Available online at www.HighTechJournal.org HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 207 ISSN: 2723-9535 Characterization of Structural Transition and Heterogeneity under Compression for Liquid Al2O3 Using Molecular Dynamics Simulation Pham Huu Kien 1 , Tran Thi Quynh Nhu 1, 2, Giap Thi Thuy Trang 1* 1 Department of Physics, Thainguyen University of Education, No. 20 Luong Ngoc Quyen, Thainguyen, Viet Nam. 2 Tuyen Quang High School for Gifted Students, Tran Hung Dao Street, Tuyenquang, Viet Nam Received 25 December 2021; Revised 13 February 2022; Accepted 18 February 2022; Available online 24 February 2022 Abstract We have performed a simulation of the structural transition and Structural Heterogeneity (SH) in liquid Al2O3 at 3500 K, in the range of 0–100 GPa. The results confirmed that the network structure of liquid alumina is built mainly from AlOx (x = 3, 4, 5, 6, 7) units, which are related to each other through the common oxygen atoms. The existence of separate AlO3-, AlO4-, AlO5-, AlO6- and AlO7- phases, where SH of the network structure can be sufficiently determined, besides, the existence of separate phases is clarified for SH in the liquid of Al2O3. In particular, at a pressure below 10 and beyond 20 GPa, AlOx units are uniformly distributed in the space and non-uniformly distributed in the range 10-20 GPa. Our study is expected to contribute to a simple way to determine the structural heterogeneity and diffusion coefficients of oxide systems. Keywords: Molecular Dynamics; Liquid; Network Structure; Phase; Cluster; Structural Transition. 1. Introduction Recently, Al2O3 has become well-known as the refractory ceramic oxide used in numerous applications, such as electronic devices, optics, and mechanical engineering, biomedical engineering, and cutting tools. Thus, liquid Al2O3 has become of great interest to researchers through both experimental and theoretical developments [1-9]. For instance, by using X-ray diffraction and scattering, Waseda et al. [10] and Ansell et al. [11] revealed that the two first peaks of the total radial distribution function (RDF) located at 2.0 and 2.8 Å as the density of 3.01 g.cm-3 and 1.76, 3.08 Å as the density of 3.175 g.cm-3. The averaged coordination number of the Al-O pair is equal to 4.5 ± 0.1. Besides, Hennet et al. [12] found out the first-, second- and third-peaks of RDF gAl-O(r) are located at 1.80 ± 0.02, 3.18 ± 0.06 and 4.36 ± 0.01 Å, respectively. These averaged coordination number of Al-O pair is approximately estimated to be 4.3 ± 0.05. To support experimental methods, simulation is also a powerful method to investigate the microstructure of melts, especially at high-temperature and/or pressure conditions [13-19]. According to the first-principles molecular dynamic (MD) simulations, Verma et al. [8] determined that the liquid Al2O3 is more sensitive to the applied compression than the temperature. The coordination number of Al atoms includes various species with disappearing three- and four- coordinated and appearing six- and seven-coordinated since the liquid is compressed. Skinner et al. [20] indicated that the melt consisted predominantly of AlO4 and AlO5 units. It can be noted that Al-O-Al connections of 83% are involved in the corner-sharing polyhedra, compared to 16% for the edge-sharing polyhedral. Miguel et al. [21] found that more than 50% of Al atoms are tetrahedral coordinated at four different temperatures. According to Hoang et al. * Corresponding author: tranggtt@tnue.edu.vn http://dx.doi.org/10.28991/HIJ-2022-03-02-08  This is an open access article under the CC-BY license (https://creativecommons.org/licenses/by/4.0/). © Authors retain all copyrights. https://creativecommons.org/licenses/by/4.0/ https://orcid.org/0000-0003-1002-9678 HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 208 [22] and Hung et al. [23], they showed the clear evidence of structural transition in liquid Al2O3 from a tetrahedral to an octahedral network. The voids created a very large hole with a volume five times bigger than that of the aluminum atom. Other simulations [24, 25] showed that the phase