Non-Equilibrium Phase Search (NEPS) method
        The Non-Equilibrium Phase Search method is designed to help elucidate the hysteresis and non-equilibrium reaction pathways associated with these conversion materials. We apply this methodology to investigate a variety of lithiation reaction pathways of Co3O4, NiO, MoS2, CuS, (Cu,Co)3O​4 by systematically exploring the energetics of a large number of equilibrium and non-equilibrium structural configurations using first-principle calculations.

The NEPS computational method involves, the following five steps, described below:
i) Starting with the host compound (which may or may not contain Li), identify all possible insertion sites. The method is initiated by searching for interstitial sites in the original transition metal oxide structures. An in-house code MINT (openly available on GitHub) was used which automates the search for insertion sites. The algorithm works by placing an analytic, exponential decaying function (Exp[-r/a]) at each atomic site and searching for geometric minima in the resulting function.
ii) Generate all symmetrically distinct configurations for Li insertion. We worked with the Enum code to generate all symmetrically-distinct configurations of Li on the unoccupied sites. All configurations were classified according to their composition Lix▢1-xMO.
iii) Compute total energies of all configurations generated in step ii). To enable a fast energy sampling, simple point-charge electrostatic calculations were usually conducted, using nominal charge states for the ions in the system. Alternatively, coarse DFT calculation can be performed to fulfill the energy sampling.
iv) Select the structures with lowest electrostatic energies to be computed more accurately and atomically-relaxed in DFT. For each composition, the structures were ranked by the electrostatic energies, and the three lowest energy structures were further relaxed using DFT. The formation energies for these selected structures were evaluated according to the following reaction: MO + xLi+ → LixMO.
v) Using all of these non-equilibrium structures derived from insertion of Li into the initial TM oxide, build the “non-equilibrium convex hull” and determine phases. For each specific system (Li-MO), we build the corresponding non-equilibrium convex hulls with the calculated formation energies at all compositions. The compositions, structures, energies located on the convex hull correspond to the identified non-equilibrium phases.

Here is an illustration of the NEPS method: Electrochemical lithiation process of Co3O4:
Figure 6. Convex hulls generated with all the calculated non-equilibrium phases for Co3O4 and the corresponding voltage profiles of the Li insertion into Co3O4. Predicted non-equilibrium reaction voltage profiles fall into the experimental lithiation voltage intervals. [Ref. 1]
Representative Publications
  1. H. Liu, Q. Li, Z. Yao, L. Li, Y. Li, C. Wolverton, M. C. Hersam, J. Wu, V. P. Dravid, Origin of Fracture-resistance to Large Volume Change in Cu-substituted Co3O4 Electrode, Advanced Materials, 1704851, 2017.
  2. Z. Yao, S. Kim, M. Aykol, Q. Li, J. Wu, J. He, C. Wolverton. Revealing the Conversion Mechanism of Transition Metal Oxide Electrodes during Lithiation from First Principles, Chemistry of Materials 29(21), 9011-9022 (2017).
  3. Q. Li†, Z. Yao†, J. Wu†, S. Mitra, S. Hao, T. S. Sahu, Y. Li, C. Wolverton, and V. P. Dravid, Intermediate Phases in Sodium Intercalation into MoS2 Nanosheets and Its Implications for Sodium-Ion Battery, Nano Energy 38, 342-349 (2017).
  4. Q. Li†, J. Wu†, Z. Yao†, M. M. Thackeray, C. Wolverton, V. P. Dravid, Dynamic Imaging of Metastable Reaction Pathways in Lithiated Metal Oxide Electrodes, Nano Energy 44, 15-22 (2018).
  5. M. Amsler, Z. Yao, C. Wolverton. Cubine, A Quasi 2-dimensional Copper-bismuth Nano Sheet, Chemistry of Materials  29(22), 9819-9828 (2017).
  6. K. He, Z. Yao, S. Hwang, N. Li, K. Sun, H. Gan, Y. Du, H. Zhang, C. Wolverton, D Su. Kinetically-Driven Phase Transformation during Lithiation in Copper Sulfide Nanoflakes, Nano Letters 17(9), 5726-5733 (2017).