Advances in Machine Learning Molecular Dynamics to Assist Materials Nucleation and Solidification Research

doi:10.11900/0412.1961.2024.00192

Acta Metall Sin

2024, Vol. 60

Issue (10): 1329-1344 DOI: 10.11900/0412.1961.2024.00192

Overview

Current Issue | Archive | Adv Search

Advances in Machine Learning Molecular Dynamics to Assist Materials Nucleation and Solidification Research

CHEN Mingyi¹^,², HU Junwei¹^,², YU Yaochen¹^,², NIU Haiyang¹^,²(

)

1 State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China
2 School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Cite this article:

CHEN Mingyi, HU Junwei, YU Yaochen, NIU Haiyang. Advances in Machine Learning Molecular Dynamics to Assist Materials Nucleation and Solidification Research. Acta Metall Sin, 2024, 60(10): 1329-1344.

Download:

HTML

PDF(2404KB)
Export: BibTeX | EndNote (RIS)

Abstract

Solidification nucleation is an everlasting research topic in the fields of materials science and condensed matter physics. Molecular dynamics (MD) and enhanced sampling methods provide a powerful means to observe the microscopic mechanisms of solidification processes in situ at the atomic level and to analyze the thermodynamic and kinetic properties of phase transitions. Recent advancements in MD simulations, particularly those incorporating machine learning (ML) techniques, have remarkably advanced our understanding of nucleation across different systems. This paper first reviews the basic theory of solidification nucleation and introduces common methods used in solidification nucleation simulation studies. It then delves into the application of ML techniques in three key areas: force fields, enhanced sampling, and order parameters. The paper further highlights several representative systems to demonstrate the practical applications of these methods. Finally, a summary and outlook on the future of ML-assisted MD simulations for studying material solidification were provided.

Key words: solidification nucleation phase transition machine learning molecular dynamics enhanced sampling

Received: 05 June 2024

ZTFLH:

TG111.4

Fund: National Natural Science Foundation of China(92370118,22003050);National Natural Science Fund for Excellent Young Scientists Fund Program (Overseas), and Research Fund of the State Key Laboratory of Solidification Proceeding (NPU) of China(2024-ZD-01)

Corresponding Authors: NIU Haiyang, professor, Tel: (029)88495240, E-mail: haiyang.niu@nwpu.edu.cn

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	CHEN Mingyi
	HU Junwei
	YU Yaochen
	NIU Haiyang

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00192 OR https://www.ams.org.cn/EN/Y2024/V60/I10/1329

Fig.1 Principles of machine learning potential
(a) Behler-Parrinello neural network (BPNN) (The subscript

i

denotes the serial number of the atom, R_i is the environmental matrix, G_i is the embedding net, D_i is the descriptor, N and N' are two fitting nets for different elements, E_i is the i-th atom's energy, E is the calculated total energy)
(b) machine learning potential based on the kernel method (x is the environmental matrix; x_i and E_i are the i-th reference configuration in the training set and the corresponding energy, respectively; α_i is the i-th fitting coefficient; k

∙

is the kernel function to measure the difference between x and x_i )

Fig.2 Machine learning to aid design of nucleation order parameters^[75] ( $d i$ is the $i$ -th input descriptor. L is the loss function. $C ∙$ is the time autocorrelation function. $λ ˜ i$ and $α i j$ are the solution of the genderized eigenvalue problem, corresponding to the eigenvalues and eigenvectors, respectively. $s$ is the collective variable established by the deep neural network. $h i θ ∙$ is the $i$ -th component of the neural network output as a function of time, where $θ$ denotes the parameter of the neural network. $t$ and $τ$ are time. CV—collective variable. TICA—time-lagged independent component analysis)
(a) Deep-LDA^[75] (b) Deep-TICA^[77]

Fig.3 Research on the nucleation mechanism of CdSe^[69]
(a) flowchart of the active learning procedure to train the deep neural network (DNN) potential (AIMD—ab initio molecular dynamics, DPMD/DP-WTMetaD—DNN-based molecular dynamics (DPMD) simulations and their variants accelerated by WTMetaD (DP-WTMetaD), DFT—density functional theory)
(b) distribution of training set configurations in the two-dimensional space mapped with the principal component analysis (PCA) (Typical structures are marked in the plot. Green and brown spheres are Se and Cd, respectively. ZB—zinc blende, WZ—wurtzite)
(c, d) error of the DNN potential relative to the DFT calculation. The values of mean absolute error (MAE) correspond to the potential energy (E) (c) and the force (F) (d) are stamped in the plot^[69] (NN—neural network)