regions of liquid Al2O3 strongly depend on compression. The mobility of atoms in different phases is different; the AlO6-phase forms immobile regions. At low temperatures, the coexistence of AlO4-, AlO5-, and AlO6-phases is the origin of the spatially dynamical heterogeneity. However, up to now, the development of structural transition and SH under compression for liquid Al2O3 is still intensively improved. In the present work, a large-scale MD simulation of an Al2O3 system consisting of 5500 atoms was performed. The structural characteristics such as the RDF, characteristics of AlOx and OAly units, visualization of simulation data have been clarified for the structural transition and SH in liquid Al2O3 under compression condition. 2. Calculation Method Models of liquid Al2O3 consisting 5500 atoms (2200 Al- and 3300 O-atoms) are constructed by MD simulation at 3500 K, in the range 0-150 GPa, with boundary conditions for all three dimensions. The Born-Mayer potential, which has been successfully used for structural and dynamic simulation of Al2O3 systems, was employed in this work. The detail about the Born-Mayer potential can be referred from Kovarik et al. (2021), Hoang & Oh (2004), and Belashchenko (1997) study [4, 15, 26]. The MD program is coded in the C language and uses the Verlet algorithm to integrate the motion equations. In this case, MD time step is selected to be 0.47 fs. Initial configuration of the model is created by randomly sowed all atoms in the simulation space. The model is heated up to 6000 K and zero pressure. Then, the model is cooled down to 3500 K within 2×104 time steps with the cooling rate of 2.0 K/ps. After that, a long relaxation (5×106 time steps) has been done in isothermal-isobaric (NPT) ensemble to equilibrate the model at 3500 K and zero pressure. From this well-equilibrated liquid Al2O3 at 3500 K and zero pressure, the proposed models at different pressures (5-100 GPa) which are labeled as M1, M2…M11, respectively (as seen in Table 1). These models were constructed by relaxing again within 5×106 time steps to reach the equilibrium in isothermal-isobaric NPT ensemble. The structural characteristics of each model are determined by averaging 1000 configurations during the last 5×104 MD steps. To calculate the clusters as well as coordination number, the cutoff distance is chosen based on the minimum position after the first peak of the RDF. Remarkably, for the Al-O pair, the cutoff distance is 2.54 Å. 3. Result and Discussion 3.1. The Structural Transition under Compression The characteristics of the constructed models, experimental, calculation and other simulation are listed in Table 1. Obviously, the major changes are a shift of distance rij to bigger value for Al-O pair and smaller value for Al-Al, O-O pairs with increasing of the applied pressure. The coordination number strongly increases with increasing of pressure. Namely, at 0 GPa, the averaged coordination numbers for Al-Al, Al-O, O-Al and O-O pairs were found to be 7.71, 4.25, 2.83 and 10.64, respectively. These numbers increased to be 13.68, 6.54, 4.36 and 16.77 as pressure increases from 0 to 100 GPa. Also, the BKS model reproduces well the structural data obtained from experimental and simulated data from Refs. [1, 2, 7, 8, 20, 22]. Thus, the prepared models are reliable to investigate the structural transition and SH of liquid Al2O3. Table 1. The structural characteristics of constructed models at different pressures, experimental and simulation data. Here T, P, ρ are temperature, pressure and density, respectively; rAl-Al , rAl-O, rO-O is the inter-atomic distance for Al-Al, Al-O and O-O pair, respectively; zAl-Al, zAl-O zO-Al, zO-O are the average coordination number for Al-Al, Al-O, O-Al and O-O pair, respectively. Models T (K) P (GPa) ρ (g/cm3) rAl-Al (Å) rAl-O (Å) rO-O (Å) zAl-Al zAl-O zO-Al zO-O M1 3500 0.01 2.78 3.14 1.68 2.78 7.71 4.25 2.83 10.64 M2 3500 5 ˗ 3.16 1.72 2.70 11.75 5.30 3.54 13.94 M3 3500 10 ˗ 3.14 1.74 2.70 11.81 5.37 3.58 14.04 M4 3500 15 ˗ 3.10 1.70 2.70 11.89 5.43 3.62 14.15 M5 3500 20 ˗ 3.12 1.72 2.64 11.97 5.51 3.67 14.36 M6 3500 25 ˗ 