Comparative computational study of the diffusion of Li, Na, and Mg in silicon including the effect of vibrations

Insertion of Mono- vs. Bi- vs. Trivalent Atoms in Prospective Active Electrode Materials for Electrochemical Batteries: An ab Initio Perspective

“…We therefore limited ourselves to the calculations of the barriers, which are expected to be quantitatively accurate with the level of theory we used [46]. The energies in the above are Gibbs free energies; however, they are typically well approximated by the electronic (internal) energies computed with DFT, as is done in nearly all ab initio studies of battery materials [9,47] with rare exceptions [14,23]. In our work, we also considered vibrational contributions to E b and E a in some of the considered systems, where such contributions were computed using the harmonic approximation as:…”

“…We produced several such studies and they are surveyed next. In references [11,12,[14][15][16]20,24], we produced comparative studies of Li, Na, and Mg insertion in crystalline and amorphous silicon. While lithiation of Si is an alloying reaction, we will further, for the sake of consistency, use the word "insertion", since for small concentrations and only interstitial sites occupied, the two mechanisms do not differ.…”

“…While lithiation of Si is an alloying reaction, we will further, for the sake of consistency, use the word "insertion", since for small concentrations and only interstitial sites occupied, the two mechanisms do not differ. Some of these studies used plane wave bases [12] and some used localized basis sets [14,20]. Specifically, when using the localized basis sets, which are more computationally efficient for many kinds of calculations, the issue of basis size and shape selection arises.…”

“…[20,67], where default basis sets of the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) program were used, with those of Ref. [14], where bases tuned in this way were used, as well as with available plane wave results [12,59,60]. This strategy was then used by us to build the basis sets for studies of Sn and TiO 2 where we also achieved good agreement between our results obtained with DZP bases and our, or others', plane wave calculations [21][22][23]28].…”

“…The insertion sites are known to be tetrahedral (Td) sites, and the hexahedral (Hex) sites serve as transition states for diffusion between Td sites [12,14,59,60]. While Li and Na strongly prefer interstitial Td sites, Mg insertion energy at the substitutional (S) site is competitive with that at the Td site.…”