches its maximum (75%) when the pressure is
5 GPa in Fig. 6(a), and it is 80% when the pressure is 10 GPa in
Fig. 6(b). The content of the 1421 and 1422 all reduce to zero when the
pressure reaches its critical value. It also can be seen from Fig. 6 that
the 1551 bond-type in the solid increases suddenly when the pressure
reaches the critical pressure, but the content of the 1541 and 1431
bond-types decrease. The content of 1551 bond-type under the pressure
30 GPa shown in Fig. 6(a) and (b) is about 47% and 48%, respectively.
It is much higher than that shown in Fig. 3(c) (about 17%). Qi et al. also
found that a more compacted local structure with more ideal icosahedra
than defected icosahedra can be obtained in PdeNi alloy under high
pressure [28]. This result suggests that the amorphous structure obtained at a low cooling rate under high pressure is different from that
obtained at a high cooling rate without pressure.
From the above results, it is actual for Ti75Al25 alloy that the
amorphous structure can be formed at a low cooling rate by adding
3
⎛ ∂G ⎞ = ⎛ ∂ (ΔG + Qn ) ⎞ = − 32πσ ⋅ Vc − Vam + ⎛ ∂Qn ⎞
∂P
3
(Gc − Gam )3
⎝ ∂P ⎠T
⎝ ∂P ⎠T ⎝
⎠T
(2)
in this formula:
ΔG =
16πσ 3
3(Gc − Gam )2
(3)
where G is the nucleation activation energy, and ΔG is the thermodynamic potential barrier of nucleation, Qn is the diffusion activation
energy, and σ is the interfacial energy (assuming it is independent of
pressure). Vc and Vam are the mole volumes of the amorphous alloy and
its crystallization phase, respectively. Gc and Gam are the Gibbs free
energy of the amorphous alloy and crystallization phase per unit volume, respectively. Because of Vam > Vc and Gc < Gam, the first term
in Eq. (2) is always negative. It implies that the pressure is beneficial to
crystallization. The second term in Eq. (2) is always positive and usually
increases with increasing pressure. It implies pressure retards crystallization. Therefore, the nucleation activation energy of the Ti75Al25
alloy increases when the value of the second term in Eq. (2) is larger
3
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
X.Y. Wang et al.
Fig. 3. H-A indices of Ti75Al25 alloy under different cooling rate without pressure: (a) 0.1 K/ps; (b) 1.0 K/ps; (c) 10 K/p.
Fig. 4. Potential energy vs temperature at different cooling rate with external pressure: (a) 0.1 K/ps; (b) 1.0 K/ps.
than that of the first one. Therefore, a qualitative conclusion can be
obtained through the Eq. (2), the crystallization process of the Ti75A25
alloy will be suppressed when pressure exceeds the critical value.
decreasing of the pressure, but the content of 1541 and 1431 bondtypes increase gradually. The total content of the 1551, 1541 and 1431
bond-types almost remains unchanged, and it is about 70%. This results
suggest that some ideal icosahedral structures transformed into the
defective icosahedral structures, but the final structure of the alloy is
still amorphous when the pressure decreases to 0 GPa. In other words,
the amorphous phase obtained during rapid solidification under high
pressure can be maintained when the pressure is removed.
3.3. The structure after removing pressure
Can the amorphous phase formed under high pressure be maintained after removing the pressure? We analyzed the change of the H-A
indices of the amorphous alloy during the external pressure decreased
from 30 GPa to 0 GPa. The pressure reduced 5 GPa per step, and then
the system runs for 100 ps at every pressure. It can be seen from Fig. 7
that the content of 1551 bond-type decreases remarkably with the
4. Conclusion
Based on the MD results of the rapid solidification of liquid Ti75Al25
4
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
X.Y. Wang et al.
Fig. 5. RDF of Ti75Al25 alloy at 300 K cooling at different rate under external pressure:
(a) 0.1 K/ps; (b) 1.0 K/ps.
Fig. 6. Relative number fi of main H-A bond-types at 300 K with different external pressure: (a) 0.1 K/ps; (b) 1.0 K/ps.
Fig. 7. The change of the relative number fi of main H-A bond-types during removing external pressure at 300 K: (a) 0.1 K/ps; (b) 1.0 K/ps.
(2) High pressure favors the formation of the ideal icosahedral structures in the amorphous Ti75Al25 alloy. The content of 1551 bondtype in the amorphous alloy formed under high pressure is much
more than the content of 1541 and 1431 bond-types.
(3) The amorphous state can be maintained if the external pressure is
removed from the amorphous alloy, but the amorphous bond-types
of the alloy change in this process. The content of 1551 bond-type
decreases with the deceasing of the pressure, but the content of
alloy at different cooling rates under high pressure, the following
conclusions are obtained:
(1) There is a critical pressure for amorphous transformation at the
certain cooling rate for Ti75Al25 alloy. The critical pressure is about
20 and 30 GPa when the cooling rate is 1.0 and 0.1 K/ps, respectively. The amorphous structure can be obtained when the pressure
exceeds the critical value during the cooling process.
5
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
X.Y. Wang et al.
1541 and 1431 bond-types increases in the process.
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Acknowledgments
This work was supported by the National Natural Science
Foundation of China (Grant No. 51531005, 51671166, and 51571174).
Natural Science Research Projects in Colleges and Universities in Hebei
province (Key Program: ZD2015048).
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