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Statistical Mechanics and Thermodynamics of Liquids and Crystals II

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 6895

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Special Issue Editor

Dr. Santi Prestipino

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Guest Editor

Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, 98166 Messina, Italy
Interests: liquid–solid transition; crystal nucleation; surface roughening; confined liquids; liquids and crystals of softly repulsive particles; self-assembly of complex fluids; superfluids and supersolids
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The thermodynamic and structural properties of liquids and crystals are a traditional subject of research in statistical mechanics. Especially the liquid–solid transition has been the focus of a great deal of theoretical and computational work in recent decades, with countless variations since the discovery of an entropy-driven freezing transition in a fluid of hard spheres in the late 1950s. Meanwhile, complex fluids and non-conventional liquids and crystals (e.g., patchy particles, hexatic fluids, crystalline membranes, and supersolids) have found their way into the field, with further types of self-assembling structures beyond those of standard crystals.

In spite of the enormous effort spent in characterizing the huge variety of condensed-matter phases, many questions remain open. To name but a few, a comprehensive understanding of the onset and growth of the crystal from the supercooled liquid, and of one crystalline phase from another, requires going beyond a merely equilibrium description. Similarly, new guiding principles need to be identified with the aim of gaining a better control of self-assembly processes in complex fluids. Like part I, this second part of the Special Issue aims to emphasize new research results in the application of statistical physics to liquids and crystals. Original manuscripts highlighting the various topics in this area, both traditional and novel, are welcome.

Prof. Dr. Santi Prestipino
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

theory of liquid structure
liquid&ndash
solid transition
translational order and bond-angle order
anisotropic liquids and their phases
crystal nucleation
water and ices
crystal polymorphism in soft matter
self-assembly of complex fluids
liquid and crystalline membranes
quantum liquids and crystals

Related Special Issue

Statistical Mechanics and Thermodynamics of Liquids and Crystals in Entropy (9 articles)

Published Papers (5 papers)

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Research

12 pages, 527 KiB

Open AccessArticle

The Solid Phase of ⁴He: A Monte Carlo Simulation Study

by Massimo Boninsegni

Entropy 2023, 25(8), 1114; https://doi.org/10.3390/e25081114 - 26 Jul 2023

Viewed by 792

Abstract

The thermodynamics of solid (hcp)

^{4}

The thermodynamics of solid (hcp)

^{4}

He is studied theoretically by means of unbiased Monte Carlo simulations at finite temperature, in a wide range of density. This study complements and extends previous theoretical work, mainly by obtaining results at significantly lower temperatures (down to 60 mK) and for systems of greater size, by including in full the effect of quantum statistics, and by comparing estimates yielded by different pair potentials. All the main thermodynamic properties of the crystal, e.g., the kinetic energy per atom, are predicted to be essentially independent of temperature below ∼ 1 K. Quantum-mechanical exchanges are virtually non-existent in this system, even at the lowest temperature considered. However, effects of quantum statistics are detectable in the momentum distribution. Comparison with available measurements shows general agreement within the experimental uncertainties. Full article

(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals II)

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23 pages, 11624 KiB

Open AccessFeature PaperArticle

Pattern Formation under Deep Supercooling by Classical Density Functional-Based Approach

