1
|
Zhang J, Zhang H, Douglas JF. A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting. J Chem Phys 2024; 160:114506. [PMID: 38511662 DOI: 10.1063/5.0197386] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2024] [Accepted: 03/05/2024] [Indexed: 03/22/2024] Open
Abstract
Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.
Collapse
Affiliation(s)
- Jiarui Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Jack F Douglas
- Material Measurement Laboratory, Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| |
Collapse
|
2
|
Baggioli M, Landry M, Zaccone A. Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory. Phys Rev E 2022; 105:024602. [PMID: 35291146 DOI: 10.1103/physreve.105.024602] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).
Collapse
Affiliation(s)
- Matteo Baggioli
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Michael Landry
- Department of Physics, Center for Theoretical Physics, Columbia University, 538 West 120th Street, New York, New York 10027, USA
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, CB30HE Cambridge, United Kingdom
| |
Collapse
|
3
|
Zaccone A, Terentjev EM. Disorder-assisted melting and the glass transition in amorphous solids. PHYSICAL REVIEW LETTERS 2013; 110:178002. [PMID: 23679782 DOI: 10.1103/physrevlett.110.178002] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2012] [Indexed: 05/12/2023]
Abstract
The mechanical response of solids depends on temperature, because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays a crucial role in materials science. In glasses, the vanishing of shear rigidity upon increasing temperature is the reverse process of the glass transition. It remains poorly understood due to the disorder leading to nontrivial (nonaffine) components in the atomic displacements. Our theory explains the basic mechanism of the melting transition of amorphous (disordered) solids in terms of the lattice energy lost to this nonaffine motion, compared to which thermal vibrations turn out to play only a negligible role. The theory is in good agreement with classic data on melting of amorphous polymers (for which no alternative theory can be found in the literature) and offers new opportunities in materials science.
Collapse
Affiliation(s)
- Alessio Zaccone
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | | |
Collapse
|
4
|
Similarities of the Collective Interfacial Dynamics of Grain Boundaries and Nanoparticles to Glass-Forming Liquids. ACTA ACUST UNITED AC 2013. [DOI: 10.1002/9781118540350.ch19] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
5
|
Zhang H, Khalkhali M, Liu Q, Douglas JF. String-like cooperative motion in homogeneous melting. J Chem Phys 2013; 138:12A538. [PMID: 23556789 PMCID: PMC3598817 DOI: 10.1063/1.4769267] [Citation(s) in RCA: 64] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2012] [Accepted: 11/06/2012] [Indexed: 02/05/2023] Open
Abstract
Despite the fundamental nature and practical importance of melting, there is still no generally accepted theory of this ubiquitous phenomenon. Even the earliest simulations of melting of hard discs by Alder and Wainwright indicated the active role of collective atomic motion in melting and here we utilize molecular dynamics simulation to determine whether these correlated motions are similar to those found in recent studies of glass-forming (GF) liquids and other condensed, strongly interacting, particle systems. We indeed find string-like collective atomic motion in our simulations of "superheated" Ni crystals, but other observations indicate significant differences from GF liquids. For example, we observe neither stretched exponential structural relaxation, nor any decoupling phenomenon, while we do find a boson peak, findings that have strong implications for understanding the physical origin of these universal properties of GF liquids. Our simulations also provide a novel view of "homogeneous" melting in which a small concentration of interstitial defects exerts a powerful effect on the crystal stability through their initiation and propagation of collective atomic motion. These relatively rare point defects are found to propagate down the strings like solitons, driving the collective motion. Crystal integrity remains preserved when the permutational atomic motions take the form of ring-like atomic exchanges, but a topological transition occurs at higher temperatures where the rings open to form linear chains similar in geometrical form and length distribution to the strings of GF liquids. The local symmetry breaking effect of the open strings apparently destabilizes the local lattice structure and precipitates crystal melting. The crystal defects are thus not static entities under dynamic conditions, such as elevated temperatures or material loading, but rather are active agents exhibiting a rich nonlinear dynamics that is not addressed in conventional "static" defect melting models.
Collapse
Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada.
| | | | | | | |
Collapse
|
6
|
Zhang H, Kalvapalle P, Douglas JF. String-Like Collective Atomic Motion in the Melting and Freezing of Nanoparticles. J Phys Chem B 2011; 115:14068-76. [DOI: 10.1021/jp203765x] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Alberta, T6G 2 V4 Canada
| | - Pranav Kalvapalle
- Department of Chemical and Materials Engineering, University of Alberta, Alberta, T6G 2 V4 Canada
| | - Jack F. Douglas
- Polymers Division, NIST, Gaithersburg, Maryland 20899, United States
| |
Collapse
|
7
|
|
8
|
Glaser MA, Clark NA. Melting and Liquid Structure in two Dimensions. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141410.ch7] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
|
9
|
Affiliation(s)
- J. P. Ibar
- a EKNET Research , P. O. Box 385, New Canaan, Connecticut, 06840
| |
Collapse
|
10
|
|
11
|
Johari GP. Glass transition and molecular motions in the glassy state of a nematic liquid. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/01418638208223543] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- G. P. Johari
- a Bell Laboratories , 600 Mountain Avenue, Murray Hill , New Jersey , 07974 , U.S.A
- b Snow and Ice Division, National Hydrology Research Institute , 562, Booth Street, Ottawa K1A 0E7, Canada
| |
Collapse
|
12
|
|
13
|
Chapter 55 The Role of Dislocations in Melting. ACTA ACUST UNITED AC 1996. [DOI: 10.1016/s1572-4859(96)80010-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2023]
|
14
|
Bettencourt LM, Rivers RJ. Interactions between U(1) cosmic strings: An analytical study. Int J Clin Exp Med 1995; 51:1842-1853. [PMID: 10018651 DOI: 10.1103/physrevd.51.1842] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
15
|
|
16
|
Lund F. Instability driven by dislocation loops in bulk elastic solids: Melting and superheating. PHYSICAL REVIEW LETTERS 1992; 69:3084-3087. [PMID: 10046721 DOI: 10.1103/physrevlett.69.3084] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
17
|
Johari GP, Goodby JW. Dielectric relaxations in a supercooled liquid and glassy smectic phase. J Chem Phys 1982. [DOI: 10.1063/1.443693] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
18
|
|
19
|
|
20
|
|
21
|
Versetzungstheorie des Schmelzens auf der Grundlage der Cluster-Entropie-Hypothese (CEH). Colloid Polym Sci 1982. [DOI: 10.1007/bf01447961] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
22
|
|
23
|
|
24
|
|