The influence of SIO2-doped concentration, temperature and pressure on the microstructure of Al2O3(SiO2)x bulk model

Abstract. This paper looks at the influence of SiO2-doped concentration, temperature and pressure on the microstructure of the Al2O3(SiO2)x (ASx) bulk model using the Molecular Dynamics (MD) method with a Born-Mayer pair interaction potential and periodic boundary conditions. The ASx model was created by changing the doping concentration (SiO2)x with x = 1, x = 2 and x = 3 at a temperature of 3,500 K and a pressure of 25 GPa. When models with the most suitable concentration were obtained, we maintained a pressure of 25 GPa and reduced the temperature to 2,500 K, 1,500 K and 500 K, or kept the temperature unchanged and reduced the pressure to 20 GPa, 15 GPa, 10 GPa, 5 GPa and 0 GPa. The models were analyzed using radial distribution functions (RDF), the coordination number, the energy, the size and the length of couplings between atoms. Obtained results showed that there was an influence of doping concentration, temperature and pressure on the microstructure of Al2O3(SiO2)x bulk model.

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2015-0046 Mathematical and Physical Sci., 2015, Vol. 60, No. 7, pp. 162-168 This paper is available online at THE INFLUENCE OF SIO2-DOPED CONCENTRATION, TEMPERATURE AND PRESSURE ON THE MICROSTRUCTURE OF Al2O3(SiO2)x BULK MODEL Nguyen Trong Dung and Nguyen Chinh Cuong Faculty of Physics, Hanoi National University of Education Abstract. This paper looks at the influence of SiO2-doped concentration, temperature and pressure on the microstructure of the Al2O3(SiO2)x (ASx) bulk model using the Molecular Dynamics (MD) method with a Born-Mayer pair interaction potential and periodic boundary conditions. The ASx model was created by changing the doping concentration (SiO2)x with x = 1, x = 2 and x = 3 at a temperature of 3,500 K and a pressure of 25 GPa. When models with the most suitable concentration were obtained, we maintained a pressure of 25 GPa and reduced the temperature to 2,500 K, 1,500 K and 500 K, or kept the temperature unchanged and reduced the pressure to 20 GPa, 15 GPa, 10 GPa, 5 GPa and 0 GPa. The models were analyzed using radial distribution functions (RDF), the coordination number, the energy, the size and the length of couplings between atoms. Obtained results showed that there was an influence of doping concentration, temperature and pressure on the microstructure of Al2O3(SiO2)x bulk model. Keywords: Microstructure, Al2O3.(SiO2)x bulk model, Molecular Dynamics. 1. Introduction Oxide materials such as Al2O3, SiO2, Fe2O3 and GeO2 are widely used in many industries. In particular, the mixed oxide Al2O3(SiO2)x (ASx) is used in ceramic technology and petrochemical technology and this material is also the basic component of the earth’s crust. Research on Al2O3, SiO2 and ASx materials are of great interest today. Some works on Al2O3(SiO2)2 (AS2) materials have shown that there was an influence of pressure on the microstructure [1] and an influence of the phase transition process on the mechanical properties [2]. In particular, studies on the influence of phase transition from one amorphous state to another one under pressure (from 14 GPa to 22 GPa [3] and from 8 GPa to 25 GPa [4]) at low temperature have found that the phase transition process occurred slowly [3]. Al atoms (molecules) have a complex structure so when they are linked to the Si-O tetrahedral lattice, the Al3+ ion has to be under a pressure which is great enough to form an AlO4 tetrahedral lattice with Al3+ and Si2+ ions that are linked together through O atoms. Some experimental methods such as Nuclear Magnetic Resonance (NMR) [5], X-ray diffraction, Raman spectrum [6] and Neutron Scattering [7] have shown that structural units 3, 4, 5 and 6 appeared in the material at 4,000 K [8]. Recently, some Received July 9, 2015. Accepted September 4, 2015. Contact Nguyen Trong Dung, e-mail address: dungntsphn@gmail.com 162 The influence of SiO2-doped concentration, temperature and pressure... theoretical and simulation methods [9] have shown the role of O atoms in the coupling to form the composites Al2O2 and AlSiO2. The results showed that the length of the Al-O coupling is in the range of 1.8 - 1.9 A˚ and the number of O atoms which are surrounded the Al atoms is in the range of 4.0 - 