Directional Monte Carlo Lattice Search Algorithm for the Structure Search of Alumina Clusters (Al2O3)n (n=1~50)

doi:10.6023/A21050207

Abstract

Alumina nanoclusters have attracted increasing attention in many technical applications due to their excellent properties in optics, electricity, thermodynamics, chemical reactions and other aspects. Therefore, it is very important to find the optimal structure for further research. In this paper, we use the directional Monte Carlo lattice search algorithm combined with Woodley's potential function to investigate the stable structures of different sizes of alumina nanoclusters in different crystal forms (α, θ and δ). In our algorithm, the lattice was chosen from supercells which the primitive lattice cell from the inorganic crystal structure database (ICSD) was duplicated to generate large supercells of α, θ and δ phases. The initial random structure generated in the lattice, then the selective probability for all chosen and empty atoms is calculated based on the Boltzmann distribution of energy. In the directional Monte Carlo exchange, at elevated temperatures, the system has enough energy to cross energy barriers and find the basins, and at low temperatures, it converges to around the global minimum. After structure searching, we analyze and compare the stable structures of different crystal forms. The results show that the α-alumina clusters consist of multiple (Al₂O₃)₁ and form a multilayer structure, as the size increased, hexagonal aluminum began to form inside the cluster. The θ and δ alumina clusters form a stable monolayer thin film structure, with the increase of size, the monolayer film structure can still be maintained. To further study the relative stability of the cluster structure, we introduced a second-order energy difference. The second-order energy difference of θ and δ alumina clusters has obvious odd-even oscillation, and the even size alumina clusters have relatively higher stability due to better symmetry. α-Alumina is the most stable crystalline phase in the bulk phase, so we take the α-alumina clusters as the benchmark to compare the relative energy of alumina clusters with different crystal types. Through the comparison of relative energy, we found that the thin film structure of θ and δ alumina clusters under the same size is more stable than that of the α-alumina clusters. Therefore, we further carried out first-principles calculations on this film structure, and we found that this film structure has good kinetic and thermodynamic stability and good oxidation resistance.

Key words: alumina cluster, directional Monte Carlo, structure search, stabilization, monolayer thin film structure

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Ji Sun, Jiuqi Yi, Longjiu Cheng. Directional Monte Carlo Lattice Search Algorithm for the Structure Search of Alumina Clusters (Al₂O₃)_n (n=1~50)[J]. Acta Chimica Sinica, 2021, 79(9): 1154-1163.

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Fig. & Tab. 14

参数	A/(eV•Å¹²)	ρ/Å	B/eV	C/(eV•Å⁶)
Al³⁺-Al³⁺	1.0		0.0	0.00
Al³⁺-O^2-	10.0	0.2649	2409.505	0.00
O^2--O^2-	1.0	0.1490	22764.000	27.88

Table 1. Buckingham interatomic pair potential parameters for Al2O3

Figure 1. α-Al2O3, θ-Al2O3 and δ-Al2O3 crystal cell structure, aluminum atoms and oxygen atoms are represented by blue gray and red respectively. All structures in this work have been rendered with VESTA

Figure 2. The flow chart of the directed Monte Carlo lattice algorithm

Figure 3. (a), (b) and (c) show the performance comparison of directional Monte Carlo and traditional Monte Carlo when α-(Al2O3)n n=10, 30 and 50, respectively. The black curve and the red curve respectively show the change of the average energy of the 10 directional Monte Carlo and the lowest energy structure based on Markov process Monte Carlo with the step size (MC steps)

Figure 4. Comparison of convergence of three different cooling strategies for (Al2O3)n, where (a) n=10, (b) n=30, and (c) n=50

Figure 5. The structure of α-(Al2O3)n cluster, (a), (b) and (c) are the structure when n=30, 50 and 1, respectively. (d) and (e) are the partial structure intercepted from the dotted line in (a)

Figure 6. (a), (b) and (c) are the structures of different crystal faces of θ-(Al2O3)n (n=8, 32 and 48), and (d), (e) and (f) are the structures of different crystal faces of δ-Al2O3 (n=8, 32 and 48), respectively

