1
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Lima EO, Pereira PCN, Apolinario SWS. Local orderings in the melting process of a square crystal and in the resulting liquid. Phys Rev E 2022; 106:054106. [PMID: 36559510 DOI: 10.1103/physreve.106.054106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 10/12/2022] [Indexed: 06/17/2023]
Abstract
Using Brownian dynamics simulations we investigate the melting processes of a square crystalline lattice of colloidal particles interacting via an isotropic potential, which comprises both a hard-core repulsion and an additional softened square-well potential. For temperatures slightly lower than the transition one, we found a proliferation of small liquid clusters surrounded by the square lattice. These clusters are not static, quite the opposite, they have an intense dynamics and are continuously formed and destroyed over time. However, no unbound topological defects are observed. At the transition temperature, one of these liquid clusters starts to grow, until the entire system becomes in the liquid phase, then, characterizing a first-order phase transition. The tetratic intermediate phase, as given by the KTHNY theory, was not observed. Moreover, the liquid phase exhibits a considerable number of crystalline clusters having square and triangular orderings, which remain present even when increasing temperature by an order of magnitude. As the temperature increases, structural changes within the liquid phase are analyzed by evaluating the number and sizes of the square and triangular clusters. A transition of the dominant clusters is observed.
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Affiliation(s)
- E O Lima
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - P C N Pereira
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - S W S Apolinario
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
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2
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Gaiduk EA, Fomin YD, Tsiok EN, Ryzhov VN. Anomalous behavior of a two-dimensional Hertzian disk system. Phys Rev E 2022; 106:024602. [PMID: 36110004 DOI: 10.1103/physreve.106.024602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 07/18/2022] [Indexed: 06/15/2023]
Abstract
The anomalous behavior of a two-dimensional system of Hertzian disks with exponent α=7/2 has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Waterlike density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also in the solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above the maximum melting point T=0.0058 of the triangular crystal.
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Affiliation(s)
- Eu A Gaiduk
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
| | - Yu D Fomin
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
| | - E N Tsiok
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
| | - V N Ryzhov
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
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3
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Abutbul D, Podolsky D. Topological Order in an Antiferromagnetic Tetratic Phase. PHYSICAL REVIEW LETTERS 2022; 128:255501. [PMID: 35802454 DOI: 10.1103/physrevlett.128.255501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2021] [Revised: 04/11/2022] [Accepted: 06/02/2022] [Indexed: 06/15/2023]
Abstract
We study lattice melting in two-dimensional systems of spinful particles that interact antiferromagnetically. We argue that, for strong spin interactions, single lattice dislocations are forbidden by magnetic frustration. This leads to a melting scenario in which a tetratic phase, containing free dislocation pairs and bound disclinations, separates the solid from the liquid. We demonstrate this phase numerically in a system of hard spheres confined between parallel plates, where spins are represented by the heights of the spheres. In the tetratic phase, the spins are shown to be as antiferromagnetically ordered as allowed by their spatial configuration.
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4
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Tsiok EN, Fomin YD, Gaiduk EA, Tareyeva EE, Ryzhov VN, Libet PA, Dmitryuk NA, Kryuchkov NP, Yurchenko SO. The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems. J Chem Phys 2022; 156:114703. [DOI: 10.1063/5.0075479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter.
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Affiliation(s)
- Elena N. Tsiok
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Yuri D. Fomin
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Eugene A. Gaiduk
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Elena E. Tareyeva
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Valentin N. Ryzhov
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Pavel A. Libet
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Nikita A. Dmitryuk
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Nikita P. Kryuchkov
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Stanislav O. Yurchenko
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
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5
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Sun YW, Li Z, Sun ZY. Multiple 2D crystal structures in bilayered lamellae from direct self-assembly of 3D systems of soft Janus particles. Phys Chem Chem Phys 2022; 24:7874-7881. [DOI: 10.1039/d1cp05894k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Numerous crystals and Frank-Kasper phases in two-dimensional (2D) systems of soft particles have been presented by theoretical investigations. How to realize 2D crystals or Frank-kasper phases by direct self-assembly of...
