^{1}, Ruchi Sharma

^{1}and Charusita Chakravarty

^{1,a)}

### Abstract

Thermodynamic properties of liquidberyllium difluoride are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be–F pair correlation function. The internal energy shows a temperature dependence. The pair correlation entropy shows a temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.

This work was financially supported by the Department of Science and Technology, New Delhi. M.A. and R.S. thank Indian Institute of Technology Delhi and Council for Scientific and Industrial Research, respectively, for financial support. The authors would like to thank Austen Angell, Peter Poole, and Ivan Saika-Voivod for clarifications with regard to computational procedures followed in their work. Computational resources and technical support provided by Computer Services Centre, IIT-Dehli is gratefully acknowledged.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

A. Potential model

B. Molecular dynamics

C. Estimation of excess entropy from pair correlation data

III. RESULTS AND DISCUSSION

A. Thermodynamic anomalies

B. Configurational energy

C. Excess entropy

D. Relationship between excess entropy and internal energy

IV. Conclusions

### Key Topics

- Entropy
- 82.0
- Silica
- 20.0
- Diffusion
- 12.0
- Molecular dynamics
- 11.0
- Simple liquids
- 7.0

## Figures

Pressure-temperature curves for different isochores from for . (a) Data from short runs of . The vertical arrows mark the highest and lowest density isochores and successive isochores differ in density by . (b) Data from long runs of . The error bars on the pressure estimated using block averaging (Ref. 52) from these long runs are of the order of .

Pressure-temperature curves for different isochores from for . (a) Data from short runs of . The vertical arrows mark the highest and lowest density isochores and successive isochores differ in density by . (b) Data from long runs of . The error bars on the pressure estimated using block averaging (Ref. 52) from these long runs are of the order of .

Mean square displacements (MSDs) for different densities along the (a) and (b) isotherms. Note the logarithmic scale along both axes of the plot.

Mean square displacements (MSDs) for different densities along the (a) and (b) isotherms. Note the logarithmic scale along both axes of the plot.

Pressure temperature curves for specific isochores in the region of the thermodynamic anomaly of : (a) , (b) , (c) , and (d) . The data points are connected by cubic splines and the minima in the plots are marked by arrows.

Pressure temperature curves for specific isochores in the region of the thermodynamic anomaly of : (a) , (b) , (c) , and (d) . The data points are connected by cubic splines and the minima in the plots are marked by arrows.

Locus of temperature of maximum density (TMD) of shown in (a) temperature-pressure plane and (b) density-temperature plane.

Locus of temperature of maximum density (TMD) of shown in (a) temperature-pressure plane and (b) density-temperature plane.

Pressure as a function of density along different isotherms for , with errors on the pressure of the order of , as discussed in Fig. 1.

Pressure as a function of density along different isotherms for , with errors on the pressure of the order of , as discussed in Fig. 1.

Density dependence of the configurational contribution to the internal energy for different isotherms of . The error bars estimated using block averaging are less than 0.05% for .

Density dependence of the configurational contribution to the internal energy for different isotherms of . The error bars estimated using block averaging are less than 0.05% for .

Configurational contribution per particle to the internal energy as a function of for different isochores of . Simulation data are shown by symbols and the solid lines are linear fits to each dataset. For clarity, all data points have been shifted by , where is . Units for are MJ/mole of . Linear fitting parameters have an error of 0.21%–2.3% with the error increasing for decreasing densities.

Configurational contribution per particle to the internal energy as a function of for different isochores of . Simulation data are shown by symbols and the solid lines are linear fits to each dataset. For clarity, all data points have been shifted by , where is . Units for are MJ/mole of . Linear fitting parameters have an error of 0.21%–2.3% with the error increasing for decreasing densities.

Static distributions of tagged particle potential energies (in ) of Be along (a) isochore, (b) isotherm.

Static distributions of tagged particle potential energies (in ) of Be along (a) isochore, (b) isotherm.

Variation of total pair correlation entropy of with density along different isotherms.

Variation of total pair correlation entropy of with density along different isotherms.

Density dependence of distinct pair correlation contributions to the excess entropy of : (a) , (b) , and (c) . Isotherm labeling is identical to that shown in Fig. 9.

Density dependence of distinct pair correlation contributions to the excess entropy of : (a) , (b) , and (c) . Isotherm labeling is identical to that shown in Fig. 9.

Pair correlation entropy vs for various densities. The dashed lines are linear fits to the two high density data sets at 2.8 and .

Pair correlation entropy vs for various densities. The dashed lines are linear fits to the two high density data sets at 2.8 and .

Correlation of pair correlation entropy with configurational energy for along different isotherms. Highest and lowest density state points for each isotherm are marked by vertical and horizontal arrows, respectively. Isotherms at 2750 and are shown as lines without any point symbols for clarity.

Correlation of pair correlation entropy with configurational energy for along different isotherms. Highest and lowest density state points for each isotherm are marked by vertical and horizontal arrows, respectively. Isotherms at 2750 and are shown as lines without any point symbols for clarity.

## Tables

TRIM potential parameters for (Refs. 7, 13, and 45).

TRIM potential parameters for (Refs. 7, 13, and 45).

Test of accuracy of the pair correlation approximation to the thermodynamic excess entropy for . The thermodynamic entropy for , calculated using thermodynamic integration is compared with the corresponding values taken from Ref. 3 and 4 at nine densities along isotherm and five temperatures along the isochore. The starred quantities refer to the values taken from the work of Saika-Voivod *et al.* (Refs. 3 and 4). is the ideal entropy, as defined in Eq. (4). is the excess entropy defined as . is estimated using Eq. (3). gives the difference between the excess entropy calculated using thermodynamic integration and using the pair correlation approximation. Unit of entropy is .

Test of accuracy of the pair correlation approximation to the thermodynamic excess entropy for . The thermodynamic entropy for , calculated using thermodynamic integration is compared with the corresponding values taken from Ref. 3 and 4 at nine densities along isotherm and five temperatures along the isochore. The starred quantities refer to the values taken from the work of Saika-Voivod *et al.* (Refs. 3 and 4). is the ideal entropy, as defined in Eq. (4). is the excess entropy defined as . is estimated using Eq. (3). gives the difference between the excess entropy calculated using thermodynamic integration and using the pair correlation approximation. Unit of entropy is .

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