Operando Raman Spectroscopy and Synchrotron X-ray Diffraction of

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Operando Raman Spectroscopy and Synchrotron X-Ray Diffraction of Lithiation/Delithiation in Silicon Nanoparticle Anodes Samuel Tardif, Ekaterina Pavlenko, Lucille Quazuguel, Maxime Boniface, Manuel Marechal, Jean-Sebastien MICHA, Laurent Gonon, Vincent Mareau, Gérard Gebel, Pascale Bayle-Guillemaud, Francois Rieutord, and Sandrine Lyonnard ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b05796 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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Operando Raman Spectroscopy and Synchrotron X-Ray Diffraction of Lithiation/Delithiation in Silicon Nanoparticle Anodes Samuel Tardif,†,§ Ekaterina Pavlenko,‡,§ Lucille Quazuguel,‡,k Maxime Boniface,† Manuel Maréchal,‡ Jean-Sébastien Micha,‡ Laurent Gonon,‡ Vincent Mareau,‡ Gérard Gébel,¶ Pascale Bayle-Guillemaud,† François Rieutord,† and Sandrine Lyonnard∗,‡ †Univ. Grenoble Alpes, CEA, INAC, MEM, F-38000 Grenoble, France ‡Univ. Grenoble Alpes, CEA, CNRS, INAC, SYMMES, F-38000 Grenoble ¶Univ. Grenoble Alpes, CEA, LITEN, F-38000 Grenoble, France §these authors contributed equally kCurrent address: Univ. Grenoble Alpes, LEPMI, F-38000 Grenoble, France E-mail: [email protected]

Abstract Operando Raman spectroscopy and synchrotron X-ray diffraction were combined to probe the evolution of strain in Li-ion battery anodes made of crystalline silicon nanoparticles. The internal structure of the nanoparticles during two discharge/charge cycles was evaluated by analyzing the intensity and position of Si diffraction peaks and Raman TO-LO phonons. Lithiation/delithiation of the silicon under limited capacity conditions triggers the formation of “crystalline core – amorphous shell” particles,

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which we evidenced as a stepwise decrease in core size, as well as sequences of compressive/tensile strain due to the stress applied by the shell. In particular, we showed that different sequences occur in the first and the second cycle, due to different lithiation processes. We further evidenced critical experimental conditions for accurate operando Raman spectroscopy measurements due to the different heat conductivity of lithiated and delithiated Si. Values of the stress extracted from both operando XRD and Raman are in excellent agreement. Long-term ex situ measurements confirmed the continuous increase of the internal compressive strain, unfavorable to the Si lithiation and contributing to the capacity fading. Finally, a simple mechanical model was used to estimate the sub-nanometer thickness of the interfacial shell applying the stress on the crystalline core. Our complete operando diagnosis of the strain and stress in SiNPs provides both a detailed scenario of the mechanical consequences of lithiation/delithiation in SiNP, and also experimental values than are much needed for the benchmarking of theoretical models and for the further rational design of SiNP-based electrodes.

Keywords strain, silicon electrodes, Li-ion batteries, operando synchrotron, operando Raman Silicon-based anodes are considered as highly promising materials for advanced Li-ion batteries (LiBs). 1,2 The specific capacity of Li15 Si4 (the endpoint compound of electrochemically lithiated silicon) and Li22 Si5 (the most lithiated equilibrium phase), are 3580 mAh/g and 4200 mAh/g, respectively, 3,4 much higher than current graphite-based electrodes (372 mAh/g for LiC6 ). 5 While lithiation in graphite is an intercalation mechanism, i.e. the Li+ ions are inserted between the graphene sheets, lithiation in silicon occurs via alloying, i.e. the Li+ ions effectively break covalent Si-Si bonds, drastically changing the crystal structure either by amorphization or by Li-rich alloy recrystallization. 6 The tremendous volume changes (up to 300% increase) associated to the phase transitions during lithiation and delithiation of silicon introduce large stresses which are detrimental to the structural integrity of the