3.08 1.72 2.62 12.02 5.55 3.70 14.43 M7 3500 30 ˗ 3.08 1.72 2.60 12.20 5.63 3.76 14.66 M8 3500 40 ˗ 3.08 1.72 2.56 12.31 5.80 3.87 15.19 M9 3500 60 ˗ 3.00 1.70 2.52 12.42 5.85 3.90 15.37 M10 3500 80 ˗ 2.84 1.72 2.50 13.74 6.45 4.30 16.26 M11 3500 100 ˗ 2.88 1.72 2.46 13.68 6.54 4.36 16.77 Exp. [11] 2500 ˗ 2.81 3.25 1.78±0.05 2.84 ˗ 4.20±0.3 ˗ ˗ Exp. [1] 2200-2650 ˗ 3.17 ˗ 1.732 3.08 ˗ 4.40±1.0 ˗ ˗ Exp. [20] 2400±50 ˗ ˗ 3.15 1.80 2.82 8.85 4.40 2.93 12.90 Sim. [22] 2500 0.05 2.80 3.20 1.77 2.80 8.00 4.20 2.80 7.44 Cal. [8] 4000 ˗ 3.683 3.02 1.79 2.61 12.4 5.52 3.69 15.60 HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 209 Figure 1. The radial distribution function of liquid Al2O3 at different pressures Figure 2. Dependence of coordination number distribution on applied pressure for: AlOx (left) and OAly (right) Figure 1 displays the RDFs gAl-O(r), gAl-Al(r) and gO-O(r) at different pressures. It can be seen that, under compression for the gAl-O(r), the position of the first peak is displaced to the right-hand side and their magnitudes are significantly decreased. In contrast, for the gO-O(r), and gAl-Al(r), the position of the first peak is displaced to the left- hand side and their magnitudes are independent on the increased pressure. Based on above analyses, the network structure of liquid Al2O3 is changed insignificantly both of intermediate- and short-range order structure, which is depended on the compression. Next, we clarified the origin of the change of the network structure of liquid Al2O3 under compression via the characteristics of AlOx and AlOy basic units. As shown in Figure 2, the fraction of AlO3, AlO4, OAl2, and OAl3 are decreased with increasing pressure while the fraction of AlO7 and OAl5 are increased. Specially, the fraction of AlO5, 0 2 4 6 0 2 4 6 8 10 M11 M7 M5 M4 Al-Al g (r ) 0 2 4 6 Al-O 0 2 4 6 M9 M3 M1 O-O r (Å) r (Å) r (Å) 0 20 40 60 80 100 0.0 0.2 0.4 0.6 0.8 AlO5 AlO6 AlO7 AlO3; AlO4 Pressure (GPa) F ra c ti o n 0 20 40 60 80 100 OAl2 OAl3 OAl4 OAl5 Pressure (GPa) HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 210 AlO5 and OAl4 creates a maximum value at 5 GPa for AlO5 and at 50 GPa for AlO5 and OAl4. This phenomenon indicated a transformation in local environment of Al ions from tetrahedral- to octahedral- coordination at 5 GPa and beyond 50 GPa, which leads to the system becomes to be denser. This result can be regarded as the bond length between O and O in AlO5 units is larger than the one in AlO6 and smaller than the one in AlO4. The bond angle and length distribution calculated separately for each type of AlOx basic units are shown in Figure 3 and 4. It showed that the angle-distributions are almost independent on pressure for AlO5. However, the deviations in the magnitude and position of main peak are observed in cases of AlO4 and AlO6 (as depicted on the left side of Figure 3). Furthermore, on the right side of Figure 3, the bond-length distribution for AlO4 and AlO6 are significantly depended on the pressure, which causes the magnitude- and position-deviations. Clearly, under compression, the shape and size of AlO4, AlO5 and AlO6 units are changed and little distorted. As presented in Figure 4, the angle distributions of OAl2, OAl3 and OAl4 units are not identical (depended on pressure). It means that the topology structure of basic- structural units is also dependent on pressure. It can be concluded that the network structure of liquid Al2O3 is formed by order parameters as follows: i/ the order parameters related to the short-range order (SRO), including AlO3, AlO4, AlO5, AlO6 and AlO7 units; ii/ the linkage OAl2, OAl3 and OAl4 are order parameters, which are related to the intermediate-range order (IRO). At low-pressure state, the number of linkages OAl3 and OAl4 is small. At high- pressure state, as most of linkages are OAl3 and OAl4, the IRO is characterized by network of interconnected tetrahedra by the edge-sharing. Clearly, the OAl2 linkages connected among AlO3 and AlO4 units causes a cluster of AlO3 and AlO4 units. In other words, this cluster is formed by the interconnected tetrahedra and the