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6
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Tsiok EN, Fomin YD, Gaiduk EA, Ryzhov VN. Structural transition in two-dimensional Hertzian spheres in the presence of random pinning. Phys Rev E 2021; 103:062612. [PMID: 34271643 DOI: 10.1103/physreve.103.062612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 06/03/2021] [Indexed: 11/07/2022]
Abstract
Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional system with the Hertz potential for α=5/2. It has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of first order, and finally, there is a continuous BKT-type transition from tetratic to the square crystal.
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Affiliation(s)
- E N Tsiok
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - Yu D Fomin
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - E A Gaiduk
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - V N Ryzhov
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
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7
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Khali SS, Chakraborty D, Chaudhuri D. Two-step melting of the Weeks-Chandler-Anderson system in two dimensions. SOFT MATTER 2021; 17:3473-3485. [PMID: 33656044 DOI: 10.1039/d0sm01484b] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We present a detailed numerical simulation study of a two-dimensional system of particles interacting via the Weeks-Chandler-Anderson potential, the repulsive part of the Lennard-Jones potential. With the reduction of density, the system shows a two-step melting: a continuous melting of solid to hexatic phase, followed by a first-order melting of hexatic to liquid. The solid-hexatic melting is consistent with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario and shows dislocation unbinding. The first-order melting of the hexatic to the liquid phase, on the other hand, displays defect-strings formed at the hexatic-liquid interfaces. We present a detailed phase diagram in the density-temperature plane.
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Affiliation(s)
- Shubhendu Shekhar Khali
- Department of Physical Science, Indian Institute Of Science Education and Research Mohali, Punjab 140306, India.
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8
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Levashov VA, Ryltsev RE, Chtchelkatchev NM. Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:025403. [PMID: 33063696 DOI: 10.1088/1361-648x/abb516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood's superposition approximation. Detailed considerations of the peaks' shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system's dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids' dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid's structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.
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Affiliation(s)
- V A Levashov
- Technological Design Institute of Scientific Instrument Engineering, 630055, Novosibirsk, Russia
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia
| | - R E Ryltsev
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia
- Institute of Metallurgy, UB RAS, 620016, 101 Amundsen str., Ekaterinburg, Russia
- Ural Federal University, 620002, 19 Mira str,, Ekaterinburg, Russia
| | - N M Chtchelkatchev
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia
- Ural Federal University, 620002, 19 Mira str,, Ekaterinburg, Russia
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9
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Boattini E, Bezem N, Punnathanam SN, Smallenburg F, Filion L. Modeling of many-body interactions between elastic spheres through symmetry functions. J Chem Phys 2020; 153:064902. [DOI: 10.1063/5.0015606] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Emanuele Boattini
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
| | - Nina Bezem
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
| | - Sudeep N. Punnathanam
- Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, Karnataka, India
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Laura Filion
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
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10
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Tsiok EN, Gaiduk EA, Fomin YD, Ryzhov VN. Melting scenarios of two-dimensional Hertzian spheres with a single triangular lattice. SOFT MATTER 2020; 16:3962-3972. [PMID: 32249869 DOI: 10.1039/c9sm02262g] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We present a molecular dynamics simulation study of the phase diagram and melting scenarios of two-dimensional Hertzian spheres with exponent 7/2. We have found multiple re-entrant melting of a single crystal with a triangular lattice in a wide range of densities from 0.5 to 10.0. Depending on the position on the phase diagram, the triangular crystal has been shown to melt through both two-stage melting with a first-order hexatic-isotropic liquid transition and a continuous solid-hexatic transition as well as in accordance with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario (two continuous transitions with an intermediate hexatic phase). We studied the behavior of heat capacity and have shown that despite two-stage melting, the heat capacity has one peak which seems to correspond to a solid-hexatic transition.
