Formation of Zintl Ions and Their Configurational ... - ACS Publications

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Formation of Zintl Ions and Their Configurational Change during Sodiation in Na−Sn Battery Yong-Seok Choi,† Young-Woon Byeon,† Jae-Pyoung Ahn,‡ and Jae-Chul Lee*,† †

Department of Materials Science and Engineering, Korea University, Seoul 136-701, Republic of Korea Advanced Analysis Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea

‡

S Supporting Information *

ABSTRACT: Despite their large theoretical storage capability, Na−Sn batteries exhibit poor round-trip energy efficiencies as compared to Li−Si batteries. Here, we report the results of a comprehensive study to elucidate how and why Na−Sn batteries exhibit such a low energy efficiency. As a convincing evidence for this behavior, we observed that the resistivity of the Sn anode increased by 8 orders of magnitude during in situ sodiation experiments, which is attributed to the formation of electrically resistive Zintl ions in the sodiated Sn. Continual sodiation induced the development of residual stresses at the Sn anode and caused the distortion of Zintl ions from their ideal configuration. This distortion caused a change in the electronic structure, resulting in the increased resistivity of the sodiated Sn. Our findings offer some solutions that can be used to improve the energy efficiency of Na−Sn batteries. KEYWORDS: Na-ion battery, resistivity, in situ sodiation experiment, ab initio simulation, FEM, Zintl ion

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of Avci and Flynn in 1979 in which the authors made an effort to explore the novel properties of the alkali alloys at various compositions.10 Additional studies were performed by Marel et al. to measure the resistivity of molten Na−xSn alloys.11 They commonly observed a marked increase in the resistivity by 2−3 orders of magnitude as the amount of Na added to the Sn increased from 0 to 50% to prepare a stress-free Na−50Sn amorphous alloy. A subsequent computational study on the Na−50Sn alloy attributed this high resistivity to the formation of covalently bonded Sn clusters, so-called Zintl ions, which is a tetrahedral structure consisting of four Sn atoms (Sn44− anions) with the ideal bond length and angle of 3.02 Å and 60°, respectively.12,13 Although these earlier studies are instructive for clarifying the electrically resistive Zintl ions as the possible origin of the low round-trip efficiency of the Na−Sn battery system, they are limited to the “stress-free” Na−50Sn alloy and thus are not sufficient to fully understand the increase in the resistivity of the Sn anode measured in the present study. This is because the maximum value of the resistivity measured from the NaSn phase during the current in situ sodiation experiment was larger than that measured from the Na−50Sn alloy used in ref 10 by more than 4 orders of magnitude. The fact that the resistivity differs significantly for materials with the same composition suggests the existence of additional factors influencing the resistivity.

a is abundant and exhibits a relatively low redox potential [Eo(Na+/Na) = −2.71 V], which makes Na ion batteries (NIBs) a primary candidate as a future alternative to Li ion batteries (LIBs).1 The growing interest in NIBs has accelerated the exploration of proper anode materials; group-IVA elements such as Sn, Sb, and Pb, are known to be suitable for use as the anode. Of these materials, Sn is the most promising candidate due to its large capacity (847 mAh/g).2−4 However, using Sn as the anode has two major drawbacks, that is, poor cyclability and low round-trip energy efficiency (also termed high voltage loss, energy loss, or high Coulombic loss, depending on the author).5−7 The short life cycle of Na−Sn batteries arises primarily from the pulverization of Sn caused by the large volume change associated with sodiation and desodiation.5 Extensive studies to improve the life cycle of Na−Sn batteries are underway.2,8 In contrast to extensive literature on the cyclability issue, the low round-trip energy efficiency of Na−Sn batteries has received only passing mention, and the physics underlying this phenomenon are not yet fully understood.8,9 During charging and discharging of a battery, the electrode materials undergo a series of phase transitions via electrochemical reactions during which electric charges are transported. This electrically driven phase transition always costs extra energy, where the amount of the energy loss associated with the phase transition depends on the difficulty of the charge transport. Therefore, the round-trip energy efficiency of a battery is closely related to the electrical resistivity of the sodiated phases. The first study on the measurement of the electrical resistivity of Na−xSn alloys is traced back to the work © XXXX American Chemical Society

