Supporting Information. Kinetically-Driven Phase Transformation during Lithiation in Copper Sulfide Nanoflakes

Transcription

1 Supporting Information Kinetically-Driven Phase Transformation during Lithiation in Copper Sulfide Nanoflakes Kai He,*,, Zhenpeng Yao, Sooyeon Hwang, Na Li, Ke Sun, Hong Gan, Yaping Du, Hua Zhang, Chris Wolverton, Dong Su*, Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11953, United States Frontier Institute of Science and Technology jointly with College of Science, State Key Laboratory for Mechanical Behavior of Materials, Xi an Jiaotong University, Xi an , China Energy Sciences Directorate, Brookhaven National Laboratory, Upton, New York 11953, United States Center for Programmable Materials, School of Materials Science and Engineering, Nanyang Technological University, Singapore , Singapore * s:

2 Supplementary Figures Figure S1. Standard procedures to acquire radially averaged electron diffraction intensity profile. A typical electron diffraction pattern (at the pristine state in Figure 1f) is shown in (a). The green curve shows an intensity profile along a specific direction. By integrating all the intensity profiles across the full 2π range, a radially averaged intensity profile is obtained as shown in (b). After background subtraction using power-law model, the final intensity profile is obtained as shown in (c).

3 Figure S2. Analysis of reaction area propagation for lithiation of CuS nanoflakes in (a) plan-view and (b) side-view. The red dashed lines outline the dark areas that are lithiated CuS phase while the rest in bright contrast represent pristine CuS phase. The lithiated areas are measured as a function of time and the derivative represent the areal propagation speed, which are shown in Figure 2f and g.

4 Intensity (a.u.) 2000 Pristine Half Lithiated Fully Lithiated Cu L 2, Energy Loss (ev) Figure S3. Evolution of Cu EELS during in situ lithiation. EELS spectra showing Cu L 2,3 edge profiles obtained at the pristine, half-lithiated, and fully-lithiated states. The pre-edge peak reduces as lithiation proceeds, indicating the evolution from Cu 2+ to Cu 0.

5 Figure S4. In situ TEM observation showing Cu extrusion and hopping during lithiation of CuS nanoflakes. (a) Time-sequential TEM images during lithiation of a CuS nanosheet indicating Cu extrusion, growth and migration. (b) Histogram of Cu particle number as a function of reaction time; the number refers to the quantity of precipitated Cu particles appearing within each time interval of 10 s. (c) Time-sequential TEM images showing evolution of Cu Particle I (red box area in a), and (d) the corresponding particle size evolution as a function of time. (e) Time-sequential TEM images showing evolution of Cu Particle II (blue box area in a), and (f) the corresponding particle size evolution as a function of time. Particle I has appeared and disappeared repeatedly for five times; and meanwhile hopping of Cu particles to multiple locations also observed, which indicates the high mobility of extruded Cu during the lithiation process.

6 Figure S5. HRTEM images of lithiation products. (a) Newly extruded Cu nanoparticle on the surface of lithiated Li x CuS; (b) Cu particles after full lithiation; (c) Li 2 S after full lithiation.

7 Figure S6. Calculated Li-Cu-S ternary phase diagram (0 K) and the equilibrium lithiation reaction path of Li-CuS. The equilibrium reaction path is presented by the red dotted line through two three-phase regions (I, II).

8 Figure S7. Calculated equilibrium and non-equilibrium lithiation voltage profiles compared to the experimentally observed counterparts. Equilibrium calculated/experimental curves are shown as red solid/dotted lines. Non-equilibrium calculated/experimental curves are shown as blue solid/dotted lines.

9 Figure S8. (a) Sampled total energies of all the configurations. (b) Non-equilibrium Li-CuS convex hull with four intermediate phases determined. (c) Predicted non-equilibrium reaction voltage profile with the equilibrium voltage profile as the reference.

10 Figure S9. (a) Averaged net charges on Cu in Li x CuS (0 < x < 2) based on the Bader charge analysis. (b) C-distance and volume evolution during the lithiation process of CuS. The error bar corresponds to the distribution of charges on specific Cu ions.

