Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed …
Elastic constants and thermodynamical quantities for crystal lattices from many-body perturbation theory
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and isothermal) and the coefficient of thermal expansion. The perturbation expansion is developed up to third-order and diagrams corresponding to the equations are represented. The present results extend the existing ones by giving expressions for the elastic constants of arbitrary order and terms which are higher-order in the interatomic force constants that have been obtained earlier. The perturbation expansion in terms of arbitrary macroscopical parameters i…
Ab initiocomputational study on the lattice thermal conductivity of Zintl clathrates[Si19P4]Cl4andNa4[Al4Si19]
The lattice thermal conductivity of silicon clathrate framework ${\mathrm{Si}}_{23}$ and two Zintl clathrates, $[{\mathrm{Si}}_{19}{\mathrm{P}}_{4}]{\mathrm{Cl}}_{4}$ and ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm{Si}}_{19}]$, is investigated by using an iterative solution of the linearized Boltzmann transport equation in conjunction with ab initio lattice dynamical techniques. At 300 K, the lattice thermal conductivities for ${\mathrm{Si}}_{23}, [{\mathrm{Si}}_{19}{\mathrm{P}}_{4}]{\mathrm{Cl}}_{4}$, and ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm{Si}}_{19}]$ were found to be 43 W/(m K), 25 W/(m K), and 2 W/(m K), respectively. In the case of ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm…
Ab initio studies on the lattice thermal conductivity of silicon clathrate frameworks II and VIII
The lattice thermal conductivities of silicon clathrate frameworks II and VIII are investigated by using ab initio lattice dynamics and iterative solution of the linearized Boltzmann transport equation(BTE) for phonons. Within the temperature range 100-350 K, the clathrate structures II and VIII were found to have lower lattice thermal conductivity values than silicon diamond structure (d-Si) by factors of 1/2 and 1/5, respectively. The main reason for the lower lattice thermal conductivity of the clathrate structure II in comparison to d-Si was found to be the harmonic phonon spectra, while in the case of the clathrate structure VIII, the difference is mainly due to the harmonic phonon spe…
Ab initiolattice dynamical studies of silicon clathrate frameworks and their negative thermal expansion
The thermal and lattice dynamical properties of seven silicon clathrate framework structures are investigated with ab initio density functional methods (frameworks I, II, IV, V, VII, VIII, and H). The negative thermal expansion (NTE) phenomenon is investigated by means of quasiharmonic approximation and applying it to equal time displacement correlation functions. The thermal properties of the studied clathrate frameworks, excluding the VII framework, resemble those of the crystalline silicon diamond structure. The clathrate framework VII was found to have anomalous NTE temperature range up to 300 K and it is suitable for further studies of the mechanisms of NTE. Investigation of the displa…