# Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition

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## Abstract

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## 1. Introduction

## 2. Approach

#### 2.1. Formulation

#### 2.2. Inverse-Power-Law Model

## 3. Results

#### 3.1. Additivity of Melting Curves

#### 3.2. Sound Velocities of the LJ System

#### 3.3. Comparison with Experiment

## 4. Discussion and Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Reduced longitudinal and transverse sound velocities at the fluid–solid coexistence of the soft sphere model versus the softness parameter s. Sound velocities are expressed in units of the thermal velocity ${v}_{\mathrm{T}}$. Upper curves are for the longitudinal mode, lower curves are for the transverse mode. Solid (dashed) curves correspond to the solid (fluid) boundary of the fluid–solid coexistence.

**Figure 3.**Reduced excess energy per particle in LJ units, ${U}_{\mathrm{ex}}/N\u03f5$, of the Lennard-Jones system versus the reduced temperature ${T}_{\ast}=T/\u03f5$. Symbols correspond to the MC results [43]. The curves are calculated using the additivity principle. Solid symbols and curve correspond to the solid side of the liquid–solid coexistence (solidus); open symbols and the dashed curve correspond to its liquid side (liquidus).

**Figure 4.**Reduced longitudinal and transverse sound velocities of the LJ model versus the reduced temperature ${T}_{\ast}$. Upper symbols and curves are for the longitudinal mode, lower symbols and curves are for the transverse mode. Symbols are the results of calculation using relations (6) and (7) using MC data from Ref. [43]. Solid and open symbols correspond to the boundaries of the solid and liquid phases, respectively. Solid (dashed) curves correspond to the solid (liquid) coexistence boundary and are plotted using the additivity principle (13).

**Figure 5.**Reduced longitudinal and transverse sound velocities in compressed solidified argon at the melting temperature in the range 123–206 K. Symbols correspond to the experimental results tabulated in Ref. [13].

$\mathcal{X}$= | ${\mathit{u}}_{\mathbf{ex}}$ | ${\mathit{p}}_{\mathbf{ex}}$ | ${\mathit{c}}_{\mathit{l}}^{2}/{\mathit{v}}_{\mathbf{T}}^{2}$ | ${\mathit{c}}_{\mathit{t}}^{2}/{\mathit{v}}_{\mathbf{T}}^{2}$ |
---|---|---|---|---|

${\mathcal{C}}_{12}$ | 2 | 8 | $\frac{296}{5}$ | $\frac{72}{5}$ |

${\mathcal{C}}_{6}$ | 2 | 4 | $\frac{76}{5}$ | $\frac{12}{5}$ |

**Table 2.**Solid-liquid coexistence data [42] and numerical values of the sums ${\mathsf{\Sigma}}_{n}$ for $n=12$ and $n=6$ IPL potentials.

n | ${\mathit{P}}_{\ast}$ | ${\mathit{\rho}}_{\ast}^{\mathbf{sol}}$ | ${\mathit{\rho}}_{\ast}^{\mathbf{liq}}$ | ${\mathbf{\Sigma}}^{\mathbf{sol}}$ | ${\mathbf{\Sigma}}^{\mathbf{liq}}$ |
---|---|---|---|---|---|

$n=12$ | 23.74 | 1.211 | 1.167 | 4.325 | 5.214 |

$n=6$ | 105.0 | 2.358 | 2.330 | 7.829 | 8.106 |

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Khrapak, S.A.
Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition. *Molecules* **2020**, *25*, 3498.
https://doi.org/10.3390/molecules25153498

**AMA Style**

Khrapak SA.
Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition. *Molecules*. 2020; 25(15):3498.
https://doi.org/10.3390/molecules25153498

**Chicago/Turabian Style**

Khrapak, Sergey A.
2020. "Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition" *Molecules* 25, no. 15: 3498.
https://doi.org/10.3390/molecules25153498