Fleur Legrain

Comparison of alpha and beta tin for lithium, sodium, and magnesium storage: An ab initio study including phonon contributions

We present a comparative ab initio study of Li, Na, and Mg storage in tin, including phononic effects and phase competition between α and β Sn. Mg doping at low concentration is found to stabilize the β phase. On the contrary, Li and Na doping is shown to reverse the stability of the phases at room temperature: Li/Na-doped α-Sn is more stable than Li/Na-doped β-Sn up to a temperature of around 380/400 K. This may rationalize the formation of α-Sn upon lithiation and delithiation of β-Sn anodes reported in experimental studies. The changes in phase stability with Li/Na/Mg doping are directly related to the intercalation energies of Li/Na/Mg in one phase versus the other: at 300 K, Li/Na is easier intercalated in α-Sn (-0.37/-0.08 eV) than in β-Sn (0.06/0.49 eV), while Mg intercalation energy is, although positive (i.e., unfavored intercalation), lower in β-Sn (0.53 eV) than in α-Sn (0.66 eV). The temperature effect is found to affect significantly the intercalation energy, by up to 0.13 eV at 300 K. Analysis of diffusion barriers shows that Li, Na, and Mg diffusion in β-Sn is anisotropic with migration barriers along the (001) direction (respectively, 0.01, 0.22, and 0.07 eV) significantly lower than those in α-Sn (respectively, 0.20, 0.52, and 0.40 eV).

A first-principles comparative study of lithium, sodium, and magnesium storage in pure and gallium-doped germanium: Competition between interstitial and substitutional sites

Thermodynamics and kinetics of Li, Na, and Mg storage in Ge are studied ab initio. The most stable configurations can consist of tetrahedral, substitutional, or a combination of the two types of sites. In the dilute limit, Li and Na prefer interstitial, while Mg prefers substitutional sites. At higher concentrations of Li, Na, and Mg, there is a combination of interstitial and substitutional sites. This is an important finding, as most previous ab initio studies of alloying type electrode materials ignored substitutional sites. Insertion energies computed at dilute concentration (x = 1/64) show that Na and Mg insertion are not thermodynamically favored in Ge vs. the formation of bulk Na and Mg, as opposed to Li insertion which is favored. We investigate the effect of p-doping of Ge (with Ga) on the thermodynamics and find that it considerably lowers the defect formation energies associated with the insertion of Li/Na/Mg at tetrahedral sites. On the other hand, the energetics associated with Li/Na/Mg insertion at substitutional sites are not significantly affected. In addition, we compute the migration energy barriers for Li/Na/Mg diffusion between two tetrahedral sites (0.38/0.79/0.66 eV), between two substitutional sites (0.77/0.93/1.83 eV), and between two sites of different types (2.15/1.75/0.85 eV).

Materials Screening for the Discovery of New Half-Heuslers: Machine Learning versus ab Initio Methods

Machine learning (ML) is increasingly becoming a helpful tool in the search for novel functional compounds. Here we use classification via random forests to predict the stability of half-Heusler (HH) compounds, using only experimentally reported compounds as a training set. Cross-validation yields an excellent agreement between the fraction of compounds classified as stable and the actual fraction of truly stable compounds in the ICSD. The ML model is then employed to screen 71 178 different 1:1:1 compositions, yielding 481 likely stable candidates. The predicted stability of HH compounds from three previous high-throughput ab initio studies is critically analyzed from the perspective of the alternative ML approach. The incomplete consistency among the three separate ab initio studies and between them and the ML predictions suggests that additional factors beyond those considered by ab initio phase stability calculations might be determinant to the stability of the compounds. Such factors can include configurational entropies and quasiharmonic contributions.

Understanding the difference in cohesive energies between alpha and beta tin in DFT calculations

The transition temperature between the low-temperature alpha phase of tin to beta tin is close to the room temperature (Tαβ = 130C), and the difference in cohesive energy of the two phases at 0 K of about ΔEcoh =0.02 eV/atom is at the limit of the accuracy of DFT (density functional theory) with available exchange-correlation functionals. It is however critically important to model the relative phase energies correctly for any reasonable description of phenomena and technologies involving these phases, for example, the performance of tin electrodes in electrochemical batteries. Here, we show that several commonly used and converged DFT setups using the most practical and widely used PBE functional result in ΔEcoh ≈0.04 eV/atom, with different types of basis sets and with different models of core electrons (all-electron or pseudopotentials of different types), which leads to a significant overestimation of Tαβ. We show that this is due to the errors in relative positions of s and p –like bands, which, comb...

Vibrational Properties of Metastable Polymorph Structures by Machine Learning

Despite vibrational properties being critical for the ab initio prediction of finite-temperature stability as well as thermal conductivity and other transport properties of solids, their inclusion in ab initio materials repositories has been hindered by expensive computational requirements. Here we tackle the challenge, by showing that a good estimation of force constants and vibrational properties can be quickly achieved from the knowledge of atomic equilibrium positions using machine learning. A random-forest algorithm trained on 121 different mechanically stable structures of KZnF3 reaches a mean absolute error of 0.17 eV/Å2 for the interatomic force constants, and it is less expensive than training the complete force field for such compounds. The predicted force constants are then used to estimate phonon spectral features, heat capacities, vibrational entropies, and vibrational free energies, which compare well with the ab initio ones. The approach can be used for the rapid estimation of stability at finite temperatures.