^{1}and G. Pastore

^{1}

### Abstract

The existence of systematic variations of isobaric fragility in different supercooled Lennard-Jones binary mixtures is revealed by molecular dynamics simulations. The connection between fragility and local structures in the bulk is analyzed by means of a Voronoi construction. It is found that clusters of particles belonging to locally preferred structures form slow, long-lived domains, whose spatial extension increases with decreasing temperature. As a general rule, a more rapid growth, upon supercooling, of such domains is associated with a more pronounced super-Arrhenius behavior, and hence to a larger fragility.

The authors would like to thank R. G. Della Valle for making available his efficient program for Voronoi analysis. Computational resources for the present work have been partly obtained through a grant from “Iniziativa Trasversale di Calcolo Parallelo” of the Italian *CNR-Istituto Nazionale per la Fisica della Materia* (CNR-INFM) and partly within the agreement between the University of Trieste and the Consorzio Interuniversitario CINECA (Italy).

I. INTRODUCTION

II. MODEL BINARY MIXTURES

A. BMLJ: Binary mixture of Lennard-Jones particles

B. : Lennard-Jones model for alloy

C. WAHN: Additive mixture of Wahnström

D. AMLJ-: Additive mixture of Lennard-Jones particles

III. QUENCHING PROTOCOLS AND SIMULATION DETAILS

IV. FRAGILITY

V. LOCALLY PREFERRED STRUCTURES

VI. CONCLUSIONS

### Key Topics

- Relaxation times
- 20.0
- Polyhedra
- 18.0
- Nickel
- 14.0
- Thermodynamic properties
- 6.0
- Diffusion
- 5.0

## Figures

Bhatia-Thornton structure factors in the deeply supercooled regime. Number-number (solid lines), number-concentration (dashed lines), and concentration-concentration (dotted lines) structure factors are shown. The concentration-concentration structure factor has been normalized to 1 by plotting . Data are shown at the lowest equilibrated temperature for each given system. Note that all structure factors are finite in the limit and that the first sharp peak of around is roughly system independent.

Bhatia-Thornton structure factors in the deeply supercooled regime. Number-number (solid lines), number-concentration (dashed lines), and concentration-concentration (dotted lines) structure factors are shown. The concentration-concentration structure factor has been normalized to 1 by plotting . Data are shown at the lowest equilibrated temperature for each given system. Note that all structure factors are finite in the limit and that the first sharp peak of around is roughly system independent.

Temperature dependence of density along isobaric quenches at (left axis, circles) and of pressure in isochoric quenches (right axis, squares). Data are shown for BMLJ (filled symbols) and WAHN (open symbols). Isochoric quenches were performed at for BMLJ and for WAHN.

Temperature dependence of density along isobaric quenches at (left axis, circles) and of pressure in isochoric quenches (right axis, squares). Data are shown for BMLJ (filled symbols) and WAHN (open symbols). Isochoric quenches were performed at for BMLJ and for WAHN.

Angell plot of relaxation times of large particles for a selection of AMLJ- mixtures. Results are shown for , 0.70, 0.73, 0.82 along the isobar . The reference temperature is described in the text. The inset shows the isobaric fragility index obtained from generalized VFT equation [see Eq. (5)] against size ratio .

Angell plot of relaxation times of large particles for a selection of AMLJ- mixtures. Results are shown for , 0.70, 0.73, 0.82 along the isobar . The reference temperature is described in the text. The inset shows the isobaric fragility index obtained from generalized VFT equation [see Eq. (5)] against size ratio .

Angell plot of relaxation times of large particles for BMLJ (black circles) and WAHN mixture (white circles) along isobaric quenches at . The inset shows results at , 10, 20, 50 for BMLJ.

Angell plot of relaxation times of large particles for BMLJ (black circles) and WAHN mixture (white circles) along isobaric quenches at . The inset shows results at , 10, 20, 50 for BMLJ.

