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Demmel F. Sodium ion self-diffusion in molten NaBr probed over different length scales. Phys Rev E 2020; 101:062603. [PMID: 32688605 DOI: 10.1103/physreve.101.062603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 05/20/2020] [Indexed: 06/11/2023]
Abstract
The single-particle dynamics of sodium ions in molten sodium bromide has been investigated with quasielastic neutron scattering. A detailed and rather extensive data analysis procedure allowed determination of the pure sodium ion dynamics with increasing wave vector. Two different evaluation procedures agree perfectly on the resulting diffusion coefficient of sodium ions on long distances. A simple kinetic theory based on binary collisions of hard spheres is not able to reproduce the sodium diffusion coefficient. The derived reduced linewidth from modeling with a Lorentzian spectral function decreases with increasing wave vector towards the first structure factor maximum. That deviation from the hydrodynamic behavior signals the hindrance of the microscopic diffusion process due to the so-called cage effect when microscopic length scales are probed in a dense fluid. The observed quadratic wave-number-dependent decrease might be evidence for a coupling to density fluctuations as the source of the changes in the diffusion process. The results indicate that in the molten salt NaBr near the melting point the self-diffusion process might be governed by similar processes as already observed in dense metallic liquids.
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Affiliation(s)
- F Demmel
- ISIS Facility, Rutherford Appleton Laboratory, Didcot, OX11 0QX, United Kingdom
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2
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Abstract
The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.
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Affiliation(s)
- Oleg Sobolev
- Institute for Physical Chemistry, Georg-August-University of Göttingen , Tammannstrasse 6, D-37077 Göttingen, Germany.,Heinz Maier-Leibnitz Zentrum , Lichtenbergstrasse 1, D-85748 Garching, Germany
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Meyer A. The measurement of self-diffusion coefficients in liquid metals with quasielastic neutron scattering. EPJ WEB OF CONFERENCES 2015. [DOI: 10.1051/epjconf/20158301002] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Giordano VM, Monaco G. Fingerprints of order and disorder on the high-frequency dynamics of liquids. Proc Natl Acad Sci U S A 2010; 107:21985-21989. [PMCID: PMC3009772 DOI: 10.1073/pnas.1006319107] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023] Open
Abstract
It is largely accepted that liquids are characterized by a short-range order usually corresponding to that of the solid phase at the same density. It is less clear to what extent dynamic properties of liquids and crystals can be compared. In particular, high-frequency collective excitations reminiscent of phonons in solids exist as well in liquids. They are however traditionally discussed in terms of relaxation processes characteristic of the liquid phase. We report here on a quantitative comparison of the collective excitations in liquid and polycrystalline sodium. We show that liquid sodium exhibits acoustic excitations of both longitudinal and transverse polarization at frequencies strictly related to those of the corresponding crystal. The only relevant difference between the liquid and the polycrystal appears in the broadening of the excitations: An additional disorder-induced contribution comes into play in the case of the liquid, which we show to be related to the distribution of local structures around the average one. These results establish a direct connection between structural and dynamic properties of liquids, with short-range order and overall structural disorder leaving very specific fingerprints.
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Affiliation(s)
- Valentina M. Giordano
- European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, B.P. 220, 38043 Grenoble Cedex, France
| | - Giulio Monaco
- European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, B.P. 220, 38043 Grenoble Cedex, France
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Abstract
Abstract
The quasielastic dynamics in liquid metals has been investigated by neutron scattering extensively during the past years. Precise measurements of the self-particle dynamics and the coherent quasielastic response provided conclusive evidence that the relaxation dynamics is governed by at least two processes. These two time scales in the correlation functions appear as two dynamical processes in their associated memory functions. One process shows a fast decay and is related to stochastic binary collisions. The second slow process stems from a non-linear coupling of slow collective modes. These slow density fluctuations arise mainly from the dynamics around the structure factor maximum. A rigorous treatment of these effects can be accomplished by mode coupling theory. A few selective experiments from monatomic metals are presented to demonstrate the influence of slow effects on the dynamics. Experiments and MD-simulations show a surprising good agreement with predictions of mode coupling theory on a quantitative level. The slow decay process appears to be related to structural arrest in the supercooled state and might indicate a link to the solidification process, starting deep in the liquid state. Accurate quasielastic neutron scattering experiments are still and will remain a fundamental pillar for elucidating the complex dynamics in the liquid state of metals.
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Pilgrim WC, Morkel C. State dependent particle dynamics in liquid alkali metals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:R585-R633. [PMID: 21690895 DOI: 10.1088/0953-8984/18/37/r01] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This paper gives a survey of the particle dynamics in the liquid alkali metals observed with inelastic x-ray and neutron scattering experiments. Liquid rubidium and sodium are chosen as model fluids to represent the behaviour of this group of fluids. In the dense metallic monatomic melt the microscopic dynamics is characterized by collective excitations similar to those in the corresponding solids. The collective particle behaviour is appropriately described using a memory function formalism with two relaxation channels for the density correlation. A similar behaviour is found for the single particle motion where again two relaxation mechanisms are needed to accurately reproduce the experimental findings. Special emphasis is given to the density dependence of the particle dynamics. An interesting issue in liquid metals is the metal to non-metal transition, which is observed if the fluid is sufficiently expanded with increasing temperature and pressure. This causes distinct variations in the interparticle interactions, which feed back onto the motional behaviour. The associated variations in structure and dynamics are reflected in the shape of the scattering laws. The experimentally observed features are discussed and compared with simple models and with the results from computer simulations.
