1
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Shi J, Wang S, Qu P, Shao J. Time series prediction model using LSTM-Transformer neural network for mine water inflow. Sci Rep 2024; 14:18284. [PMID: 39112684 PMCID: PMC11306369 DOI: 10.1038/s41598-024-69418-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2024] [Accepted: 08/05/2024] [Indexed: 08/10/2024] Open
Abstract
Mine flooding accidents have occurred frequently in recent years, and the predicting of mine water inflow is one of the most crucial flood warning indicators. Further, the mine water inflow is characterized by non-linearity and instability, making it difficult to predict. Accordingly, we propose a time series prediction model based on the fusion of the Transformer algorithm, which relies on self-attention, and the LSTM algorithm, which captures long-term dependencies. In this paper, Baotailong mine water inflow in Heilongjiang Province is used as sample data, and the sample data is divided into different ratios of the training set and test set in order to obtain optimal prediction results. In this study, we demonstrate that the LSTM-Transformer model exhibits the highest training accuracy when the ratio is 7:3. To improve the efficiency of search, the combination of random search and Bayesian optimization is used to determine the network model parameters and regularization parameters. Finally, in order to verify the accuracy of the LSTM-Transformer model, the LSTM-Transformer model is compared with LSTM, CNN, Transformer and CNN-LSTM models. The results prove that LSTM-Transformer has the highest prediction accuracy, and all the indicators of its model are well improved.
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Affiliation(s)
- Junwei Shi
- College of Management Science and Engineering, Shandong Technology and Business University, Yantai, 264000, China.
| | - Shiqi Wang
- College of Management Science and Engineering, Shandong Technology and Business University, Yantai, 264000, China
| | - Pengfei Qu
- College of Management Science and Engineering, Shandong Technology and Business University, Yantai, 264000, China
| | - Jianli Shao
- College of Management Science and Engineering, Shandong Technology and Business University, Yantai, 264000, China
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2
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Zhou C, Dong Z, Zhou C, Fu P, Luo S. Mechanical mechanism analysis of rockburst in deep-buried tunnel with high in-situ stress. Sci Rep 2024; 14:18076. [PMID: 39103442 DOI: 10.1038/s41598-024-69274-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2024] [Accepted: 08/02/2024] [Indexed: 08/07/2024] Open
Abstract
The Qinling water conveyance tunnel has a large buried depth and high in-situ stress level, and rockburst disasters frequently occurred during excavation. In order to find out the mechanical mechanism of rockburst, the research work in this paper is as follows: (1) In-situ three-dimensional hydraulic fracturing method was used to measure the in-situ stress of the deep buried tunnel crossing the ridge. (2) Based on the measured in-situ stress results, the stress distribution characteristics of the tunnel crossing the ridge were obtained by the multiple linear regression method, and the rockburst tendency during construction was predicted. (3) A three-dimensional numerical model of tunnel excavation was established to analyze the dynamic adjustment characteristics of the surrounding rock stress and elastic strain energy during TBM excavation, and to clarify the mechanical mechanism of rockburst. The research results show that the maximum principal stress of the deep-buried tunnel crossing the ridge of Qinling is 40-66 MPa, which belongs to extremely high in-situ stress level, and medium-strong rockburst may occur during excavation. In the process of TBM excavation, the stress of the surrounding rock in the range of 2.6 times the diameter of the tunnel before and after the working face is adjusted violently, and the concentrated zones after the stress redistribution are mainly distributed in the arch roof and arch bottom, and the stress concentration coefficient can reach 2.06. The arch roof, arch waist, and arch bottom are susceptible to immediate rockburst due to stress transient unloading at the moment of excavation. After the elastic strain energy of the surrounding rock at the arch roof and the arch bottom is released and accumulated, it is easy to cause time delayed rockburst, and the depth of the rockburst pit can reach 3.5 m, which is consistent with the rockburst phenomenon in the field.