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electrode material and to the stability of the Solid Electrolyte Interphase (SEI), causing dramatic capacity fading. 7 The adverse structural effects of the silicon lithiation may be partially mitigated using crystalline nanoparticles (SiNPs) 8–12 or nanowires, 13 as well as other shapes with large surface/volume ratios. 14 Recent advances have shown the importance of considering the stress in such confined nanostructures, not only to predict the mechanical failure of the electrode (by fracture or debonding from the current collector) but also because stress, electrochemistry and Li+ ions diffusion dynamics are intimately coupled. 15–20 For example, the effect of the stress on the potential was estimated to be on the order of 60-120 mV/GPa 21 using the LarchÃľ-Cahn formalism, 22 which can be quite significant given that crystalline silicon can withstand stresses in the GPa range, especially when nanosized. 23 Several theoretical models have further been developed to predict the stress and strain distribution in SiNPs for different situations: for the first lithiation of Si as a function of the imposed potential sweep rate and particle size 24,25 or considering the Li diffusion; 26 for two-phase and single-phase reaction during the initial and subsequent lithiations, respectively; 27–30 as a function of the particle morphology; 31 or including stress relaxation mechanisms. 32 Analytical solutions of the stress distribution in a compressed core-shell structure have recently been derived as well. 33 Simultaneously, different in situ and operando techniques have been developed for the study of the lithiation mechanisms in LiBs, as reviewed in Ref 34. For instance, electron energy loss spectroscopy in a scanning transmission electron microscope (TEM) was used to probe the composition distribution of the SEI on SiNPs, 35 while the SEI formation and evolution was observed in situ using atomic force microscopy. 36 The two-phase mechanism of the initial lithiation of nano-sized crystalline Si was irrefutably demonstrated using operando TEM. 37,38 Measurements of the strain during lithiation/delithiation were achieved in operando conditions by monitoring the deflection of multilayered cantilevers; 26,39 by measuring the curvature of Si wafers, either bare or covered with a thin composite Si

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electrode; 40–44 or by in situ digital image correlation. 45 Yet, such strain measurements were performed in model electrodes, quite different from actual devices. Anodes and cathodes in real or close-to-real LiBs have also been probed using operando Raman spectroscopy to measure the stress and strain in crystalline materials as well as the local disorder, 46–50 with a very recent study dedicated to the investigation of the first lithiation of SiNPs. 14 Coin cells were also modified to probe operando Si microparticles anodes using scanning electron microscopy. 51 Others have used X-rays and synchrotron radiation as reviewed in Ref 52, or neutrons to probe the lithiation/delithiation mechanisms using reflectivity, 53–55 imaging, 56–59 Bragg coherent imaging, 60 tomography, 61 or diffraction. 62–66 However, no experimental results have been reported so far on the study of strain and stress in crystalline SiNPs during repetitive lithiation/delithiation and the results from stress/strain models have yet to be experimentally demonstrated over several cycles. Here we report on the combination of operando Raman spectroscopy and synchrotron X-ray diffraction (XRD) to study the stress and elastic strain in SiNPs during the first two cycles, under limited capacity cycling conditions. We provide a comprehensive, continuous understanding of the core-shell SiNPs structure by analyzing the intensity and position variations of the XRD and Raman peaks. Such measurements allow one to test how efficient is the general strategy to reduce size (increase surface/volume ratio) on limiting the stress on these systems. The cross-correlated Raman/XRD real-time results are complemented by mechanical stress calculations to rationalize the compression and extension sequences observed within the particles. We evidence that the pressure exerted from the âĂĲbreathingâĂİ amorphized shell onto the continuously shrinking crystalline core is responsible for electrochemically-driven variations of the internal stress. Our results provide experimental evidence of the stress and strain evolution during the first and subsequent lithiation, as predicted by the initial two-phase and subsequent single-phase lithiation mechanisms in confined volumes.

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Results and discussion In order to monitor the structural evolution and to determine the internal strain and stress in the SiNPs, we performed operando measurements using both X-ray diffraction (XRD, sensitive to the bulk of the SiNPs) and Raman spectroscopy (sensitive to the outer part of the SiNPs).

Amorphization and strain in SiNPs by operando XRD It is known that upon the first lithiation at room temperature, Si crystals are gradually amorphized by an electrochemically-driven solid-state reaction before they eventually form a Li-rich crystalline phase. 1,3,67,68 This structural change is accompanied with a dramatic volume expansion (about 300%) which can result in large stress and strain in the electrode material. 69 In order to simultaneously investigate the amorphization process and the resulting strain in the remaining crystalline electrode material, we performed operando synchrotron X-ray diffraction in SiNPs electrodes. The geometry of the measurement and the custom cell design are shown in Fig. 1(a) and Fig. 1(b). At the same time as the battery was cycled (Fig. 1(c)), the Bragg reflections from the SiNP and from the Cu collector were measured (Fig. 1(d)) and fit by a Lorentzian function, thus providing direct information on the volume of crystalline Si in the nanoparticles (from the reflection integrated intensity) and on the strain state (from the reflection angle). From the simultaneous measurement of the cell potential, Bragg reflection intensity and scattering vector, we can access in real time the sequential effects of the lithiation/delithiation mechanisms on the SiNP. Fig. 2 shows the time dependence of (a) the cell potential and the transferred specific capacity along the two cycles, (b) the integrated X-ray diffraction intensity and (c) the strain ε (= −∆q/q where q is the scattering vector) relative to the initial state. By analyzing (a), (b) and (c), we are able to identify the successive steps of the lithiation/delithiation, related to distinct mechanisms that are schematically shown in (d).

