Strong stress-composition coupling in lithium alloy nanoparticles

The stress inevitably imposed during electrochemical reactions is expected to fundamentally affect the electrochemistry, phase behavior and morphology of electrodes in service. Here, we show a strong stress-composition coupling in lithium binary alloys during the lithiation of tin-tin oxide core-shell nanoparticles. Using in situ graphene liquid cell electron microscopy imaging, we visualise the generation of a non-uniform composition field in the nanoparticles during lithiation. Stress models based on density functional theory calculations show that the composition gradient is proportional to the applied stress. Based on this coupling, we demonstrate that we can directionally control the lithium distribution by applying different stresses to lithium alloy materials. Our results provide insights into stress-lithium electrochemistry coupling at the nanoscale and suggest potential applications of lithium alloy nanoparticles.

mapping of Li-K spectra reveal that the void is not Li rich phases formed via phase separation 70 within the particle. f-g The thickness profile obtained by EELS spectra across the particle 71 diameter show that the void is indeed a void with significantly reduced material thickness. 72 The scale bar in a indicates 100 nm.
Modest volume expansion in shell upon solute addition = Small interfacial energy between core and shell = Large particle and small surface energy

= .
Poisson ratio of the core

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Poisson ratio of the shell

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Core to shell thickness ratio indicates the total incident current intensity, which is sum of the total energy loss in an 224 EELS spectrum (Supplementary Fig. 20). and respectively indicate the background-  Fig. 5). The average portion of voids increases from 4.3% to 9.7% as the nominal composition increases from Li 2 Sn to Li 3.5 Sn ( Supplementary Fig. 6), which suggests 247 that the void size is affected by Li concentration in lithiated Sn-SnO 2 nanoparticles. The 248 voided morphology is consistently observed among different-sized particles with radii 249 ranging from 50 nm to 150 nm. For the fully lithiated particle, we confirm the void formed 250 inside the lithiated shell ( Supplementary Fig. 7). After the galvanostatic delithiation, the 251 particles exhibit similar core morphology, but with noticeably thinner shells than those in 252 lithiated particles (Supplementary Fig. 5e). The area of the core-shell nanoparticles was measured by counting the pixel number of 256 the selected contrast contour using ImageJ (National Institutes of Health). The error bound 257 for measuring lithiation-induced areal changes in nanoparticles were ±3.4% (Fig. 2). 258 The electron beam-induced C-rate during our in situ GLC tests were calculated based on The estimated C-rate is thus 17 C. 274 Using the same method, we estimate the lithiation rate for the other two core-shell 275 nanoparticles in Fig. 2k  A nm -2 , the estimated C-rate decreases accordingly. When the electron irradiation is 280 maintained the same, we still observe different lithiation rates for different-sized particles. 281 For smaller particles, the C-rate increases as the Li intake current is identical. Following our 282 analysis on the constant inelastic scattering cross section, this result suggests that we can 283 control the lithiation rate by the irradiated electron beam density for given nanomaterials.  Fig. 2k exhibits 288 rapid initial increase in particle size, followed by a slow yet steady increase before core 289 dealloying begins (pointed by dashed line for each curve). The observed step-wise increase in 290 particle size is similar to those reported for Sn nanowires during potentiostatic lithiation 9 . It is 291 also noted that this distinct two-stage kinetics is observed for both oxide-shelled and pristine 292 Sn particles suggesting that compressive stress does not significantly affect the lithiation 293 kinetics ( Fig. 2k and Supplementary Fig. 4b). 294 It means that the initial lithiation behavior is controlled by lithiation of Sn core. The 295 consistent lithiation kinetics, observed in Sn particles with or without oxide shell, might be 296 due to rapid Li insertion into Sn core through defective grain boundaries 10 . This continuous 297 two-step lithiation dynamics, observed in both oxide-shelled and pristine Sn particles, differs 298 from the initial two phase dynamics in Si. 299 At the areal expansion up to 100% for the three nanoparticles in Fig. 2k, the rigid oxide 300 shell is expected to break apart. Instead, the shell thickens continuously and demonstrates that 301 Li intake occurs in the shell as well as in the core. As the shell remains intact, the expanding 302 core presumably imposes tensile hoop stress on the shell while the shell imposes compressive 303 hydrostatic stress on the core. 304 305 6. Elasticity models for core-shell particles 306 To identify when the elastic limit is reached for the SnO 2 shell during lithiation, we 307 employed the diffusion-induced elasticity model by Verbrugge et al. 11 . Understanding the 308 elastic stress of core-shell geometry during lithiation involves solving the following set of 309 dimensionless differential equations in terms of the displacement ( ). The particle geometry 310 is assumed to be spherically symmetric.
The dimensionless displacement is defined as the following: Here, α refers to the core phase and β the shell phase. ̅ and ̅ refer to the 315 dimensionless radii and interface position. , and , refer to the particle radius, partial 316 molar volume of Li in the core and the relative composition x in Li x Sn, respectively. we may express the dimensionless stresses as the following: The dimensionless stress components may be converted back to the stress components as the 338 following: We thus obtain the elastic stresses in the particle at Here, and refer to the core and particle radii, respectively. Similarly, in the core, we 357 obtain the following expressions for the stress states: The solutions to the plasticity model only contains one materials parameter, the yield stress of 359 the shell. Solving the equations for the particle's materials parameters gives the stress states 360 in Fig. 4a with respect to the shell thickness. At the thin shell limit, the shell-imposed stress on the core 385 (and the equivalent stress potential) converges to zero. The shell experiences stress potential 386 corresponding to the yield stress.
Increasing the shell thickness results in enlarged potential drop on the core. In the thin 388 shell case, the potential drop on the core is negligible, while the potential increase on the shell 389 remains significant. The difference between the two potential curves, labeled as the overall 390 potential difference, increases with increasing shell thickness.
Here, and indicate the molar volume of the diffusing species and the surface layer 413 thickness, respectively. refers to the characteristic feature size, here the void size. is