Abstract. The microstructure and dynamic in aluminum-silicate melt has been studied using
molecular dynamics (MD) simulation. The model consisting of 5500 particles and using
Born–Mayer potentials has been constructed at a temperature of 3500 K and pressure varing
from 0-20 GP. The analysis is carried out for separate subsets of oxygen, silicon and
aluminum. Further, we use the simplex to clarify the structure heterogeneity. The simulation
reveals two patterns of atom movement: the free motion for aluminum and the correlation
motion for oxygen and silicon. The dynamics heterogeneity (DH) is found for the lowpressure configuration of the melt. The mechanism of densification to the melt is presented and
discussed.

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2017-0042
Mathematical and Physical Sci. 2017, Vol. 62, Iss. 8, pp.142-147
This paper is available online at
THE DYNAMIC HETEROGENEITY OF ALUMINUM-SILICATE
UNDER COMPRESSION
Nguyen Thi Thanh Ha, Mai Thi Lan and Pham Khac Hung
Department of Computational Physics, Hanoi University of Science and Technology
Abstract. The microstructure and dynamic in aluminum-silicate melt has been studied using
molecular dynamics (MD) simulation. The model consisting of 5500 particles and using
Born–Mayer potentials has been constructed at a temperature of 3500 K and pressure varing
from 0-20 GP. The analysis is carried out for separate subsets of oxygen, silicon and
aluminum. Further, we use the simplex to clarify the structure heterogeneity. The simulation
reveals two patterns of atom movement: the free motion for aluminum and the correlation
motion for oxygen and silicon. The dynamics heterogeneity (DH) is found for the low-
pressure configuration of the melt. The mechanism of densification to the melt is presented and
discussed.
Keywords: Molecular dynamic, dynamics heterogeneity, structure, immobile and mobile.
1. Introduction
Silicate liquids play a signiﬁcant role in many geochemical and geophysical phenomena [1-6].
The silicate liquids have certain peculiar properties. That is, silica-rich liquids have negative
pressure dependence (diffusion anomaly) on shear viscosity although silica-poor liquids have
positive pressure dependence [2, 7-8]. Further, silica liquids exhibit dynamics heterogeneity (DH)
and dynamical slowdown near the glass transition point [9-11]. It was shown that there are
distinguishable regions where the mobility of atoms is fast or slow. To clarify the mechanism at
the atomic level on DH and diffusion anomaly molecular dynamics (MD) simulation is widely
used. Numerous MD simulation studies have attempted to clarify the dependence of silicate liquid
on negative pressure [12-14]. DH has been detected by multi-correlation function, visualization
and analysis of specific subset of particles [15-17]. The experimental and simulation results show
that TOx the structure of SiO2, GeO2, and Al2O3 comprises basic structural units TOx (Here T is the
cation (Si, Al, Mg ...); (x = 4, 5, 6) [18-20].
In recent decades, aluminum-silicate has been studied. However because our knowledge of
their microstructure and dynamic is still quite limited, more studies are needed [17, 21, 22]. In
this work, the microstructure, DH and structure heterogeneity of aluminum-silicate liquid at five
different pressure conditions have been investigated using the MD method. The aim of this work
is to clarify the origin of DH in aluminum-silicate.
Received December 7, 2016. Accepted August 24, 2017.
Contact Mai Thi Lan, email: ha.nguyenthithanh1@hust.edu.vn
The dynamic heterogeneity of aluminum-silicate under compression
143
2. Content
2.1. Computational procedure
MD simulation is conducted for 5500-atom models (1000 Si, 3500 O and 1000 Al atoms)
with periodic boundary conditions. The Born-Mayer type pair potential used here is given as [21]
ij
ijjiij
R
r
B
r
e
zzru exp
2
Initial configuration was generated by random placing of all atoms in a simulation box. This
configuration is heated to 6000 K. A well-equilibrated model (M1) has been constructed at a
temperature of 3500 K at ambient pressure (0 GPa). The model at ambient pressure has been
compressed to different pressures and then relaxed for a long time to reach the equilibrium. In this
way, four models compressed to 5, 10, 15 and 20 GPa are constructed.