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Eight different steps were identified, as indicated in Fig. 2 by the colored shadowed areas (steps i to vii, step iii being split into iiia and iiib ). These steps correspond (1) to different amounts of crystalline materials and (2) to different compressive or tensile strain states. We clearly see that the first and second lithiations are very different, which we describe in more details hereafter and explain by the formation of core-shell particles during the first lithiation and core-double-shell particles during the second lithiation. In the following, we analyze the main features of each step by correlating the electrochemical state (specific capacity on charge and discharge) to the structural evolution of the SiNPs. Indeed, at any point in time, quantitative information on the relative thicknesses of the core and shells can be obtained using relatively simple relations based on geometrical considerations and assumptions regarding the amount of lithium incorporated and the corresponding alloyed phase. A sketch describing the dimensions introduced hereafter is shown in Fig. S2 in the Supplementary Information. During lithiation, the Li concentration will increase in the SiNPs. Let the overall amount of Li ions in a SiNP be NLi = ρVSiN P xSiN P , where ρ is the atomic density of Si, VSiN P =

4π 3 R 3

is the (initial) volume of the SiNP of radius R and

xSiN P is the Li fraction (number of Li ion per Si atom) in the overall SiNP, measured from the specific capacity increase. If the lithiation is limited to an outer shell, we also have NLi = ρVshell xshell , where Vshell =

4π 3

(R3 − (R − h)3 ) is the (initial) volume of the lithiated

shell of thickness h and xshell is the Li fraction in this shell. Thus we can write R3 − (R − h)3 xSiN P Vshell = = . 3 VSiN P R xshell

(1)

The relative thicknesses of the core and shells can then be expressed in terms of relative Li fraction as h xSiN P =1− 1− R xshell

1/3

.

(2)

Additionally, the integrated diffracted intensity is proportional to the volume of the

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crystalline core, hence Iprist. ≈ R3 , Ilith. ≈ (R − h)3 and Ilith. h =1− R Iprist.

!1/3

(3)

,

where Iprist. and Ilith. are the measured diffracted intensities of the pristine and lithiated SiNP, respectively. From Eq. 2 and Eq. 3, we can estimate the Li fraction in the shell as

xshell = xSiN P

!

Iprist. . Iprist. − Ilith.

(4)

Using Eq. 2, Eq. 3 and Eq. 4 we can describe in more details the observed steps and the effects of the first and second lithiation/delithiation on the SiNP microstructure hereafter. Step i: Open circuit The open-circuit voltage (OCV) of the as-prepared cell is about 2.8 V, consistent with similar Si-based Li-batteries. Step ii: Initial voltage drop (SEI formation) When the galvanostatic measurement starts, i.e. a negative current (-148 µA) is applied and the potential with respect to Li+ /Li redox couple drops from the OCV value to less than 100 mV in about 3300s (218 mAh/g). This step corresponds to the SEI formation and the lithiation of the surface silicon oxide. Step iii: First lithiation plateau The relatively flat plateau between 50 and 75 mV (step iii) is typical of the lithiation of a Si-based electrode 38 and is indicative of a two-phase process: the outer shell of the SiNP is highly lithiated and amorphized, while the core is relatively unaffected. The two phases are separated by a sharp lithiation front that progresses inwards. 37,43,67,70–72 The beginning

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Figure 2: (a) Cell potential, (b) intensity of the SiNP Bragg reflection and (c) strain in the SiNP over the first two partial lithiation/delithiation cycles, as well as (d) a schematic view of the lithiation/delithiation process in the SiNP. Different steps corresponding to variations in the integrated intensity and/or the strain are identified (colored areas, green for lithiation, purple for delithiation). For each step (i to vii), values of the current amplitude, incremental and cumulative specific capacities are reported. In the cartoon representing the single-core shell (first cycle) and double-core-shell (second cycle) mechanisms, compressive and tensile states are schematized using red and blue arrows, respectively. The crystalline core is colored in grey, and the outer amorphized shell in green on lithiation and purple on delithiation.