Figure 7. The second order energy difference of (a) θ-(Al2O3)n, (b) δ-(Al2O3)n and (c) α-(Al2O3)n (n=1~50) clusters, respectively. Figure (d) shows the relative energy comparison of θ-(Al2O3)n and δ-(Al2O3)n with α-(Al2O3)n at (n=1~50)

Figure 8. (a), (b) and (c) are the stable structures of θ, δ and α alumina with large second order difference energies, respectively

Figure 9. Single cell left view (a), main view (b), top view (c) of θ-Al2O3 monolayer structure. The red is O, and the gray green is Al

Figure 10. Phonon dispersion curve of θ-Al2O3 monolayer in the first Brillouin region

Figure 12. The θ-Al2O3 monolayer was simulated with oxygen molecules in molecular dynamics, during a timescale of 5 ps

Figure 13. Diagram of the process of stripping a single layer from its body phase on the left (a), peel energy under different peel distances on the right (b)

References 55

[1]	Brey, W. S.; Krieger, K. A. J. Am. Chem. Soc. 1949, 71, 3637. doi: 10.1021/ja01179a016
[2]	Ernst, M.; Lurot, F.; Schrotter, J.-C. Appl. Catal. B-Environ. 2004, 47, 15. doi: 10.1016/S0926-3373(03)00290-X
[3]	Qin, Y. Acta Phys.-Chim. Sin. 2019, 35, 1305. (in Chinese) doi: 10.3866/PKU.WHXB201906082
	( 覃勇, 物理化学学报, 2019, 35, 1305.)
[4]	Lukin, E. S.; Tarasova, S. V.; Korolev, A. V. Glass Ceram. 2001, 58, 105. doi: 10.1023/A:1010999432041
[5]	Schembri, V.; Heijmen, B. J. M. Med. Phys. 2007, 34, 2113. pmid: 17654914
[6]	Martínez, A.; Sansores, L. E.; Salcedo, R.; Tenorio, F. J.; Ortiz, J. V. J. Phys. Chem. A 2002, 106, 10630. doi: 10.1021/jp0213102
[7]	Turco, R. P.; Toon, O. B.; Whitten, R. C.; Cicerone, R. J. Nature 1982, 298, 830. doi: 10.1038/298830a0
[8]	Magg, N.; Giorgi, J. B.; Schroeder, T.; Bäumer, M.; Freund, H.-J. J. Phys. Chem. B 2002, 106, 8756. doi: 10.1021/jp0204556
[9]	Silva, F. T.; Silva, M. X.; Belchior, J. C. Front. Chem. 2019, 7, 707. doi: 10.3389/fchem.2019.00707
[10]	Jäger, M.; Schäfer, R.; Johnston, R. L. Nanoscale 2019, 11, 9042. doi: 10.1039/c9nr02031d pmid: 31025685
[11]	Yañez, O.; Báez-Grez, R.; Inostroza, D.; Rabanal-León, W. A.; Pino-Rios, R.; Garza, J.; Tiznado, W. J. Chem. Theory Comput. 2019, 15, 1463. doi: 10.1021/acs.jctc.8b00772
[12]	Zhou, L.-Q.; Yan, Z.-H.; Yue, Z.-Y.; Liang, X.-Q.; Zhao, J.-J. J. At. Mol. Phys. 2017, 34, 441. (in Chinese)
	( 周丽琴, 闫兆鸿, 岳子渝, 梁晓庆, 赵纪军, 原子与分子物理学报, 2017, 34, 441.)
[13]	Zhao, J.; Shi, R.; Sai, L.; Huang, X.; Su, Y. Mol. Simulat. 2016, 42, 809. doi: 10.1080/08927022.2015.1121386
