Neural Network Molecular Dynamics Study of Ultrafast Laser-Induced Melting of Copper Nanofilms
GAO Tianyu1,2, ZENG Qiyu1,2(), CHEN Bo1,2, KANG Dongdong1,2, DAI Jiayu1,2()
1 College of Science, National University of Defense Technology, Changsha 410072, China 2 Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410072, China
Cite this article:
GAO Tianyu, ZENG Qiyu, CHEN Bo, KANG Dongdong, DAI Jiayu. Neural Network Molecular Dynamics Study of Ultrafast Laser-Induced Melting of Copper Nanofilms. Acta Metall Sin, 2024, 60(10): 1439-1450.
Exploring ultrafast structural transitions in materials triggered by femtosecond laser pulses—from their condensed states to high-temperature, high-pressure conditions, and potentially to ideal plasmas—is a crucial scientific endeavor with profound implications for fields such as inertial confinement fusion, metal additive manufacturing, and laser processing. These extreme conditions, which are challenging to replicate and directly observe in experiments due to temporal and spatial resolution limitations, require theoretical models and simulations to decode the underlying microscopic mechanisms. Molecular dynamics (MD) simulations, especially when paired with advanced potential energy surfaces, are effective tools for addressing these challenges. However, maintaining a balance between computational efficiency and physical accuracy, particularly when simulating excited states induced by laser interactions, remains a formidable task. In this context, neural network potential energy surfaces (NNPES) have demonstrated exceptional capability for capturing the complex interactions and properties of materials under extreme conditions, providing vital links between quantum mechanics and macroscale phenomena. Using Cu as a prototypical example, the ability of NNPES to accurately depict lattice vibrations, thermophysical properties, and complex dynamics during laser-matter interactions has been demonstrated. By seamlessly integrating NNPES with a two-temperature MD model, this study directly simulates the atomic-scale dynamics of Cu thin films subjected to intense pulsed laser irradiation. This innovative approach, which combines quantum-level accuracy with large-scale thermodynamics and detailed microstructural evolution, provides unprecedented insights into the fundamental mechanisms of laser-induced melting. Our findings reveal two distinct melting behaviors in Cu, dependent on laser fluence. At fluences near the melting threshold, a heterogeneous melting process initiated at the film surface because of the lower free energy barrier was observed. The solid-liquid interface then moves inward at velocities of tens of meters per second, requiring hundreds of picoseconds for melting to complete. Conversely, at fluences well above the threshold, Cu films experience rapid and homogeneous melting, markedly different from conventional heating-induced melting. Here, the lattice temperature almost instantaneously exceeds the thermal stability limit, leading to uniform liquid nucleation and rapid growth throughout the film, culminating in complete melting within just tens of picoseconds. This study not only illuminates the atomic-scale dynamics of laser-induced melting but also underscores the transition from heterogeneous to homogeneous melting mechanisms as a function of laser fluence. This study serves as an invaluable research tool for enhancing our understanding of laser-matter interactions and their potential applications in optimizing laser-based manufacturing processes and predicting material behavior under extreme conditions. Moreover, the reliability and versatility of NNPES set the stage for extending the research to more complex systems, including alloys and amorphous materials. This expansion fosters robust connections between microscopic theories and macroscale applications, deepening our understanding of material responses to intense laser irradiation. Future studies employing this framework could explore complex physical phenomena such as explosive boiling and material disintegration during laser ablation, offering unique atomic-scale insights that could pave the way for groundbreaking discoveries and technological advancements.