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Affiliation(s)
- Chao Zhou
- Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan, 430010, Hubei, China
- State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, 430072, Hubei, China
- Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan, 430072, China
| | - Zhihong Dong
- Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan, 430010, Hubei, China.
| | - Chunhua Zhou
- Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan, 430010, Hubei, China
| | - Ping Fu
- Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan, 430010, Hubei, China
| | - Sheng Luo
- Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan, 430010, Hubei, China
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3
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He M, Wang Y, Fan Y. Metastable grain boundaries: the roles of structural and chemical disorders in their energetics, non-equilibrium kinetic evolution, and mechanical behaviors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:343001. [PMID: 38740049 DOI: 10.1088/1361-648x/ad4aab] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2024] [Accepted: 05/13/2024] [Indexed: 05/16/2024]
Abstract
Complex environments in advanced manufacturing usually involve ultrafast laser or ion irradiation which leads to rapid heating and cooling and drives grain boundaries (GBs) to non-equilibrium states, featuring distinct energetics and kinetic behaviors compared to conventional equilibrium or near-equilibrium GBs. In this topical review, we provide an overview of both recent experimental and computational studies on metastable GBs, i.e. their energetics, kinetic behaviors, and mechanical properties. In contrast to GBs at thermodynamic equilibrium, the inherent structure energy of metastable GBs exhibits a spectrum instead of single value for a particular misorientation, due to the existence of microstructural and chemical disorder. The potential energy landscape governs the energetic and kinetic behaviors of metastable GBs, including the ageing/rejuvenating mechanism and activation barrier distributions. The unique energetics and structural disorder of metastable GBs lead to unique mechanical properties and tunability of interface-rich nanocrystalline materials. We also discuss that, in addition to structural disorder, chemical complexity in multi-components alloys could also drive the GBs away from their ground states and, subsequently, significantly impact on the GBs-mediated deformation. And under some extreme conditions such as irradiation, structural disorders and chemical complexity may simultaneously present at interfaces, further enriching of metastability of GBs and their physical and mechanical behaviors. Finally, we discuss the machine learning techniques, which have been increasingly employed to predict and understand the complex behaviors of metastable GBs in recent years. We highlight the potential of data-driven approaches to revolutionize the study of disorder systems by efficiently extracting the relationship between structural features and material properties. We hope this topical review paper could shed light and stimulate the development of new GBs engineering strategies that allow more flexibility and tunability for the design of nano-structured materials.
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Affiliation(s)
- Miao He
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, United States of America
| | - Yuchu Wang
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, United States of America
| | - Yue Fan
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, United States of America
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4
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Yu HB, Gao L, Gao JQ, Samwer K. Universal origin of glassy relaxation as recognized by configuration pattern matching. Natl Sci Rev 2024; 11:nwae091. [PMID: 38577671 PMCID: PMC10989661 DOI: 10.1093/nsr/nwae091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Revised: 01/28/2024] [Accepted: 03/07/2024] [Indexed: 04/06/2024] Open
Abstract
Relaxation processes are crucial for understanding the structural rearrangements of liquids and amorphous materials. However, the overarching principle that governs these processes across vastly different materials remains an open question. Substantial analysis has been carried out based on the motions of individual particles. Here, as an alternative, we propose viewing the global configuration as a single entity. We introduce a global order parameter, namely the inherent structure minimal displacement (IS Dmin), to quantify the variability of configurations by a pattern-matching technique. Through atomic simulations of seven model glass-forming liquids, we unify the influences of temperature, pressure and perturbation time on the relaxation dissipation, via a scaling law between the mechanical damping factor and IS Dmin. Fundamentally, this scaling reflects the curvature of the local potential energy landscape. Our findings uncover a universal origin of glassy relaxation and offer an alternative approach to studying disordered systems.
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Affiliation(s)
- Hai-Bin Yu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Liang Gao
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jia-Qi Gao
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Konrad Samwer
- I. Physikalisches Institut, Universität Göttingen, Göttingen D-37077, Germany
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5
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Zella L, Moon J, Egami T. Ripples in the bottom of the potential energy landscape of metallic glass. Nat Commun 2024; 15:1358. [PMID: 38355602 PMCID: PMC10866862 DOI: 10.1038/s41467-024-45640-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 01/29/2024] [Indexed: 02/16/2024] Open
Abstract
In the absence of periodicity, the structure of glass is ill-defined, and a large number of structural states are found at similar energy levels. However, little is known about how these states are connected to each other in the potential energy landscape. We simulate mechanical relaxation by molecular dynamics for a prototypical [Formula: see text] metallic glass and follow the mechanical energy loss of each atom to track the change in the state. We find that the energy barriers separating these states are remarkably low, only of the order of 1 meV, implying that even quantum fluctuations can overcome these potential energy barriers. Our observation of numerous small ripples in the bottom of the potential energy landscape puts many assumptions regarding the thermodynamic states of metallic glasses into question and suggests that metallic glasses are not totally frozen at the local atomic level.