Fig.4 Research on the nucleation process of Si^[66]
(a) distributions of the order parameters using local structure factor S_i (q₁) in the liquid and solid phase (Inset shows the structure factor patterns and the position of the module of the wave number

q 1

, which corresponds to the first peak of the XRD spectrum shown in the inset)
(b) distributions of the configurations as a function of the structure factor at the first peak in well-tempered sampling, liquid phase, and solid phase, respectively (Insets present the typical configuration, whose structure factor peak corresponds to the position of abscissa. Disordered configurations are colored in grey, and ordered ones, i.e., ice-like structures, are colored in blue. The same applies to Fig.4c)
(c) free energy surface of the solidification at different temperatures (k_B—Boltzmann constant, T—temperature)
(d) snapshots of Si nuclei

Fig.5 Molecular dynamics simulation of the homogeneous ice nucleation with ab-initio accuracy^[91] (The areas wrapped in orange are the ice nuclei. The areas wrapped in green are high-mobile regions. Solid-like, liquid-like, and imperfect coordinated water molecules are colored in blue, pink, and red, respectively)

Fig.6 Nucleation behaviors of Ga^[98]
(a) temperature vs critical sizes (N_c) of α-Ga and β-Ga
(b) temperature vs nucleation free energy barriers (ΔG) of α-Ga and β-Ga

Fig.7 Research on crystal structure of vaterite CaCO₃^[102]
(a) theoretically grown vaterite with an intergrowth of different polytypic structures (The symbols “+” and “-” inserted indicate the stacking sequences of carbonate layers)
(b) selected area electron diffraction (SAED) pattern of vaterite along [103]_m,_{where the subscript letter “m” denotes the monolithic crystal system
(c) two-dimensional free energy surface of vaterite as a function of order parameter and temperature}