[14]	Zhou, Y.; Zhao, Z.; Cheng, D. Comput. Phys. Commun. 2020, 247, 106945. doi: 10.1016/j.cpc.2019.106945
[15]	Mai, G.; Hong, Y.; Fu, S.; Lin, Y.; Hao, Z.; Huang, H.; Zhu, Y. Swarm Evol. Comput. 2020, 57, 100710. doi: 10.1016/j.swevo.2020.100710
[16]	Li, M.-S.; Huang, X.-Y.; Liu, H.-S.; Liu, B.-X.; Wu, Y.; Ai, F.-R. Acta Chim. Sinica 2013, 71, 1053. (in Chinese) doi: 10.6023/A13020193
	( 李孟山, 黄兴元, 柳和生, 柳炳祥, 武燕, 艾凡荣, 化学学报, 2013, 71, 1053.) doi: 10.6023/A13020193
[17]	Liu, T.-D.; Chen, J.-R.; Hong, W.-P.; Shao, G.-F.; Wang, T. N.; Zheng, J.-W.; Wen, Y.-H. Acta Phys. Sin. 2013, 62, 192. (in Chinese)
	( 刘暾东, 陈俊仁, 洪武鹏, 邵桂芳, 王婷娜, 郑骥文, 文玉华, 物理学报, 2013, 62, 192.)
[18]	Wang, Y.-C.; Lv, J.; Ma, Y.-M. Chin. Sci. Bull. 2015, 60, 2580. (in Chinese) doi: 10.1360/N972015-00575
	( 王彦超, 吕健, 马琰铭, 科学通报, 2015, 60, 2580.)
[19]	Gao, P.-Y.; Lv, J.; Wang, Y.-C.; Ma, Y.-M. Physics 2017, 46, 582. (in Chinese)
	( 高朋越, 吕健, 王彦超, 马琰铭, 物理, 2017, 46, 582.)
[20]	Zhang, J.; Dolg, M. Phys. Chem. Chem. Phys. 2015, 17, 24173. doi: 10.1039/c5cp04060d pmid: 26327507
[21]	Zhang, J.; Dolg, M. Phys. Chem. Chem. Phys. 2016, 18, 3003. doi: 10.1039/c5cp06313b pmid: 26738568
[22]	Zhang, J.; Glezakou, V.-A.; Rousseau, R.; Nguyen, M.-T. J. Chem. Theory Comput. 2020, 16, 3947. doi: 10.1021/acs.jctc.9b01107 pmid: 32364725
[23]	Wang, Q.-W.; Li, X.-Q.; Chen, H.-J.; Zhang, J.-W. 2017, 34, 1040. (in Chinese)
	( 王全武, 李喜全, 陈恒杰, 张家伟, 原子与分子物理学报, 2017, 34, 1040.)
[24]	Shao, X.; Cheng, L.; Cai, W. J. Comput. Chem. 2004, 25, 1693. doi: 10.1002/(ISSN)1096-987X
[25]	Shao, X.; Yang, X.; Cai, W. J. Comput. Chem. 2008, 29, 1772. doi: 10.1002/jcc.20938
[26]	Wu, X.; He, C. Chem. Phys. 2012, 405, 100. doi: 10.1016/j.chemphys.2012.06.015
[27]	Wu, X.; Cheng, W. J. Chem. Phys. 2014, 141, 124110. doi: 10.1063/1.4896152
[28]	Wei, D.; Ma, W.; Wu, X.; Cheng, L. Chem. Phys. 2021, 543, 111097. doi: 10.1016/j.chemphys.2021.111097
[29]	Siddique, N.; Adeli, H. Int. J. Artif. Intell. Tools 2016, 25, 1630001. doi: 10.1142/S0218213016300015
[30]	Karabin, M.; Stuart, S. J. J. Chem. Phys. 2020, 153, 114103. doi: 10.1063/5.0018725 pmid: 32962382
[31]	Rondina, G. G.; Da Silva, J. L. F. J. Chem Inf. Model. 2013, 53, 2282. doi: 10.1021/ci400224z
[32]	Huang, R.; Bi, J.-X.; Li, L.; Wen, Y.-H. J. Chem Inf. Model. 2020, 60, 2219. doi: 10.1021/acs.jcim.0c00130 pmid: 32203652
[33]	Liu, T.-D.; Li, Z.-P.; Ji, Q.-S.; Shao, G.-F.; Fan, T.-E.; Wen, Y.-H. Acta Phys. Sin. 2017, 66, 57. (in Chinese)
	( 刘暾东, 李泽鹏, 季清爽, 邵桂芳, 范天娥, 文玉华, 物理学报, 2017, 66, 57.)
