^{1}, Sean M. Cleary

^{2}and Howard R. Mayne

^{2,a)}

### Abstract

We have carried out parallel tempering Monte Carlo calculations on the binary six-atom mixed Lennard-Jones clusters, . We have looked at the classical configurational heat capacity as a probe of phase behavior. All three clusters show a feature in the heat capacity in the region of . The cluster exhibits a further peak in the heat capacity near . We have also investigated dynamical properties of the cluster as a function of temperature using molecular dynamics. We report the interbasin isomerization rate and the bond fluctuation parameter obtained from these calculations. At , the isomerization rate is on the order of ; at , the isomerization rate is greater than . Furthermore, at , the bond fluctuation parameter is less than 3%; at , it is in the range of 10–15% (depending on the sampling time used). Using this information, together with Monte Carlo quenching data, we assign the feature in the heat capacity to a solid-liquidphase change and the peak to a solid-solidphase change. We believe this is the smallest Lennard-Jones cluster system yet shown to exhibit solid-solidphase change behavior.

Support for this work in the form of a student research assistantship (SMC) from NSF Grant No. 0425826 (NSF-NSEC: The Center for High-Rate Nanomanufacturing) is gratefully acknowledged.

I. INTRODUCTION

II. CALCULATIONS

A. Potential-energysurface

B. Parallel tempering Monte Carlo calculations

C. Molecular-dynamics calculations

III. RESULTS AND DISCUSSION

A. Potential-energysurfaces

B. Parallel tempering Monte Carlo calculations

C. Molecular-dynamics simulations

IV. CONCLUSIONS

### Key Topics

- Phase transitions
- 37.0
- Solid solid phase transitions
- 27.0
- Isomerization
- 24.0
- Cluster phase transitions
- 18.0
- Solid liquid phase transitions
- 16.0

## Figures

Energies of the local minima (isomers) for , , , , and . Energies are given as in units of Kelvin relative to the GM for each individual cluster. The highest-energy level shown has .

Energies of the local minima (isomers) for , , , , and . Energies are given as in units of Kelvin relative to the GM for each individual cluster. The highest-energy level shown has .

Schematic of the local minima (isomers) and connecting transition states of the potential-energy surface for . Local minima are designated by a solid line; transition states by a dashed line. Transition states between minima are shown only if they have energy less than . If more than one transition state links two minima, only the lowest in energy is shown. Minima and transition states are joined by a dashed line if they are connected. The geometries of the isomers (local minima) are also shown in the figure. The energies of the local minima are given in Table II.

Schematic of the local minima (isomers) and connecting transition states of the potential-energy surface for . Local minima are designated by a solid line; transition states by a dashed line. Transition states between minima are shown only if they have energy less than . If more than one transition state links two minima, only the lowest in energy is shown. Minima and transition states are joined by a dashed line if they are connected. The geometries of the isomers (local minima) are also shown in the figure. The energies of the local minima are given in Table II.

Disconnectivity graphs for , , , and . The vertical scales are arbitrary. The numbers on the graph refer to the isomer labels of Fig. 2.

Disconnectivity graphs for , , , and . The vertical scales are arbitrary. The numbers on the graph refer to the isomer labels of Fig. 2.

Heat-capacity curves as a function of for (a) , , and and (c) , , and . (b) for repeated together with (multiplied by ten for clarity).

Heat-capacity curves as a function of for (a) , , and and (c) , , and . (b) for repeated together with (multiplied by ten for clarity).

Probability of occupation of the minima of the system as a function of temperature. In the top panel each of the minima is shown individually. In the middle panel the data for isomers **1**–**3** are shown separately, together with the sum of probabilities in isomers **4**–**8**. The label “square planar core” refers to the geometry of the core in local minimum 1 and “tetrahedral core” refers to the geometry of the core in isomers **2** and **3**. In the lower panel **1**–**3** are summed and **4**–**8** are shown separately.

Probability of occupation of the minima of the system as a function of temperature. In the top panel each of the minima is shown individually. In the middle panel the data for isomers **1**–**3** are shown separately, together with the sum of probabilities in isomers **4**–**8**. The label “square planar core” refers to the geometry of the core in local minimum 1 and “tetrahedral core” refers to the geometry of the core in isomers **2** and **3**. In the lower panel **1**–**3** are summed and **4**–**8** are shown separately.

(Lower) Mean temperature for as a function of total energy for MD trajectories initiated in isomer **1** (filled circles) and isomer **2** (open circles). (Upper) Isomerization rate constant as a function of mean temperature for MD trajectories initiated in isomer **1** (the GM; filled circles) and isomer **2** (the first “excited state,” open circles).

(Lower) Mean temperature for as a function of total energy for MD trajectories initiated in isomer **1** (filled circles) and isomer **2** (open circles). (Upper) Isomerization rate constant as a function of mean temperature for MD trajectories initiated in isomer **1** (the GM; filled circles) and isomer **2** (the first “excited state,” open circles).

Bond fluctuation parameter as a function of temperature for . Data are for a single trajectory. Open symbols are the results obtained by initiating the trajectory in the local minimum No. **2**; filled symbols are the results obtained by initiating the trajectory in the GM, No. **1**. Circles are the results obtained by sampling the trajectory every ; squares are the results obtained by sampling every .

Bond fluctuation parameter as a function of temperature for . Data are for a single trajectory. Open symbols are the results obtained by initiating the trajectory in the local minimum No. **2**; filled symbols are the results obtained by initiating the trajectory in the GM, No. **1**. Circles are the results obtained by sampling the trajectory every ; squares are the results obtained by sampling every .

## Tables

Lennard-Jones parameters for Ar–Ar, Xe–Xe, and Ar–Xe interactions.

Lennard-Jones parameters for Ar–Ar, Xe–Xe, and Ar–Xe interactions.

Local minima on the PES. The total potential energy is found from Eq. (1) relative to the atoms at infinity. Also given in the first column are the symmetry of the cluster and that of the core. (Local minima—or isomers—6 and 8 have structures which are not similar to stationary points of the isolated .) The third column gives the potential energy relative to the global minimum No. 1. Energies are given in units of Kelvin.

Local minima on the PES. The total potential energy is found from Eq. (1) relative to the atoms at infinity. Also given in the first column are the symmetry of the cluster and that of the core. (Local minima—or isomers—6 and 8 have structures which are not similar to stationary points of the isolated .) The third column gives the potential energy relative to the global minimum No. 1. Energies are given in units of Kelvin.

Saddle points on the surface. The eight lowest energy saddle points are listed in order of increasing potential energy. In the second column, the total potential energy is given. In the third column, the energy relative to the global minimum is given. (As in Table II and elsewhere in this paper, energies are given in Kelvin.) In the fourth column listed the two local minima connected by the saddle point.

Saddle points on the surface. The eight lowest energy saddle points are listed in order of increasing potential energy. In the second column, the total potential energy is given. In the third column, the energy relative to the global minimum is given. (As in Table II and elsewhere in this paper, energies are given in Kelvin.) In the fourth column listed the two local minima connected by the saddle point.

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