1	Alder B J. Studies in molecular dynamics. III. A mixture of hard spheres [J]. J. Chem. Phys., 1964, 40: 2724
2	Alder B J, Wainwright T E. Studies in molecular dynamics. I. General method [J]. J. Chem. Phys., 1959, 31: 459
3	Alder B J, Wainwright T E. Phase transition for a hard sphere system [J]. J. Chem. Phys., 1957, 27: 1208
4	Car R, Parrinello M. Unified approach for molecular dynamics and density-functional theory [J]. Phys. Rev. Lett., 1985, 55: 2471 pmid: 10032153
5	Blank T B, Brown S D, Calhoun A W, et al. Neural network models of potential energy surfaces [J]. J. Chem. Phys., 1995, 103: 4129
6	Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces [J]. Phys. Rev. Lett., 2007, 98: 146401
7	Zeng J Z, Zhang D, Lu D H, et al. DeePMD-kit v2: A software package for deep potential models [J]. J. Chem. Phys., 2023, 159: 054801
8	Wang H, Zhang L F, Han J Q, et al. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics [J]. Comput. Phys. Commun., 2018, 228: 178
9	Zhang L F, Wang H, Car R, et al. Phase diagram of a deep potential water model [J]. Phys. Rev. Lett., 2021, 126: 236001
10	Qiu R, Zeng Q Y, Wang H, et al. Anomalous thermal transport across the superionic transition in ice [J]. Chin. Phys. Lett., 2023, 40: 116301
11	Wang Y, Wang J J, Hermann A, et al. Electronically driven 1D cooperative diffusion in a simple cubic crystal [J]. Phys. Rev., 2021, 11X: 011006
12	Wang X Y, Wang Z Y, Gao P Y, et al. Data-driven prediction of complex crystal structures of dense lithium [J]. Nat. Commun., 2023, 14: 2924 doi: 10.1038/s41467-023-38650-y pmid: 37217498
13	Guo F Y, Chen B, Zeng Q Y, et al. Microstructure evolution under thermo-mechanical operating of rocksalt-structure TiN via neural network potential [J]. J. Chem. Phys., 2023, 159: 204702
14	Hu T P, Tian J X, Dai F Z, et al. Impact of the local environment on Li ion transport in inorganic components of solid electrolyte interphases [J]. J. Am. Chem. Soc., 2023, 145: 1327 doi: 10.1021/jacs.2c11521 pmid: 36576963
15	Zeng J Z, Giese T J, Ekesan Ş, et al. Development of range-corrected deep learning potentials for fast, accurate quantum mechanical/molecular mechanical simulations of chemical reactions in solution [J]. J. Chem. Theory Comput., 2021, 17: 6993 doi: 10.1021/acs.jctc.1c00201 pmid: 34644071
16	Li P F, Jia X Y, Pan X L, et al. Accelerated computation of free energy profile at ab initio quantum mechanical/molecular mechanics accuracy via a semi-empirical reference potential. I. Weighted thermodynamics perturbation [J]. J. Chem. Theory Comput., 2018, 14: 5583 doi: 10.1021/acs.jctc.8b00571 pmid: 30336015
17	Volmer M, Weber A. Kinetic theory for nucleation of supersaturated structures [J]. Z. Phys. Chem., 1926, 119: 277
18	Farkas L. Keimbildungsgeschwindigkeit in übersättigten Dämpfen [J]. Z. Phys. Chem., 1927, 125U: 236
19	Becker R, Döring W. Kinetische behandlung der keimbildung in übersättigten dämpfen [J]. Ann. Phys., 1935, 416: 719
20	Zeldovich Y B. On the theory of new phase formation: Cavitation [J]. Acta Physicochem. USSR, 1943, 18: 1
21	Pruppacher H R, Klett J D, Wang P K. Microphysics of clouds and precipitation [J]. Aerosol Sci. Technol., 1998, 28: 381
22	Wang J C, Guo C, Zhang Q, et al. Recent progresses in modeling of nucleation during solidification on the atomic scale [J]. Acta Metall. Sin., 2018, 54: 204 doi: 10.11900/0412.1961.2017.00425
	王锦程, 郭灿, 张琪等. 原子尺度下凝固形核计算模拟研究的进展 [J]. 金属学报, 2018, 54: 204 doi: 10.11900/0412.1961.2017.00425
23	Sosso G C, Chen J, Cox S J, et al. Crystal nucleation in liquids: Open questions and future challenges in molecular dynamics simulations [J]. Chem. Rev., 2016, 116: 7078 doi: 10.1021/acs.chemrev.5b00744 pmid: 27228560
24	Zahn D. Thermodynamics and kinetics of prenucleation clusters, classical and non-classical nucleation [J]. ChemPhysChem, 2015, 16: 2069 doi: 10.1002/cphc.201500231 pmid: 25914369
25	Gebauer D, Kellermeier M, Gale J D, et al. Pre-nucleation clusters as solute precursors in crystallisation [J]. Chem. Soc. Rev., 2014, 43: 2348 doi: 10.1039/c3cs60451a pmid: 24457316
