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Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

### Abstract

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.

© 2016 AIP Publishing LLC

Received 22 October 2015
Accepted 15 February 2016
Published online 03 March 2016

Acknowledgments:
We would like to thank M. G. Stepanov for several very useful discussions.^{29}

Article outline:

I. INTRODUCTION
II. STRESS TENSOR ELLIPSOIDS
A. Elements of the atomic stress tensors in the spherical representation
III. TWO RANDOM REFERENCE MODELS
A. *RIλ* approach
B. *RIσ*^{sph} approach
IV. CORRELATION FUNCTIONS
A. Directional coordinate frame associated with the direction from atom *i* to atom *j*
B. Correlation function in the directional coordinate frame
C. Correlation function in an arbitrary frame
D. Correlation function invariants
V. STUDIED SYSTEM AND THE DETAILS OF MOLECULAR DYNAMICS SIMULATIONS
A. Studied system
B. Mean square particles’ displacement and the partial pair density correlation functions
VI. CORRELATIONS BETWEEN THE STRESS COMPONENTS AND EIGENVALUES OF THE INDIVIDUAL ATOMIC STRESS TENSORS
A. Distributions of the atomic stress components
B. Eigenvalues of the atomic stress matrices and correlations between the eigenvalues
C. Correlations between the eigenvalues and the random and independent approximations
1. From independent and random spherical stress components to the Cartesian stress components and eigenvalues
2. Random distributions of eigenvalues vs. the distributions of eigenvalues from MD simulations
3. The distributions of the spacings between the eigenvalues
VII. CORRELATION FUNCTIONS BETWEEN DIFFERENT ATOMS
A. Partial pair density functions and the stress-stress correlation function invariants related to viscosity
VIII. CONCLUSIONS

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/content/aip/journal/jcp/144/9/10.1063/1.4942863

2016-03-03

2016-10-26

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