Abstract
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•A method is proposed to extract phonons using covariance matrix of atomic velocities.•This method relates the real space data with the reciprocal space data.•The eigenvectors with lowest eigenvalues has strong relation to the reciprocal space.•We named the eigenvectors with lowest eigenvalues as reciprocal eigenvectors.•Plotting the lowest eigenvectors presents special patterns.•Each atom has three specific numbers in the reciprocal eigenvectors.
The analysis of phonons is a well-established tool in the study of materials. The phonon frequency spectrum is sensitive to the local environment and provides an assessment as to material structure and quality. Yet it is challenging to quantify the impact of environmental factors on individual phonons and sometimes to identify the source of individual phonon peaks. The determination of the phonon frequency spectrum from atomic trajectories obtained from molecular dynamics simulations allows, in principle, anharmonicity, boundaries, defects, strain and other effects to be interpreted at realistic temperatures. However, it is difficult to associate particular atomic displacements with specific phonons. An efficient method to identify phonon peaks at a given wavevectors using simulation trajectories is presented. We use the eigenvectors with the smallest eigenvalues of the covariance matrix of the atomic trajectories. We demonstrated its usability on phonon modes at two wavevectors of the Brillouin zone of a graphene nanoribbon. The method isolates the transverse, longitudinal, and out-of-plane phonons of the ribbon. This method highlights the ability to analyze reciprocal space data by the covariance matrix of the real space data using the eigenvectors with the lowest eigenvalues.