4.8. The structure of the AS2 system is made up of AlO4 tetrahedral and AlO8 octahedral blocks with the rate depending on the research methodology and procedures of experimental processes. P. Lamparter and his colleagues studied the microstructure of Al2O3 using experimental methods (X-ray diffraction and neutron diffraction) and the Monte Carlo simulation method [10] and found that with 20% Al atoms, 3 were surrounded by O atoms, with 56% Al atoms 4 were surrounded by O atoms and with 22% Al atoms 5 were surrounded by O atoms. Until today, there has been no adequate explanation for the microstructure change in the AS2 model under the influence of temperature, pressure and SiO2-doped concentration. There are still many problems to be studied in detail. In this paper, the influence of SiO2-doped concentration, temperature and pressure on the microstructure (radial distribution function, coordination number, energy, size and the length of the couplings between pairs of atoms) of the ASx model was studied. 2. Content 2.1. Method of calculation The (Al2O3)(SiO2)x (ASx) bulk model is constructed with x = 1, x = 2 and x = 3, corresponding to AS1, AS2, AS3 models which have atomic numbers as shown in Table 1. Table 1. ASx bulk model with doping concentrations x = 1(AS1), x = 2(AS2) and x = 3(AS3) Model n (atomic) nAl nSi nO AS1 1200 300 150 750 AS2 1650 300 300 1050 AS3 2100 300 450 1350 The Molecular Dynamics method is used to study the Born - Mayer pair interaction potential and periodic boundary conditions Uij(r) = qiqj rij +Aij exp(−Bijrij), where the parameters are given in Table 2. Table 2. The coefficient of the Born - Mayer pair interaction potential used in the ASx bulk model Si-Si Si-O O-O Si-Al O-Al Al-Al Aij (eV) 0 1729.5 1479.86 0 1500 0 Bij (A˚−1) 0 3.4483 3.4483 0 3.4483 0 qij 0 qSi = +4.0 qAl = +3.0 0 qO = -2.0 0 (NA = 6.022.10 23; p = 2.6.10−24; mSi = 26.98154; mO = 15.999; mAl = 28.085; n = nAl + nSi + nO) The ASx bulk model (x = 1, x = 2 and x = 3) was initially put randomly in a cubic box, then run with the statistical recovery of 10,000 steps by the Born-Mayer pair interaction potential with periodic boundary conditions so that the atoms (molecules) were not stuck together. After that, the model was run with 5.105 NPT steps with moving step dr = 0.01 at temperature dT = 1.0 and pressure dP = 0.01e−4 until the model reached a stable state at the temperature 3500 K and 163 Nguyen Trong Dung and Nguyen Chinh Cuong pressure 25 GPa. Then, the model was continued to run with 5.104 NVE steps to keep the energy unchanged. Keeping the pressure at 25 GPa, the model was run with 5.104 NVT steps so that the temperature would drop from 3500 K to 2500 K, 1500 K and 500 K. Alternatively, we kept the temperature at 3500 K with moving step dr = 0.01, dT = 1.0, and the model was run with 5.104 NVP steps so that the pressure would drop from 25 GPa to 20 GPa, 15 GPa, 10 GPa, 5 GPa and 0. After obtaining models that were at the desired temperature and pressure, all models were run simultaneously with 5.105 NPT steps with moving step dr = 0.01, temperature at dT = 1.0 and pressure at dP = 0.01e−4 until the models reached a stable state. Then they were continued to run with 5.104 NVE steps to keep the energy unchanged. All models were analyzed using the radial distribution function, the coordination number, the energy, the size and the length of couplings. Results showed that there was an influence of SiO2-doped concentration, temperature and pressure on the microstructure of the ASx bulk model. 2.2. Results and discussion The (Al2O3)(SiO2)x bulk model with x = 1, x = 2 and x = 3 corresponds to AS1, AS2 and AS3 models obtained at the temperature 3500 K and pressure 25 GPa that were analyzed using radial distribution functions, with the obtained results shown in Tables 3 and 4. Table 3. The first peak position (rij) of radial distribution functions with the ASx model at different doping concentrations N r(Si-Si) r (Si-O) r (O-O) r(Si-Al) r(O-Al) r(Al-Al) AS1 3.16 1.64 2.5 3.1 1.74 3.08 AS2 3.14 1.64 2.5 3.08 1.72 3.00 AS3 3.14 1.64 2.48 3.12 1.74 3.08 simulation [1] 1.61 1.74 Table 4. The first peak height g(r) of radial distribution functions with the ASx model at different doping concentrations n g(Si-Si) g(Si-O) g(O-O) g(Si-Al) g(O-Al) g(Al-Al) AS1 3.84 5.58 2.41 3.80 3.77 3.72 AS2 3.20 5.48 2.34 3.03 3.72 2.79 AS3 4.05 5.25 2.51 3.94 3.48 3.98 Results in Tables 3 and 4 show that there primarily existed the couplings of Si-Si, Si-O, O-O, Si-Al, O-Al, Al-Al atomic pairs in the (Al2O3).