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Affiliation(s)
- Leo Zella
- Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA
| | - Jaeyun Moon
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14853, USA
| | - Takeshi Egami
- Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA.
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA.
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996, USA.
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6
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Lieou CKC, Egami T. Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses. Sci Rep 2023; 13:15979. [PMID: 37749128 PMCID: PMC10520023 DOI: 10.1038/s41598-023-42685-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 09/13/2023] [Indexed: 09/27/2023] Open
Abstract
It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearrangements and the local atomic environment as measured by the atomic-level stresses, kinetic and potential energies, and the per-atom Voronoi volume. In addition, there is only a weak correlation between atomic rearrangements and the largest and smallest eigenvalues of the dynamical matrix. Our results confirm the transient nature of dynamical heterogeneities and suggest that the notion of defects may be less relevant than that of a propensity for rearrangement.
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Affiliation(s)
- Charles K C Lieou
- Department of Nuclear Engineering, University of Tennessee, Knoxville, TN, USA
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA
| | - Takeshi Egami
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA.
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA.
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA.
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7
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Egami T, Ryu CW. World beyond the nearest neighbors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:174002. [PMID: 36812595 DOI: 10.1088/1361-648x/acbe24] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 02/22/2023] [Indexed: 06/18/2023]
Abstract
The structure beyond the nearest neighbor atoms in liquid and glass is characterized by the medium-range order (MRO). In the conventional approach, the MRO is considered to result directly from the short-range order (SRO) in the nearest neighbors. To this bottom-up approach starting with the SRO, we propose to add a top-down approach in which global collective forces drive liquid to form density waves. The two approaches are in conflict with each other, and the compromise produces the structure with the MRO. The driving force to produce density waves provides the stability and stiffness to the MRO, and controls various mechanical properties. This dual framework provides a novel perspective for description of the structure and dynamics of liquid and glass.
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Affiliation(s)
- Takeshi Egami
- Shull-Wollan Center and Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, United States of America
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, United States of America
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States of America
| | - Chae Woo Ryu
- Shull-Wollan Center and Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, United States of America
- Department of Materials Science and Engineering, Hongik University, Seoul 04066, Republic of Korea
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8
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Zhang DM, Sun DY, Gong XG. Angell plot from the potential energy landscape perspective. Phys Rev E 2022; 106:064129. [PMID: 36671189 DOI: 10.1103/physreve.106.064129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 11/22/2022] [Indexed: 12/24/2022]
Abstract
Within the scenario of the potential energy landscape (PEL), a thermodynamic model has been developed to uncover the physics behind the Angell plot. In our model, by separating the barrier distribution in PELs into a Gaussian-like and a power-law form, we obtain a general relationship between the relaxation time and the temperature. The wide range of the experimental data in the Angell plot, as well as the molecular-dynamics data, can be excellently fitted by two characteristic parameters, the effective barrier (ω) and the effective width (σ) of a Gaussian-like distribution. More importantly, the fitted ω and σ^{2} for all glasses are found to have a simple linear relationship within a very narrow band, and fragile and strong glasses are well separated in the ω-σ^{2} plot, which indicates that glassy states appear only in a specific region of the PEL.
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Affiliation(s)
- D M Zhang
- Key Laboratory for Computational Physical Sciences (MOE), Institute of Computational Physics, Fudan University, Shanghai 200433, China
| | - D Y Sun
- Engineering Research Center for Nanophotonics & Advanced Instrument (MOE), School of Physics and Electronic Science, East China Normal University, 200241 Shanghai, China.,Shanghai Qi Zhi Institution, Shanghai 200030, China
| | - X G Gong
- Key Laboratory for Computational Physical Sciences (MOE), Institute of Computational Physics, Fudan University, Shanghai 200433, China.,Shanghai Qi Zhi Institution, Shanghai 200030, China
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9
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Yang M, Li W, Liu X, Wang H, Wu Y, Wang X, Zhang F, Zeng Q, Ma D, Ruan H, Lu Z. Configurational Entropy Effects on Glass Transition in Metallic Glasses. J Phys Chem Lett 2022; 13:7889-7897. [PMID: 35979998 DOI: 10.1021/acs.jpclett.2c01234] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Configurational entropy (Sconf) is known to be a key thermodynamic factor governing a glass transition process. However, this significance remains speculative because Sconf is not directly measurable. In this work, we demonstrate the role of Sconf theoretically and experimentally by a comparative study of a Zr-Ti-Cu-Ni-Be high-entropy metallic glass (HE-MG) with one of its conventional MG counterparts. It is revealed that the higher Sconf leads to a glass that is energetically more stable and structurally more ordered. This is manifested by ab initio molecular dynamics simulations, showing that ∼60% fewer atoms are agitated above Tg, and experimental results of smaller heat capacity jump, inconspicuous stiffness loss, insignificant structural change during glass transition, and a more depressed boson peak in the HE-MG than its counterpart. We accordingly propose a model to explain that a higher Sconf promotes a faster degeneracy-dependent kinetics for exploration of the potential energy landscape upon glass transition.