Fund: National Natural Science Foundation of China(12104507);Science and Technology Innovation Program of Hunan Province(2021RC4026);Postgraduate Technology Innovation Program of Hunan Province(CX20220070)
Corresponding Authors:
DAI Jiayu, professor, Tel: (0731)87001006, E-mail: jydai@nudt.edu.cn; ZENG Qiyu, Tel: 18374847919, E-mail: zengqiyu@nudt.edu.cn
Table 1 Details of the exploration strategy for the deep potential (DP) model of Cu system under different thermodynamics conditions
Fig.1 Comparisions of DP model predicted energy from DP model (EDP),force (fDP), and virial tensor (VDP) of Cu with the energy (EDFT), force (fDFT), and virial tensor (VDFT) on the training set calculated by density functional theory (DFT) (a) EDP-EDFT (b) fDP-fDFT (c) VDP-VDFT
Item
a0 / nm
Tm / K
ΔHm / (kJ·kg-1)
εm / (kJ·kg-1)
Relative error / %
1.12
0.39
0.52
0.40
DP result
0.3655
1275 ± 25
232.3 ± 11.2
658.7 ± 49.1
Experiment result
0.3615[48]
1280[51]
231.1[53]
661.3[51,53-56]
Table 2 Lattice constant (a0), melting point (Tm), latent heat of phase transition (ΔHm), and melting threshold (εm) of Cu obtained by using deep potential, and experimental results [48,51,53-56] for comparison
Fig.2 Phonon spectrum of solid copper obtained using DP model, and the experimental result[50] for comparison (The horizontal axis shows the value of the in-plane wave vector, along the Γ-X-W-X-U-Γ-L paths in the frst Brillouin zone)
Fig.3 DP model results and experimental results of Cu melting point under different pressure conditions (The red dots are the melting points under different pressure conditions calculated using DP, the red curve is the melting curve fitted using Simon-Glatzel equation[52], and the silver squares are the experimental result[51])
Fig.4 Lattice heat capacity (cp ) and electron heat capacity (ce) of Cu (a) cp of Cu varied with ionic temperature (T) (The red dots are the result obtained using the DP potential, and the silver squares are the experimental result[54]) (b) ce of Cu varied with electron temperature (Te) (The red dots are the result of this work, the dashed blue lines are Smirnov's KS-DFT result[55] and the silver squares are the experimental result[56])
Fig.5 Evolutionary dynamics of Cu thin films at the laser flux of 18 mJ/cm2 (a) evolution of ion temperature (Ti) and (Te) over time (b1-b4) evolutions of Te (b1), Ti (b2), density (ρ) (b3), and pressure (P) (b4) in different regions in the z direction of the Cu film with time (c1-c6) atomic scale structural evolutions at time t = 0 ps (c1), 50 ps (c2), 100 ps (c3, c6), 150 ps (c4), and 200 ps (c5) (Fig.5c6 is the locally enlarged view of Fig.5c3, and polyhedral surface meshes (white interface) around fcc-type (brass) and liquid-type (gray) particles are constructed to highlight the heterogeneous phase transition)
Fig.6 Evolutionary dynamics of Cu thin films at the laser flux of 30 mJ/cm2 (a) evolutions of Ti and Te over time (b1-b4) evolutions of Te (b1), Ti (b2), ρ (b3), and P (b4) in different regions in the z direction of the Cu film with time (c1-c6) atomic scale structural evolutions at t = 0 ps (c1), 4 ps (c2), 8 ps (c3, c6), 12 ps (c4), and 16 ps (c5) (Fig.6c6 is the locally enlarged view of Fig.6c3, and polyhedral surface meshes (white interface) around fcc-type (brass) and liquid-type (gray) particles are constructed to highlight the homogeneous phase transition)
1
Abu-Shawareb H, Acree R, Adams P, et al. Lawson criterion for ignition exceeded in an inertial fusion experiment [J]. Phys. Rev. Lett., 2022, 129: 075001
2
Shugaev M V, Wu C P, Armbruster O, et al. Fundamentals of ultrafast laser-material interaction [J]. MRS Bull., 2016, 41: 960
3
Roy N K, Dibua O G, Jou W, et al. A comprehensive study of the sintering of copper nanoparticles using femtosecond, nanosecond, and continuous wave lasers [J]. J. Micro Nano-Manuf., 2018, 6: 010903
4
Cheng C W, Chang C L, Chen J K, et al. Femtosecond laser melting of silver nanoparticles: Comparison of model simulations and experimental results [J]. Appl. Phys., 2018, 124A: 371
5
Zhang H, Li C, Bevillon E, et al. Ultrafast destructuring of laser-irradiated tungsten: Thermal or nonthermal process [J]. Phys. Rev., 2016, 94B: 224103
