Theory of self-diffusion in alkali metals: I. Results for monovacancies in Li, Na, and K

Abstract

The phonon dispersion curves for perfect crystals of bcc Li, Na, and K are calculated by the ab initio force-constant method in a supercell approach. It is shown that the coupling constants of Li decay much more slowly in space than those for Na and K, so for Li the phonon spectrum could not be reliably determined with the supercell sizes used in the calculations. From the phonon spectra of the perfect supercell and the supercell with a monovacancy the vacancy formation entropy is calculated for Na (1.36 k B ) and K (0.78 k B ). Furthermore, the formation energy (0.53, 0.34, and 0.30 eV) and the formation volume (about 0.5 0 ) are obtained for Li, Na, and K, and the temperature and pressure dependences of the formation entropy and volume are investigated for the case of Na; a strong decrease of the formation volume with increasing pressure is found. The migration energies and volumes are determined within the framework of the transition-state theory. The migration energies are small (about 0.05 eV) for Li, Na, and K, and the migration volumes are small and negative for Li and Na. The calculated activation energies for self-diffusion (0.58, 0.39, and 0.35 eV) agree well with experimental data. Neglecting the migration entropy and inserting Flynn's ansatz for the attempt frequency, the absolute values of the self-diffusion coefficients are determined as a function of temperature. For Na these values agree well with experimental data, whereas for K the calculated values are too small except for low temperatures.

Quenching Studies of Lattice Vacancies in High-Purity Aluminium

“…Examples are calculations on Li, 1, 2) Na 2,3) and, in particular, on Al, the subject of the present paper. Based on the density functional theory (DFT), 4) the majority of the computations make use of the local density approximation (LDA) of Kohn and Sham,5) whose reliability in this context can at present not be judged by theoretical arguments alone.…”

“…13) Therefore the tracer self-diffusivity, D T (T ), may be obtained accurately even at temperatures T that are so low that a substantial fraction of the thermalequilibrium vacancies is associated with impurities. (2) In contrast to bcc metals such as Li, Na, etc., fcc metals do not undergo low-temperature phase transformations that affect the self-diffusivity by fluctuation enhancement. 14,15) Whereas in quite a few fcc metals H SD 1V is known from experiment with an accuracy of about 1%, it is much more difficult to obtain the quantities on the left-hand side of eq.…”

Suppressing void formation in all-solid-state batteries: the role of interfacial adhesion on alkali metal vacancy transport

“…35,36 Experimental and computational studies have shown that the self-diffusion mechanism in bulk Li and Na metal is dominated by monovacancy transport. 37 Under thermal equilibrium, the overall activation energy for self-diffusion = is , + , given as the sum of the vacancy formation energy, , and the activation energy, . DFT calculations have indicated that the activation energies of monovacancies in Li ( 0.053 eV) = and Na ( 0.053 eV) are considerably smaller than the = formation energies ( =0.506 eV and =0.334 eV).…”

Atomistic simulation of phonon dispersion for body-centred cubic alkali metals

“…For instance, the phonon dispersion of alkali metals has been calculated by many model methods, such as pair potentials [2][3][4], the general tensor force model [5], the embedded atom method (EAM) [6], analytic EAM (AEAM) [7,8], ab initio [9][10][11][12], and pseudopotential theory [13]. For instance, the phonon dispersion of alkali metals has been calculated by many model methods, such as pair potentials [2][3][4], the general tensor force model [5], the embedded atom method (EAM) [6], analytic EAM (AEAM) [7,8], ab initio [9][10][11][12], and pseudopotential theory [13].…”