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Affiliation(s)
- Ming Yang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
- Neutron Science Platform, Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wenyue Li
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Xiongjun Liu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Hui Wang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Yuan Wu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Xianzhen Wang
- Institute for Advanced Materials and Technology, University of Science and Technology Beijing, Beijing 100083, China
| | - Fei Zhang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Qiaoshi Zeng
- Center for High Pressure Science and Technology Advanced Research, Pudong, Shanghai 201203, China
| | - Dong Ma
- Neutron Science Platform, Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Haihui Ruan
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
| | - Zhaoping Lu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
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10
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Ryu CW, Egami T. Medium-range atomic correlation in simple liquids. I. Distinction from short-range order. Phys Rev E 2022; 104:064109. [PMID: 35030901 DOI: 10.1103/physreve.104.064109] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 11/19/2021] [Indexed: 11/07/2022]
Abstract
Physical properties of liquids and glasses are controlled not only by the short-range order (SRO) in the nearest-neighbor atoms but also by the medium-range order (MRO) observed for atoms beyond the nearest neighbors. In this article the nature of the MRO as the descriptor of point-to-set atomic correlation is discussed focusing on simple liquids, such as metallic liquids. Through the results of x-ray diffraction and simulation with classical potentials we show that the third peak of the pair-distribution function, which describes the MRO, shows a distinct change in temperature dependence at the glass transition, whereas the first peak, which represents the SRO, changes smoothly through the glass transition. The result suggests that the glass transition is induced by the freezing of the MRO rather than that of the SRO, implying a major role of the MRO on the viscosity of supercooled liquid.
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Affiliation(s)
- Chae Woo Ryu
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Takeshi Egami
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA.,Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA.,Materials Sciences and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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11
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Liu C, Fan Y. Emergent Fractal Energy Landscape as the Origin of Stress-Accelerated Dynamics in Amorphous Solids. PHYSICAL REVIEW LETTERS 2021; 127:215502. [PMID: 34860096 DOI: 10.1103/physrevlett.127.215502] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Revised: 08/23/2021] [Accepted: 10/05/2021] [Indexed: 06/13/2023]
Abstract
The ageing dynamics in a multiplicity of metastable glasses are investigated at various thermomechanical conditions. By using data analytics to deconvolute the integral effects of environmental factors (e.g., energy level, temperature, stress), and by directly scrutinizing the minimum energy pathways for local excitations, we demonstrate external shear would make the system's energy landscape surprisingly fractal and create an emergent low-barrier mode with highly tortuous pathways, leading to an accelerated relaxation. This finding marks a departure from the classic picture of shear-induced simple bias of energy landscape. The insights and implications of this study are also discussed.
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Affiliation(s)
- Chaoyi Liu
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Yue Fan
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
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12
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Zhang Y, Osetsky YN, Weber WJ. Tunable Chemical Disorder in Concentrated Alloys: Defect Physics and Radiation Performance. Chem Rev 2021; 122:789-829. [PMID: 34694124 DOI: 10.1021/acs.chemrev.1c00387] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The development of advanced structural alloys with performance meeting the requirements of extreme environments in nuclear reactors has been long pursued. In the long history of alloy development, the search for metallic alloys with improved radiation tolerance or increased structural strength has relied on either incorporating alloying elements at low concentrations to synthesize so-called dilute alloys or incorporating nanoscale features to mitigate defects. In contrast to traditional approaches, recent success in synthesizing multicomponent concentrated solid-solution alloys (CSAs), including medium-entropy and high-entropy alloys, has vastly expanded the compositional space for new alloy discovery. Their wide variety of elemental diversity enables tunable chemical disorder and sets CSAs apart from traditional dilute alloys. The tunable electronic structure critically lowers the effectiveness of energy dissipation via the electronic subsystem. The tunable chemical complexity also modifies the scattering mechanisms in the atomic subsystem that control energy transport through phonons. The level of chemical disorder depends substantively on the specific alloying elements, rather than the number of alloying elements, as the disorder does not monotonically increase with a higher number of alloying elements. To go beyond our knowledge based on conventional alloys and take advantage of property enhancement by tuning chemical disorder, this review highlights synergistic effects involving valence electrons and atomic-level and nanoscale inhomogeneity in CSAs composed of multiple transition metals. Understanding of the energy dissipation pathways, deformation tolerance, and structural stability of CSAs can proceed by exploiting the equilibrium and non-equilibrium defect processes at the electronic and atomic levels, with or without microstructural inhomogeneities at multiple length scales. Knowledge of tunable chemical disorder in CSAs may advance the understanding of the substantial modifications in element-specific alloy properties that effectively mitigate radiation damage and control a material's response in extreme environments, as well as overcome strength-ductility trade-offs and provide overarching design strategies for structural alloys.