Received: September 2, 2016 Revised: December 29, 2016

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Figure 1. (a−d) Representative snapshots captured from a movie (Supplementary Movie 1) showing the morphological changes of a Sn particle subjected to sodiation for (a) 0, (b) 800, (c) 9000, and (d) 18 000 s. (e) TEM image of a Sn particle subjected to the first-stage sodiation, showing the presence of the two distinct regions of the NaSn shell (dark) and the Sn core (bright). The regions denoted by “A” correspond to chipped-out grains. (f,g) A set of EDS maps for (f) Na and (g) Sn obtained from (e). (h) Cross-sectional view of a sodiated Sn particle subjected to second-stage sodiation, showing that the particle constructed an a-NaSn/a-Na0.2Sn/Sn core−shell structure.

sodiation is characterized by a volume expansion of up to ∼520% (Figure 1d), which in most cases9,14 promotes the formation of cracks on the surface of the sodiated Sn particle. In order to identify the phases formed during each stage of sodiation, the sodiation of pristine Sn particles was promoted inside an FIB instrument to prepare sodiated particles corresponding to the first-stage sodiation. When the moving phase boundary reached the equator of the Sn particle (Figure 1b), sodiation was interrupted intentionally by exposing the particle to oxygen, leaving the particle partially covered with a thin layer of oxidized NaxSn (for the detailed procedures, see Method). The particle was then milled to a thin slice and analyzed to identify the composition of the a-NaxSn phases using TEM equipped with energy-dispersive spectroscopy (EDS). Figure 1e shows the cross-sectional view of the sodiated particle subjected to the first-stage sodiation, in which the presence of a very thin reaction layer (∼100 nm) is observed. When analyzed using EDS (Figures 1f−g), it was found that this layer consisted of an a-NaxSn phase with an average composition close to that of NaSn. We next prepared another particle by promoting second-stage sodiation. The particle was cut in half to estimate the phases using EDS analysis. The image in Figure 1h shows that Na atoms continued to diffuse across the particle, increasing the thickness of the a-NaSn surface layer and at the same time producing a new a-Na0.2Sn phase at the interior. The cross section of the partially sodiated Sn particle consisted of the three distinct regions separated by the phase boundaries, that is, the inner core of the unreacted Sn, an intermediate layer of a-Na0.2Sn, and an outer shell of a-NaSn, thus constructing a typical aNaSn/a-Na0.2Sn/Sn “core−shell” structure (Figure 1h). The final stage of sodiation was characterized by the formation of the a-Na3.75Sn (equivalent to Na15Sn4) phase, as evidenced by the volume expansion of ∼520% and EDS analysis (data not shown).9

In this study, using a combined technique of the in situ sodiation experiment based on electron microscopy, the firstprinciples calculation, the finite element method (FEM), we performed a comprehensive study to elucidate how and why Na−Sn batteries exhibit such a low energy efficiency. This paper addresses four issues and is organized as follows: (1) We first described the in situ measurement of the sodiation behavior using a focused ion-beam (FIB) system to measure simultaneously the change in the electrical resistivity and the morphology of the sodiated Sn particles. (2) Using firstprinciples calculations on the Na−Sn alloy system, we calculated the structural evolution of the Sn anode in order to confirm that the formation of Zintl ions is feasible during sodiation. (3) Using FEM analysis, we assessed the development of the residual stresses induced by sodiation to clarify their role in the configurational changes of the Zintl ions. (4) Finally, by evaluating the structural changes of Zintl ions and their effect on the electronic structure, we reveal that sodiationinduced stresses are an important factor affecting the energy efficiency of Na−Sn batteries. On the basis of the present findings, we also address some likely solutions that can improve the round-trip energy efficiency of the Na−Sn battery system. Direct Observation of Sodiation of the Sn Anode. Figure 1a−d show snapshots captured from a video (Supplementary Movie 1) showing the continuous and spontaneous insertion of Na, which takes place in three stages. Each stage is distinguished by a characteristic volume expansion. The first stage of sodiation is dominated by the surface diffusion of Na to Sn and proceeds with a minor change in the volume (Figure 1b). During this stage, the sodiated and unsodiated regions are clearly distinguished by the moving phase boundary (denoted by the dotted line in Figure 1b) advancing across the surface. After the phase boundary completely sweeps over the entire surface of the Sn particle, second-stage sodiation takes place, accompanied by a volume expansion of up to ∼220% (Figure 1c). The final stage of B

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Figure 2. (a) Changes in the electrical resistance and the morphology of the sodiated particle recorded as a function of the sodiation time using (b) the setup installed in an FIB system. The two W tips holding the Na and Sn particles are arranged such that the Sn particle is in contact with the Na particle, whereas the other tips (probes) are positioned near the Na particle to measure the change in the resistivity during sodiation. (c−g) The morphologies of the particle corresponding to the regions denoted by “○” in the resistance curve. Note that sodiation was significantly suppressed when the sodiated layer reached the positions of the W probes, and therefore all the resistance values [denoted by the dots in (a)] measured beyond 4000 s were obtained separately from the particle sodiated for a designated time without attaching the probes.