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of step iii (iiia ) is marked by a constant diffracted intensity, while we would expect it to decrease over time since the amorphous lithiated shell does not contribute to the diffraction anymore. The constant diffracted intensity may be explained either by the concentration of Li+ in the SEI or by the lithiation of smaller SiNPs. Since the intensity of diffraction goes as the third power of the particle radius, small SiNPs do not significantly contribute to the total diffracted intensity compared to the larger ones. A small tensile stress appears during step iiia and is explained by the formation of the thin, highly lithiated, amorphous layer around the SiNP core. The large volume expansion in that amorphous layer results in an initial pull on the crystalline core. During the step iiib (starting after a specific capacity increase of about 584 mAh/g), the diffracted intensity of all Bragg peaks starts to decrease over time, i.e. the core amorphization starts to become significant and the surrounding lithiated amorphous layer turns into a shell. The stress changes sign, since the lithiation front is now at the interface between the core and the shell: the strain due to the volume expansion at this interface is now bound by the core and the shell. Whether we consider the total specific capacity increase over the potential plateau (≈ 979 mAh/g) or only during step iiib i.e. when the diffracted intensity decreases (≈ 613 mAh/g), we find that the inserted Li fraction is xSiN P = 1.03 or xSiN P = 0.64 Li ion per Si atom respectively, which corresponds to xshell = 3.7 or xshell = 2.3 Li/Si using Eq. 4. These results are quite consistent with previous reports of the Li fraction in the shell, on the order of xshell = 3.4 ± 0.2. 1 Note that if only 90% of the SiNP are active (Iprist. = 0.9), we find that the specific capacity increase during step iiib corresponds to xshell = 3.2 Li/Si. Considering xshell = 3.4 ± 0.2 and using Eq. 2 we find that h/R = 6.7% ± 1.2%, while solving Eq. 3 at the end of step iiib with Ilith. /Iprist. = 0.72 ± 0.05 gives h/R = 10% ± 2%, i.e. the SiNP are lithiated up to about 7 to 10% of their radius. The maximum compressive strain ε reached at the end of step iii is about −3.5 × 10−4 . Considering that the bulk modulus B of Si is about 98 GPa, 73 we can estimate that the hydrostatic compressive stress in the core is on the order of 3Bε ≈ 100 MPa, which is comparable with the observations by

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Zeng et al. using Raman spectroscopy on similar electrodes. 14 Step iv: First delithiation As soon as the current is reversed (step iv), Li+ ions are removed from the shell to the electrolyte. Concomitantly, the diffracted intensity stops decreasing and remains constant, showing that the Si crystals are not amorphized anymore. A compressive strain is measured in the core and is explained by the fact that the delithiated shell deflates and applies a compressive stress to the core. The total specific capacity decrease before the potential reaches 1 V (the condition for current reversal in our protocol) is -529 mAh/g, which is less than half the total specific capacity increase during the lithiation step (steps ii + iii, 1197 mAh/g). Step v: Beginning of second lithiation, relithiation of the amorphous shell During the first part of the second lithiation (step v), the amorphized shell is lithiated again. Contrary to the first lithiation where the material being lithiated was crystalline Si, this time amorphous Si is being lithiated and this lithiation step is a single phase process. As a result, the amorphous shell is lithiated through its overall thickness. It expands again and applies a tensile stress on the crystalline core, in contrast with the first lithiation. The constant diffracted intensity indicates that no amorphization occurs during that step and that all the Li+ ions are indeed inserted in the shell. The decreasing tensile strain rate (i.e. the change in strain with time or, equivalently, with lithiation) during this step can be explained by the decreasing yield strength of the amorphous Si shell upon lithiation, 41 resulting in plastic relaxation at the core/shell interface. Step vi: Second lithiation plateau, lithiation of the crystalline core Once the shell has been filled with Li+ ions, the lithiation of the crystalline Si core resumes (step vi). This translates into a drop of the potential to about the same plateau value 11


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as step iii (≈ 60 mV), indicating that a similar electrochemical reaction is occurring. The diffracted intensity decreases, as expected from the gradual amorphization of the core, similar to step iiib . Again, the stress reverses and an increasing compressive stress is applied to the SiNP core. This is explained by the first lithiation of an inner shell of new material, trapped between the already lithiated outer shell and the crystalline core, with no free boundary to expand. Part of the outward expansion of this inner shell is probably absorbed by elastic and/or plastic deformation of the outer shell, but some stress is applied to the inner crystalline core. This compressive stress increases gradually, until the current is reversed. At the end of step vi, the diffracted intensity amounts to 42% of the initial intensity, which corresponds to h/R = 25% according to Eq. 3. An upper bound of the Li fraction in the SiNP can be estimated from the total transferred specific capacity (366 + 613 − 529 + 494 + 1178 = 2122 mAh/g) to be around 2.2 Li per Si atom in the SiNP. From Eq. 4, we obtain xshell = 3.8 Li/Si in the outer shell, similar to the first lithiation. Interestingly, the slope of the potential during step vi is negative, which is consistent with an increasing compressive stress over time since compressive stress lowers the lithiation potential of Si. 40 Conversely, the potential slightly rises over time during step iiia , when a small tensile stress is applied. The total specific capacity increase during this second lithiation is 1672 mAh/g. By the end of step vi, the compressive strain has reached −11.5×10−4 , which converts to an hydrostatic compressive stress in the core on the order of 340 MPa. From the above considerations and detailed inspection of the various steps, we can draw several conclusions. First, the weighting of the different reactions (Si lithiation, reductions of the electrolyte and of possible traces) are clearly distinct from the first to the second cycle, due to the pre-existent shell already formed at the beginning of the second lithiation. In fact, it is well-established that the first cycle is peculiar due to initial SEI formation and first sequence of amorphization. Second, we observe that the strain exerted onto the core is increasing on cycling, with values on the order of 300 MPa already attained after only two charge/discharge cycles limited to 1/3 capacity. As the compressed state of crystalline

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Si is not favorable to lithium alloying, this situation is most probably limiting the efficiency of the following cycles of the battery. We now compare the XRD findings to the operando Raman characterization for further confirmation of these effects.

