Density Affects the Nature of the Hexatic-Liquid Transition in Two-Dimensional Melting of Soft-Core Systems

Mengjie Zu, Jun Liu, Hua Tong, and Ning Xu

Phys. Rev. Lett. 117, 085702 – Published 15 August 2016

Abstract

We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature $T_{m}$ happening at a crossover density $ρ_{m}$ . The hexatic-liquid transition at a density smaller than $ρ_{m}$ is discontinuous. Liquid and hexatic phases coexist in a density interval, which becomes narrower with increasing temperature and tends to vanish approximately at $T_{m}$ . Above $ρ_{m}$ , the transition is continuous, in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For these soft-core systems, the nature of the hexatic-liquid transition depends on density (pressure), with the melting at $ρ_{m}$ being a plausible transition point from discontinuous to continuous hexatic-liquid transition.

Received 2 May 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.085702

Physics Subject Headings (PhySH)

Crystal melting Phase transitions

Liquids

Molecular dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mengjie Zu, Jun Liu, Hua Tong, and Ning Xu^*

CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale, and Department of Physics, University of Science and Technology of China, Hefei 230026, People’s Republic of China

^*ningxu@ustc.edu.cn

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Issue

Vol. 117, Iss. 8 — 19 August 2016

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Images

Figure 1
Phase diagram for $N = 1024$ Hertzian disks in the temperature $T$ and density $ρ$ plane. Here, we only show the density region with triangular and square solid structures. There are more structures at higher densities. The solid circles are approximate phase boundaries, above which are pure liquid states. The lines are a guide for the eye. The images for triangular and square structures are taken from simulation snapshots, with the particle diameters shown here being half of the actual values. (Inset) $ρ (T)$ curves across the transitions at $P = 0.12$ (dot dashed), 0.14 (solid), and 0.16 (dashed). The solid and dashed lines are shifted vertically by $- 0.06$ and $- 0.117$ , respectively. The solid circles demonstrate how the phase boundaries in the main panel are determined.
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Figure 2
(a) Isothermal equation of state $P (ρ)$ calculated at $T = 3.00 \times 1 0^{- 3}$ across the melting at $ρ < ρ_{m}$ for $N = 102 400$ Herztian disks. We use different symbols as explained in the legend to distinguish different states. The solid line is a tenth-order polynomial fit to the data. The dashed line demonstrates the Maxwell construction. (b) System size dependence of the interface free energy per particle $f$ for Hertzian disks calculated at $T = 3.00 \times 1 0^{- 3}$ . The area encircled by the solid and dashed lines in (a) determines $f$ . The line shows the scaling: $f \sim N^{- 1 / 2}$ . (c) Temperature dependence of the density interval of phase coexistence $Δ ρ_{coex}$ for Herztian (circles) and harmonic (squares) repulsions. The lines show the scaling: $Δ ρ_{coex} \sim (T_{m}^{*} - T)^{γ}$ , with $T_{m}^{*} = 3.86 \times 1 0^{- 3}$ ( $7.06 \times 1 0^{- 3}$ ) and $γ = 0.70$ (0.50) for Herztian (harmonic) repulsion. (d) Isothermal equation of state $P (ρ)$ calculated for the same system and at the same temperature as (a), but across the transitions at $ρ > ρ_{m}$ . The symbols have the same meaning as in (a). The line is a guide for the eye.
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Figure 3
System size dependence of the density $ρ (T)$ , enthalpy per particle $H (T) / N$ , and average bond-orientational order $Ψ_{6} (T)$ for Hertzian disks calculated at $P = 0.058$ ( $< P_{m}$ , left column) and 0.263 ( $> P_{m}$ , right column). The lines are a guide for the eye.
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Figure 4
Isothermal equation of state $P (ρ)$ across the transitions for $N = 25 600$ Gaussian-core disks calculated at $T = 1.80 \times 1 0^{- 3}$ and at (a) $ρ < ρ_{m}$ and (b) $ρ > ρ_{m}$ . The line in (a) is the tenth-order polynomial fit to the data, while in (b) is a guide for the eye. The legend in (b) explains the meaning of the symbols in both panels. The inset in (a) shows the temperature dependence of the density interval of phase coexistence $Δ ρ_{coex}$ . The data can be well fitted with $Δ ρ_{coex} \sim (T_{m}^{*} - T)^{γ}$ , where $T_{m}^{*} = 0.0114$ and $γ = 2.0$ .
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