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Affiliation(s)
- Yanwen Zhang
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States.,Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Yuri N Osetsky
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - William J Weber
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
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13
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Trachenko K, Zaccone A. Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:315101. [PMID: 34034250 DOI: 10.1088/1361-648x/ac04cd] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 05/25/2021] [Indexed: 06/12/2023]
Abstract
We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential decay at high temperature. Finally, we reproduce SER to CER crossover across the glass transition recently observed in metallic glasses.
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Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom
| | - A Zaccone
- Department of Physics 'A Pontremoli', University of Milan, Italy
- Cavendish Laboratory, University of Cambridge, CB3 0HE, Cambridge, United Kingdom
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14
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Tang L, Liu H, Ma G, Du T, Mousseau N, Zhou W, Bauchy M. The energy landscape governs ductility in disordered materials. MATERIALS HORIZONS 2021; 8:1242-1252. [PMID: 34821917 DOI: 10.1039/d0mh00980f] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Based on their structure, non-crystalline phases can fail in a brittle or ductile fashion. However, the nature of the link between structure and propensity for ductility in disordered materials has remained elusive. Here, based on molecular dynamics simulations of colloidal gels and silica glasses, we investigate how the degree of structural disorder affects the fracture of disordered materials. As expected, we observe that structural disorder results in an increase in ductility. By applying the activation-relaxation technique (an open-ended saddle point search algorithm), we demonstrate that the propensity for ductility is controlled by the topography of the energy landscape. Interestingly, we observe a power-law relationship between the particle non-affine displacement upon fracture and the average local energy barrier. This reveals that the dynamics of the particles upon fracture is encoded in the static energy landscape, i.e., before any load is applied. This relationship is shown to apply to several classes of non-crystalline materials (oxide and metallic glasses, amorphous solid, and colloidal gels), which suggests that it may be a generic feature of disordered materials.
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Affiliation(s)
- Longwen Tang
- State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China.
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15
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Structural relaxation and crystallization in supercooled water from 170 to 260 K. Proc Natl Acad Sci U S A 2021; 118:2022884118. [PMID: 33790015 DOI: 10.1073/pnas.2022884118] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The origin of water's anomalous properties has been debated for decades. Resolution of the problem is hindered by a lack of experimental data in a crucial region of temperatures, T, and pressures where supercooled water rapidly crystallizes-a region often referred to as "no man's land." A recently developed technique where water is heated and cooled at rates greater than 109 K/s now enables experiments in this region. Here, it is used to investigate the structural relaxation and crystallization of deeply supercooled water for 170 K < T < 260 K. Water's relaxation toward a new equilibrium structure depends on its initial structure with hyperquenched glassy water (HQW) typically relaxing more quickly than low-density amorphous solid water (LDA). For HQW and T > 230 K, simple exponential relaxation kinetics is observed. For HQW at lower temperatures, increasingly nonexponential relaxation is observed, which is consistent with the dynamics expected on a rough potential energy landscape. For LDA, approximately exponential relaxation is observed for T > 230 K and T < 200 K, with nonexponential relaxation only at intermediate temperatures. At all temperatures, water's structure can be reproduced by a linear combination of two, local structural motifs, and we show that a simple model accounts for the complex kinetics within this context. The relaxation time, τ rel , is always shorter than the crystallization time, τ xtal For HQW, the ratio, τ xtal /τ rel , goes through a minimum at ∼198 K where the ratio is about 60.
