Role of anisotropy in determining stability of electrodeposition at solid-solid interfaces

Zeeshan Ahmad and Venkatasubramanian Viswanathan

Phys. Rev. Materials 1, 055403 – Published 24 October 2017

Abstract

We investigate the stability of electrodeposition at solid-solid interfaces for materials exhibiting an anisotropic mechanical response. The stability of electrodeposition or resistance to the formation of dendrites is studied within a linear stability analysis. The deformation and stress equations are solved using the Stroh formalism and faithfully recover the boundary conditions at the interface. The stability parameter is used to quantify the stability of different solid-solid interfaces incorporating the full anisotropy of the elastic tensor of the two materials. Results show a high degree of variability in the stability parameter depending on the crystallographic orientation of the solids in contact, and point to opportunities for exploiting this effect in developing Li metal anodes.

Received 6 July 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.055403

Physics Subject Headings (PhySH)

Electrochemical properties Electrochemistry

Batteries Solid-solid interfaces

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zeeshan Ahmad

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

Venkatasubramanian Viswanathan^*

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA and Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

^*venkvis@cmu.edu

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Issue

Vol. 1, Iss. 5 — October 2017

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Images

Figure 1

Schematic of the electrodeposition problem with a metal electrode-solid electrolyte interface. The metal surface $x_{2} = f (x_{1}, t)$ grows on deposition of metal ions, the rate of which is proportional to the current. The local geometry alters the kinetics of deposition at the interface.
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Figure 2

Transformation of the elastic tensor for anisotropic analysis. The rotation brings the required crystallographic directions $v_{2}$ and $u_{2}$ along $e_{2}$ and $e_{1}$ . Note that the rotation operation is performed on the crystallographic axes of the material and not on the actual axes considered in the problem $e_{1}$ and $e_{2}$ .
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Figure 3

Deformation profiles obtained for different mechanical properties at the interface. (a) Initial position and deformed positions for one wavelength $λ = 2 π / k = 62.8$ nm of an interface on application of a sinusoidal perturbation: (b) isotropic-isotropic interface, (c) isotropic-anisotropic interface, and (d) anisotropic-anisotropic interface. The interface $x_{2} = 0$ is located in the middle (red line) with an electroyte above $(x_{2} > 0)$ and an electrode below $(x_{2} < 0)$ . The materials at the interface are the Li electrode and LiI electrolyte. In (c), the (010) Li surface is in contact with isotropic LiI, and in (d), the (010) Li surface is in contact with the (010) LiI surface with $v_{2} = V ([0 1 0]), u_{2} = V ([1 0 0])$ as in Fig. 2. The deformations are nonzero at the ends $(x_{2} = \pm 20$ nm) and vanish only at $x_{2} = \pm \infty$ .
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Figure 4

Stability parameter of a solid electrolyte-Li electrode system as a function of the shear modulus of solid electrolyte for $v_{2} = V ([0 1 0]), V ([1 1 0])$ , and $V ([1 1 1])$ and $v = 0.1$ , 3.85, respectively.
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Figure 5

Stability diagram of isotropic solid electrolyte-anisotropic Li electrode system for $v_{2} = V ([1 0 0]), V ([1 1 0])$ , and $V ([1 1 1])$ showing the range of shear modulus of an electrolyte over which electrodeposition is stable and its dependence on the volume ratio $v$ of the cation and metal atom.
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