In the present work we present a phase-field modeling (PFM) study of (electro-)chemical sodiation of SnSb thin-film electrodes. The PFM is developed and applied to explore the sodium diffusion/intercalation and its influence on the evolution of SnSb grain structure. The PFM was developed using the MOOSE Framework.1,2 The model was validated against our experimental measurements, where SnSb thin films are prepared using ball-milling techniques and are deposited onto a carbon film/copper mesh transmission electron microscopy (TEM) grid (EMS CF-400-Cu) using DC magnetron sputtering. In-situTEM and electron diffraction experiments are used to directly image sodium diffusion and to determine the local structures.
Employong the PFM an electrochemical free energy function, considering sodium diffusion within the grains and the grain boundary (GB) along with the elastic stress field associated with Na intercalation, is established. The phase-field GB model is used to generate thin-film grain structures and subsequently to study their evolution under the sodium diffusion. Results show that Na diffusion first proceeds through the GB and then through the grains, and that the electrochemical sodiation is much faster than the chemical sodiation due to an applied electric potential, which drives more Na-ions towards the electrode. The elastic strain energy associated with the sodium intercalation slows down Na diffusion due to the stress build-up. At the first glance, the generated stress has the detrimental effect on the sodiation; however, by slowing down the diffusion process it provides a stabilization function, as less Na is available inside a grain, thus avoiding a potential for irreversible crystallization. In addition, to increase the fundamental understanding of sodium diffusion/intercalation and the GB evolution, sensitivity analysis was performed. Thus, the present modeling work (in conjunction with the experimental work) allows a mechanistic interpretation of the origin of different mechanical, electrochemical and transport phenomena occurring during the sodiation of thin films SnSb electrodes.
1. M. R. Tonks, D. Gaston, P. C. Millett, D. Andrs, and P. Talbot, Comput. Mater. Sci., 51, 20–29 (2012).
2. M. R. Tonks, Y. Zhang, A. Butterfield, and X. M. Bai, Model. Simul. Mater. Sci. Eng., 23, 045009 (2015).