A Numerical algorithm for finding pressure induced Acoustic phonon instabilities in crystals

In this talk, I will present a fast-efficient computational Pseudo code to find acoustic phonon instabilities in crystals [1]. The code use the stress-strain relations to numerical find sound velocities in terms of second-order elastic constants for various wave modes in uniaxial and hydrostatically compressed crystals for a given wave direction $k$ [2,3]. I use Tantalum as the testing material and the results are compared with Molecular dynamics simulations using the EAM potential formalism [4,5], DFT calculations via VASP and via a stability of the lattice as a function of uniaxial compression by determining the phonon-dispersion relation over the entire BZ [6] . All three methods predict that the lattice first goes unstable at 25{\%} of uniaxial compression along the \textless 100\textgreater direction. The implementation of the code is discussed using the free open source software OCTAVE and the symbolic program MATHEMATICA\\ \\ 1. Guerrero, ETD Collection for University of Texas, El Paso. Paper AAI1477789. \\ 2. Eur. Phys. J. B \textbf{5}, 7-13 (1998) \\ 3. Nature 418.6895 (2002): 307-310 \\ 4. Phys. Rev. B \textbf{88}, 134101 \\ 5. Guerrero et al Journal of Materials Science and Engineering B, 2013. \textbf{3}(3): p. 153-160 6. Phys. Rev. B \textbf{8}