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Affiliation(s)
- W-C Pilgrim
- Department of Chemistry, Physical-Chemistry, Philipps-University of Marburg, D-35032 Marburg, Germany
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Monaco A, Scopigno T, Benassi P, Giugni A, Monaco G, Nardone M, Ruocco G, Sampoli M. Collective dynamics in molten potassium: An inelastic x-ray scattering study. J Chem Phys 2004; 120:8089-94. [PMID: 15267728 DOI: 10.1063/1.1689641] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The high-frequency collective dynamics of molten potassium has been investigated by inelastic x-ray scattering, disclosing an energy/momentum transfer region unreachable by previous inelastic neutron scattering (INS) experiments. We find that a two-step relaxation scenario, similar to that found in other liquid metals, applies to liquid potassium. In particular, we show how the sound velocity determined by INS experiments, exceeding the hydrodynamic value by approximately 30%, is the higher limit of a speedup, located in the momentum region 1 < Q < 3 nm(-1), which marks the departure from the isothermal value. We point out how this phenomenology is the consequence of a microscopic relaxation process that, in turn, can be traced back to the presence of "instantaneous" disorder, rather than to the crossover from a liquid to solidlike response.
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Affiliation(s)
- A Monaco
- Dipartimento di Fisica and INFM, Universita di L'Aquila, I-67010, L'Aquila, Italy
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Chiba A, Ohmasa Y, Yao M. Vibrational, single-particle-like, and diffusive dynamics in liquid Se, Te, and Te50Se50. J Chem Phys 2003. [DOI: 10.1063/1.1615234] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Scopigno T, Filipponi A, Krisch M, Monaco G, Ruocco G, Sette F. High-frequency acoustic modes in liquid gallium at the melting point. PHYSICAL REVIEW LETTERS 2002; 89:255506. [PMID: 12484899 DOI: 10.1103/physrevlett.89.255506] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2002] [Indexed: 05/24/2023]
Abstract
The microscopic dynamics in liquid gallium at melting has been studied by inelastic x-ray scattering. We demonstrate the existence of acousticlike modes up to wave vectors above one-half of the first maximum of the static structure factor, at variance with earlier results from inelastic neutron scattering [F. J. Bermejo et al., Phys. Rev. E 49, 3133 (1994)]. Despite structural (extremely rich polymorphism) and electronic (mixed valence) peculiarities, the collective dynamics is strikingly similar to the one of van der Waals and metallic fluids. This result speaks in favor of the universality of the short time dynamics in monatomic liquids rather than of system-specific dynamics.
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Affiliation(s)
- T Scopigno
- Dipartimento di Fisica and INFM, Universitá di Roma La Sapienza, Italy
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Scopigno T, Ruocco G, Sette F, Viliani G. Evidence of short-time dynamical correlations in simple liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:031205. [PMID: 12366104 DOI: 10.1103/physreve.66.031205] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2002] [Revised: 05/16/2002] [Indexed: 05/23/2023]
Abstract
We report a molecular dynamics study of the collective dynamics of a simple monatomic liquid--interacting through a two-body potential that mimics that of lithium--across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones glasses. The origin of this process is ascribed to the topological disorder, i.e., to the dephasing of the different momentum Q Fourier components of the actual normal modes of vibration of the disordered structure. More important, we find that the fast relaxation persists in the liquid phase with almost no temperature dependence of its characteristic parameters (strength and relaxation time). We conclude, therefore, that in the liquid phase well above the melting point, at variance with the usual assumption of uncorrelated binary collisions, the short time particle motion is strongly correlated and can be described via a normal mode expansion of the atomic dynamics.
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Affiliation(s)
- T Scopigno
- Dipartimento di Fisica and INFM, Università di Roma La Sapienza, I-00185 Roma, Italy
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Scopigno T, Balucani U, Ruocco G, Sette F. Inelastic x-ray scattering study of the collective dynamics in liquid sodium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:031205. [PMID: 11909038 DOI: 10.1103/physreve.65.031205] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2001] [Indexed: 05/23/2023]
Abstract
Inelastic x-ray scattering data have been collected for liquid sodium at T=390 K, i.e., slightly above the melting point. Owing to the very high instrumental resolution, pushed up to 1.5 meV, it has been possible to determine accurately the dynamic structure factor S(Q,omega) in a wide wave-vector range, 1.5-15 nm(-1), and to investigate on the dynamical processes underlying the collective dynamics. A detailed analysis of the line shape of S(Q,omega), similarly to other liquid metals, reveals the coexistence of two different relaxation processes with slow and fast characteristic time scales. The present data lead to the conclusion that (i) the picture of the relaxation mechanism based on a simple viscoelastic model fails and (ii) although the comparison with other liquid metals reveals similar behavior, the data do not exhibit an exact scaling law as the principle of the corresponding state would predict.
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Affiliation(s)
- T Scopigno
- Dipartimento di Fisica and INFM, Università di Roma "La Sapienza," I-00185, Roma, Italy
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Wuttke J, Chang I, Randl OG, Fujara F, Petry W. Tagged-particle motion in viscous glycerol: Diffusion-relaxation crossover. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:5364-5369. [PMID: 9965721 DOI: 10.1103/physreve.54.5364] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Morkel C, Gronemeyer C. Determination of the low ? cusp in the velocity autocorrelation spectrum of liquid sodium. ACTA ACUST UNITED AC 1988. [DOI: 10.1007/bf01314523] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Morkel C, Gronemeyer C, Gläser W, Bosse J. Experimental evidence for the long-time decay of the velocity-autocorrelation in liquid sodium. PHYSICAL REVIEW LETTERS 1987; 58:1873-1876. [PMID: 10034560 DOI: 10.1103/physrevlett.58.1873] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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