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16
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Tang L, Ma G, Liu H, Zhou W, Bauchy M. Bulk Metallic Glasses' Response to Oscillatory Stress Is Governed by the Topography of the Energy Landscape. J Phys Chem B 2020; 124:11294-11298. [PMID: 33231456 DOI: 10.1021/acs.jpcb.0c08794] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
When subjected to cyclic loading, bulk metallic glasses tend to exhibit fatigue-induced damage. Although fatigue is a key limitation of metallic glasses, its atomic origin remains elusive. Here, based on molecular dynamics simulations, we investigate the response of metallic glasses prepared with varying cooling rates to oscillatory stress. We find that fatigue manifests itself as an accumulation of residual strain, which results from some nonaffine displacement of the atoms. Such local reorganizations are promoted under a high cooling rate. Importantly, we demonstrate that the fatigue-induced dynamics of the atoms is encoded in the topography of the static energy landscape, i.e., before any load is applied.
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Affiliation(s)
- Longwen Tang
- State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China.,Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095, United States
| | - Gang Ma
- State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
| | - Han Liu
- Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095, United States
| | - Wei Zhou
- State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
| | - Mathieu Bauchy
- Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095, United States
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17
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Ryu CW, Egami T. Origin of liquid fragility. Phys Rev E 2020; 102:042615. [PMID: 33212574 DOI: 10.1103/physreve.102.042615] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 10/12/2020] [Indexed: 11/07/2022]
Abstract
Liquid fragility characterizes how steeply the viscosity of a glass-forming liquid decreases with increasing temperature above the glass transition. It is one of the most fundamental properties of a liquid, with high importance for science and application. Yet, its origin is unclear. Here we show that it is directly related to the structural coherence of the medium-range order (MRO) in liquid defined by the decay of the pair-distribution function with distance. The MRO can also be evaluated from the first peak of the structure function determined by x-ray or neutron diffraction, and it is a measure of the cooperativity of atomic motion in a diffusive event in supercooled liquids. These findings shed light on the mechanism of atomic transport in supercooled liquids.
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Affiliation(s)
- Chae Woo Ryu
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Takeshi Egami
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA.,Materials Sciences and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.,Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
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18
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Egami T, Ryu CW. Why Is the Range of Timescale So Wide in Glass-Forming Liquid? Front Chem 2020; 8:579169. [PMID: 33134277 PMCID: PMC7550744 DOI: 10.3389/fchem.2020.579169] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 08/27/2020] [Indexed: 11/13/2022] Open
Abstract
The viscosity and the relaxation time of a glass-forming liquid vary over 15 orders of magnitude before the liquid freezes into a glass. The rate of the change with temperature is characterized by liquid fragility. The mechanism of such a spectacular behavior and the origin of fragility have long been discussed, but it remains unresolved because of the difficulty of carrying out experiments and constructing theories that bridge over a wide timescale from atomic (ps) to bulk (minutes). Through the x-ray diffraction measurement and molecular dynamics simulation for metallic liquids we suggest that large changes in viscosity can be caused by relatively small changes in the structural coherence which characterizes the medium-range order. Here the structural coherence does not imply that of atomic-scale structure, but it relates to the coarse-grained density fluctuations represented by the peaks in the pair-distribution function (PDF) beyond the nearest neighbors. The coherence length is related to fragility and increases with decreasing temperature, and it diverges only at a negative temperature. This analysis is compared with several current theories which predict a phase transition near the glass transition temperature.
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Affiliation(s)
- Takeshi Egami
- Department of Materials Science and Engineering, Shull-Wollan Center - Joint Institute for Neutron Sciences, University of Tennessee, Knoxville, Knoxville, TN, United States.,Department of Physics and Astronomy, University of Tennessee, Knoxville, Knoxville, TN, United States.,Materials Sciences and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, United States
| | - Chae Woo Ryu
- Department of Materials Science and Engineering, Shull-Wollan Center - Joint Institute for Neutron Sciences, University of Tennessee, Knoxville, Knoxville, TN, United States
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19
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Torregrosa Cabanilles C, Molina-Mateo J, Sabater i Serra R, Meseguer-Dueñas JM, Gómez Ribelles JL. Non-Markovian Methods in Glass Transition. Polymers (Basel) 2020; 12:E1997. [PMID: 32887333 PMCID: PMC7565281 DOI: 10.3390/polym12091997] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Revised: 08/29/2020] [Accepted: 08/31/2020] [Indexed: 11/16/2022] Open
Abstract
A model for the heterogeneity of local dynamics in polymer and other glass-forming materials is provided here. The fundamental characteristics of the glass transition phenomenology emerge when simulating a condensed matter open cluster that has a strong interaction with its heterogeneous environment. General glass transition features, such as non-exponential structural relaxations, the slowing down of relaxation times with temperature and specific off-equilibrium glassy dynamics can be reproduced by non-Markovian dynamics simulations with the minimum computer resources. Non-Markovian models are shown to be useful tools for obtaining insights into the complex dynamics involved in the glass transition phenomenon, including whether or not there is a need for a growing correlation length or the relationship between the non-exponentiality of structural relaxations and dynamic heterogeneity.
