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In amorphous alloys, the atomic arrangement exhibits short-range order while lacking long-range order. Despite the lack of long-range order, the local atomic arrangements and interactions can still significantly affect the motion of atoms. The microstructural features and structural evolution mechanisms of amorphous materials are key areas of research, and the dynamics of amorphous alloys can provide insights into their formation process and structural evolution. The cage effect refers to the phenomenon where atoms are trapped by their surrounding atoms, making them difficult to migrate or diffuse freely. This leads to slower diffusion rates and higher viscosities in these materials. Atomic concentration is one of the crucial factors that influence the structures and properties of amorphous materials. Variation in concentration can significantly change the material’s structure. Adjusting the atomic concentration can lead to the difference in diffusion rate between elements in the amorphous alloys, resulting in heterogeneous distributions of elements in different regions, which in turn affects the deformation characteristics of amorphous materials. This study aims to investigate the effect of Pd atomic concentration on the diffusion hindrance of Si atoms, as well as its influence on the local symmetry and order of the system. To achieve this objective, molecular dynamics simulations are employed to explore the relaxation process of atoms in Pd-Si amorphous alloys at different Pd atomic concentrations, and parameters related to atomic diffusion, displacement distribution, system symmetry, and order are analyzed. The results show that increasing the concentration of Pd atoms leads to a more significant hindrance to the diffusion of Si atoms, manifested as an increase in the abnormal peak values of the non-Gaussian parameters and a decrease in the standard deviation of the displacement. This indicates that a higher Pd atom concentration enhances the cage effect of Si atoms, thus restricting their diffusion. Additionally, the increase in Pd concentration promotes the transition from unsaturated to saturated bond type in the Pd-Si amorphous alloy, and also leads the system’s configurational entropy to decrease. This consequently enhances the local symmetry and order of the Pd-Si amorphous alloys, leading Si atoms to be located in the center of more closed, higher-symmetry, and more compact cluster structure, which strengthens their cage effect and local symmetry. This study investigates the influence of Pd atom concentration on the diffusion behavior and local environment of Si atoms, providing a new insight into the structural evolution of amorphous alloys.
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Keywords:
- molecular dynamics /
- Pd-Si amorphous alloys /
- atomic concentration /
- cage effect /
- local symmetry
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图 1 Pd-Si非晶合金弛豫过程中Pd原子和Si原子的均方位移随时间的变化 (a) Pd; (b) Si
Figure 1. Time-dependent evolution of mean square displacement of Pd and Si atoms during the relaxation in Pd-Si amorphous alloys: (a) Pd; (b) Si.
图 2 Pd-Si非晶合金弛豫过程中Si原子的非高斯参数随时间的变化 (a) 不同浓度体系Si原子的非高斯参数; (b) 不同浓度体系Si原子非高斯参数异常峰峰值
Figure 2. Variation of non-Gaussian parameters of Si atoms in different systems during the relaxation of Pd-Si amorphous alloys: (a) Non-Gaussian parameters; (b) abnormal peak values of non-Gaussian parameters.
图 3 Pd-Si非晶合金中Si原子在0.08 ps内的Von Hove相关函数的自部分
Figure 3. Self-part of the Von Hove correlation function for the time evolution of Si atoms in Pd-Si amorphous alloys during 0.08 ps.
图 4 Pd-Si非晶合金中Si原子的平均位移与位移标准差
Figure 4. Average displacement and displacement standard deviation of Si atoms in Pd-Si amorphous alloys.
图 5 Pd-Si非晶合金在300 K时的结构特征 (a) 偏双体分布函数gPd-Si(r); (b) 结构示意图
Figure 5. Structural characteristics of Pd-Si amorphous alloys at 300 K: (a) The pair distribution function; (b) visual displays.
图 6 Si原子的近邻Pd原子个数 (a) 以第一峰为截断距离; (b) 以第一谷为截断距离
Figure 6. Number of neighboring Pd atoms for Si atoms: (a) The first peak value as the truncation distance; (b) the first valley value as the truncation distance.
图 7 Pd-Si非晶合金在300 K时的H-A键型分析 (a) 典型H-A键型所占百分比; (b) 典型H-A键型结构示意图
Figure 7. Analysis of H-A bond types of Pd-Si amorphous alloys at 300 K: (a) Percentage of typical H-A bond types; (b) visual displays of H-A bond types.
图 8 Pd-Si非晶合金中在300 K时体系中以Si原子为中心的典型团簇分析 (a) 团簇数目; (b) 团簇结构示意图
Figure 8. Analysis of typical cluster centered on Si atoms in Pd-Si amorphous alloys at 300 K: (a) Number of clusters; (b) visual displays of cluster structure.
图 9 Pd-Si非晶合金的构型熵
Figure 9. Configuration entropy of Pd-Si amorphous alloys.