(SiO2) model with x = 1, x = 2 and x = 3. When the SiO2-doped concentration in the (Al2O3).(SiO2)x model was increased, the first peak position of the radial distribution function changed insignificantly. This proves that the SiO2-doped concentration did not change the length of couplings between atoms. But, the first peak height of the radial distribution function changed significantly. The couplings of Si-Si, O-O, Si-Al and Al-Al atomic pairs tended to increase while the couplings of Si-O and O-Al atomic pairs tended to decrease. The first peak height of the radial distribution function of the AS2 model reached minimum value. That means that the AS2 model had significant changes in its microstructure. 164 The influence of SiO2-doped concentration, temperature and pressure... To observe the shape of the AS2 model, some visualization tools were used to determine the shape of the Al2O3.2(SiO2) model at temperature 3500 K and pressure 25 GPa. The size of the ASx model (x = 1, x = 2 and x = 3) is shown in Figure 1 and Table 5. Figure 1. The shape of the Al2O3.2(SiO2) model at temperature 3500 K and pressure 25 GPa (Al atoms are red, O atoms are blue and Si atoms are green) Table 5. Sizes of models with different atomic numbers Model AS1 AS2 AS3 Size (nm) 2.211 2.463 2.663 Figure 1 and Table 5 show that the model was determined with 3 atomic types (Al, Si and O) at a nano-scale. When the SiO2-doped concentration was increased, the size of the model increased from 2.211 nm to 2.663 nm. The microstructure of the AS2 model is shown in Figure 2. Figure 2. Radial distribution functions of the AS2 model with 1,650 atoms Figure 2 shows that there primarily existed the first peaks of radial distribution function for the couplings of Si-Si, Si-O, O-O, Si-Al, O-Al and Al-Al atomic pairs in the AS2 model. There only existed the near range interaction in the AS2 model. Table 3 shows values of the lengths of the two couplings Si-O and O-Al in the AS2 model, which were consistent with simulation values of 1.61 A˚ and 1.74 A˚ [1]. This shows that the selection of SiO2-doped concentration for the ASx model at x = 2 is consistent with previous simulation results. The simulation results of the influence of temperature on the microstructure of the AS2 model at 25 GPa when the temperature was lowered from 3500 K to 2500 K, 1500 K and 500 K are shown in Tables 6 and 7. 165 Nguyen Trong Dung and Nguyen Chinh Cuong Table 6. The first peak position (rij) of radial distribution functions with the AS2 model at different temperatures T(K) r(Si-Si) r (Si-O) r (O-O) r(Si-Al) r(O-Al) r(Al-Al) 3500 3.14 1.64 2.5 3.08 1.72 3.00 2500 3.14 1.66 2.48 3.08 1.74 3.02 1500 3.14 1.66 2.48 3.10 1.74 3.02 500 3.12 1.64 2.48 3.08 1.76 3.06 Table 7. The first peak height g(r) of radial distribution functions with the AS2 model at different temperatures T(K) g(Si-Si) g(Si-O) g(O-O) g(Si-Al) g(O-Al) g(Al-Al) 3500 3.20 5.48 2.34 3.03 3.72 2.79 2500 3.54 5.95 2.55 3.44 4.11 2.93 1500 3.81 6.67 2.71 3.53 4.70 3.03 500 4.35 7.99 2.92 3.91 6.00 3.40 Results in Tables 6 and 7 show that there primarily existed couplings of Si-Si, Si-O, O-O, Si-Al, O-Al and Al-Al atomic pairs in the AS2 model. When the temperature was decreased, the first peak position of the radial distribution function changed insignificantly. That means that the temperature did not change the length of couplings between the atoms. In particular, the first peak height of the radial distribution function for the couplings Si-Si, Si-O, O-O, Si-Al, O-Al and Al-Al changed significantly. This proved that temperature had a great influence on the microstructure of the AS2 model. Table 8. The first peak position (rij) of radial distribution functions with the AS2 model at different pressures P(GPa) r(Si-Si) r (Si-O) r (O-O) r(Si-Al) r(O-Al) r(Al-Al) 25 3.14 1.64 2.5 3.08 1.72 3.00 20 3.12 1.62 2.50 3.10 1.72 3.04 15 3.14 1.60 2.54 3.10 1.70 3.06 10 3.14 1.60 2.58 3.12 1.70 3.08 5 3.14 1.58 2.60 3.14 1.66 3.08 0 3.16 1.58 2.64 3.18 1.64 3.16 Table 9. The first peak height g(r) of the radial distribution functions with the AS2 model at different pressures P(GPa) g(Si-Si) g(Si-O) g(O-O) g(Si-Al) g(O-Al) g(Al-Al) 25 3.20 5.48 2.34 