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Affiliation(s)
- E N Tsiok
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia.
| | - E A Gaiduk
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia.
| | - Yu D Fomin
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia. and Moscow Institute of Physics and Technology, 9 Institutskiy Lane, Dolgoprudny City, Moscow Region, Russia
| | - V N Ryzhov
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia.
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11
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Mandal BK, Mishra P. Pair correlation function and freezing transitions in a two-dimensional system of model ultrasoft colloids. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1706774] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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12
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Nowack L, Rice SA. Sequential phase transitions and transient structured fluctuations in two-dimensional systems with a high-density Kagome lattice phase. J Chem Phys 2019; 151:244504. [DOI: 10.1063/1.5130558] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Linsey Nowack
- Department of Chemistry and the Chicago Center for Theoretical Chemistry, James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Stuart A. Rice
- Department of Chemistry and the Chicago Center for Theoretical Chemistry, James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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13
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Munaò G, Saija F. Monte Carlo simulation and integral equation study of Hertzian spheres in the low-temperature regime. J Chem Phys 2019; 151:134901. [PMID: 31594317 DOI: 10.1063/1.5121007] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the behavior of Hertzian spheres in the fluid phase and in proximity of the freezing threshold by using Monte Carlo (MC) simulations and integral equation theories, based on the Ornstein-Zernike (OZ) approach. The study is motivated by the importance of the Hertzian model in representing a large class of systems interacting via soft interactions, such as star polymers or microgels. Radial distribution functions, structure factors, and excess entropy clearly show the reentrant behavior typical of the Hertzian fluid, well caught by both MC simulations and OZ theory. Then, we make use of some phenomenological one-phase criteria for testing their reliability in detecting the freezing threshold. All criteria provide evidence of the fluid-solid transition with different degrees of accuracy. This suggests the possibility to adopt these empirical rules to provide a quick and reasonable estimate of the freezing transition in model potentials of wide interest for soft matter systems.
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Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Franz Saija
- CNR-IPCF, Viale F. Stagno Alcontres 37, I-98158 Messina, Italy
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14
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Fomin YD, Ryzhov VN, Tsiok EN. The influence of long-range interaction on the structure of a two-dimensional multi scale potential system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:315103. [PMID: 31039557 DOI: 10.1088/1361-648x/ab1df6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We present the results of a computer simulation study of a finite temperature phase diagram of two-dimensional and quasi two-dimensional core-softened systems both taking into account long-range Coulomb-like forces and ignoring them. The system structure was determined from analysis of the behavior of radial distribution functions, order parameters and number of nearest neighbors. The system has been shown to have a large number of different phases. We have found that long-range forces substantially affected the structure and the melting point of the system at low and moderate densities, while at high densities the effect of long-range forces was negligible.
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15
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Gaiduk EA, Fomin Y, Tsiok EN, Ryzhov VN. The influence of random pinning on the melting scenario of two-dimensional soft-disk systems. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1607917] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- E. A. Gaiduk
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
| | - Yu.D. Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
| | - E. N. Tsiok
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
| | - V. N. Ryzhov
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
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16
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Azizi I, Rabin Y. Identity ordering and metastable clusters in fluids with random interactions. J Chem Phys 2019; 150:134502. [PMID: 30954053 DOI: 10.1063/1.5083218] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We use Langevin dynamics simulations to study dense two-dimensional systems of particles where all binary interactions are different in the sense that each interaction parameter is characterized by a randomly chosen number. We compare two systems that differ by the probability distributions from which the interaction parameters are drawn: uniform (U) and exponential (E). Both systems undergo neighborhood identity ordering and form metastable clusters in the fluid phase near the liquid-solid transition, but the effects are much stronger in E than in U systems. Possible implications of our results for the control of the structure of multicomponent alloys are discussed.
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Affiliation(s)
- Itay Azizi
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel
| | - Yitzhak Rabin
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel
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