Fig. 1. The schematic illustration of linkage and cluster
a) a linkage, b), c), d) clusters and set of 5 atoms
We employ simplexes and linkages. Two atoms have a linkage, if their distance is less than a
defined distance rlk. Here rlk is equal to 4.5 and 5.63 Å for oxygen and the cation (silicon or
aluminum), respectively. A cluster is defined as a set of atoms where each atom connects to
another one through a path consisting of linkages. The maximal number of linkages for an cluster
comprising m atoms is m(m-1)/2. The size of the cluster is defined by the number of atoms in the
cluster. Fig.1 schematically represents the linkage and cluster. One can see that the cluster with 9
linkages (Fig.1c) can be placed in a smaller volume than the cluster with 5 linkages (Fig.1b),
although the number of atom in both clusters is equal to 5. Moreover, a set of five atoms forming
three small clusters has only 4 linkages (Fig.1d). Therefore, the number of linkages characterizes
the clustering of atoms and packing of cluster in the space.
We consider the subset of 10% atoms which have highest mean square displacement <rt
2
>
(mobile atoms). Here <rt
2
> are determined from the positions of mobile atoms in a starting
configuration and the configuration at time t. Then we find the clusters and linkages for mobile
atoms in the starting configuration. We also conduct the same analysis of 10% of the atoms taken
b)
d) c)
r < rlk
a)
Nguyen Thi Thanh Ha, Mai Thi Lan and Pham Khac Hung
144
Fig.3. The time dependence of and NCL for the subset of oxygens (left) and the
distributions of cluster size for configuration at 96.5 ps for the subset of oxygens (right) at
0 GPa
0 20 40 60 80 100
40
80
120
160
0.0
0.5
1.0
1.5
2.0
N
C
L
The time, ps
A1 A2 A3
<
N
LK
>
0 10 20 30 40 50 60 70 80
0
20
40
60
80
0
20
40
60
80
100
A1 A3T
he
n
um
be
r
of
c
lu
st
er
s
The size of cluster
A1 A2
96.5 ps
randomly from the system. A comparison between two subsets of mobile and random atoms
provides the clustering of mobile atoms. We also examine the clustering for the subset of
immobile atoms which have lowest square displacement <rt
2
>. For convenience we denote the
subset of random, immobile and mobile atoms to A1, A2 and A3, respectively. We analyze the
subset of oxygen, silicon and aluminum separately. This allows a clarification of the role of
different sort atoms for the specific pattern of atom motion. Hence, the subset of oxygen atoms
contains 350 atoms; while the subset of aluminum or silicon has 100 atoms
2.2. Results and discussion
The time dependence of characteristics for the subset of oxygens at ambient pressure is
shown in Fig. 2 and 3. Here <rt
2
> is the mean square displacement; NCL is the number of clusters;
is the mean number of linkages per atom. Within 96.5 ps the mobile atoms make on
average a displacement of 5.83 Å, while the immobile atoms move over 0.49 Å. Focusing first on
NCL and we find that those quantities for immobile and mobile atoms significantly differ
from that for random atoms. In particular for A1 is always smaller; but NCL in contrast is
larger than that for A2 and A3. This is clear evidence of a clustering of atoms of A2 and A3. Such
clustering is also evidenced from the size distribution of cluster.
Fig. 2. The time dependence of <rt
2
> for A1, A2, A3 oxygen subsets and all oxygen atoms at 0 GPa
0 20 40 60 80 100
0
5
10
15
20
25
30
35
<
r t
2
>
,
Å
2
Time, ps
All oxygens
A
1
A
2
A
3
The dynamic heterogeneity of aluminum-silicate under compression
145
As shown in Fig.3, the size distribution for A1 is spread in a narrow interval from 1 to 14
atoms. The number of one-oxygen clusters (clusters with one oxygen) is bigger than 80. In
contrast to A1, the number of one-oxygen clusters for A2 and A3 is about 40 which is half as small.
Moreover, A2 and A3 form a number of clusters having more 20 atoms. This difference indicates
that the mobile and immobile atoms tend to form larger clusters. As a result, of those atoms
is bigger and NCL is smaller than that of random atoms. It follows that the dynamics of oxygen is
spatially heterogeneous. Regarding silicon and aluminum we find the similar behaviors. Namely,
NCL for A1 is bigger and is smaller than that for A2 and A3 (see Fig.4). Therefore, within
the timeframe of this study DH is also observed for both aluminum and silicon. In Fig.5 we plot
the time dependence of NCL for oxygen subsets in high-pressure configurations. As the pressure
becomes larger 5 GPa, NCL for A1 is closer to that for A2 and A3. Similar behavior is observed for
silicon and aluminum subsets. This means that DH is not observed for high-pressure configuration
within the timeframe of this study.
To clarify the pattern of atom motion we examine the neighbors for atoms of subsets A1, A2
and A3 in the configuration at ambient pressure. The neighbor is defined as the atom that forms a
linkage with the given atom. Then we determine the mean square displacement <rt
2
> for
neighbors while the average number of neighbors for atoms of subsets was considered.