6
Chen Z, Mo M, Soulard L, et al. Interatomic potential in the nonequilibrium warm dense matter regime [J]. Phys. Rev. Lett., 2018, 121: 075002
7
Ernstorfer R, Harb M, Hebeisen C T, et al. The formation of warm dense matter: Experimental evidence for electronic bond hardening in gold [J]. Science, 2009, 323: 1033
doi: 10.1126/science.1162697
pmid: 19164708
8
Mo M Z, Chen Z, Li R K, et al. Heterogeneous to homogeneous melting transition visualized with ultrafast electron diffraction [J]. Science, 2018, 360: 1451
doi: 10.1126/science.aar2058
pmid: 29954977
9
Mo M Z, Murphy S, Chen Z J, et al. Visualization of ultrafast melting initiated from radiation-driven defects in solids [J]. Sci. Adv., 2019, 5: eaaw0392
10
Wu J, Tang M X, Zhao L R, et al. Ultrafast atomic view of laser-induced melting and breathing motion of metallic liquid clusters with MeV ultrafast electron diffraction [J]. Proc. Natl. Acad. Sci. USA, 2022, 119: e2111949119
11
Mahieu B, Jourdain N, Ta Phuoc K, et al. Probing warm dense matter using femtosecond X-ray absorption spectroscopy with a laser-produced betatron source [J]. Nat. Commun., 2018, 9: 3276
doi: 10.1038/s41467-018-05791-4
pmid: 30115918
12
Jourdain N, Lecherbourg L, Recoules V, et al. Ultrafast thermal melting in nonequilibrium warm dense copper [J]. Phys. Rev. Lett., 2021, 126: 065001
13
Chen Z, Curry C B, Zhang R, et al. Ultrafast multi-cycle terahertz measurements of the electrical conductivity in strongly excited solids [J]. Nat. Commun., 2021, 12: 1638
doi: 10.1038/s41467-021-21756-6
pmid: 33712576
14
Hohlfeld J, Wellershoff S S, Güdde J, et al. Electron and lattice dynamics following optical excitation of metals [J]. Chem. Phys., 2000, 251: 237
15
Lin Z B, Zhigilei L V. Thermal excitation of d band electrons in Au: Implications for laser-induced phase transformations [A]. Proceedings of SPIE 6261, High-Power Laser Ablation VI [C]. Taos: SPIE, 2006: 62610U
16
Lin Z B, Zhigilei L V, Celli V. Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium [J]. Phys. Rev., 2008, 77B: 075133
17
Lee J W, Kim M, Kang G, et al. Investigation of nonequilibrium electronic dynamics of warm dense copper with femtosecond X-ray absorption spectroscopy [J]. Phys. Rev. Lett., 2021, 127: 175003
18
Grolleau A, Dorchies F, Jourdain N, et al. Femtosecond resolution of the nonballistic electron energy transport in warm dense copper [J]. Phys. Rev. Lett., 2021, 127: 275901
19
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
20
Molina J M, White T G. A molecular dynamics study of laser-excited gold [J]. Matter Radiat. Extremes, 2022, 7: 036901
21
Ivanov D S, Zhigilei L V. Effect of pressure relaxation on the mechanisms of short-pulse laser melting [J]. Phys. Rev. Lett., 2003, 91: 105701
22
Daraszewicz S L, Giret Y, Naruse N, et al. Structural dynamics of laser-irradiated gold nanofilms [J]. Phys. Rev., 2013, 88B: 184101
23
Murphy S T, Daraszewicz S L, Giret Y, et al. Dynamical simulations of an electronically induced solid-solid phase transformation in tungsten [J]. Phys. Rev., 2015, 92B: 134110
24
Murphy S T, Giret Y, Daraszewicz S L, et al. Contribution of electronic excitation to the structural evolution of ultrafast laser-irradiated tungsten nanofilms [J]. Phys. Rev., 2016, 93B: 104105
25
Arefev M I, Shugaev M V, Zhigilei L V. Kinetics of laser-induced melting of thin gold film: How slow can it get? [J]. Sci. Adv., 2022, 8: eabo2621
26
Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces [J]. Phys. Rev. Lett., 2007, 98: 146401
27
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
28
Zeng Q Y, Chen B, Yu X X, et al. Towards large-scale and spatiotemporally resolved diagnosis of electronic density of states by deep learning [J]. Phys. Rev., 2022, 105B: 174109
29
Zeng Q Y, Yu X X, Yao Y P, et al. Ab initio validation on the connection between atomistic and hydrodynamic description to unravel the ion dynamics of warm dense matter [J]. Phys. Rev. Res., 2021, 3: 033116
30
Yang F H, Zeng Q Y, Chen B, et al. Lattice thermal conductivity of MgSiO3 perovskite and post-perovskite under lower mantle conditions calculated by deep potential molecular dynamics [J]. Chin. Phys. Lett., 2022, 39: 116301
