Operando Scanning Force Microscopy for Lithium-Ion Dynamics in Solid Electrolytes

All scanning force microscopy (SFM) measurements including operando KFPM and tr-EFM (MFP-3D Asylum Research, Oxford Instrument, USA)) were performed in a glove box (GS, Germany) filled with argon (purity 99.9999%). The inert argon gas environment prevents battery degradation, including LLZO and lithium electrodes reacting with O₂, N₂, CO₂, N₂, and H₂O. SFM measurements were taken with PtIr-coated cantilevers, having a nominal spring constant of 2 N/m and a nominal resonance frequency of 75 kHz (SCM-PIT-V2, Bruker, USA). A homemade holder was used to fix and connect the battery sample to the potentiostat. The potentiostat was operated outside the glove box with electrical connections through the glove box wall. Photographs of the equipment are shown in Supplementary Fig. 33.
1) Operando KPFM: KPFM measurements were carried out in heterodyne frequency modulation (FM) mode with an external lock-in amplifier (Zurich Instruments HF2LI-MOD) to measure contact potential difference (CPD) between SFM tip and sample. More details about the KPFM working principle and interpretation is provided in Supplementary Note 9.
We first performed KPFM measurements on the LLZO or the Li₃PO₄ surface at position x without any external potential applied to the Li-CE. x is the distance to the Li-CE. Upon applying a constant external current or potential to the symmetric Li|LLZO|Li cell, we measured a CPD change at a specific position x on LLZO surface. It is defined as: ${CPD\left(x\right)}_{\mathrm{applied}}-{CPD\left(x\right)}_{\mathrm{OCV}}=k\left(x\right)\cdot {\varphi }_{\mathrm{applied}}+△\mathrm{\Phi }\left(x\right),$
Here, ${CPD\left(x\right)}_{\mathrm{OCV}}$ is the contact potential difference in the OCV state. ${CPD\left(x\right)}_{\mathrm{applied}}$ is the contact potential difference with an applied potential ${\varphi }_{\mathrm{applied}}$ . $△\mathrm{\Phi }\left(x\right)$ is work function change of the LLZO surface at position x, which changes with a material’s composition change.
2) Tr-EFM: Tr-EFM measurements were performed with the external lock-in amplifier (Zurich Instruments HF2LI-MOD) as well. Details are provided in Supplementary Note 10. Briefly, we performed tr-EFM measurements as follows. First, the cantilever was excited to vibrate at its first resonance frequency with an internal piezoelectric oscillator. A feedback electronic regulates the height between tip and measured points on the sample by keeping the vibration amplitude at the first resonance frequency constant. In this way, a topographic image of the sample was obtained in tapping mode. In addition, we applied an AC voltage at the second resonance frequency to generate an electrostatic force between SFM tip and the LLZO sample.
Next, we brought the tip into contact with the surface and applied a DC bias voltage of −3 V for 1.5 s to induce ion displacements in LLZO. Then, we grounded the tip for 1.5 s to allow ion relaxation, after which we retracted the tip and repeated this sequence at the next position. During this sequence, we recorded the vibration amplitude of the cantilever at its second resonance frequency (ω) to track changes of the electrostatic force $F_{\mathrm{es}\left(\mathrm{t},\mathrm{\omega }\right)}$ . As lithium ions are the main mobile charges in LLZO, we attribute changes of the electrostatic force to lithium-ion displacement. In solid ionic conductors, the ionic transport follows a stretched-exponential time response due to the electric field between the sample and tip^{60 (link)–63 (link)}: $\mathrm{\Delta }{A}_{\left(\mathrm{t},\omega \right)}=\mathrm{\Delta }{A}_{\mathrm{slow}}\exp \left[-{\left(\mathrm{t}/\tau \right)}^{\beta }\right]+\mathrm{\Delta }{A}_{\mathrm{fast}},$
Here, $\mathrm{\Delta }{A}_{\left(\mathrm{t},\omega \right)}$ is the total amplitude change at frequency ω, $\mathrm{\Delta }{A}_{\mathrm{fast}}$ is the amplitude change, before ionic relaxation due to ultrafast vibrational and electronic polarization^{44 (link),64 (link)}, $\mathrm{\Delta }{A}_{\mathrm{slow}}$ is the amplitude change until the system reaches a saturation state due to ionic relaxation, τ is a time constant and β is a stretch exponent representing ion diffusion properties^{44 (link)}. For simplicity, we set β to 1 to fit the $\mathrm{\Delta }{A}_{\left(\mathrm{t},\omega \right)}$ vs. time curve. Differences in ion diffusivity ( $D~1/\tau$ ) can be measured by fitting Eq. (5) to measurements recorded at different positions on a freshly prepared LLZO surface^{65 (link)}.
The comparison of tr-EFM results on LLZO and Au shows that tr-EFM can effectively track ion diffusivity in ionic conductors (Supplementary Fig. 34). The magnitude of the applied DC voltage on the tip does not alter the calculated relaxation time of the sample (Supplementary Fig. 35).