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Affiliation(s)
- Constantino Torregrosa Cabanilles
- Center for Biomaterials and Tissue Engineering, Universitat Politècnica de València, 46022 València, Spain; (J.M.-M.); (R.S.i.S.); (J.M.M.-D.); (J.L.G.R.)
| | - José Molina-Mateo
- Center for Biomaterials and Tissue Engineering, Universitat Politècnica de València, 46022 València, Spain; (J.M.-M.); (R.S.i.S.); (J.M.M.-D.); (J.L.G.R.)
| | - Roser Sabater i Serra
- Center for Biomaterials and Tissue Engineering, Universitat Politècnica de València, 46022 València, Spain; (J.M.-M.); (R.S.i.S.); (J.M.M.-D.); (J.L.G.R.)
- CIBER-BBN, Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine, 46022 València, Spain
| | - José María Meseguer-Dueñas
- Center for Biomaterials and Tissue Engineering, Universitat Politècnica de València, 46022 València, Spain; (J.M.-M.); (R.S.i.S.); (J.M.M.-D.); (J.L.G.R.)
- CIBER-BBN, Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine, 46022 València, Spain
| | - José Luis Gómez Ribelles
- Center for Biomaterials and Tissue Engineering, Universitat Politècnica de València, 46022 València, Spain; (J.M.-M.); (R.S.i.S.); (J.M.M.-D.); (J.L.G.R.)
- CIBER-BBN, Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine, 46022 València, Spain
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20
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Jay A, Huet C, Salles N, Gunde M, Martin-Samos L, Richard N, Landa G, Goiffon V, De Gironcoli S, Hémeryck A, Mousseau N. Finding Reaction Pathways and Transition States: r-ARTn and d-ARTn as an Efficient and Versatile Alternative to String Approaches. J Chem Theory Comput 2020; 16:6726-6734. [DOI: 10.1021/acs.jctc.0c00541] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Antoine Jay
- LAAS-CNRS, Université de Toulouse, CNRS, F-31555 Toulouse, France
| | - Christophe Huet
- ISAE-SUPAERO, Université de Toulouse, F-31555 Toulouse, France
| | - Nicolas Salles
- CNR-IOM, Democritos National Simulation Center, Istituto Officina dei Materiali, c/o SISSA, via Bonomea 265, IT-34136 Trieste, Italy
| | - Miha Gunde
- LAAS-CNRS, Université de Toulouse, CNRS, F-31555 Toulouse, France
| | - Layla Martin-Samos
- CNR-IOM, Democritos National Simulation Center, Istituto Officina dei Materiali, c/o SISSA, via Bonomea 265, IT-34136 Trieste, Italy
| | | | - Georges Landa
- LAAS-CNRS, Université de Toulouse, CNRS, F-31555 Toulouse, France
| | - Vincent Goiffon
- ISAE-SUPAERO, Université de Toulouse, F-31555 Toulouse, France
| | - Stefano De Gironcoli
- CNR-IOM, Democritos National Simulation Center, Istituto Officina dei Materiali, c/o SISSA, via Bonomea 265, IT-34136 Trieste, Italy
- SISSA, via Bonomea 265, IT-34136 Trieste, Italy
| | - Anne Hémeryck
- LAAS-CNRS, Université de Toulouse, CNRS, F-31555 Toulouse, France
| | - Normand Mousseau
- Département de Physique and Regroupement québécois sur les matriaux de pointe, Département de Physique, Université de Montréal, C.P. 6128, succursale Centre-ville H3C 3J7 Montréal Canada Montréal, Canada
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21
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Zhang S, Liu C, Fan Y, Yang Y, Guan P. Soft-Mode Parameter as an Indicator for the Activation Energy Spectra in Metallic Glass. J Phys Chem Lett 2020; 11:2781-2787. [PMID: 32191474 DOI: 10.1021/acs.jpclett.0c00495] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The activation energy (EA) spectra of the potential energy landscape (PEL) provide a convenient perspective for interpreting complex phenomena in amorphous materials; however, the link between the EA spectra and other physical properties in metallic glasses is still mysterious. By systematically probing the EA spectra for numerous metallic glass samples with distinct local geometric ordering, which correspond to broad processing histories, we found that the shear moduli of the samples are strongly correlated with the arithmetic mean of the EA spectra rather than with the local geometrical ordering. Furthermore, we studied the correlation of the obtained EA spectra and various well-established physical parameters. The outcome of our research clearly demonstrates that the soft-mode parameter Ψ and the EA spectrum are correlated; therefore, this could be a good indicator of metallic glass properties and sheds important light on the structure-property relationship in metallic glass through the medium of the PEL.