26	Langer J S. Theory of spinodal decomposition in alloys [J]. Ann. Phys., 1971, 65: 53
27	Rosenbluth M N, Rosenbluth A W. Further results on Monte Carlo equations of state [J]. J. Chem. Phys., 1954, 22: 881
28	Jones J E. On the determination of molecular fields. —II. From the equation of state of a gas [J]. Proc. R. Soc., 1924, 106A: 463
29	Jones J E. On the determination of molecular fields. —I. From the variation of the viscosity of a gas with temperature [J]. Proc. R. Soc., 1924, 106A: 441
30	Baskes M I. Application of the embedded-atom method to covalent materials: A semiempirical potential for silicon [J]. Phys. Rev. Lett., 1987, 59: 2666 pmid: 10035617
31	Baskes M I, Nelson J S, Wright A F. Semiempirical modified embedded-atom potentials for silicon and germanium [J]. Phys. Rev., 1989, 40B: 6085
32	Tersoff J. New empirical approach for the structure and energy of covalent systems [J]. Phys. Rev., 1988, 37B: 6991
33	Chenoweth K, Van Duin A C T, Goddard W A. ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation [J]. J. Phys. Chem., 2008, 112A: 1040
34	Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects [J]. Phys. Rev., 1965, 140: A1133
35	Hiberty P C, Leforestier C. Expansion of molecular orbital wave functions into valence bond wave functions. A simplified procedure [J]. J. Am. Chem. Soc., 1978, 100: 2012
36	Ercolessi F, Adams J B. Interatomic potentials from first-principles calculations: The force-matching method [J]. Europhys. Lett., 1994, 26: 583
37	Zhang L F, Han J Q, Wang H, et al. Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics [J]. Phys. Rev. Lett., 2018, 120: 143001
38	Jia W L, Wang H, Chen M H, et al. Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning [A]. SC20: International Conference for High Performance Computing, Networking, Storage and Analysis [C]. Atlanta: IEEE, 2020: 1
39	Zhang L F, Wang H, Muniz M C, et al. A deep potential model with long-range electrostatic interactions [J]. J. Chem. Phys., 2022, 156: 124107
40	Bartók A P, Kondor R, Csányi G. On representing chemical environments [J]. Phys. Rev., 2013, 87B: 184115
41	Jinnouchi R, Karsai F, Verdi C, et al. Descriptors representing two- and three-body atomic distributions and their effects on the accuracy of machine-learned inter-atomic potentials [J]. J. Chem. Phys., 2020, 152: 234102
42	Jinnouchi R, Karsai F, Kresse G. On-the-fly machine learning force field generation: Application to melting points [J]. Phys. Rev., 2019, 100B: 014105
43	Jinnouchi R, Lahnsteiner J, Karsai F, et al. Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on the fly with Bayesian inference [J]. Phys. Rev. Lett., 2019, 122: 225701
44	Skilling J. Maximum Entropy and Bayesian Methods [M]. Dordrecht: Springer, 1989: 89
45	Zhang Y Z, Wang H D, Chen W J, et al. DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models [J]. Comput. Phys. Commun., 2020, 253: 107206
46	Invernizzi M, Piaggi P M, Parrinello M. Unified approach to enhanced sampling [J]. Phys. Rev., 2020, 10X: 041034
47	Laio A, Parrinello M. Escaping free-energy minima [J]. Proc. Natl. Acad. Sci. USA, 2002, 99: 12562 pmid: 12271136
48	Barducci A, Bussi G, Parrinello M. Well-tempered metadynamics: A smoothly converging and tunable free-energy method [J]. Phys. Rev. Lett., 2008, 100: 020603
49	Swendsen R H, Wang J S. Replica Monte Carlo simulation of spin-glasses [J]. Phys. Rev. Lett., 1986, 57: 2607 pmid: 10033814
50	Gao Y Q. An integrate-over-temperature approach for enhanced sampling [J]. J. Chem. Phys., 2008, 128: 064105
51	Yang Y I, Niu H Y, Parrinello M. Combining metadynamics and integrated tempering sampling [J]. J. Phys. Chem. Lett., 2018, 9: 6426 doi: 10.1021/acs.jpclett.8b03005 pmid: 30354148
52	Dellago C, Bolhuis P G, Csajka F S, et al. Transition path sampling and the calculation of rate constants [J]. J. Chem. Phys., 1998, 108: 1964
53	Allen R J, Frenkel D, Ten Wolde P R. Simulating rare events in equilibrium or nonequilibrium stochastic systems [J]. J. Chem. Phys., 2006, 124: 024102