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[1] Qiao J C, Pelletier J M 2014 J. Mater. Sci. Technol. 30 523
Google Scholar
[2] Abrosimova G E 2011 Phys. Usp. 54 1227
Google Scholar
[3] Cornet A, Garbarino G, Zontone F, Chushkin Y, Jacobs J, Pineda E, Deschamps T, Li S, Ronca A, Shen J, Morard G, Neuber N, Frey M, Busch R, Gallino I, Mezouar M, Vaughan G, Ruta B 2023 Acta Mater. 255 119065
Google Scholar
[4] Zella L, Moon J, Keffer D, Egami T 2022 Acta Mater. 239 118254
Google Scholar
[5] 陈贝, 邓永和, 祁青华, 高明, 文大东, 王小云, 彭平 2024 物理学报 73 026101
Google Scholar
Chen B, Deng Y H, Qi Q H, Gao M, Wen D D, Wang X Y, Peng P 2024 Acta Phys. Sin. 73 026101
Google Scholar
[6] Gao M , Wen D D, Cao G Q, Zhang Y W, Deng Y H, Hu J H 2023 Appl. Surf. Sci. 640 158286
Google Scholar
[7] Faruq M, Villesuzannea A, Shao G S 2018 J. Non-Cryst. Solids 487 72
Google Scholar
[8] Zhou Z Y, Yang Q, Yu H B 2024 Prog. Mater Sci. 145 101311
Google Scholar
[9] Deng Y H, Chen B, Qi Q H, Li B B, Gao M, Wen D D, Wang X Y, Peng P 2024 Chin. Phys. B 33 047102
Google Scholar
[10] Raya I, Chupradit S, Kadhim M M, Mahmoud M Z, Jalil A T, Surendar A, Ghafel S T, Mustafa Y F, Bochvar A N 2022 Chin. Phys. B 31 016401
Google Scholar
[11] Jiang J, Sun W F, Luo N 2022 Mater. Today Commun. 31 103861
Google Scholar
[12] Laws K J, Granata D, Löffler J F 2016 Acta Mater. 103 735
Google Scholar
[13] Fernández R, Carrasco W, Zúñiga A 2010 J. Non-Cryst. Solids 356 1665
Google Scholar
[14] Chen Y X, Pan S P, Lu X Q, Kang H, Zhang Y H, Zhang M, Feng S D, Ngai K L, Wang L M 2022 J. Non-Cryst. Solids 590 121699
Google Scholar
[15] Gao Q, Jiang Y, Liu Z, Zhang H, Jiang C, Zhang X, Li H 2020 Mater. Sci. Eng., A 779 139139
Google Scholar
[16] Liu C Y, Maaß R 2018 Adv. Funct. Mater. 28 1800388
Google Scholar
[17] Pourasghar A, Kamarian S 2015 J. Vib. Control 21 2499
Google Scholar
[18] Celtek M, Sengul S, Domekeli U, Guder V 2023 J. Mol. Liq. 372 121163
Google Scholar
[19] Nandam S H, Adjaoud O, Schwaiger R, Ivanisenko Y, Chellali M R, Wang D, Albe K, Hahn H 2020 Acta Mater. 193 252
Google Scholar
[20] Verlet L 1967 Phys. Rev. 159 98
Google Scholar
[21] Available at https://www.google.com/site/eampotentials/Table/PdSi
[22] Priezjev N V 2020 Comput. Mater. Sci. 174 109477
Google Scholar
[23] Moon J 2021 J. Appl. Phys. 130 055101
Google Scholar
[24] Sun L, Peng C, Cheng Y, Song K, Li X, Wang L 2021 J. Non-Cryst. Solids 563 120814
Google Scholar
[25] Li Y G, Suleiman K, Xu Y 2024 Phys. Rev. E 109 014139
Google Scholar
[26] Wen T Q, Sun Y, Ye B L, Tang L, Yang Z J, Ho K M, Wang C Z, Wang N 2018 J. Appl. Phys. 123 045108
Google Scholar
[27] Deng Y H, Wen D D, Li Y, Liu J, Peng P 2018 Philos. Mag. 98 2861
Google Scholar
[28] Wen D D, Deng Y H, Liu J, Tian Z A, Peng P 2017 Comput. Mater. Sci. 140 275
Google Scholar
[29] Feng S D, Chan K C, Zhao L, Pan S P, Qi L, Wang L M, Liu R P 2018 Mater. Des. 158 248
Google Scholar
[30] Liu R S, Liu H R, Dong K J, Hou Z Y, Tian Z A, Peng P, Yu A B 2009 J. Non-Cryst. Solids 355 541
Google Scholar
[31] Zhou Y, Liang Y C, Zhou L L, Mo Y F, Wu R L, Tian Z A 2023 J. Non-Cryst. Solids 612 122354
Google Scholar
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