Amorphization and strain in SiNPs by operando and ex situ Raman spectroscopy Operando Raman spectroscopy measurements were conducted on similar SiNP electrodes to monitor the evolution of the stresses generated in the crystalline cores of the core-shell structures during lithiation/delithiation (Fig. 3(a)). In contrast with the operando XRD measurements, the amount of active SiNP connected to the Cu mesh collector could not be easily controlled. We therefore cycled the cell in potentiostatic mode, between 1 V and 0.01 V vs Li+ /Li with a scan rate of 0.1 mV/s. The lower potential limit was chosen to avoid the formation of the crystalline Li15 Si4 phase as well as lithium plating. Fig. 3(b,e) represent the electrochemical cycling sequence corresponding to the initial one and a half cycles. The reduction peak at ≈ 1.1 V indicates the formation of the SEI upon the first lithiation. The onset of the reduction current is observed in the first cycle at ≈ 0.2 V, corresponding to the initial alloying of the crystalline SiNPs with lithium, while in the second cycle the lithiation reduction peak shifts to ≈ 0.3 V and increases in magnitude, which can be attributed to the increase of the amount of electrochemically active silicon. The two anodic peaks at ≈ 0.3 V and ≈ 0.5 V are associated with Li dealloying. A typical Raman spectrum of the pristine SiNP electrode taken at a low laser power of 0.017 mW exhibits a narrow peak (full width at half maximum (FWHM) ≈ 3.2 cm−1 ) centered at 520.6 cm−1 corresponding to the transverse optical (TO) and longitudinal optical (LO) phonons of crystalline silicon (c-Si). The evolution of the c-Si peak over the initial one and a half cycles is shown in Fig. 3d. We found that the absolute intensity of the c-Si Raman signal dropped significantly upon lithiation but recovered (although not completely) upon delithiation. This intensity drop results from two effects: (1) the amorphization of the crystalline Si, such as observed in the 13


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operando XRD measurements; and (2) the changes in the optical skin depth that occur upon the formation of the Li-Si alloy. 74 We never observed a complete disappearance of the c-Si peak since cycling was performed at limited capacity. From the data shown in Fig. 3(d) we could also follow the evolution of the position of the c-Si peak during cycling. To determine the average spectral positions and the intensities of the TO-LO phonon peak, all spectra where fitted with a Lorentzian line shape. Fig. 3(f,g) presents the evolution of the intensity and position with the applied voltage. No significant changes in spectral position are observed during the first lithiation, while upon delithiation the spectra are clearly upshifted. The upshift is followed by a continuous downshift upon the second lithiation. The observed up and down spectral shifts can be related to the internal strains inside the crystalline particles: compressive stresses in c-Si result in an upshift of the spectral position of the TO-LO peak while tensile stresses lead to a downshift. 75 Therefore, the operando Raman measurements show that the crystalline SiNPs experience little to no stress during the first lithiation and are compressed during the following delithiation, which is in excellent agreement with the previously described operando XRD results. The stress is released at the start of the second cycle, similarly to the XRD data. Hence, the continuous spectral modulations of the c-Si peak measured by Raman spectroscopy strongly support our interpretation of the time-resolved XRD analysis. Operando measurements were complemented by ex situ Raman measurements performed on samples subjected to more prolonged cycling , i.e. after 1, 10 and 100 cycles ending after either the last lithiation or delithiation (denoted further as Li1, Li10, Li100 and deLi1, deLi10, deLi100, respectively). The samples were cycled in a galvanostatic mode at cycling rate of C/2 and the capacity was limited at 1200 mAh/g to avoid the formation of the crystalline Li15 Si4 phase as well as lithium plating, similarly to the operando measurements. In addition to the c-Si peak, a typical Raman spectrum of the sample after the 1st delithiation exhibits an amorphous silicon (a-Si) Raman signal composed of four broad characteristic contributions positioned at 155 (TA), 310 (LA), 400 (LO) and 475 cm−1 (TO) (Fig. 3(c).