[34]	Northby, J. A. J. Chem. Phys. 1987, 87, 6166. doi: 10.1063/1.453492
[35]	Rahm, J. M.; Erhart, P. Nano Lett. 2017, 17, 5775. doi: 10.1021/acs.nanolett.7b02761
[36]	He, C.-C.; Liao, J.-H.; Yang, X.-B. Acta Phys. Sin. 2017, 66, 85. (in Chinese)
	( 何长春, 廖继海, 杨小宝, 物理学报, 2017, 66, 85.)
[37]	Gutiérrez, G.; Johansson, B. Phys. Rev. B 2002, 65, 104202. doi: 10.1103/PhysRevB.65.104202
[38]	Woodley, S. M. Proc. R. Soc. A 2011, 467, 2020. doi: 10.1098/rspa.2011.0009
[39]	Bush, T. S.; Gale, J. D.; Catlow, C. R. A.; Battle, P. D. J. Mater. Chem. 1994, 4, 831. doi: 10.1039/jm9940400831
[40]	Romero, D.; Barrón, C.; Gómez, S. Comput. Phys. Commun. 1999, 123, 87. doi: 10.1016/S0010-4655(99)00259-3
[41]	Momma, K.; Izumi, F. J. Appl. Crystallogr. 2011, 44, 1272. doi: 10.1107/S0021889811038970
[42]	Lewis, J.; Schwarzenbach, D.; Flack, H. D. Acta Crystallogr. Sect. A 1982, 38, 733. doi: 10.1107/S0567739482001478
[43]	Zhou, R.-S.; Snyder, R. L. Acta Crystallogr. Sect. B 1991, 47, 617. doi: 10.1107/S0108768191002719
[44]	Repelin, Y.; Husson, E. Mater. Res. Bull. 1990, 25, 611. doi: 10.1016/0025-5408(90)90027-Y
[45]	Yu, K.; Wang, X.; Chen, L.; Wang, L. J. Chem. Phys. 2019, 151, 214105. doi: 10.1063/1.5127913
[46]	Paleico, M. L.; Behler, J. J. Chem. Phys. 2020, 152, 094109. doi: 10.1063/1.5142363
[47]	Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169. pmid: 9984901
[48]	Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15. doi: 10.1016/0927-0256(96)00008-0
[49]	Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. pmid: 10062328
[50]	Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188. doi: 10.1103/PhysRevB.13.5188
[51]	Togo, A.; Tanaka, I. Scr. Mater. 2015, 108, 1. doi: 10.1016/j.scriptamat.2015.07.021
[52]	Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. doi: 10.1063/1.3382344
[53]	Laurens, G.; Amans, D.; Lam, J.; Allouche, A.-R. Phys. Rev. B 2020, 101, 045427. doi: 10.1103/PhysRevB.101.045427
[54]	Van den Bossche, M.; Noguera, C.; Goniakowski, J. Nanoscale 2020, 12, 6153. doi: 10.1039/c9nr10487a pmid: 32133480
[55]	McHale, J. M.; Auroux, A.; Perrotta, A. J.; Navrotsky, A. Science 1997, 277, 788. doi: 10.1126/science.277.5327.788

定向Monte Carlo格点搜索算法用于氧化铝团簇(Al₂O₃)_n (n=1~50)的结构搜索

Directional Monte Carlo Lattice Search Algorithm for the Structure Search of Alumina Clusters (Al₂O₃)_n (n=1~50)

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定向Monte Carlo格点搜索算法用于氧化铝团簇(Al2O3)n (n=1~50)的结构搜索