corner-sharing, which characterizes the low-density phase. The network structure of high-density phase is produced from OAl3 and OAl4 linkages. Consequently, the OAl3 and OAl4 linkages connect among AlOx (x = 5, 6, 7) units forming a cluster of AlO5, AlO6 and AlO7 units. Figure 3. Bond angle O-Al-O (left) and length (right) distribution in coordination units AlOx at different pressures 0.00 0.05 0.10 0.15 M1 M2 M3 M4 M5 M6 M7 AlO4 0.00 0.02 0.04 0.06 M1 M2 M3 M4 M5 M6 M7 AlO4 0.00 0.05 0.10 M2; M3 M4; M5 M6; M7 M8 AlO5 0.00 0.02 0.04 M2; M3 M4; M5 M6; M7 M8 AlO5 60 90 120 150 180 0.00 0.05 0.10 M4; M5 M6; M7 M8; M10 M11 AlO6 1.5 1.8 2.1 2.4 0.00 0.02 0.04 F ra c ti o n F ra c ti o n F ra c ti o n Bond length(Å) M4; M5 M6; M7 M8; M10 M11 AlO6 Angle (degree) HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 211 Figure 4. Bond angle Al-O-Al (left) and length (right) distribution in coordination units OAly at different pressures 3.2. The structural heterogeneity under compression The SH for liquid Al2O3 through the analysis Voronoi volume of atoms, the link-cluster function, visualization of simulation data and the consideration the mean square displacement (MSD) of atoms are clarified in this part. As presented in Figure 5, in comparison with Al, the fraction curve of O ion spreads in wider intervals. When the pressure increase, the graphs shift to the left. This phenomenon indicated that O occupies significantly larger volume compared to Al result, therefore, the Voronoi volume is decreased with increasing pressure. Clearly, Figure 6 displays the average Voronoi volumes of Al- and O-atoms under compression. Consequently, and are monotonously decreased, in which is decreased stronger than . These results confirmed that the IRO is modified stronger than the SRO upon compression. To characterize the cluster of atoms, we proposed the link-cluster function Flink(r,t) and the exploited calculated algorithm can be found from Hung et al. (2018) and Lan et al. (2019) study [27, 28]. Here, we considered sets of mobiles, immobiles and random atoms (SMA, SIMA and SRA), which contains total atoms of 20%. It can be noted that the SMA has the mean-square-displacement (MSD), which is larger than that of remaining atoms. Conversely, the SIMA has the MSD smaller than that of remaining atoms. The SRAs are randomly chosen from the proposed models. The atoms of SMA, SIMA and SRA are determined from the atom position in the configuration at t = 2×105 time steps. Figure 7 shows the link-cluster function Flink(r,t) at 5, 15, 20 and 80 GPa. It is clearly seen that, at 5 and 80 GPa, the function Flink(r,t) for SMA, SIMA and SRA is very identical. As r varies from 1.5 to 2.55 Å, Flink(r, t) for SMA, SIMA and SRA drops drastically to 689, 745; 521 at 15 GPa and 663, 740 and 551 at 20 GPa, respectively. Meanwhile, SIMA, SMA and SRA drops drastically to the same values, namely, to 558, 615 and 648 at 5 GPa and 521 at 15 GPa; 331, 353 and 325 at 80 GPa, respectively. Moreover, with further increasing r, a shoulder is appeared, then Flink(r, t) is decreased gradually. We concluded that at 5 and beyond 80 GPa, AlOx units are uniformly distributed in 0.00 0.05 0.10 0.15 M1 M2 M3 M4 M5 M6 M7 OAl2 OAl3 0.00 0.04 0.08 M1 M2 M3 M4 M5 M6 M7 OAl2 0.00 0.05 0.10 M2; M3 M4; M5 M6; M7 M8 0.00 0.02 0.04 M2; M3 M4; M5 M6; M7 M8 OAl3 60 90 120 150 180 0.00 0.05 0.10 0.15 M4; M5 M6; M7 M8; M10 M11 OAl4 Bond length (Å) F ra c ti o n F ra c ti o n F ra c ti o n Angle (degree) 1.5 1.8 2.1 2.4 0.00 0.02 0.04 M4; M5 M6; M7 M8; M10 M11 OAl4 HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 212 the space. Meanwhile, in the range 15-20 GPa, the spatial distribution of AlOx units is non- uniformly. This is caused by strongly rearrangement of atoms in the range 10-20 GPa compared to that of below 15 and beyond 20 GPa. Figure 5. Dependence of fraction of Al and O on Voronoi volume at 0, 10, 20 and 40 GPa. Fraction of Al, O is given respectively by m(υAl)/mAl and m(υO)/mO with m(υAl), m(υO) is the number of Al and O having volume υAl and υO, respectively. mAl and mO are the total number of Al and O, respectively. Figure 