31
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
32
Santos-Florez P A, Yanxon H, Kang B, et al. Size-dependent nucleation in crystal phase transition from machine learning metadynamics [J]. Phys. Rev. Lett., 2022, 129: 185701
33
Chen B, Zeng Q Y, Yu X X, et al. Three-step formation of diamonds in shock-compressed hydrocarbons: Decomposition, species separation, and nucleation [J]. arXiv: 2208. 01830, 2022
34
Chen B, Zeng Q Y, Wang H, et al. Atomistic mechanism of phase transition in shock compressed gold revealed by deep potential [J]. arXiv: 2006. 13136, 2021
35
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
36
Zeng Q Y, Chen B, Zhang S, et al. Full-scale ab initio simulations of laser-driven atomistic dynamics [J]. npj Comput. Mater., 2023, 9: 213
37
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
38
Zhang L F, Lin D Y, Wang H, et al. Active learning of uniformly accurate interatomic potentials for materials simulation [J]. Phys. Rev. Mater., 2019, 3: 023804
39
Zhang Y Z, Gao C, Liu Q R, et al. Warm dense matter simulation via electron temperature dependent deep potential molecular dynamics [J]. Phys. Plasmas, 2020, 27: 122704
40
Zeng Q Y, Dai J Y. Structural transition dynamics of the formation of warm dense gold: From an atomic scale view [J]. Sci. China Phys. Mech. Astron., 2020, 63: 263011
41
Dai J Y, Hou Y, Yuan J M. Unified first principles description from warm dense matter to ideal ionized gas plasma: Electron-ion collisions induced friction [J]. Phys. Rev. Lett., 2010, 104: 245001
42
Dai J Y, Kang D D, Zhao Z X, et al. Dynamic ionic clusters with flowing electron bubbles from warm to hot dense iron along the hugoniot curve [J]. Phys. Rev. Lett., 2012, 109: 175701
43
Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Phys. Rev., 1996, 54B: 11169
Blöchl P E. Projector augmented-wave method [J]. Phys. Rev., 1994, 50B: 17953
46
Ivanov D S, Zhigilei L V. Combined atomistic-continuum modeling of short-pulse laser melting and disintegration of metal films [J]. Phys. Rev., 2003, 68B: 064114
47
Plimpton S. Fast parallel algorithms for short-range molecular dynamics [J]. J. Comput. Phys., 1995, 117: 1
48
Kittel C. Kittel's Introduction to Solid State Physic [M]. Beijing: Machine Press, 2020: 86
49
Tadano T, Gohda Y, Tsuneyuki S. Anharmonic force constants extracted from first-principles molecular dynamics: Applications to heat transfer simulations [J]. J. Phys.: Condens. Matter., 2014, 26: 225402
50
Nilsson G, Rolandson S. Lattice dynamics of copper at 80 K [J]. Phys. Rev., 1973, 7B: 2393
51
Japel S, Schwager B, Boehler R, et al. Melting of copper and nickel at high pressure: The role of d electrons [J]. Phys. Rev. Lett., 2005, 95: 167801
52
Simon F, Glatzel G. Bemerkungen zur schmelzdruckkurve [J]. Z. Anorg. Allg. Chem., 1929, 178: 309
53
Cagran C, Wilthan B, Pottlacher G. Enthalpy heat of fusion and specific electrical resistivity of pure silver, pure copper and the binary Ag-28Cu alloy [J]. Thermochim. Acta, 2006, 445: 104
54
Nizomov Z, Saidov R H, Gulov B N, et al. Temperature dependence of the heat capacity of aluminium, copper, silicon, magnesium, zinc and comparison with Debye theory [J]. Interconf, 2021, 55: 307
55
Smirnov N A. Copper, gold, and platinum under femtosecond irradiation: Results of first-principles calculations [J]. Phys. Rev., 2020, 101B: 094103
56
Cho B I, Ogitsu T, Engelhorn K, et al. Measurement of electron-ion relaxation in warm dense copper [J]. Sci. Rep., 2016, 6: 18843
doi: 10.1038/srep18843
pmid: 26733236
57
Hohlfeld J, Müller J G, Wellershoff S S, et al. Time-resolved thermoreflectivity of thin gold films and its dependence on film thickness [J]. Appl. Phys., 1997, 64B: 387
58
Zhang Y W, Chen J K. Ultrafast melting and resolidification of gold particle irradiated by pico- to femtosecond lasers [J]. J. Appl. Phys., 2008, 104: 054910
CHEN Kai;YU Menghuai;HU Shangxu (Zhejiang University; Hangzhou 310027)YU Sirong; HE Zhenming(Jilin University of Technology; Changchun 130025)(Manuscript received 1996-04-30; in revise form 1996-09-28). SIMULATION OF ROOM-TEMPERATURE STRENGTH OF ZA22/Al_20_3(F) COMPOSITES[J]. 金属学报, 1997, 33(4): 437-442.