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Figure 3: (a) Experimental operando Raman setup and electrochemical cell. (b)Linear sweep cyclic voltammograms. (c) Typical Raman spectra including crystalline and amorphous Silicon peaks. (d) Evolution of the c-Si TO-LO peak as a function of the scan number during the open-circuit (OCV), discharge (green) and charge (purple) cycles. The shadow on the left panel shows the variation of the Raman peak intensity over cycling time and the intensity map on the lower panel indicates the shift of the peak position (highlighted by the black line). Evolution of the (e) current, (f) Raman peak intensity and (g) spectral position as a function of time and applied voltage. Dashed lines indicate the end of the (de)lithiation processes.

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For delithiated samples where the changes in the optical skin depth due to alloying is no longer an issue we observe that the absolute intensity of the c-Si peak drops significantly after the first cycle and then continues decreasing with the increasing number of cycles (see supplementary Information) indicating a gradual transformation of the initially crystalline silicon into an amorphous one. When recording Raman spectra, one should care about sample heating by the illuminating laser beam which in turn affects the Raman spectra. 76–79 This issue is crucial when dealing with nanoparticles as the thermal conductivity is lower than in bulk. In crystalline Si, heating leads to a downshift and broadening of its first order Raman peak (LO-TO phonon). To better understand the influence of the laser power (i.e. heating) on the Raman response of our systems we Raman mapped a pristine Si electrode and samples after 1Li and 1deLi at 0.017 mW and 1.7 mW. For each Raman map we obtained 70 spectra that were further fitted with a Lorentzian line shape to obtain the spectral positions and FWHMs for each LO-TO c-Si phonon. Fig. 4(a,b) represents the Raman shifts and FWHMs obtained from the Raman maps. It is important to note that the number of points presented for each sample is the same. As expected the increase in laser power to 1.7 mW caused a considerable downshift in positions and increase in FWHM with respect to the values obtained at lower laser power of 0.017 mW. Additionally, when comparing the absolute shifts we find that they differ for lithiated, delithiated and pristine (crystalline) silicon. In Fig. 4(a) one can observe smaller downshifts and broadenings indicating a lower temperature (better heat dissipation) for the lithiated sample (crystalline core with an a-Lix Si shell (green circles)) than for the delithiated (crystalline core with an amorphous shell (purple circles)) and pristine (crystalline (black circles)) ones. Moreover an upshift with respect to the spectral position of the pristine c-Si sample is observed for the delithiated sample at lower laser power, indicating a compressive stress in the core, but is not observed when using higher power. On the contrary we observe a downshift caused by heating of the sample due to worse heat dissipation in a-Si compared to crystalline one. We also observe a significant dispersion of Raman peak positions and

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FWHMs at higher laser power indicating an inhomogeneous heating of the samples by the laser beam, while for spectra taken at lower laser power the dispersion is almost negligible allowing for a precise estimation of the generated stresses. Thus laser heating can mask sample modifications that could be revealed by Raman spectroscopy. To precisely measure the Raman spectral shifts due to lithiation/delithiation, we acquired 70 spectra from the pristine Si electrode as well as Li1, Li10, Li100, deLi1, deLi10 and deLi100 samples at a laser power of 0.017 mW. Fig. 4(b) presents the average value of the TO-LO peak position. We observe that the spectral positions for all samples subjected to electrochemical cycling are upshifted with respect to the one of the pristine silicon electrode. This suggests that compressive stresses in the crystalline core systematically increase upon cycling. Moreover, at the same number of cycles, the delithiated samples are compressed more than the lithiated ones, consistently with the operando measurement. A maximum shift of about 4 cm−1 is observed for the delithiated sample after 100 cycles. Here we note that the position upshifts obtained ex situ are greater than those obtained operando. This is attributed to the states of charge of the SiNPs that cannot be exactly the same for the ex situ and operando cycling protocols, due to different potential of the electrodes (galvanostatic for ex situ vs potentiostatic for operando). Thus, ex situ Raman spectroscopy provides an additional confirmation of the compression/tension of SiNPs crystalline core induced by the extraction/insertion of lithium and shows the build-up of compressive stress in the still-crystalline core. Along with the upshift we observe a broadening of the Raman peak with the number of cycles, indicating contributions arising from various core-shells with diverse stresses, as well as a stress-free contribution corresponding to some SiNP that did not undergo an amorphization process (i.e. no core-shell structure and therefore only a native c-Si contribution). However, as for the XRD measurements, the modulated dependence of the elastic internal strain upon applied voltage remains a robust finding. To further quantify the impact of cycling on the structure of the SiNPs, we can evaluate the magnitude of the stress as revealed by the Raman shifts. The magnitude of such stress can be estimated

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the initial two-phase lithiation. 81 In the early stages of the lithiation, the lithiated and amorphized layer is still very thin and the hoop stress in the SiNP is small and tensile, while when the lithiated shell is thick enough, a compressive stress is imposed on the crystalline core, ahead of the lithiation front. We use a simple mechanical model to estimate the required thickness of the stress-imposing interfacial shell (i.e., the lithiation front), assuming it is still crystalline but already being lithiated. We can approximate the displacement in the core and front u(r) by considering an isotropic core-shell structure with a Li concentration gradient: 82 1+ν u(r) = − 3(1 − ν)

