  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 model 3D binary liquid using the eigenvalues and
eigenvectors of the atomic stress tensors. Thus correlations relevant to the
Green-Kubo expression for viscosity are interpreted 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: $\lambda_1 \geq \lambda_2 \geq
\lambda_3 \geq 0$. We found that, for the particles of a given type, the
probability distributions of the ratios $(\lambda_2/\lambda_1)$ and
$(\lambda_3/\lambda_2)$ are essentially identical to each other in the liquids
state. We also found that $\lambda_2$ tends to be equal to the geometric
average of $\lambda_1$ and $\lambda_3$. In our view, correlations between the
eigenvalues may represent "the Poisson ratio effect" at the atomic scale.
