Ab Initio Molecular Dynamics and Elastic Properties of TiC and TiN Nanoparticles
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Ab initio Molecular Dynamics and Elastic Properties of TiC and TiN Nanoparticles A. V. Postnikov and P. Entel Theoretical Low-Temperature Physics, FB10, Gerhard Mercator University Duisburg, D-47048 Duisburg, Germany
ABSTRACT The results of first-principles simulations of relaxed ground-state structure and vibrational modes are presented for titanium carbide and titanium nitride clusters of nearly stoichiometric composition and compared to frozen phonon and molecular dynamics calculations for crystalline TiC and TiN. The calculations have been done with the SIESTA method, using norm-conserving pseudopotentials and the basis of strictly localized numerical pseudoatomic orbitals. The dominant vibration mode corresponding to the zone-center TO phonon (14 THz) persists and gets hardened (21 THz) in the small Ti4C4 cluster. The increase of the cluster size to Ti14C13 leads to an enhancement of vibrational density of states in the intermediate range of frequencies, including the phonon band gap of pure crystalline TiC (near 15 THz). Similar trends can be noted for the Ti-N system, with the vibration spectrum slightly scaled upwards but otherwise very close to that of TiC. The clusters studied are yet too small to perform a reliable analysis of acoustic modes. INTRODUCTION Titanium carbide and nitride prepared as nanoparticles find many applications. Among their peculiar properties different from those in the bulk phase, a considerable softness could be expected. Elastic properties of nanoparticles are difficult to access in direct experimental measurements, but hopefully due to their relation with electronic structure thay can be reasonably estimated from first-principles calculations, as is known to be the case for many crystalline materials. The meaning of strain or homogeneous external pressure may not be so straightforward in a computational experiment on small clusters as it is for bulk crystals. However, different vibrational modes may be induced in a simulation and give a clue e.g. of the sound velocity in nanoparticles. For a detailed analysis it is advantageous to have accumulated data from sufficiently long molecular dynamics (MD) simulations, that would permit to project out various modes of interest, with respect to their frequency and/or wavenumber, and reconstruct the vibrational density of states. The present study is a preliminary attempt towards such analysis, where we present data on very small TiC and TiN particles and concentrate on their quite general vibrational behavior, as compared to that in corresponding bulk systems.
CALCULATION METHOD The central element in first-principle calculations of vibration frequencies and patterns is a reliable and precision method to extract total energy and/or forces for any distorted (e.g., lowsymmetric) configuration of a system of interest. (Linear reasponse schemes that provide directly dynamical matrice without actually displacing the atoms may provide a more elegant, albeit W6.3.1
methodically much more involved, alternative - see Ref.[1] for a recent revie
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