6. Pressure dependence of average Voronoi volume of Al-, O-atom 6 12 18 24 30 0.0 0.1 0.2 0.3 Al O F ra ct io n o f a to m s M1 8 12 16 20 M3 Al O 4 8 12 16 0.0 0.1 0.2 0.3 0.4 M5 Al O Volume (Å3) F ra ct io n o f a to m s Volume (Å3) 4 6 8 10 M8 Al O 0 20 40 60 80 100 6 9 12 15 O Si A v e ra g e V o ro n o i v o lu m e ( Å 3 ) Pressure (GPa) HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 213 Figure 7. The link-cluster function at 5, 15, 20 and 80 GPa Figure 8 displays the partial distribution of AlOx in the liquid Al2O3 at different pressures. Obviously, the distribution of AlOx units is not uniform and it tends to form clusters (subnets) of AlO3, AlO4, AlO5, AlO6 and AlO7. It means that the structure of liquid Al2O3 comprises the mixture of AlO3, AlO4, AlO5, AlO6 or AlO7 clusters. Namely, the structure of liquid Al2O3 is the mixture of regions with different SRO. The structure of liquid Al2O3 consists of structural phases is that AlO3-, AlO4, AlO5-, AlO6- or AlO7 -phases, AlOx (x = 3, 4, 5, 6, 7) phases are formed by the AlOx units, respectively. It can be seen that at 0 GPa, the regions with AlO3, AlO4, AlO5 -phase are linked to each other to create a large region with the expanse almost whole model. The region with AlO6- and AlO7-phases is small and localized at different locations leading to separated regions. As pressure is increased, the regions with AlO5-, AlO6- and AlO7 -phases are expanded and the regions with AlO3 and AlO4-phase are shrunk. At pressure of 10, 20 GPa, the regions with AlO5- and AlO6-phase are expanded the whole model. At pressure of 100 GPa, the regions with AlO3-, AlO4-, AlO5-phases are shrunk, whereas the regions with AlO6- and AlO7 -phases are expanded almost the whole model. It is noted that the coexistence of different phases in network-forming liquids under compression can be examined by the neutron and X-ray diffraction experiments [29, 30]. To clarify the distribution of AlOx (x = 3, 4, 5, 6, 7) units in proposed models, the structures at different pressures are visualized in the 3D space (as shown in Figure 9). At 0 GPa, most of structural units are AlO4, AlO5 and some AlO3, AlO6 and AlO7 units. The spatial distribution of AlO4, AlO5 is not uniform but it tends to form AlO4- and AlO5- clusters. At pressure of 10, 15, 20 and 60 GPa, most of structural units are AlO5, AlO6 and they also tend to form AlO5- and AlO6-clusters. At pressure of 100 GPa, in particular, most of structural units are AlO6, AlO7 and they are also tended to form of AlO6-, AlO7-clusters. 0 200 400 600 800 1000 SMA SIMA SRA F L in k (r ,t ) M2 M4 1 2 3 4 5 6 7 0 200 400 600 800 1000 M5 F L in k (r ,t ) r (Å) 1 2 3 4 5 6 7 M10 r (Å) HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 214 Figure 8. Spatial distribution of AlO3, AlO4, AlO5, AlO6 and AlO7 in the liquid Al2O3 at different pressure and 3500 K. Al and O atoms are in red and blue color, respectively Further, the network topology, the immediate structural phase and SH can be analyzed by the corner-sharing, the edge-sharing, the face-sharing bonds and their clustering behavior. The distribution of corner-, edge- and face-sharing links (CSL, ESL and FSL) are calculated using the following algorithm: If Al atom connects with Al atom via one bridge O atom, which can be regarded as a corner-sharing bond (Al-O-Al). Also, Al atom connects to Al atom through two bridge O atoms, which is defined as an edge-sharing bond (Al-O-,-O-Al). In case of Al atom connects with Al atom via three bridge O atoms, which is defined as a face-sharing bond (Al-O-,-O-,-O-Al). The employed calculated algorithm is similar with that in Guignard & Cormier (2008) study [31]. AlO3 AlO6 AlO4 M1 AlO5 AlO6 AlO7 AlO4 M5 AlO5 AlO7 AlO6 AlO4 M3 AlO5 AlO7 AlO6 AlO4 M11 AlO5 HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 215 Figure 9. Snapshots of spatial distribution of AlO3 units (in black spheres), AlO4 (in blue spheres), AlO5 (in red spheres), AlO6 (in pink spheres) and AlO7 (in turquoise spheres) for liquid Al2O3 at pressures of 0, 10, 15, 20, 60 and 100 GPa (M1, M3, M4, M5, M9, M11) and 3500 K. Figure 10 displays the