54	Allen R J, Frenkel D, Ten Wolde P R. Forward flux sampling-type schemes for simulating rare events: Efficiency analysis [J]. J. Chem. Phys., 2006, 124: 194111
55	Abrams J B, Tuckerman M E. Efficient and direct generation of multidimensional free energy surfaces via adiabatic dynamics without coordinate transformations [J]. J. Phys. Chem., 2008, 112B: 15742
56	Yu T Q, Chen P Y, Chen M, et al. Order-parameter-aided temperature-accelerated sampling for the exploration of crystal polymorphism and solid-liquid phase transitions [J]. J. Chem. Phys., 2014, 140: 214109
57	Grafke T, Vanden-Eijnden E. Numerical computation of rare events via large deviation theory [J]. Chaos, 2019, 29: 063118
58	Hartmann C, Kebiri O, Neureither L, et al. Variational approach to rare event simulation using least-squares regression [J]. Chaos, 2019, 29: 063107
59	Valsson O, Parrinello M. Variational approach to enhanced sampling and free energy calculations [J]. Phys. Rev. Lett., 2014, 113: 090601
60	Zhang J, Yang Y I, Noé F. Targeted adversarial learning optimized sampling [J]. J. Phys. Chem. Lett., 2019, 10: 5791 doi: 10.1021/acs.jpclett.9b02173 pmid: 31522495
61	Petitjean M. On the root mean square quantitative chirality and quantitative symmetry measures [J]. J. Math. Phys., 1999, 40: 4587
62	Niu H Y, Piaggi P M, Invernizzi M, et al. Molecular dynamics simulations of liquid silica crystallization [J]. Proc. Natl. Acad. Sci. USA, 2018, 115: 5348 doi: 10.1073/pnas.1803919115 pmid: 29735667
63	Sellberg J A, Huang C, McQueen T A, et al. Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature [J]. Nature, 2014, 510: 381
64	Debye P. Zerstreuung von röntgenstrahlen [J]. Ann. Phys., 1915, 351: 809
65	Lin Z B, Zhigilei L V. Time-resolved diffraction profiles and atomic dynamics in short-pulse laser-induced structural transformations: Molecular dynamics study [J]. Phys. Rev., 2006, 73B: 184113
66	Bonati L, Parrinello M. Silicon liquid structure and crystal nucleation from ab initio deep metadynamics [J]. Phys. Rev. Lett., 2018, 121: 265701
67	Zhang Y Y, Niu H Y, Piccini G M, et al. Improving collective variables: The case of crystallization [J]. J. Chem. Phys., 2019, 150: 094509
68	Yang M Y, Karmakar T, Parrinello M. Liquid-liquid critical point in phosphorus [J]. Phys. Rev. Lett., 2021, 127: 080603
69	Zhang L S, Yang M Y, Zhang S W, et al. Unveiling the crystallization mechanism of cadmium selenide via molecular dynamics simulation with machine-learning-based deep potential [J]. J. Mater. Sci. Technol., 2024, 185: 23 doi: 10.1016/j.jmst.2023.09.059
70	Niu H Y, Yang Y I, Parrinello M. Temperature dependence of homogeneous nucleation in ice [J]. Phys. Rev. Lett., 2019, 122: 245501
71	Li M D, Zhang J, Niu H Y, et al. Phase transition between crystalline variants of ordinary ice [J]. J. Phys. Chem. Lett., 2022, 13: 8601 doi: 10.1021/acs.jpclett.2c02176 pmid: 36073968
72	Deng J, Niu H Y, Hu J W, et al. Melting of MgSiO₃ determined by machine learning potentials [J]. Phys. Rev., 2023, 107B: 064103
73	Ahlawat P, Hinderhofer A, Alharbi E A, et al. A combined molecular dynamics and experimental study of two-step process enabling low-temperature formation of phase-pure α-FAPbI₃ [J]. Sci. Adv., 2021, 7: eabe3326
74	Mendels D, Piccini G M, Parrinello M. Collective variables from local fluctuations [J]. J. Phys. Chem. Lett., 2018, 9: 2776 doi: 10.1021/acs.jpclett.8b00733 pmid: 29733652
75	Bonati L, Rizzi V, Parrinello M. Data-driven collective variables for enhanced sampling [J]. J. Phys. Chem. Lett., 2020, 11: 2998 doi: 10.1021/acs.jpclett.0c00535 pmid: 32239945
76	Naritomi Y, Fuchigami S. Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: The case of domain motions [J]. J. Chem. Phys., 2011, 134: 065101
77	Bonati L, Piccini G M, Parrinello M. Deep learning the slow modes for rare events sampling [J]. Proc. Natl. Acad. Sci. USA, 2021, 118: e2113533118
78	Yuan J H, Chen Y, Duan X M, et al. CdSe optical parametric oscillator operating at 12.07 µm with 170 mW output [J]. Opt. Laser Technol., 2017, 92: 1