The result is shown in Fig.6 and 7. One can see that <rt
2
> decreases in the order: A2 - A1 - A3. This
means that the neighbors of mobile atoms move quickly, but the neighbors of immobile atoms
move slowly. It follows that the mobile atoms tend to locate in micro-regions where atom
mobility is large. The immobile atoms in contrast, are in micro-regions where the atom mobility is
small. Obviously this indicates DH. The existence of micro-regions with different mobility is
related to structural heterogeneity in the liquid. This fact is evidenced from the mean number of
neighbors shown in Fig.7. One can see that for oxygen and aluminum of A3 is bigger than
that of A1 and A2. The of A2 is smaller than A1. In the case of the silicon subset,
for A1 is close to A2, but the value of this quantity for A3 is smaller than it is for A1 and A2. Thus,
the atom motions in the liquid are correlated which is caused by the structure heterogeneity.
Fig. 4. The time dependence of NLKCL and for aluminum and silicon subsets at 0 GPa
0 20 40 60 80 100
20
40
60
80
20
40
60
80
N
L
K
C
L
Silicon
A
1
A
2
A
3
Time, ps
Aluminum
0 20 40 60 80 100
0.3
0.6
0.9
1.2
0.3
0.6
0.9
1.2
Time, ps
<
N
L
K
>
Silicon
A
1
A
2
A
3
Aluminum
Nguyen Thi Thanh Ha, Mai Thi Lan and Pham Khac Hung
146
To obtain more details about the correlation motion we find A2 and A3 in the configuration at
t = 95.6 ps (final configuration). Then we find all neighbors for atoms of A2 and A3 in the starting
configuration. Let Bi be the subset of neighbors that correspond to Ai (i = 2, 3). Next we find the
linkages between atoms from Ai and Bi in the starting configuration. These linkages are denoted to
Fig.5. The time dependence of NLK for the oxygen subsets in the high-pressure configurations.
0 20 40 60 80 100
80
120
160
80
120
160
The time, ps
N
C
L
5GPa
A1 A2 A3
10GPa
0 20 40 60 80 100
15GPa
A1 A2 A3
20GPa
Fig. 7. The time dependence of averaged number
of neighbors of A1 , A2 and A3
Fig. 6. The mean square displacement for
neighbors of A1 , A2 and A3 as a function of time
20 40 60 80 100
0
2
4
0
4
8
12
4
8
12
16
The time, ps
<
r t
2
>
,
A
2
Aluminum
Oxygen
A1 A2 A3
Silicon
0 20 40 60 80 100
7
8
9
11
12
13
14
6
8
10
12
The time, ps
Silicon
Oxygen
T
h
e
a
v
e
ra
g
e
d
n
u
m
b
e
r
o
f
n
e
ig
h
b
o
rs
,
<
N
N
G
H
>
Aluminum
A1 A2 A3
The dynamic heterogeneity of aluminum-silicate under compression
147
initial linkage. At 95.6 ps the atoms from subsets are thought to lose a part of their initial linkage
due to atom rearrangement. Next we determine the clusters in the final configuration which are
formed by the initial linkages. For example, we find a cluster form of atoms 1 and 2 from A2 and 4,
and 5 from B2 in the final configuration. In addition this cluster is formed by initial linkages 14, 15
and 25. This means that there is a cluster in the starting configuration which is formed by atoms 1,
2, 4 and 5 and linkages 14, 15 and 25. A calculation shows that clusters found from A2 and B2
consists of slow atoms. Meanwhile clusters from A3 and B3 shows a motion of fast groups of
atoms. We found a number of large clusters of slow atoms and the movement of fast atoms by
groups. This phenomenon is caused by the correlation of motion mentioned above.
3. Conclusions
The structure and dynamics of aluminum-silicate melt were investigated using new analysis
on MD models. We used the linkages and clusters consisting of atoms of the same sort. The DH
has been detected by comparing the characteristics of subsets of mobile, immobile and random
atoms. We separately examined the subsets of oxygen, aluminum and silicon atoms. The DH is
observed for all subsets in the low-pressure configurations. We found that the atom motion in
these configurations is spatially correlated. That is, the neighbors of fast atoms move an average
distance that is significantly larger than the neighbors of slow atoms. This result indicates the
existence of separate regions where atom mobility is quite different. That the averaged number of
neighbors for fast atoms is larger than that for slow atoms is clear evidence of structural
heterogeneity in the liquid. The correlated motion is responsible for both the DH and the diffusion
anomaly observed.
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