spatial distribution of CSL, ESL and FSL of liquid Al2O3. It can be observed that the distribution of CSL, ESL and FSL is not uniform. Obviously, this phenomenon represents structural heterogeneity in liquid Al2O3. In principle, the clusters of face-sharing links form immobile regions and the clusters of corner-sharing links, corresponding mobile regions. The mentioned analysis demonstrated that the coexistence of separate structural phases in network forming is origin of spatially SH with micro-scaled phase separation in liquid Al2O3. M1 M3 M4 M5 M9 M11 Edg Face Cor M2 M4 Face Edg Cor HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 216 Figure 10. Distribution of corner, edge, face-sharing of Al2O3 at pressure of 5, 15, 30 and 80 GPa and 3500 K. Al and O atoms are in red and blue color, respectively In general, the SH is the main cause of dynamic heterogeneity. Figure 11 shows the mean square displacement (MSD) of Al and O ions as a function of time (at 5, 15, 20, 80, and 100 GPa). It can be seen that O is always more mobile than Al atoms. Consequently, the O-rich regions will be more mobile than the Al-rich regions. It means that the OAl1-, OAl2-cluster is more stable than OAl3-, OAl4-cluster. This phenomenon confirmed the dynamics of OAly- clusters is very interested. Figure 11. MSD of Al (left) and O (right) atom as a function of time at pressure of 5, 15, 20, 60 and 100 GPa M10 Face Edg Cor M7 Face Edg Cor 0 15000 30000 45000 0 300 600 900 1200 M2; M4 M5; M9 M11 M S D ( x1 0 -4 c m 2 ) Time (fs) Al 0 15000 30000 45000 0 500 1000 1500 2000 2500 M2; M4 M5; M9 M11 M S D ( x1 0 -4 c m 2 ) Time (fs) O HighTech and Innovation Journal Vol. 3, No. 2, June, 2022 217 4. Conclusion The structural transition and SH under compression are investigated in detail. The obtained result realized the structure organization of liquid Al2O3 comprises AlO3, AlO4-, AlO5-, AlO6 or AlO7- phases, which depend on the applied pressure. At lower pressures, liquid Al2O3 comprises two main AlO4-, AlO5-phases and scattering AlO3-, AlO6-, AlO7-phases. In the range of 10-20 GPa, two main AlO5-, AlO6- and scattering AlO3-, AlO4-, AlO7-phases are comprised. In case of beyond 20 GPa, two main AlO6-, AlO7- and scattering AlO3-, AlO4-, AlO5-phases are comprised. Under compression conditions, the topology of AlOx is slightly changed and distorted. In the AlO3- and AlO4-phases, the AlO3- and AlO4-units mainly link to each other through the corner-sharing bonds, for AlO5-, AlO6-, AlO7-phases through corner-, edge-, face-sharing bonds. The existence of separate phases is evidence of SH in liquid Al2O3. Furthermore, the Voronoi volumes of O atoms are detected to decrease faster than those of Si, indicating the existence of free-volume regions in liquid Al2O3. The atoms in AlO3-, AlO4-phases are more mobile than the ones in AlO6-, AlO7-phases. Importantly, at pressure below 10 and beyond 20 GPa, AlOx units are uniformly distributed. Meanwhile, in the range of 10-20 GPa, the spatial distribution of AlOx units is more homogeneous in space. 5. Declarations 5.1. Author Contributions Conceptualization and methodology, T.T.Q.N.; formal analysis and investigation, P.H.K.; writing—original draft preparation, G.T.T.T.; writing—review and editing, P.H.K. All authors have read and agreed to the published version of the manuscript. 5.2. Data Availability Statement The data presented in this study are available in article. 5.3. Funding This research is funded by the Thainguyen University of Education, and Thai Nguyen University under project number ĐH2022-TN04-02. 5.4. Institutional Review Board Statement Not Applicable 5.5. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 6. References [1] Landron, C., Hennet, L., Jenkins, T. E., Greaves, G. N., Coutures, J. P., & Soper, A. K. (2001). Liquid alumina: Detailed atomic coordination determined from neutron diffraction data using empirical potential structure refinement. Physical Review Letters, 86(21), 4839–4842. doi:10.1103/PhysRevLett.86.4839. [2] Neuville, D. R., Ligny, D. de, Cormier, L., Henderson, G. 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