Na Diffusion in Hard Carbon Studied with Positive Muon Spin Rotation and Relaxation

Kazuki Ohishi; Daisuke Igarashi; Ryoichi Tatara; Shoichiro Nishimura; Akihiro Koda; Shinichi Komaba; Jun Sugiyama

doi:10.1021/acsphyschemau.1c00036

Na Diffusion in Hard Carbon Studied with Positive Muon Spin Rotation and Relaxation

ACS Phys Chem Au. 2021 Nov 15;2(2):98-107. doi: 10.1021/acsphyschemau.1c00036. eCollection 2022 Mar 23.

Authors

Kazuki Ohishi¹, Daisuke Igarashi², Ryoichi Tatara^{2

3}, Shoichiro Nishimura⁴, Akihiro Koda⁴, Shinichi Komaba^{2

3}, Jun Sugiyama^{1

5}

Affiliations

¹ Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society (CROSS), Tokai, Ibaraki 319-1106, Japan.
² Department of Applied Chemistry, Tokyo University of Science, Shinjuku-ku, Tokyo 162-8601, Japan.
³ Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Nishikyo-ku, Kyoto 615-8245, Japan.
⁴ Muon Science Laboratory, Institute of Materials Structure Science, KEK, Tokai, Ibaraki 319-1106, Japan.
⁵ Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan.

Abstract

The diffusive nature of Na⁺ in Na-inserted hard carbon (C _x Na), which is the most common anode material for a Na-ion battery, was studied with a positive muon spin rotation and relaxation (μ⁺SR) technique in transverse, zero, and longitudinal magnetic fields (TF, ZF, and LF) at temperatures between 50 and 375 K, where TF (LF) denotes the applied magnetic field perpendicular (parallel) to the initial muon spin polarization. At temperatures above 150 K, TF-μ⁺SR measurements showed a distinct motional narrowing behavior, implying that Na⁺ begins to diffuse above 150 K. The presence of two different muon sites in C _x Na was confirmed with ZF- and LF-μ⁺SR measurements; one is in the Na-inserted graphene layer, and the other is in the Na-vacant graphene layer adjacent to the Na-inserted graphene layer. A systematic increase in the field fluctuation rate (ν) with increasing temperature also evidenced a thermally activated Na diffusion, particularly above 150 K. Assuming the two-dimensional diffusion of Na⁺ in the graphene layers, the self-diffusion coefficient of Na⁺ (D _Na ^J) at 300 K was estimated to be 2.5 × 10^-11 cm²/s with a thermal activation energy of 39(7) meV.