Angell plot of total diffusion coefficient for a selection of AMLJ- mixtures. Results are shown for , 0.70, 0.73, 0.82 along the isobar . The reference temperature is obtained from fit to Eq. (7). The inset shows the isobaric fragility index obtained from Eq. (7) against size ratio .

Angell plot of total diffusion coefficient for a selection of AMLJ- mixtures. Results are shown for , 0.70, 0.73, 0.82 along the isobar . The reference temperature is obtained from fit to Eq. (7). The inset shows the isobaric fragility index obtained from Eq. (7) against size ratio .

Angell plot of total diffusion coefficient for BMLJ (black circles) and WAHN mixture (white circles) along isobaric quenches at . The inset shows results at , 10, 20, 50 for BMLJ.

Angell plot of total diffusion coefficient for BMLJ (black circles) and WAHN mixture (white circles) along isobaric quenches at . The inset shows results at , 10, 20, 50 for BMLJ.

Temperature dependence of the fraction of small particles at the center of (0,0,12) polyhedra in AMLJ- for selected values of . Results are shown for instantaneous configurations (main plot) and local minima (inset) along isobaric quenches at .

Temperature dependence of the fraction of small particles at the center of (0,0,12) polyhedra in AMLJ- for selected values of . Results are shown for instantaneous configurations (main plot) and local minima (inset) along isobaric quenches at .

Variation of icosahedral ordering with size ratio in additive mixtures AMLJ-. The fraction of small particles at the center of (0,0,12)-polyhedra in local minima is shown as a function of size ratio , at (black circles) and at the lowest equilibrated temperatures (open circles).

Variation of icosahedral ordering with size ratio in additive mixtures AMLJ-. The fraction of small particles at the center of (0,0,12)-polyhedra in local minima is shown as a function of size ratio , at (black circles) and at the lowest equilibrated temperatures (open circles).

Examples of locally preferred structures found in local minima of supercooled Lennard-Jones mixtures. Small and large particles are shown as dark and pale spheres respectively. (a) (0,2,8) polyhedron (twisted bicapped square prism) in BMLJ. This is the most frequent chemical coordination, incidentally one or two small particles can form the cap. (b) (0,3,6) polyhedron (capped trigonal prism) in . In this case, one of the caps is often formed by a small particle. (c) (0,0,12) polyhedron (icosahedron) in WAHN. On average, the coordination around the central particle is equimolar.

Examples of locally preferred structures found in local minima of supercooled Lennard-Jones mixtures. Small and large particles are shown as dark and pale spheres respectively. (a) (0,2,8) polyhedron (twisted bicapped square prism) in BMLJ. This is the most frequent chemical coordination, incidentally one or two small particles can form the cap. (b) (0,3,6) polyhedron (capped trigonal prism) in . In this case, one of the caps is often formed by a small particle. (c) (0,0,12) polyhedron (icosahedron) in WAHN. On average, the coordination around the central particle is equimolar.

Bond-angle distributions around small particles for WAHN (upper plot), BMLJ (middle plot), and (lower plot). The bond-angle distribution is shown as a solid line. Also shown is the bond-angle distribution restricted to small particles which are at the center of the locally preferred structure of the system, as given by Fig. 9. Data refer to the lowest equilibrated temperature of each given system. The sharp peaks in the distributions filtered for locally preferred structures reflect the ideal angles of the corresponding geometry.

Bond-angle distributions around small particles for WAHN (upper plot), BMLJ (middle plot), and (lower plot). The bond-angle distribution is shown as a solid line. Also shown is the bond-angle distribution restricted to small particles which are at the center of the locally preferred structure of the system, as given by Fig. 9. Data refer to the lowest equilibrated temperature of each given system. The sharp peaks in the distributions filtered for locally preferred structures reflect the ideal angles of the corresponding geometry.

Temperature dependence of the fraction of small particles at the center of selected Voronoi polyhedra in instantaneous configurations (main plot) and local minima (inset). The fraction of (0,2,8) polyhedra in BMLJ (white symbols) and (0,0,12) polyhedra in WAHN mixture (black symbols) is shown along isobaric quenches at . Data for are close to those for BMLJ, but are not shown for clarity.

