^{1,a)}, Jérôme Delhommelle

^{2}and Claude Millot

^{3,b)}

### Abstract

Classical nucleation theory pictures the homogeneous nucleation of a crystal as the formation of a spherical crystalline embryo, possessing the properties of the macroscopic crystal, inside a parent supercooled liquid. In this work we study crystal nucleation in moderately supercooled sulfur hexafluoride by umbrella sampling simulations. The nucleationfree energy evolves from at to at . The corresponding critical nucleus size ranges from at at . Both nucleationfree energy and critical nucleus size are shown to evolve with temperature according to the equations derived from the classical nucleation theory. Inspecting the obtained nuclei we show, however, that they present quite anisotropic shapes in opposition to the spherical assumption of the theory. Moreover, even though the critical nuclei possess the structure of the stable bcc plastic phase, the only mechanically stable crystal phase for in the temperature range investigated, they are shown to be less ordered than the corresponding macroscopic crystal. Their crystalline order is nevertheless shown to increase regularly with their size. This is confirmed by a study of a nucleus growth from a critical size to a size of the order of . Similarly to the fact that it does not affect the temperature dependence of the nucleationfree energy and of the critical nucleus size, the ordering of the nucleus with size does not affect the growth rate of the nucleus.

Support of the University Henri Poincaré and the CNRS and access to the supercomputers of the Centre Informatique National de l’Enseignement Superieur (Project No. lct2248) are gratefully acknowledged.

I. INTRODUCTION

II. METHODS

III. SIMULATION RESULTS

IV. DISCUSSION AND CONCLUSION

### Key Topics

- Nucleation
- 62.0
- Free energy
- 25.0
- Liquid crystals
- 19.0
- Carbon nanotubes
- 16.0
- Crystal structure
- 16.0

## Figures

Evolution of the nucleation free energy (top) and of the critical nucleus size (bottom) with temperature. Symbols are umbrella sampling results; straight lines are fit to CNT equations [Eq. (5): ; Eq. (4): ].

Evolution of the nucleation free energy (top) and of the critical nucleus size (bottom) with temperature. Symbols are umbrella sampling results; straight lines are fit to CNT equations [Eq. (5): ; Eq. (4): ].

(Color online) Snapshots of critical nuclei taken along the 100 (left) and 111 (right) directions of the body centered cubic structure. Only sulfur atoms are displayed for clarity. a: ; b: ; c: ; d: ; e: ; f: .

(Color online) Snapshots of critical nuclei taken along the 100 (left) and 111 (right) directions of the body centered cubic structure. Only sulfur atoms are displayed for clarity. a: ; b: ; c: ; d: ; e: ; f: .

(Color) Projections along the 100 (left, blue) and 111 (right, purple) directions of ideal clusters created from spherical chunks of a perfect bcc crystal. A: ; B: 27; C: 51 and 59; D: 65; E: 89; F: 113; G: 137; H: 169; I: 181; J: 229; K: 259; L: 283; M: 307; N: 1211; O: 5521; P: 146 399. Some 3D shapes of the corresponding polyhedron (D, G, H, J, M, and P), obtained by arbitrarily increasing the particle diameters, are shown in yellow on black background.

(Color) Projections along the 100 (left, blue) and 111 (right, purple) directions of ideal clusters created from spherical chunks of a perfect bcc crystal. A: ; B: 27; C: 51 and 59; D: 65; E: 89; F: 113; G: 137; H: 169; I: 181; J: 229; K: 259; L: 283; M: 307; N: 1211; O: 5521; P: 146 399. Some 3D shapes of the corresponding polyhedron (D, G, H, J, M, and P), obtained by arbitrarily increasing the particle diameters, are shown in yellow on black background.

(Color online) Distribution of local order parameters. Straight line is bcc crystal ; dashed line is liquid ; symbols are critical nuclei at (circles), , (squares) and (diamonds).

(Color online) Distribution of local order parameters. Straight line is bcc crystal ; dashed line is liquid ; symbols are critical nuclei at (circles), , (squares) and (diamonds).

(Color online) Individual effect of temperature (left) and nucleus size (right) on the nucleus local order parameter distributions. Left plots: nuclei at (circles), (squares), and (diamonds). Right plots: Nuclei of 50 (circles), 100 (squares), and 300 (diamonds) molecules at . Distributions for the bcc crystal (straight line) and the supercooled liquid (dashed lines) at are shown for comparison.

(Color online) Individual effect of temperature (left) and nucleus size (right) on the nucleus local order parameter distributions. Left plots: nuclei at (circles), (squares), and (diamonds). Right plots: Nuclei of 50 (circles), 100 (squares), and 300 (diamonds) molecules at . Distributions for the bcc crystal (straight line) and the supercooled liquid (dashed lines) at are shown for comparison.

(Color) Time evolution of the nucleus local order parameter distributions during a growth trajectory at in a 21 296 molecules system. Circles are for time and average nucleus size ; squares are for and ; diamonds are for and ; up triangles are for and ; left triangles are for and ; down triangles are for and . Distributions for the critical nucleus (straight lines) and the bcc crystal (dashed line) at are given for comparison.

(Color) Time evolution of the nucleus local order parameter distributions during a growth trajectory at in a 21 296 molecules system. Circles are for time and average nucleus size ; squares are for and ; diamonds are for and ; up triangles are for and ; left triangles are for and ; down triangles are for and . Distributions for the critical nucleus (straight lines) and the bcc crystal (dashed line) at are given for comparison.

(Color online) Evolution of the nucleus size during a growth trajectory at . Circles are simulation results; straight line is fit to a constant growth rate law.

(Color online) Evolution of the nucleus size during a growth trajectory at . Circles are simulation results; straight line is fit to a constant growth rate law.

## Tables

Temperature and radius of the biased subsystem used in umbrella sampling simulations together with the resulting nucleation free energies and critical nuclei sizes .

Temperature and radius of the biased subsystem used in umbrella sampling simulations together with the resulting nucleation free energies and critical nuclei sizes .

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