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Affiliation(s)
- Shan Zhang
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Chaoyi Liu
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Yue Fan
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Yong Yang
- Centre for Advanced Structural Materials, Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong, China
| | - Pengfei Guan
- Beijing Computational Science Research Center, Beijing 100193, China
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22
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Hoy RS. Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:2. [PMID: 30617641 DOI: 10.1140/epje/i2019-11763-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Accepted: 12/03/2018] [Indexed: 06/09/2023]
Abstract
We discuss issues related to thermalization of plastic flow in the context of soft glassy rheology (SGR) theory. An apparent problem with the theory in its current form is that the stationarity of thermomechanical equilibrium obtained by requiring that its flow rule satisfy detailed balance in the absence of applied deformation requires plastic flow to be athermal. This prevents proper application of SGR to small-molecule and polymer glasses where plastic flow is often well thermalized. Clearly, one would like to have a SGR-like theory of thermalized plastic flow that satisfies stationarity. We discuss reasons why such a theory could prove very useful and clarify obstacles that must be overcome in order to develop it.
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Affiliation(s)
- Robert S Hoy
- Department of Physics, University of South Florida, 33620, Tampa, FL, USA.
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23
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Xu B, Falk ML, Li JF, Kong LT. Predicting Shear Transformation Events in Metallic Glasses. PHYSICAL REVIEW LETTERS 2018; 120:125503. [PMID: 29694058 DOI: 10.1103/physrevlett.120.125503] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Revised: 12/26/2017] [Indexed: 06/08/2023]
Abstract
Shear transformation is the elementary process for plastic deformation of metallic glasses, the prediction of the occurrence of the shear transformation events is therefore of vital importance to understand the mechanical behavior of metallic glasses. In this Letter, from the view of the potential energy landscape, we find that the protocol-dependent behavior of shear transformation is governed by the stress gradient along its minimum energy path and we propose a framework as well as an atomistic approach to predict the triggering strains, locations, and structural transformations of the shear transformation events under different shear protocols in metallic glasses. Verification with a model Cu_{64}Zr_{36} metallic glass reveals that the prediction agrees well with athermal quasistatic shear simulations. The proposed framework is believed to provide an important tool for developing a quantitative understanding of the deformation processes that control mechanical behavior of metallic glasses.
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Affiliation(s)
- Bin Xu
- State key Laboratory of Metal Matrix Composites, School of Materials Science & Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Michael L Falk
- Department of Materials Science and Engineering, Mechanical Engineering, and Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - J F Li
- State key Laboratory of Metal Matrix Composites, School of Materials Science & Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - L T Kong
- State key Laboratory of Metal Matrix Composites, School of Materials Science & Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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24
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Barbot A, Lerbinger M, Hernandez-Garcia A, García-García R, Falk ML, Vandembroucq D, Patinet S. Local yield stress statistics in model amorphous solids. Phys Rev E 2018; 97:033001. [PMID: 29776106 DOI: 10.1103/physreve.97.033001] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Indexed: 06/08/2023]
Abstract
We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.
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Affiliation(s)
- Armand Barbot
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Matthias Lerbinger
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Anier Hernandez-Garcia
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Reinaldo García-García
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Michael L Falk
- Departments of Materials Science and Engineering, Mechanical Engineering, and Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Damien Vandembroucq
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
| | - Sylvain Patinet
- PMMH, ESPCI Paris/CNRS-UMR 7636/University Paris 6 UPMC/University Paris 7 Diderot, PSL Research University, 10 rue Vauquelin, 75231 Paris cedex 05, France
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