! 2(1 − 2ν) r Z Rc 1 Zr 2 2 βc(r)r dr + βc(r)r dr , r2 0 1 + ν Rc3 0

(6)

where ν is an isotropic Poisson ratio, Rc is the radius of the crystal (core and lithiation front), c(r) is the normalized radial Li concentration profile (c = 0 in the pristine Si core and c = 1 in fully lithiated Si, i.e. 3.75 Li per Si) and β = 0.6 is the lithiation expansion coefficient (βc(r) is equivalent to αT (r) in a thermal model). 81 The initial lithiation mechanism can be described by c(r) = 0 for 0 ≤ r ≤ Rc − t, where t is the thickness of the lithiation front, and c(r) goes quite abruptly from 0 to 1 between Rc − t and Rc . Further assuming that c(r) = c0 for Rc − t ≤ r ≤ Rc , the strain in the crystalline core is constant and given by the slope of the right hand term in Eq. 6:

ε≈−

2(1 − 2ν) t βc0 . 3(1 − ν) Rc

(7)

Thus, at the end of the first lithiation where ε = âĹŠ3.5 × 10−4 and considering an isotropic Poisson ratio ν = 0.17, we find that c0 t/Rc = 0.1%. Since c0 is bound between 0 and 1 (and probably closer to 1), such a low value indicates that t/Rc is quite small, i.e. the stressing region is limited to a very thin but finite lithiation front of sub-nanometer size. This is consistent with a picture of a lithiation front rich in Li but not yet saturated, so that the coherent crystal structure with the underlying Si core is maintained and stress can applied to the core without plastic relaxation at the interface, while the highly lithiated,

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amorphized Si outer shell is plastically relaxed. Similarly, the hoop stress in the stressing layer can be derived from the same elastic expression: 2µ σθθ (r) = λ divu(r) + r where λ =

Eν (1+ν)(1−2ν)

and µ =

∂uθ 1+ν 2µ (r) + ur (r) = λ βc(r) + ur (r), ∂θ 3(1 − ν) r !

E 2(1+ν)

(8)

are the Lamé coefficients and E is the Young

modulus of the material. At the stressing layer position, r = Rc − t, the rightmost term in ur (Rc − t)/(Rc − t) is proportional to t/Rc and thus is negligible. As a result we can approximate

σθθ (Rc − t) ≈ Eβc0

ν . 3(1 − ν)(1 − 2ν)

(9)

Assuming the values presented before, we can estimate σθθ ≈ 0.062E. If we consider the Young modulus of the stressing layer in the hundreds of GPa range, we obtain a hoop stress on the order of the GPa, comparable to previous studies and consistent with a picture where plastic relaxation occurs behind the lithiation front, in the Li-rich amorphous shell. As a result, this simple mechanical model can account for a thin interfacial shell corresponding to the lithiation front during the first lithiation, which applies the stress to the crystalline core.

Conclusion We have evidenced in real-time the effects of lithiation and delithiation on crystalline Si nanoparticles for Li-ion batteries with operando X-ray diffraction and Raman spectroscopy. Using progressive limited capacity cycling, we show that the initial lithiation of crystalline Si (a two-phase reaction) and subsequent lithiation of amorphous Si (a single-phase reaction) in a confined core-shell geometry result in different strain profile during the battery cycling, as expected from theoretical models. Initial lithiation of the outer shell of the SiNP

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results in a small tensile stress, which is reverted to a compressive stress upon delithiation. Further relithiation of the amorphized Si introduces an additional tensile component, which is then compensated by a stronger compressive stress that is applied when the lithiation front reaches the crystalline core and traps the lithiation reaction front between the outer amorphized shell and still pristine inner core. A simple mechanical model was used to estimate the sub-nanometer thickness of the stress-imposing interfacial shell between the amorphous lithiated outer shell and the pristine crystalline Si core. Additionally, powerdependent Raman measurements have shown how the combination of local sample heating and a difference in heat conductivity could artificially reverse the measured Raman spectral shifts in lithiated and delithiated SiNPs. In fine, our operando diagnosis of the strain and stress in SiNPs provides experimental figures that are much needed for the benchmarking of theoretical models of lithiation/delithiation in SiNPs and for the further rational design of SiNP-based electrodes minimizing the internal stresses via morphology and surface/volume ratios optimization.