Temperature dependence of the fraction of small particles at the center of selected Voronoi polyhedra in instantaneous configurations (main plot) and local minima (inset). The fraction of (0,2,8) polyhedra in BMLJ (white symbols) and (0,0,12) polyhedra in WAHN mixture (black symbols) is shown along isobaric quenches at . Data for are close to those for BMLJ, but are not shown for clarity.

Domains formed by locally preferred structures in local minima at the lowest equilibrated temperature at (WAHN: . BMLJ: ). Particles forming (a) (0,2,8) polyhedra in BMLJ and (b) (0,0,12) polyhedra in WAHN are shown as spheres of the same radius, irrespective of chemical species.

Domains formed by locally preferred structures in local minima at the lowest equilibrated temperature at (WAHN: . BMLJ: ). Particles forming (a) (0,2,8) polyhedra in BMLJ and (b) (0,0,12) polyhedra in WAHN are shown as spheres of the same radius, irrespective of chemical species.

Distribution of the size of domains formed by locally preferred structures in BMLJ (left plots) and WAHN (right plots) at different . Results refer to isobaric quenches at .

Distribution of the size of domains formed by locally preferred structures in BMLJ (left plots) and WAHN (right plots) at different . Results refer to isobaric quenches at .

Dynamical impact of locally preferred structures, as identified by the temperature dependence of the ratio (main plot) and (insets) at . See the text for definition of , , and . Upper plot: AMLJ- mixtures for , 0.70, 0.73, 0.82. Lower plot: BMLJ (filled circles), WAHN (open circles), and (stars). The dotted line drawn at 1 indicates the high-temperature limit.

Dynamical impact of locally preferred structures, as identified by the temperature dependence of the ratio (main plot) and (insets) at . See the text for definition of , , and . Upper plot: AMLJ- mixtures for , 0.70, 0.73, 0.82. Lower plot: BMLJ (filled circles), WAHN (open circles), and (stars). The dotted line drawn at 1 indicates the high-temperature limit.

## Tables

Parameters of Lennard-Jones potentials for binary mixtures. Also shown are the masses and of the two species and the concentration of particles of species 1. In the case of additive mixtures AMLJ-, the following values of size ratio have been used: 0.60, 0.64, 0.70, 0.73, 0.76, 0.82, 0.88, 0.92, 0.96, 1.00.

Parameters of Lennard-Jones potentials for binary mixtures. Also shown are the masses and of the two species and the concentration of particles of species 1. In the case of additive mixtures AMLJ-, the following values of size ratio have been used: 0.60, 0.64, 0.70, 0.73, 0.76, 0.82, 0.88, 0.92, 0.96, 1.00.

Fitted parameters for relaxation times of large particles according to the generalized Vogel-Fulcher-Tammann given by Eq. (5), and for total diffusion coefficient according to Eq. (7). The reference temperature and the onset temperature are described in the text.

Fitted parameters for relaxation times of large particles according to the generalized Vogel-Fulcher-Tammann given by Eq. (5), and for total diffusion coefficient according to Eq. (7). The reference temperature and the onset temperature are described in the text.

Most frequent Voronoi polyhedra around small particles. The percentage is computed with respect to the number of small particles in the system. Also shown is the average number of neighbors of species and . Results refer to local minima along the isobar and are shown for and slightly above the reference temperature , i.e., for the lowest equilibrated temperature.

Most frequent Voronoi polyhedra around small particles. The percentage is computed with respect to the number of small particles in the system. Also shown is the average number of neighbors of species and . Results refer to local minima along the isobar and are shown for and slightly above the reference temperature , i.e., for the lowest equilibrated temperature.

Lifetime of most frequent Voronoi polyhedra around small particles. Results are obtained from local minima at the lowest equilibrated temperatures . Also shown is the ratio , where is the relaxation time obtained from the condition .

Lifetime of most frequent Voronoi polyhedra around small particles. Results are obtained from local minima at the lowest equilibrated temperatures . Also shown is the ratio , where is the relaxation time obtained from the condition .

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