Atomic Physics Seminars

We employ a variational approach by optimizing the free energy of an anharmonic Hamiltonian with respect to strain tensor, interatomic coordinates and force constants in an interacting electron-phonon system. The goal is to predict possible phase transitions in crystal structures at finite temperatures. The variational method is based on Bogoliubov inequality to get an approximation to the Helmholtz free energy in a lattice with anharmonic potential energy terms. A harmonic trial Hamiltonian is used for the minimization. The optimization will give the set of equations corresponding to atomic displacements, lattice strain, IFCs and other order parameters, leading to phonon frequencies at each k-point for every temperature. The reliability of the approach is then checked in 1D/3D cases, comparing to available computational/experimental results and by applying DFT method to compute free energies of various phases at different temperatures.