79	Yuan J H, Duan X M, Yao B Q, et al. Tunable 10- to 11-μm CdSe optical parametric oscillator pumped by a 2.1-μm Ho: YAG laser [J]. Appl. Phys., 2016, 122B: 202
80	Ninomiya S, Adachi S. Optical properties of cubic and hexagonal CdSe [J]. J. Appl. Phys., 1995, 78: 4681
81	Park S H, Casey M P, Falk J. Nonlinear optical properties of CdSe quantum dots [J]. J. Appl. Phys., 1993, 73: 8041
82	Steininger J. Growth of CdSe single crystals by temperature gradient solution zoning in excess Se [J]. Mater. Res. Bull., 1968, 3: 595
83	Štich I, Car R, Parrinello M. Structural bonding, dynamical, and electronic properties of liquid silicon: An ab initio molecular-dynamics study [J]. Phys. Rev., 1991, 44B: 4262
84	Bartels-Rausch T. Ten things we need to know about ice and snow [J]. Nature, 2013, 494: 27
85	Matsumoto M, Saito S, Ohmine I. Molecular dynamics simulation of the ice nucleation and growth process leading to water freezing [J]. Nature, 2002, 416: 409
86	Tanaka H. Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids [J]. Eur. Phys. J., 2012, 35E: 113
87	Bullock G, Molinero V. Low-density liquid water is the mother of ice: On the relation between mesostructure, thermodynamics and ice crystallization in solutions [J]. Faraday Discuss., 2013, 167: 371 pmid: 24640501
88	Moore E B, Molinero V. Structural transformation in supercooled water controls the crystallization rate of ice [J]. Nature, 2011, 479: 506
89	Fitzner M, Sosso G C, Cox S J, et al. Ice is born in low-mobility regions of supercooled liquid water [J]. Proc. Natl. Acad. Sci. USA, 2019, 116: 2009 doi: 10.1073/pnas.1817135116 pmid: 30670640
90	Haji-Akbari A, Debenedetti P G. Direct calculation of ice homogeneous nucleation rate for a molecular model of water [J]. Proc. Natl. Acad. Sci. USA, 2015, 112: 10582 doi: 10.1073/pnas.1509267112 pmid: 26240318
91	Chen M Y, Tan L, Wang H, et al. Imperfectly coordinated water molecules pave the way for homogeneous ice nucleation [DB/OL]. arXiv: 2304. 12665, 2023
92	Piaggi P M, Weis J, Panagiotopoulos A Z, et al. Homogeneous ice nucleation in an ab initio machine-learning model of water [J]. Proc. Natl. Acad. Sci. USA, 2022, 119: e2207294119.
93	Sanchez-Burgos I, Tejedor A R, Vega C, et al. Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations [J]. J. Chem. Phys., 2022, 157: 094503
94	Gong X G, Chiarotti G L, Parrinello M, et al. α-gallium: A metallic molecular crystal [J]. Phys. Rev., 1991, 43B: 14277
95	Narten A H. Liquid gallium: Comparison of x-ray and neutron-diffraction data [J]. J. Chem. Phys., 1972, 56: 1185
96	Daeneke T, Khoshmanesh K, Mahmood N, et al. Liquid metals: Fundamentals and applications in chemistry [J]. Chem. Soc. Rev., 2018, 47: 4073 doi: 10.1039/c7cs00043j pmid: 29611563
97	Heine V. Crystal structure of gallium metal [J]. J. Phys., 1968, 1C: 222
98	Niu H Y, Bonati L, Piaggi P M, et al. Ab initio phase diagram and nucleation of gallium [J]. Nat. Commun., 2020, 11: 2654 doi: 10.1038/s41467-020-16372-9 pmid: 32461573
99	Bosio L. Crystal structures of Ga(II) and Ga(III) [J]. J. Chem. Phys., 1978, 68: 1221
100	Piaggi P M, Parrinello M. Multithermal-multibaric molecular simulations from a variational principle [J]. Phys. Rev. Lett., 2019, 122: 050601
101	Espinosa J R, Vega C, Valeriani C, et al. Seeding approach to crystal nucleation [J]. J. Chem. Phys., 2016, 144: 034501
102	San X Y, Hu J W, Chen M Y, et al. Unlocking the mysterious polytypic features within vaterite CaCO₃ [J]. Nat. Commun., 2023, 14: 7858 doi: 10.1038/s41467-023-43625-0 pmid: 38030637
103	Zhang D, Liu X Z J, Zhang X Y, et al. DPA-2: Towards a universal large atomic model for molecular and material simulation [DB/OL]. arXiv: 2312. 15492, 2023
104	Mo P H, Li C, Zhao D, et al. Accurate and efficient molecular dynamics based on machine learning and non von Neumann architecture [J]. npj Comput. Mater., 2022, 8: 107
105	Su Y J, Fu H D, Bai Y, et al. Progress in materials genome engineering in China [J]. Acta Metall. Sin., 2020, 56: 1313 doi: 10.11900/0412.1961.2020.00199
	宿彦京, 付华栋, 白洋等. 中国材料基因工程研究进展 [J]. 金属学报, 2020, 56: 1313 doi: 10.11900/0412.1961.2020.00199
106	AIS square [EB/OL].