3.03 3.72 2.79 20 3.13 5.74 2.29 3.05 3.82 2.69 15 3.32 6.35 2.28 2.90 4.03 2.90 10 3.30 7.30 2.30 2.98 4.38 2.82 5 3.75 9.46 2.44 3.07 5.31 3.03 0 4.91 13.03 2.94 3.53 7.43 3.30 166 The influence of SiO2-doped concentration, temperature and pressure... The simulation results of the influence of pressure on the microstructure of the AS2 model at 3,500 K with pressure lowered from 25 GPa to 20 GPa, 15 GPa, 10 GPa, 5 GPa and 0 are shown in Tables 8 and 9. Results in Tables 8 and 9 show that there primarily existed the couplings of Si-Si, Si-O, O-O, Si-Al, O-Al and Al-Al atomic pairs. When the pressure was decreased, the first peak position of the radial distribution function increased significantly with the couplings Si-Si, O-O, Si-Al and Al-Al and decreased significantly with the couplings Si-O and O-Al. This proved that pressure changed the length of couplings between the atoms. The first peak height of the radial distribution function for the couplings Si-Si, Si-O, O-O, Si-Al, O-Al and Al-Al had significantly increased and that means that pressure had a great influence on the length of couplings between atoms and on the microstructure of the AS2 model. Influence of temperature and pressure on the microstructure of models is also considered through the energy and size of models and these results are shown in Table 10. Table 10. The energy and size of models at different temperatures and pressures Model Temperature (K) Pressure (GPa) 3500 2500 1500 500 25 20 15 10 5 0 Energy(eV) -61396.70 -61909.52 -62317.42 -62715.41 -61396.70 -61432.21 -61490.02 -61561.44 -61682.97 -61768.87 Size(nm) 2.463 2.444 2.435 2.432 2.463 2.493 2.543 2.609 2.748 2.998 Results in Table 10 show that when the temperature and pressure of models were decreased, the energy of models tended to decrease. This is completely consistent with experimental data. When the temperature was decreased, the size of the models tended to decrease and the density of atoms increased. When the pressure was decreased, the size of the models increased, the density of the atoms decreased and the microstructure of the models moved to durable equilibrium state corresponding to the lowest energy level. The change in microstructure of the models when the temperature and pressure of models were decreased is shown in Figure 3 and Table 11. Figure 3. The couplings between T (Si or Al) atoms with O atoms in the AS2 model at temperature 3500 K and pressure 25 GPa (3a, 3b and 3c), the couplings between Si and Al atoms through O atoms (3d) Table 11. Coordination numbers in models corresponding to different temperatures and pressures Temperature (K) 4 5 6 Pressure (GPa) 4 5 6 3500 124 726 703 25 124 726 703 2500 94 581 916 20 242 787 564 1500 74 618 897 15 391 784 367 500 103 708 797 10 658 675 136 5 971 316 21 0 1130 48 0 167 Nguyen Trong Dung and Nguyen Chinh Cuong Results in Figure 3 and Table 11 show that the microstructure of the AS2 model at temperature 2.500 K and pressure 25 GPa had the prevailing coordination number 6 while at temperature 3500 K and zero pressure it had the prevailing coordination number 4. It is proved that when temperature and pressure were decreased, the coordination number 4 increased and the coordination number 6 decreased. This confirms that SiO2-doped concentration, temperature and pressure have a significant influence on the microstructure of the ASx model. 3. Conclusion Studying influencing factors on the microstructure of the Al2O3(SiO2)x (ASx) bulk model using Molecular Dynamics (MD) with Born-Mayer pair interaction potential and boundary conditions has given some important results. The choice of Born-Mayer (BM) pair interaction potential with parameters for the simulation of Al2O3(SiO2)x bulk models have given results which are consistent with previous simulation results. When the temperature is decreased, the size of the model decreases and its energy increases while the decrease in pressure leads to an increase in both size and energy of the model. There are differences in terms of microstructure of the couplings Si-Si, Si-O, OO, Si-Al, O-Al and Al-Al in models when the temperature and pressure are lowered. REFERENCES [1] Hoang V. V., Linh N. N. and Hung N. H. 2007. Structure and dynamics of liquid and amorphous Al2O3.2SiO2. Eur. Phys. J. 111: 37-48. [2] Matthew H. F., 2004. 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