Density functional tight-binding and cluster expansion studies of lithiated/sodiated silicon anodes for high-energy-density batteries

Abstract

This work presents a computational modelling workflow that uniquely combines several techniques, proposed as a means for studying and designing high-energy-density electrodes for the next-generation of rechargeable batteries within the era of the fourth industrial revolution (4IR). The Self-Consistent Charge Density Functional-based Tight Binding (SCC-DFTB) parameterisation scheme for the Li-Si and Na-Si systems is presented. By using the Li-Si system, a procedure for developing the Slater-Koster based potentials is shown. Using lessons learned from the Li-Si framework, the parameterisation of the Na-Si is reported. The Li-Si SCC-DFTB parameter set has been developed to handle environments that consist of Si-Si, Li-Si and Li-Li interactions; and the Na-Si SCC DFTB parameter set is developed for Na-Na, Na-Si, and Si-Si interactions. Validations and applications of the developed sets are illustrated and discussed. By calculating equilibrium lattice constants, the Li-Si set is shown to be compatible with various phases in the crystalline Li-Si system. The results were generally within a margin of less than 8% difference, with some values such as that of the cubic Li22Si5 being in agreement with experiments to within 1%. The volume expansion of Si as a function of Li insertion was successfully modelled via the Li-Si SCC-DFTB parameter set. It was shown that Si gradually expands in volume from 53.6% for the LiSi phase composed of 50 atm % Li, to 261.57% for Li15Si4 with 78.95 atm % Li, and eventually shoots over 300% for the Li22Si5 phase with the expansion at 316.45%, which agrees with experiments. Furthermore, the ability of the Li-Si SCC-DFTB parameter set to model the mechanical properties of Si is evaluated by calculating the mechanical properties of pristine cubic Si. The parameter set was able to produce the mechanical properties of Si, which agree with experiments to within 6%. The SCC-DFTB parameter set was then used to model the volume expansion of amorphous silicon (a-Si) as a result of lithiation within concentrations ranging from 33 – 50 atm % Li. Consistent with experiments, the a-Si was found to marginally expand in a linear form with increase in Li content. a-Si was observed to exhibit a lower expansion compared to c-Si. Additionally, the structural stability of the amorphous Li-Si alloys was examined, and observations agree with experiments.vi The Na-Si SCC-DFTB parameter set produced equilibrium lattice parameters that agree with experiments to within 4% for reference structures, and the transferability was tested on three Na-Si clathrate compounds (i.e. the Pm-3n Na8Si46, the Cmcm NaSi6 and Fd-3m Na24Si136). By employing the approach used when lithiating Si, the sodiation of crystalline silicon (c-Si) was modelled. It was predicted that c-Si expands by over 400% at 77 atm% Na and shoots above 500% for concentrations exceeding 80 atm% of Na. By comparing how c-Si expands as a result of lithiation to the expansion consequent to sodiation for concentrations ranging from 66.6 – 81.4 atm%, c-Si is shown to be unsuitable for Na-ion batteries. As a test, the ability of the developed Na-Si SCC DFTB parameter set to handle large and complex geometries was shown by modelling the expansion of a-Si at 33 atm% Na. It was deduced that a-Si would be more preferable for Na-ion batteries since at 33 atm% Na, a-Si expanded a lot less than when c-Si was used. Using the Li-Si and the Na-Si SCC-DFTB parameter sets, it was noted that amorphisation appears to lower the magnitude by which Si expands, therefore agreeing with experiments in that amorphous structures are reported to exhibit a buffering effect towards volume expansion. The material space for the Li-Si alloy system is explored through crystal structure predictions conducted via a machine learning powered cluster expansion (CE). Using the FCC and BCC – based parent lattice in the grid search, 12 thermodynamically stable Li-Si alloys were predicted by the genetic algorithm. Viz. the trigonal Li4Si (R-3m), tetragonal Li4Si (I4/m), tetragonal Li3Si (I4/mmm), cubic Li3Si (Fm-3m), monoclinic Li2Si3 (C2/m), trigonal Li2Si (P-3m1), tetragonal LiSi (P4/mmm), trigonal LiSi2 (P-2m1), monoclinic LiSi3 (P2/m), cubic LiSi3 (Pm-3m), tetragonal LiSi4 (I4/m) and monoclinic LiSi4 (C2/m). The structural stabilities of the predicted Li-Si alloys are further studied. With focus on pressure, the thermodynamic conditions under which the Li-rich phase, Li4Si (R 3m), would be stable are tested. Li4Si (R-3m) was subjected to pressures during geometry optimization and found to globally maintain its structural stability within the range 0 – 25GPa. Hence, Li4Si was predicted to be a low pressure phase. In studying the PDOS, the Li4Si (I4/m) was noted to be more stable around 40GPa and vii 45GPa, which is consistent with the prediction made from other works, wherein intelligence-based techniques were used. A test for exploring the Na-Si material space was done using insights acquired from the Li-Si framework. Three thermodynamically stable Na-Si (i.e. the I4/mmm Na3Si, P4/nmm NaSi and Immm NaSi2) were predicted. Using the Na-Si SCC-DFTB parameter set, a correlation of the total DOS in the vicinity of the Fermi level (Ef) with the structural stability of the three Na-Si alloys is done. NaSi (P4/nmm) was shown to be unstable at 0GPa, NaSi2 (Immm) is found to be stable, and the Na-rich Na3Si exhibited metastability. The stability of Na3Si was seen to improve when external pressure ranging from 2.5 – 25GPa was applied; hence, suggesting Na3Si (I4/mmm) to be a high-pressure phase. Furthermore, expanding on the groundwork laid from the Li-Si and Na-Si CE, the Mg-Si system was tested to illustrate that the approach can be used to rapidly screen for new materials. The ground-state crystal structure search predicted 4 thermodynamically stable Mg-Si alloys. Viz. Mg3Si (Pm-3m), MgSi (P4/mmm), MgSi2 (Immm) and MgSi3 (Pmmm). Lastly, to highlight the power of combining various computational techniques to advance material discovery and design, a framework linking SCC-DFTB and CE is illustrated. Candidate electrode materials with nano-architectural features were simulated by designing nanospheres comprised of more than 500 atoms, using the predicted Li-Si and Na-Si crystal structures. The stability of the nanospheres was examined using SCC-DFTB parameters developed herein. The workflow presented in this work paves the way for rapid material discovery, which is sought for in the era of the fourth industrial revolution.