11 Figure S10. Searching for the non-equilibrium phases through the Li-CuS reactions. The searching process proceeds as follows: (a) Identify possible insertion sites (A, B, and C) for Li from the original CuS structure. (b) All symmetrically different configurations of Li on unoccupied sites were generated for each composition (Li x CuS, 0 < x < 2) using Enum (Li and vacancy ordering are shown by green circles with the CuS structure visualized by the blue polyhedral). Total energies of all configurations were sampled by DFT using settings as described in the method section. For the specific composition, corresponding structures were ranked by their total energy with the lowest three energy structures were further relaxed in DFT with more strict settings. Formation energies of these selected structures were then evaluated. Non-equilibrium convex hull was built with these formation energies and compositions located on the hull were determined to be the non-equilibrium intermediate phases.

12 Supplementary Movies Movie S1. In situ STEM observation showing lithiation of CuS nanoflakes along both plan-view and side-view. The movie clip is accelerated by 100 times. Movie S2. In situ TEM observation showing Cu extrusion and hopping during lithiation of CuS nanoflakes. The movie clip is accelerated by 50 times. Movie S3. In situ STEM observation showing another representative lithiation of CuS nanoflakes. The movie clip is accelerated by 100 times. Movie S4. In situ STEM observation showing delithiation of the CuS nanoflakes after the lithiation in Movie S3. The movie clip is accelerated by 150 times.

13 Supplementary Information of Calculations Construction of the Li-Cu-S phase diagram and equilibrium reaction path. Phase diagram represents the thermodynamic phase equilibria of a multicomponent system and offers significant information on material synthesis and reactions. The construction of phase diagrams can be accelerated remarkably using computational tools like DFT. Through calculating the energies of all known compounds in certain chemical space, we can therefore determine the phase diagram of that system. In this study, we construct the Li-Cu-S phase diagram using structures from the Inorganic Crystal Structure Database (ICSD). 1 The reference states (Li, Cu, and S) were obtained by fitting 2 to experiment data from SGTE substance database (SSUB). 3 The equilibrium lithiation/delithiation reaction paths can be determined directly from the ground state convex hull between Li and CuS which is obtained using a linear programming approach. 4 Calculation of voltage profiles. In a two-phase reaction between Li x CuS and Li y CuS: Li x CuS + (y-x) Li Li y CuS, the averaged voltage relative to Li/Li + is given by the difference of the reaction free energy per Li: V = G f F N Li where F is the Faraday constant, N Li is the amount of Li added/removed and G f is the (molar) change in free energy of the reaction. We approximated G with total energies (E) from DFT calculations neglecting the entropic and enthalpic (pv m ) contributions (0 K, atmospheric pressure): E = E(Li y CuS) - E(Li x CuS) - (y-x)e(li metal ). In practical batteries, the (de)lithiation reactions do not necessarily to proceed strictly through two-phase reactions. Accordingly, the voltage profile obtained should be viewed as approximate and small voltage steps should not be taken as significant. At the same time, voltage drops in the predicted voltage profile would become rounded and smooth as finite temperatures (e.g. room temperature) considering the entropic contributions. 5

14 Supplementary References 1. Belsky, A.; Hellenbrandt, M.; Karen, V. L.; Luksch, P. Acta Cryst. B 2002, 58, Grindy, S.; Meredig, B.; Kirklin, S.; Saal, J. E.; Wolverton, C. Phys. Rev. B 2013, 87, Scientific Group Thermodate Europe (SGTE). Thermodynamic Properties of Inorganic Materials vol. 19; Lehrstuhl für Werkstoffchemie, RWTH, Aachen, Ed.; Springer: Berlin, Akbarzadeh, A. R.; Ozoliņš, V.; Wolverton, C. Adv. Mater. 2007, 19, Wolverton, C.; Zunger, A. Phys. Rev. Lett. 1998, 81,