by Kun Wang, Wenjin Chen, Shifang Xiao, Jun Chen and Wangyu Hu

Entropy 2023, 25(5), 708; https://doi.org/10.3390/e25050708 - 24 Apr 2023

Viewed by 1157

Abstract

Solidification patterns during nonequilibrium crystallization are among the most important microstructures in the natural and technical realms. In this work, we investigate the crystal growth in deeply supercooled liquid using the classical density functional-based approaches. Our result shows that the complex amplitude expanded phase-field crystal (APFC) model containing the vacancy nonequilibrium effects proposed by us could naturally reproduce the growth front nucleation (GFN) and various nonequilibrium patterns, including the faceted growth, spherulite, symmetric and nonsymmetric dendrites among others, at the atom level. Moreover, an extraordinary microscopic columnar-to-equiaxed transition is uncovered, which is found to depend on the seed spacing and distribution. Such a phenomenon could be attributed to the combined effects of the long-wave and short-wave elastic interactions. Particularly, the columnar growth could also be predicted by an APFC model containing inertia effects, but the lattice defect type in the growing crystal is different due to the different types of short-wave interactions. Two stages are identified during the crystal growth under different undercooling, corresponding to diffusion-controlled growth and GFN-dominated growth, respectively. However, compared with the second stage, the first stage becomes too short to be noticed under the high undercooling. The distinct feature of the second stage is the dramatic increments of lattice defects, which explains the amorphous nucleation precursor in the supercooled liquid. The transition time between the two stages at different undercooling is investigated. Crystal growth of BCC structure further confirms our conclusions. Full article

(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals II)

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15 pages, 1393 KiB

Open AccessArticle

Ultrasoft Classical Systems at Zero Temperature

by Matheus de Mello, Rogelio Díaz-Méndez and Alejandro Mendoza-Coto

Entropy 2023, 25(2), 356; https://doi.org/10.3390/e25020356 - 15 Feb 2023

Viewed by 1121

Abstract

At low temperatures, classical ultrasoft particle systems develop interesting phases via the self-assembly of particle clusters. In this study, we reach analytical expressions for the energy and the density interval of the coexistence regions for general ultrasoft pairwise potentials at zero temperatures. We use an expansion in the inverse of the number of particles per cluster for an accurate determination of the different quantities of interest. Differently from previous works, we study the ground state of such models, in two and three dimensions, considering an integer cluster occupancy number. The resulting expressions were successfully tested in the small and large density regimes for the Generalized Exponential Model α, varying the value of the exponent. Full article

(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals II)

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19 pages, 2502 KiB

Open AccessArticle

A Glimpse into Quantum Triplet Structures in Supercritical ³He

by Luis M. Sesé

Entropy 2023, 25(2), 283; https://doi.org/10.3390/e25020283 - 2 Feb 2023

Viewed by 937

Abstract

A methodological study of triplet structures in quantum matter is presented. The focus is on helium-3 under supercritical conditions (4 < T/K < 9; 0.022 <

ρ_{N} / Å^{- 3}

< 0.028), for which strong quantum diffraction effects dominate the [...] Read more.

A methodological study of triplet structures in quantum matter is presented. The focus is on helium-3 under supercritical conditions (4 < T/K < 9; 0.022 <

ρ_{N} / Å^{- 3}

< 0.028), for which strong quantum diffraction effects dominate the behavior. Computational results for the triplet instantaneous structures are reported. Path integral Monte Carlo (PIMC) and several closures are utilized to obtain structure information in the real and the Fourier spaces. PIMC involves the fourth-order propagator and the SAPT2 pair interaction potential. The main triplet closures are: AV3, built as the average of the Kirkwood superposition and the Jackson–Feenberg convolution, and the Barrat–Hansen–Pastore variational approach. The results illustrate the main characteristics of the procedures employed by concentrating on the salient equilateral and isosceles features of the computed structures. Finally, the valuable interpretive role of closures in the triplet context is highlighted. Full article

(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals II)

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15 pages, 2596 KiB

Open AccessFeature PaperArticle

Condensation and Crystal Nucleation in a Lattice Gas with a Realistic Phase Diagram

by Santi Prestipino and Gabriele Costa

Entropy 2022, 24(3), 419; https://doi.org/10.3390/e24030419 - 17 Mar 2022

Cited by 1 | Viewed by 1911

Abstract

We reconsider model II of Orban et al. (J. Chem. Phys. 1968, 49, 1778–1783), a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: Upon closer inspection, the alleged liquid–vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier relative to crystal nucleation from the “liquid”. Full article

(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals II)

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