Resistance Measurement during the in Situ Sodiation Experiment. Inspired by our success in observing the sodiation process of the Na−Sn system using in situ electron microscopy,15 we then simultaneously recorded the change in the electrical resistance and the morphology of a sodiated Sn particle during a prolonged period of time (see Figure 2a and Supplementary Movies 2 and 3). This was achieved by positioning a pristine Sn particle (∼10 μm) and the four W tips in the FIB system as shown in Figure 2b (also outlined in detail in Methods) to allow the spontaneous diffusion of Na to Sn. The in situ sodiation experiment showed that the spontaneous and continuous insertion of Na to the Sn particle caused a substantial increase in the electrical resistance (Figure 2a). When the measured resistance was converted to the resistivity by incorporating the geometry of the sodiated particle, three plateaus representing the characteristic resistivity values were observed; the resistivity measured from the firststage sodiation (10−3 Ω·cm) was greater than that of the pristine Sn (10−5 Ω·cm) by approximately 2 orders of magnitude. Considering that the electric current tends to flow across the surface, the resistivity measured from the first-stage sodiation is considered to arise from the formation of the thin a-NaSn phase on the surface of the Sn particle (Figure 2e). This measurement is roughly consistent with that measured for the amorphous Na−50Sn alloy in ref 10. The second stage sodiation is characterized by a marked increase in the resistivity, such that the resistivity measured from this stage (∼10 Ω·cm) was higher than that of the pristine Sn by more than 6 orders of magnitude. Considering that the phase formed at this stage is the same as that formed during the first-stage sodiation (Figure 1h), the resistivity measured at the second stage is unusual and thus of academic and practical interest. An additional increase in the resistivity (by 2 orders of magnitude as compared to that measured from the second stage) was measured during in the final/third stage. Final-stage sodiation was characterized by the

formation of the a-Na3.75Sn phase, which corresponds to the volume expansion of up to ∼520%.9 This change in the volume promoted the formation of cracks on the surface of the sodiated Sn particle. Cracks formed at the surfaces of the sodiated particles are known to scatter electrons and thus to disturb the charge transfer. This, in general, causes an increase in the resistivity of a typical alloy as much as 2 orders of magnitude, 16,17 which is in good agreement with the experimentally observed value. When we combine the increase in the resistivity measured from all three stages, the resistivity of the pristine Sn increased by 8 orders of magnitude after full sodiation. Considering that the resistivity of the LIB counterpart decreases slightly during the lithiation process,18 the high resistivity measured from the Sn anode is unexpected and is thought to have a close relationship with the structural change associated with the phase transition of the Sn particle. In the following, the phase transition behavior associated with sodiation is discussed with particular emphasis on the second-stage sodiation, which is characterized by the formation of a thick-layered a-NaSn phase and accounts for the largest portion (more than 50%) of the resistivity increase. Formation Mechanism of the Zintl Ion during Sodiation. Owing to their capacity to depict atomic-scale structures and their corresponding properties, atomic simulations have been a powerful technique for exploring the structure−property relationship of a material. Of all the simulation techniques presently available, the first-principles calculation approach provides the most reliable information regarding interatomic interactions. In this section, we explore the structural evolution of the Sn anode of the Na−Sn battery system to investigate the mechanism for the observed change in the resistivity associated with sodiation. Figure 3a shows the full-scale computational cell of the laminated Na−Sn slab used to elucidate the structural evolution of the Sn anode associated C

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Figure 3. (a) Full-scale calculation cell of the laminated Na−Sn slab used for the first-principles calculations. (b−e) Snapshots captured from the simulation results, showing the structural evolution of the Na−Sn slab at the region near the Na/Sn interface during sodiation at (b) 0, (c) 1.2, (d) 8.4, and (e) 28.8 ps. The large and small spheres in (b−e) correspond to the Sn and Na atoms, respectively. In these figures, the chemical bonds within the cutoff distance of 3.2 Å are indicated for the Sn atoms to show the Sn structures, whereas the Sn atoms are colored differently to distinguish the atoms constructing different configurations, that is, networked (in gray) and clustered (in red) structures. (f) Partial RDF and (g) BDF computed for the Sn atoms comprising the structure of the a-NaxSn phase (e) with differing Na contents. Black vertical sticks denote the reference peaks of the ideal Zintl ion, i.e., Sn44− tetrahedron.

Interpretation of the Resistivity Measurement. Referring back to Figure 1, the second-stage behavior associated with the thickening of the a-NaSn phase is of particular interest because it accounts for the largest portion of the resistivity increment during the whole sodiation process. The firstprinciples calculations showed that this increment in the resistivity observed from the second stage arises from the formation of the electrically resistive Zintl ions in the a-NaSn phase (Figure 3f,g). However, the resistivity of the a-NaSn phase formed from the second-stage sodiation (∼10 Ω·cm) is higher than the highest resistivity (3 × 10−3 Ω·cm) of the stress-free Na-50Sn amorphous alloy10 prepared by quenching by approximately 4 orders of magnitude, which is nearly comparable to the typical values exhibited by a semiconducting material. The different resistivities shown by the two different amorphous materials with the same composition suggests the existence of additional factors other than the Zintl ion formation. It is noted from Figure 1 that sodiation is always accompanied by a large volume expansion, which in many cases causes the development of surface cracks on the sodiated particle. This suggests the existence of sodiation-induced stress states, which in turn can distort the shape of the Zintl ion from its ideal configuration. The configurational change of the Zintl ion alters its electronic structure and causes the change in the electrical resistivity of the a-NaSn phase. In order to interpret the high resistivity of the a-NaSn phase formed during secondstage sodiation in conjunction with the stress state, it is necessary to deal with a complex and comprehensive problem that was tackled in this study in three steps: (1) modeling of the core−shell structure of the sodiated particle that incorporates the time-dependent volume change of the constituent phases, (2) calculation of the local stresses using the core−shellstructured model based on the experimentally identified sodiation mechanism, and (3) calculation of the electronic

with sodiation. As shown in the magnified views of the snapshots captured from the simulation results (Figure 3b−e), Na and Sn atoms spontaneously diffuse into each other due to the chemical potential gradients. This spontaneous insertion of Na into Sn proceeds by breaking the Sn bonds, which causes the Na and Sn crystals to evolve into a disordered structure (Figure 3b−e); the structure of the Sn anode is first transformed from a crystal to a networked amorphous structure and eventually to the clustered structure of the Sn atoms (denoted by the red spheres in Figure 3d,e). We next elucidate whether the structural disruption of the Sn anode (Figure 3b−e) promotes the formation of Zintl ions. For this purpose, the model cell in Figure 3e was divided into the three regions according to the Na content in the a-NaxSn phase, with x ranging 0.1 < x < 0.4, 0.4 < x < 1.0, and 1.0 < x < 3.75 (see Supporting Information Figure S1 for the composition profiles). For these three regions, the partial radial distribution function [RDF, g(r)] and the bond-angle distribution function [BDF, g(θ)] were calculated to determine how the structures of the Sn anode evolve to form Zintl ions. With increasing Na content beyond x > 1.0, the interatomic distance and the bond angle of the nearest Sn atom pairs in the sodiated a-NaxSn alloy tended to approach those of the ideal Zintl ion, that is, r = 3.02 Å and θ = 60°, as shown in the RDF and BDF in Figure 3f,g, respectively. This indicates that the tetrahedral Sn clusters have formed in the a-NaSn phase with their atomic configuration slightly distorted from the ideal Zintl ion. An important conclusion drawn here is that the formation of the Zintl ion is feasible in the sodiated Sn particle, even within a very short time. Therefore, Zintl ions can form in large quantity during a real-world sodiation reaction because much longer time is allowed for the formation of the stable phase associated with sodiation. This phase transition would alter the electrical resistivity of the Sn anode, which is discussed in detail in the below. D

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Figure 4. (a) The stress components defined in a spherical coordinate system used for the FE analyses and (b) the analysis results, showing the changes in the radial (σr) and hoop (σθ = σφ) stresses at the subsurface region located at r/R = 0.97 evaluated as a function of the degree of sodiation. (c−e) The schematics in the graph are the sodiated particles corresponding to the three representative stages, where the marked changes in the stress states are observed. Colors are used in the model particles to distinguish the position of the moving phase boundary separated by the two phases, that is, a-Na0.2Sn (in orange) and a-NaSn (in blue).

evaluated at the subsurface region of the particle as defined by r/R = 0.97 (Figure 4), where r and R are the distance measured from the particle center and the radius of the particle, respectively. This treatment is reasonable because, as discussed earlier, the electric current tends to flow across the outer surface layer and thus the electrical resistivity is mainly influenced by the atomic-scale structure of the outer region. Figure 4 shows the results of the FE analyses (for the detailed formulations, refer to Supporting Information Computational Methods), where the stress state evaluated from the subsurface region (r/R = 0.97) continually changes with sodiation (for the stress states calculated for other regions, see Supporting Information Figure S2). These changes are attributed to the relative thickness of the shells, which changed with increasing degree of sodiation; the radial stress evolved to the tension at the initial stage of sodiation, quickly changed to the small compression and converged to zero with the completion of sodiation. On the other hand, the hoop stress exhibited a drastic stress reversal from the initial tension to compression and eventually to tension again upon completion of sodiation. This reversal, exhibited by the hoop stress, is related to the three sequential steps shown in Figure 3; in the early stage of sodiation, when the a-NaSn phase begins to form on the particle surface (Figures 1b and 4c), a tensile stress state develops along the hoop direction. With continuous insertion of Na, the a-NaSn layer thickens and proceeds toward the interior of the particle by forming an a-NaSn/a-Na0.2Sn phase boundary (Figure 4d). The difference in the volume expansions between the two neighboring phases causes the development of compressive stress at the outer surface in the hoop direction (i.e., a biaxial compressive stress of approximately −2 GPa) due to the constraining effect of the interior a-Na0.2Sn phase. When sodiation proceeds over a prolonged period of time, the sodiated particle mainly consists of a thick a-NaSn phase (Figure 4e). At this stage, the newly formed a-NaSn phase at the phase boundary pushes the pre-existing a-NaSn shell outward, resulting in the development of tensile stress along the hoop direction. Continued sodiation intensifies this “push-out” effect19 until the value of the biaxial tensile stress converges to saturation at ∼2 GPa along the hoop direction. The existence of the tensile hoop stress on the surface is evidenced by the formation of surface cracks developed on the

structure (or band gap) and the corresponding resistivity of the Zintl ion under the sodiation-induced stress states. Modeling of the Sodiated Sn Particle for the Residual Stress Calculation. During sodiation, Na diffusion to the Sn particle always proceeds from the surface to the interior, during which various NaxSn phases form. Because the compositions of the phases are different from each other, the volume expansion rates of the phases are also different, leading to the development of locally inhomogeneous stresses. FEM is a large-scale simulation technique, which makes it suitable for predicting and tracing the evolution of the stress states in the sodiated Sn particle as a function of the degree of sodiation. To construct a simple FEM model that well describes the structural evolution of the sodiated particle, we once more discussed the structures of the sodiated particles obtained from the first and second stages of sodiation. This is because the Zintl ions formed at these stages account for 75% of the resistivity increase (see the analysis for Figure 3). Although the actual core−shell structure of the sodiated particle may consist of more than three phases (Figure 1h), we simplified this multilayered core−shell structure to a twolayered structure consisting of an outer a-NaSn shell and an inner a-Na0.2Sn core. This is because the stress development and its evolution within the sodiated particle are mainly governed by the combined effects of the relative thicknesses of the a-NaSn shell and the a-Na0.2Sn core and the differences in their volume expansions. Furthermore, the electrical resistivity is largely governed by the structure of the Zintl ions formed at the outer shell of the sodiated particle through which the majority of the electric current would flow. Therefore, this twolayer simplification is considered to be reasonable for tracing the evolution of the stresses. Stress Evolution in the Sodiated Sn Particle. From observation of the morphological changes in the Sn particle during sodiation (Figure 1 and Supplementary Movies 1, 2 and 3), the sodiated particle swells in a spherically symmetric manner with no significant distortion from its initial shape, indicating that normal stresses are the dominant type of stress in the spherical coordinate system. Therefore, we ignored the shear stress and only calculated the principle stresses, that is, the radial stress (σr) and hoop (or tangential) stress (σθ = σφ), as a function of the degree of sodiation. These stresses were E

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Nano Letters sodiated Sn particle (Figure 1d). Upon the generation of cracks, constraints responsible for the formation of the biaxial stress state are relieved, which can transform the biaxial stress state to a uniaxial stress state. From a mechanics perspective, any stress state other than the hydrostatic state can produce a deviatoric stress component and thus can distort the shape of the Zintl ion from its ideal configuration. This change in the structure of the Zintl ion would then alter its band gap and the corresponding resistivity of the sodiated particle. This scenario may serve as the basis of why the sodiated particle exhibits unusually high resistivity associated with the formation of the aNaSn phase, which is tested in detail in the following by correlating the level of the local stress states to the band gap and the resistivity of the Zintl ion. Effects of the Sodiation-Induced Stresses on the Band Gap of the Zintl Ion. In order to assess the effect of stress on the increased resistivity of the a-NaSn phase, it is necessary to evaluate the electronic structures of the a-NaSn phase or, more specifically, the band gap of the electrically resistive Zintl ion. However, modeling the a-NaSn phase by direct simulation of the sodiation process requires enormous computational time and , if not impossible, a significant challenge. Furthermore, Zintl ions in the a-NaSn phase are present as distorted Sn clusters embedded in randomly arranged Na atoms, leading to complicated electronic structures (referred to as the “pseudogap”12) that make it difficult to establish the residual stress versus resistivity relation of the a-NaSn phase. An alternative approach to evaluating the stress dependence of the electronic structure of the a-NaSn phase is, therefore, to use the crystalline NaxSn phase, which not only has a chemical composition and atomic configuration similar to those of the a-NaSn phase but also allows the estimation of its band gap. Of all known NaxSn phases, the β-NaSn phase, which is the low-temperature crystalline phase with the same composition as the a-NaSn phase, has an atomic structure similar to that of the a-NaSn phase as evaluated by the RDF and BDF analyses (Supporting Information Figure S3). Furthermore, unlike other NaxSn phases, the β-NaSn phase has a band gap that mainly originates from its ideal Zintl ion (Supporting Information Figure S4). Therefore, the evaluation of the stress dependence on the value of the band gap of the β-NaSn phase would provide insight into how the sodiation-induced stresses influence the resistivity of the a-NaSn phase. Figure 5a shows the model cell of the β-NaSn phase used to predict the changes in the structure of the Zintl ions and their band gap as a function of different levels of the uniaxial (σuni) and the biaxial (σbi) stress. Before evaluating the band gap of the Zintl ion, the structural change (or distortion) of the Zintl ion was quantified by the difference in the bond length (|Δl|) between the atomic pairs in the ideal and the distorted Zintl ions. Figure 5b shows the changes in |Δl| of the Zintl ions evaluated as a function of the stress. As the uniaxial and the biaxial stress were applied to the model alloy, the value of |Δl| increased linearly to 0.02 Å. The increment in the |Δl| values was more pronounced under uniaxial stress, indicating that the structural change became greater after the formation of surface cracks in the sodiated Sn. Considering that the bond length is directly related to the relative positions of the conduction and the valence band,21 this structural change can influence the band gap of the Zintl ion and thus the electrical resistivity of the a-NaSn phase. Figure 5c shows the changes in the band gap of the Zintl ion calculated as a function of the stress. As the stress increased from 0 to 2 GPa, the band gap of the Zintl ion

Figure 5. (a) Supercell structure of the β-NaSn crystal, which is fully of with the ideal Zintl phase (for a detailed configuration of the ideal Zintl phase, see ref 20). The effect of the uniaxial and biaxial stresses on the change in (b) the structure (|Δl|) and (c) the band gap (Eg) of the Zintl ion.

increased from 0.28 to 0.37 eV under biaxial stress and from 0.23 to 0.45 eV under uniaxial stress. Considering that the resistivity (ρ) of a semiconducting material is related to its band gap according to the canonical equation ρ = ρoT−3/2exp(Eg/ kT),22 the increased band gap evaluated in this study is equivalent to an increase in the resistivity of 2−3 orders of magnitude. Although the present analysis underestimates the actual increment in the resistivity of the a-NaSn phase obtained from experiments, it explains why the a-NaSn phase formed during second-stage sodiation exhibits a resistivity higher than those of the a-NaSn phase formed during first-stage sodiation and the Na−50Sn amorphous alloy prepared by quenching. Further molecular orbital analysis showed that the increment in the band gap of the Zintl ion stemmed from the change of the Sn 2p orbitals, which are the main components of the conduction and valence orbitals (Supporting Information Figure S5). When the bond length of the Zintl ion increased, the conduction level greatly increased due to its concentrated Sn 2p bonding orbitals, causing the band gap to increase (Supporting Information Figure S6). The present interpretation on second-stage (and third-stage) sodiation shows that the stress developed during sodiation is the major reason for the increased resistivity of the Sn anode, accounting for nearly 75% of the resistivity increase. In order to improve the energy efficiency of Na−Sn batteries, it is therefore necessary to develop the structure of anode materials that can diminish the sodiation-induced stress. The use of the nanostructured Sn anode (e.g., hollow nanoparticle, porous structure)23,24 or/and the mechanical buffers (e.g., graphene, wood fiber)8,25−27 have been applied to LIBs as a means of reducing the stress and thus improving the energy efficiency of the batteries. Therefore, these two methods can also yield a F

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Density Functional Theory Calculations. Car−Parrinello simulations28 were performed under a canonical ensemble to simulate the sodiation process. Norm-conserving pseudopotentials with Perdew−Burke−Ernzerhof (PBE)29 exchangecorrelation developed by Troullier and Martins were treated as implemented in Quantum Espresso.30 A cutoff energy of 30 Ryd was set for the plane wave expansion and only the gamma point was sampled. The energy convergence was achieved down to 0.2 Ry/unit cell. The temperature during our calculations was fixed at 300 K using the Nosé−Hoover thermostat technique.31 The Verlet algorithm was used to solve classical equations of motion for 28.8 ps with a time step of 0.12 fs. RDF and bond-angle distributions obtained from the CPMD calculations were averaged over a time interval of 1.2 ps. The detailed atomic configurations of the Na−Sn slabs are provided in the description of the computational method in the Supporting Information. We further evaluated the effects of external stress on the band gap of the Zintl ion to evaluate the effect of the sodiationinduced stress on the resistivity of the a-NaSn phase. This calculation was performed using density functional theory with the plane-wave basis set and projector augmented wave (PBE− PAW) pseudopotentials29,32 as implemented in the Vienna ab initio simulation package (VASP).33 We used the Monkhorst− Pack scheme for the Brillouin zone sampling, and the k-point mesh was set to 6 × 6 × 6. The plane wave cutoff energy was set to 300 eV and the total energy convergence was achieved within 10−5 eV. Finite Element Analyses. The sodiation-induced stresses of the sodiated particle were calculated using a simplified twophase core−shell model consisting of the a-Na0.1Sn core and the a-NaSn shell. The stress state of the sodiated particle was computed by FEM using the COMSOL package.34 Following the study on stress generation during lithiation by Huang et al.,35 the sodiation-induced stress was calculated by solving three coupled partial differential equations and the parameters (see Supporting Information for detailed calculation methods). Note that providing precise parameters for stress analyses is difficult due to the lack of experimental measurements on the Na−Sn system. Instead, we focused on the essential physical effects of sodiation on the stress generation by assuming reasonable values for the target parameters. The Young’s modulus E (GPa) of the a-NaxSn phase was assumed to follow the mixture rule, which incorporates the Young’s modulus of Sn (50 GPa) and Na (10 GPa) and the relative Na composition c that varies from 0 (pure Sn) to 1 (pure Na). For example, as the value of c increased from 0.16 (a-Na0.2Sn) to 0.50 (a-NaSn), the Young’s modulus decreased from 43.33 to 30 GPa. The yield stress, σY, and Poisson’s ratio, v, were chosen to be 0.05E and 0.3, respectively. On the basis of a previous study on the volumetric expansion of sodiated Sn,9 the sodiated expansion coefficient βr (= βθ) was assumed to be ∼0.24, which yielded a volume increase of ∼90%. Assuming that the stress states induced by the sodiation process are rate-independent, the rate sensitivity exponent, m, and the effective strain rate constant,

likely solution for rational design of anode materials for NIBs because they are the structure that can readily accommodate the stress caused by the volume expansion associated with charging and discharging. A systematic future work is necessary on this issue. In conclusion, in situ sodiation experiments on the Na−Sn battery system showed that the continuous and spontaneous insertion of Na takes place in three characteristic stages. Sodiation begins by the formation of a thin a-NaSn layer at the surface. Over time, the a-NaSn layer grows thicker with the formation of a new a-Na0.2Sn phase at the interior, resulting in a core−shell structure. Further sodiation transforms the a-NaSn phase to the a-Na3.75Sn phase, which in most cases induces cracks on the particle surface. The phase transition observed for each stage of sodiation causes the resistivity to increase, such that after full sodiation, the resistivity of the sodiated Sn is higher than that of pristine Sn by 8 orders of magnitude. This increment is largely attributed to the formation of the a-NaSn phase (the Zintl ions), which is formed at the surface of the Sn anode during the first- and the second-stage sodiation. However, the increment in the resistivity is more pronounced in the second-stage, during which the a-NaSn/a-Na0.2Sn core− shell structure forms. The core−shell structure develops the residual stresses to a significant level (∼2 GPa) at the surface of the sodiated Sn particle. The stress, in turn, induces the distortion of the Zintl ion from its ideal configuration, causing the change in the band gap structure, thus resulting in the increased resistivity of the sodiated Sn. Methods. In Situ Sodiation Experiment. In order to promote in situ sodiation of Sn while preventing the oxidation of Na, Na and Sn metals were prepared inside an air-free chamber with dual-beam FIB (Quanta3D FEG, FEI) and a nanomanipulator (MM3A-EM, Kleindiek Nanotechnik). Lumps of pure Na (>99%) and Sn particles (>99%, ∼10 μm) were used as the target materials. They were moved using the nanomanipulator with W tips (100 nm in diameter). In order to circumvent the oxidation of Na during the sampling process, we manually sealed Na with high purity Ar (>99.999%) and transferred it into the FIB chamber by using cryotransfer (ALTO 2500, Gatan Inc.). Using two-point probe method, the change in the resistance of the Sn particle was measured during sodiation while simultaneously observing the morphological change. The resistance measurement of the sodiated Sn was carried out by connecting the W probes to a potentiostat (B1500A, Keysight Technologies Ltd.) at a fixed potential of 0.1 V. The measured resistance was then converted to the resistivity value by incorporating the geometry of the sodiated Sn particle. The resistivity was then calibrated by comparing it to that of the pristine Sn. In order to identify the composition of the a-NaxSn phases inside the sodiated Sn particle, we first manually interrupted the sodiation process by exposing it to oxygen. We then coated the sodiated Sn particle with Pt, cut by ion milling (PIPS Model 691, Gatan lnc.), and measured the composition of all possible elements (Na, Sn, O, Pt, and Ga) by using energy dispersive Xray spectroscopy (EDS, SDD Sirius SD, EDAX Inc.). The composition of the sodiated layer was identified by extracting the composition of O, Pt, and Ga from the measurement. The electric current applied by SEM and EDS was controlled to be lower than usual (5 keV and 37 pA for SEM and 5 keV, 3.9 nA for EDS) to minimize electron beam damage on the target materials.15

·

ε0p, were chosen to be 0.01 and 0.001, respectively.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b03690. G

DOI: 10.1021/acs.nanolett.6b03690 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

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Additional information and figures (PDF)

(22) https://www.sccs.swarthmore.edu/users/02/lisal/physics/labs/ lowtemp.pdf, accessed on [01-06-2017]. (23) Kim, C.; Lee, K.-Y.; Kim, I.; Park, J.; Cho, G.; Kim, K.-W.; Ahn, J.-H.; Ahn, H.-J. J. Power Sources 2016, 317, 153−158. (24) Sun, H.; Xin, G.; Hu, T.; Yu, M.; Shao, D.; Sun, X.; Lian, J. Nat. Commun. 2014, 5, 4526. (25) Zhang, C.; Wang, X.; Liang, Q.; Liu, X.; Weng, Q.; Liu, J.; Yang, Y.; Dai, Z.; Ding, K.; Bando, Y. Nano Lett. 2016, 16, 2054−2060. (26) Sun, J.; Lee, H.-W.; Pasta, M.; Sun, Y.; Liu, W.; Li, Y.; Lee, H. R.; Liu, N.; Cui, Y. Energy Storage Mater. 2016, 4, 130−136. (27) Sun, J.; Lee, H.-W.; Pasta, M.; Yuan, H.; Zheng, G.; Sun, Y.; Li, Y.; Cui, Y. Nat. Nanotechnol. 2015, 10, 980−985. (28) Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471. (29) Perdew, J.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396. (30) Troullier, N.; Martins, J. L. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 43, 1993. (31) Hoover, W. G. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695. (32) Kresse, G.; Joubert, D. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758. (33) Kresse, G.; Furthmüller, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169. (34) Multiphysics, C. Structural Mechanics Module User’s Guide; 2013. http://hpc.mtech.edu/comsol/pdf/Structural_Mechanics_Module/ StructuralMechanicsModuleUsersGuide.pdf (accessed Jan 12, 2017). (35) Huang, S.; Fan, F.; Li, J.; Zhang, S.; Zhu, T. Acta Mater. 2013, 61, 4354−4364.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Young-Woon Byeon: 0000-0003-2684-7720 Jae-Chul Lee: 0000-0002-9294-2163 Author Contributions

Y.S.C. and Y.W.B. contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the computational supports provided by KIST, Korea and IMR at Tohoku University, Japan. We are also grateful to Dr. Kahyun Hur and Dr. Seung-Yeol Jeon at KIST for their computational supports to the present study. This work was supported by the institutional program (Grant K1617531) funded from Korea University and the institutional program (Project No. 2E26330) funded from KIST.

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REFERENCES

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DOI: 10.1021/acs.nanolett.6b03690 Nano Lett. XXXX, XXX, XXX−XXX