Experimental SiNP Electrodes Pristine SiNPs electrodes were provided by VARTA Micro Innovation. They were prepared in an aqueous slurry that comprised 80 wt.% active crystalline nanoparticles (about 100 nm diameter, from Nanostructured & Amorphous Materials, Inc.; see Refs 11,12 and corresponding Supplementary Information for a study on a similar electrodes), 12 wt.% carbon black as conductive additive and 8 wt% carboxymethylcellulose (Sigma-Aldrich) as binder. More details on the TEM characterization of the SiNPs can be found in the supplementary information. The Si electrodes were inserted in custom-designed air-tight battery cells developed for X-ray diffraction and Raman spectroscopy measurements. For the Raman measurements, the aqueous slurry described above was spread over a copper mesh (DEXMET Corp.) and 21


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dried at 90 ◦ C for 2h before placing it into the glove box. For the XRD diffraction measurements, the slurry was spread and dried on a Cu sheet and then cut in 10 mm diameter disks. Li metal was used as counter and quasi-reference electrode (diameter = 10 mm, thickness = 300 µm). Cycling was performed using standard carbonate electrolyte (1M lithium hexafluorophosphate in 1:1 (vol.%) ethylene carbonate:diethylcarbonate with 10% fluoroethylene carbonate additive (Solvionic). For Raman measurements, a 30 µm-thick woven Celgard 2500 separator (Celgard) and a three layered fleece separators (diameter = 1.2 cm, thickness = 100 µm, Freudenberg) were used while the XRD experiments were performed without separators. Both Raman and XRD measurements were performed in custom-designed cells. Electrochemical cycling was performed using a BioLogic VMP-300 potentiostat.

Operando Synchrotron X-ray Diffraction The XRD experiments were conducted on the French CRG beamline BM32 at the European Synchrotron Radiation Facility (ESRF, Grenoble, France). The incident energy was set to 27 keV (0.4592 ˚ A) to minimize absorption through the electrochemical cell. The beamsize at the sample position was 50 µm (V) × 700 µm (H) and the cell was mounted in reflection geometry, at an incidence of 4◦ (i.e. a surface footprint of about 0.7 mm along the beam). A Ge 111 crystal analyzer was used to maximize angular resolution and the diffracted intensity was recorded on photomultiplier coupled to a NaI scintillator. The XRD cell was made of two stainless steel electrodes and a polyetheretherketone body with a 360◦ × 20◦ 200 µm-thin window for high chemical stability and low background contribution. The Bragg reflections were recorded in the two-theta range from 8 to 22◦ which corresponds to Si 111, 220, 311, 400 and 331 from the SiNPs to reduce experimental errors and evidence the isotropic strain, as well as Cu 111, 200 and 220 from the underlying current collector, used as references. It was checked that the latter do not vary in shape, position nor intensity during the experiments to assess the reliability and accuracy of the measurements performed on the SiNP. The mass of active material (Si) was 0.620 mg over a 10 mm diameter circular electrode. The cell was 22


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cycled in galvanostatic mode with a constant current of 148 µA (i.e. the cycling rate was C/4).

Operando Raman spectroscopy Confocal Raman spectroscopy was carried out on a LabRam HR instrument (Horiba JobinYvon) in back-scattering geometry. The electrode was assembled in a glove box and mounted in a custom electrochemical cell equipped with a glass window transparent to the Raman laser. The electrochemical cell was then transferred from the glove box to a glove bag under argon atmosphere and placed in the spectrometer. For Raman measurements we used a 100X long working distance optical objective that resulted in a laser spot of approximately 3 µm2 on the Si electrode. Thus, an obtained Raman spectrum represented an average spectrum taken from all Si nano-particles contained in the volume defined by the focal spot (about 3 µm2 ) times the penetration depth (depending on the Si probed: ∼1000 nm in crystalline, 83 ∼ 100nm in amorphous 84 and ≪100 nm in lithiated Si 74 ). The experiments were performed using a 632 nm laser excitation wavelength at very low laser power (0.1% filter ≈ 0.017 mW, corresponding to about 570 W/cm2 ). It resulted in long acquisition times (15 minutes per spectrum) to obtain a sufficient signal-to-noise ratio but was mandatory to avoid heating of the SiNPs by the laser beam.

Acknowledgement The authors thank the ESRF EC-Lab for access to the laboratory to prepare the cell during the operando XRD measurements. Funding from the European Research Council (ERC), EU FP7 Energy.2013.7.3.3 program on “Understanding interfaces in rechargeable batteries and supercapacitors through in situ methods”, Grant award No. 608491 on project “Battery and Supercapacitors Characterization and Testing” (BACCARA) is acknowledged.

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Supporting Information Available Transmission Electron Microscopy and Electron Energy-Loss Spectroscopy in the SiNPs, detailed geometry of the mechanical model, deformation measured in both the SiNP and the Cu current collector during the operando XRD experiments and Raman spectra measured in SiNPs in different lithiation stages. This material is available free of charge via the Internet at http://pubs.acs.org/.

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