[1]	WANG Lin, WEI Chen, WANG Lei, WANG Jun, LI Jinshan. Simulation of Core-Shell Structure Evolution of Cu-Co Immiscible Alloys[J]. 金属学报, 2024, 60(9): 1239-1249.
[2]	CAO Shuting, ZHAO Jian, GONG Tongzhao, ZHANG Shaohua, ZHANG Jian. Effects of Cu Content on the Microstructure and Tensile Property of K4061 Alloy[J]. 金属学报, 2024, 60(9): 1179-1188.
[3]	DONG Weixia, YAO Zhongzheng, LIU Sinan, CHEN Guoxing, WANG Xun-Li, WU Zhenduo, LAN Si. Evolution of Short-to-Medium Range Orders During the Liquid-Liquid Phase Transition of a Pd-Si Metallic Glass[J]. 金属学报, 2024, 60(8): 1119-1129.
[4]	ZHU Shaoxiang, WANG Qingjiang, LIU Jianrong, CHEN Zhiyong. Macrosegregation of Zr and Mo in TC19 Titanium Alloy Ingot[J]. 金属学报, 2024, 60(7): 869-880.
[5]	GAO Xinliang, BA Wenyue, ZHANG Zheng, XI Shiping, XU Dong, YANG Zhinan, ZHANG Fucheng. Model and Analysis of Solute Microsegregation in Bainite Rail Steel During Continuous Casting Process[J]. 金属学报, 2024, 60(7): 990-1000.
[6]	CHEN Cheng, YANG Guangyu, JIN Menghui, WANG Qiang, TANG Xin, CHENG Huimin, JIE Wanqi. Effect of the Mold Positive and Negative Rotation on the Microstructure and Room-Temperature Mechanical Properties of K4169 Superalloy[J]. 金属学报, 2024, 60(7): 926-936.
[7]	BAI Zhiwen, DING Zhigang, ZHOU Ailong, HOU Huaiyu, LIU Wei, LIU Feng. Molecular Dynamics Simulation of Thermo-Kinetics of Tensile Deformation of α-Fe Single Crystal[J]. 金属学报, 2024, 60(6): 848-856.
[8]	LIU Zhuangzhuang, DING Minglu, XIE Jianxin. Advancements in Digital Manufacturing for Metal 3D Printing[J]. 金属学报, 2024, 60(5): 569-584.
[9]	MENG Zikai, MENG Zhichao, GAO Changyuan, GUO Hui, CHEN Hansen, CHEN Liutao, XU Dongsheng, YANG Rui. Molecular Dynamics Simulation of Creep Mechanism in Nanocrystalline α-Zirconium Under Various Conditions[J]. 金属学报, 2024, 60(5): 699-712.
[10]	WANG Jinxin, YAO Meiyi, LIN Yuchen, CHEN Liutao, GAO Changyuan, XU Shitong, HU Lijuan, XIE Yaoping, ZHOU Bangxin. High Temperature Steam Oxidation Behavior of Zr-1Nb- xFe Alloy Under Simulated LOCA Condition[J]. 金属学报, 2024, 60(5): 670-680.
[11]	DONG Shihu, ZHANG Hongwei, LÜ Wenpeng, LEI Hong, WANG Qiang. Numerical Simulation on Macrosegregation in Fe-C Alloy Under Solidification Shrinkage Through Interface Tracking-Dynamic Mesh Technique[J]. 金属学报, 2024, 60(3): 388-404.
[12]	ZHU Rui, WANG Junjie, ZHANG Yunhu, TIAN Zhichao, MIAO Xincheng, ZHAI Qijie. Flow and Solidification Microstructure in Metal Melts Driven by a Combined Magnetic Field[J]. 金属学报, 2024, 60(2): 231-246.
[13]	LIU Yong, ZENG Gang, LIU Hong, WANG Yu, LI Jianlong. Grain Refinement Mechanism and Research Progress of Magnesium Alloy Incorporating Zr[J]. 金属学报, 2024, 60(2): 129-142.
[14]	REN Junqiang, SHAO Shan, WANG Qi, LU Xuefeng, XUE Hongtao, TANG Fuling. Molecular Dynamics Simulation of Tensile Mechanical Properties and Deformation Mechanism of Oxygen-Containing Nano-Polycrystalline α-Ti[J]. 金属学报, 2024, 60(2): 220-230.
[15]	WEI Chen, WANG Jun, YAN Yujie, FAN Jiayi, LI Jinshan. Solidification Microstructure and Wear Properties of Undercooled Cu-Co/Cu-Co-Fe Alloys Under a High Magnetic Field[J]. 金属学报, 2024, 60(11): 1571-1583.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed