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Journal of Power Sources 285 (2015) 29e36

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Journal of Power Sources

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High capacity group-15 alloy anodes for Na-ion batteries:Electrochemical and mechanical insights

Majid Mortazavi, Qiongjie Ye, Nick Birbilis, Nikhil V. Medhekar*

Department of Materials Engineering, Monash University, Clayton, Victoria 3800, Australia

h i g h l i g h t s

� High-capacity group-15 alloy anodes have been characterized for Na-ion batteries.� Electrochemical properties of the alloy anodes have been obtained.� Elastic behavior of the alloy anodes upon increasing sodiation has been studied.� Sodiation-induced elastic softening up to 60% is found for these alloys anodes.� Our results provide preliminary steps towards the design of failure-free anodes.

a r t i c l e i n f o

Article history:Received 17 December 2014Received in revised form1 February 2015Accepted 8 March 2015Available online 14 March 2015

Keywords:Na-ion batteries (NIBs)Alloy anodesElectrochemical propertiesElastic propertiesDensity functional theory (DFT)

* Corresponding author.E-mail address: nikhil.medhekar@monash.edu (N.

http://dx.doi.org/10.1016/j.jpowsour.2015.03.0510378-7753/© 2015 Published by Elsevier B.V.

a b s t r a c t

Group-15 elements phosphorus, arsenic, antimony and bismuth offer the prospect of serving as func-tional alloying elements for developing high-capacity alloy anodes for sodium-ion batteries (NIBs). Herewe obtain concentration-dependent electrochemical properties of sodium (Na) alloys with group-15elements using first principles calculations. Since Na intercalation in these alloys is accompanied by asubstantial volume expansion that can lead to mechanical failure and loss of capacity, we have alsoobtained a full set of concentration-dependent elastic properties for a single crystal as well as a poly-crystalline microstructure. We find that sodiation of these alloys results in their significant elasticsoftening by as large as 60%. In contrast to the group-14 alloys that are also being explored as anodes ofNIBs, the elastic softening in group-15 alloys varies in a non-monotonic manner with Na concentration,and more importantly, the maximum degradation of elastic properties does not necessarily occur at fullsodiation. Our results provide crucial insights into the electrochemical and mechanical response of thesealloys to Na intercalation, thus contributing to the design of failure-resistant architectures of high ca-pacity NIBs.

© 2015 Published by Elsevier B.V.

1. Introduction

Lithium-ion batteries, on account of their high volumetric andgravimetric capacities, are currently seen as the only viable next-generation energy storage solutions for portable electronic de-vices and hybrid vehicles [1,2]. Despite their increasingly wide-spread use, concerns regarding the availability of lithium resourcesand their uneven distribution across the world are growing [3]. Asan alternative to lithium-ion batteries, sodium-ion batteries (NIBs)are particularly attractive due to the abundance of sodium (Na) aswell as its electrochemical similarities with lithium. In addition, Na

V. Medhekar).

is environmentally benign, thus promising a safer and more sus-tainable energy storage [4]. Although NIBs are unlikely to outper-form lithium-ion batteries in terms of volumetric and gravimetricenergy densities, they are being actively pursued for applicationslike low-cost grid-based energy storage where the size or weight ofa battery is not the most critical factor [4,5].

In spite of a significant progress in developing positive elec-trodes (cathodes) for NIBs, identifying a high-performing negativeelectrode (anode) remains a key challenge [5,6]. Materials investi-gated so far as active materials for Na-ion anodes can generally beclassified into three categories: (i) layered materials such as tita-nates, phosphates and transition metal dichalcogenides with aspecific capacity in the range of 50e250 mA h g�1 [7,8], (ii) carbon-based materials, for example, hard carbons with a maximumreversible capacity of 350 mAh g�1 [5,8], and (iii) nanostructures

M. Mortazavi et al. / Journal of Power Sources 285 (2015) 29e3630

like hollow nanowires and spheres, reduced graphene oxide anddoped carbon nanosheets offering a maximum capacity of300 mAh g�1 [5,8]. Despite these advances, practical application ofthese materials remains limited due to a low specific capacity aswell as a poor rate performance [8,9]. In contrast, various alloys ofNa can potentially enable the design of high-performance anodesfor NIBs due to their excellent specific capacity for Na ion [8,9].

A number of recent experimental studies have establishedintercalation of Na under electrochemical setting (sodiation) ingroup-14 and group-15 elements [10e14]. For example, anodes ofNa alloys with group-14 elements Si, Ge, Sn and Pb show amaximum specific capacity in the range of 350e850 mA h g�1 atroom temperature in an electrochemical setting with NaClO4 pro-pylene carbonate electrolyte, fluoroethylene carbonate additiveand polyacrylate binder [10e12,15e18]. Very recent experimentshave demonstrated that alloying with group-15 elements such as P,As, Sb and Bi allows for even greater specific capacities than ingroup-14 elements [9,13,14]. For instance, elemental black phos-phorus (P) with polycarbonate electrolyte gives a maximum spe-cific capacity of 2560 mAh g�1dthe highest specific capacity everreported for anodes of NIBs [13]. Similarly, a maximum capacity inexcess of 1073, 600 and 385mAh g�1 can be obtained for As, Sb andBi at full sodiation, respectively [13,14,19e21]. Furthermore, Dar-wiche et al. recently reported an unexpectedly better cycling per-formance of Na ions compared with Li ions at room temperature inSb with 1 M NaClO4 in PC or 1 M LiPF6 in EC:PC:3DMC electrolyte[19]. Their results suggest that alloys of group-15 elements as an-odes for NIBs may outperform those for Li-ion batteries. These earlyreports of a promising electrochemical performance motivate thedevelopment of Na alloys with group-15 elements as high perfor-mance anodes for NIBs.

While a large specific capacity of Na alloys with group-15 ele-ments underpins their potential application as anodes, ion incor-poration in such alloys is generally characterized with substantialvolume expansion during charge and equivalent contraction duringdischarge. These repetitive volume changes under the constraintsimposed by the battery packaging give rise to complex mechanicalstresses in active particles, ultimately leading to their fracture orpulverization [8,9,22]. Experiments have conclusively shown thatsuch mechanical failures are responsible for a complete loss ofelectrochemical capacity in alloy anodes, and thus largely hindertheir practical application in rechargeable batteries [8,9,22e25]. Itis therefore vital to fully understand the mechanistic behavior ofalloy anodes during cycles of charge and discharge. To this end, anumber of models have been developed to analyze intercalationinduced mechanical deformation at the macroscopic level [26e29].These models typically require the knowledge of the intrinsicelastic behavior upon intercalation as a fundamental preliminaryinput, which can then be used to predict the stress evolution andthe mechanisms of subsequent mechanical failure [26e29]. Whilestudies so far investigating the mechanical stability of alloy anodeshave focused on high-capacity Li-ion anodes [30e35], the me-chanical response of Na alloys to sodiation and desodiation remainslargely unexplored. In an earlier work, we investigated the funda-mental elastic properties of the group-14 alloys [16]. More recently,Zhu et al. presented a continuum chemo-mechanical model toexplore morphology and stress evolution of Sn during sodiationand desodiation [36]. However, a systematic understanding of themechanical response of high capacity group-15 alloys to sodiationis yet unknown.

Here we investigated the intrinsic, concentration-dependentelectrochemical and elastic behavior of Nax M (M ¼ P, As, Sb andBi) alloy anodes using first principles calculations. All crystallinephases that appear in the equilibrium binary phase diagrams of Nawith group-15 elements were considered. It has been reported that

alloying P with Na leads to the formation of Na3 P11, NaP and Na3 Pphases [37]. Three binary phases exist for NaeAs system, namely,Na3 As7, NaAs and Na3 As [38], while only two intermetallic phasesare formed upon mixing Sb or Bi with Na, namely, NaSb and NaSb3,and NaBi and NaBi3, respectively [39,40]. For all these phases, weobtained fundamental electrochemical properties along with theelastic constants for single crystal as well as polycrystalline mi-crostructures. Our calculated values of the electrode potentials andvolumetric energy densities agree well with experimental mea-surements. Our results show that while the elastic strength ofgroup-15 alloys generally degrades upon sodiation, the evolution ofthe elastic properties is highly distinct fromwhat has been reportedin the case of group-14 Na alloys.

2. Methodology

All calculations were performed using spin-polarized densityfunctional theory (DFT) within the GGA-PBE approximation asimplemented in Vienna Ab Initio Simulation Package [41,42].Projector-augmented wave potentials were used to describe coreand valence electrons [43]. The 2p63s1, 3s23p3, 4s24p3, 5s25p3 and6s26p3 states were treated as valence electrons for Na, P, As, Sb andBi, respectively. We used a plane-wave kinetic energy cutoff of600 eV and the Gamma-centered k-point mesh method for sam-pling the Brillouin zone for all structural phases. Convergence testswith respect to kinetic energy cutoff and k-point meshwere carriedout to ensure the total energy converges within 1 meV/atom. Theinitial crystal structures for all phases were taken from the CrystalStructure Database [37e40]. The crystal structures were thenoptimized by allowing the lattice cell vectors and the ionic posi-tions to relax until the HellmanneFeynman forces were less than0.01 eV/Å. Bader charge population analysis was used to calculatethe net charges on each atom [44].

For each optimized structure, we calculated the formation en-ergy Ef with respect to Na/Naþ as Ef¼ E(NaxM)�[xE(Na)þ E(M)].Here, x is the number of Na atoms per M atoms of Nax M phase,E(NaxM) is the total energy per M atom of Nax M phase, E(Na) is theper atom total energy Na in bcc crystal structure, and E(M) is the peratom total energy of M in its elemental crystal structure. The valuesof the optimized structural parameters, formation energy, and thek-pointmesh used for sampling the Brillouin zone of each phase aregiven in Table 1. The lattice parameters obtained from our calcu-lations are in close agreement with earlier experimental andtheoretical studies [37e40,45,46]. Next, we calculated the electrodepotential for the Nax M phases with respect to Na/Naþ as F¼�Ef/x,and the specific capacity as q ¼ nF=

PM, where n is the total

number of electrons transferred, F is Faraday's constant(26.802 Ah mol�1) and

PM is the molecular weight of the asso-

ciated phase. The volumetric energy density for the Nax M phasewas then obtained as

Q ¼ FkVavg

xf

1þ xf

!; (1)

where k is the volume occupied by Na (17.8 ml mol�1), Vavg is theaverage potential of all NaeM phases obtained from our DFT cal-culations versus a hypothetical 3.75 V cathode, and xf is the finalvolume expansion at full sodiation [47].

In order to calculate the second order elastic constants of Nax Mphases, a specific set of small deformations was applied dependingon the crystal symmetry of each phase [48]. The internal strainenergy of the crystal U as a function of the homogeneous strain fieldε can be written in a simplified-form as

Table 1Equilibrium lattice parameters (a, b, and c, in Å), volume of the unit cell (in�A

3) and

formation energy Ef (in eV) for Nax M (M ¼ P, As, Sb and Bi) alloys as obtained fromour DFT calculations. The details of k-points mesh used for sampling the irreducibleBrillouin zone of each phase are also given.

Phase x Spacegroup

a b c Volume Ef k-pointsmesh

NaePP 0.00 Cmce 3.32 10.46 4.42 153.77 0.00 11� 5� 11Na3 P11 0.27 Pcnb 9.92 12.63 10.61 1329.41 �0.25 5� 5� 5NaP 1.00 P21 21 21 5.67 6.06 10.16 349.09 �0.39 11� 11� 5Na3 P 3.00 P63/mmc 4.97 4.97 8.86 189.83 �0.34 11� 11� 7Na ∞ Im3m 4.21 4.21 4.21 74.63 0.00 11� 11� 11NaeAsAs 0.00 R 3 m 3.81 3.81 10.83 136.51 0.00 11� 11� 5Na3 As7 0.43 P21/c 15.76 11.17 14.48 2295.21 �0.27 3� 5� 3NaAs 1.00 P21 21 21 6.00 6.30 10.58 400.18 �0.39 7� 7� 5Na3 As 3.00 P63 cm 8.83 8.83 9.06 612.51 �0.42 7� 7� 7Na ∞ Im3m 4.21 4.21 4.21 74.63 0.00 11� 11� 11NaeSbSb 0.00 R 3 m 4.37 4.37 11.49 190.81 0.00 11� 4� 11NaSb 1.00 P21/c 6.82 6.42 12.59 490.07 �0.31 11� 4� 11Na3 Sb 3.00 P63/mmc 5.38 5.38 9.51 238.94 �0.44 11� 4� 11Na ∞ Im3m 4.21 4.21 4.21 74.63 0.00 11� 4� 11NaeBiBi 0.00 R 3 m 4.58 4.58 12.15 221.16 0.00 11� 11� 5NaBi 1.00 P4/mmm 3.45 3.45 4.91 58.57 �0.30 11� 11� 11Na3 Bi 3.00 P63/mmc 5.48 5.48 9.75 254.56 �0.38 11� 11� 7Na ∞ Im3m 4.21 4.21 4.21 74.63 0.00 11� 11� 11

Fig. 1. Calculated electrode potential profiles with respect to Na/Naþ for Nax M phases.Experimental data for NaeP [13], NaeSb [19], and NaeBi [14] phases at room tem-perature with respect to metallic Na/Naþ are also shown.

M. Mortazavi et al. / Journal of Power Sources 285 (2015) 29e36 31

UðεÞ ¼ Uð0Þ þ V0

2

Xij

Cijεiεj þ O�ε3i

�; (2)

whereU(0) and V0 are the internal energy and volume of the crystalat zero strain [49], respectively, and ε and Cij are the strain and thesecond order elastic constants in Voigt notation, respectively [48].The internal energy of the crystal obtained from our DFT calcula-tions can also be expressed in the form of a second-order poly-nomial as a function of the applied strain. By comparing the secondorder coefficients of the polynomial with the components of Eq. (2),the elastic constants Cij s of the crystalline phase can be readilyobtained [49]. Following the determination of all single crystalelastic constants, we calculated polycrystalline elastic propertiessuch as Young's, bulk and shear moduli of Nax M phases as afunction of Na concentration by employing Hill's averaging tech-nique [50]. Finally, the evolution of electronic charge distributionand interatomic bonding was studied to explain the concentration-dependent elastic behavior of Nax M phases.

Fig. 2. Volumetric energy density (Wh cc�1) as a function of volume expansion for NaxM (M¼ P, As, Sb and Bi) phases. The values for the volumetric energy density of Na15Sn4 [15] and hard carbon [51] are shown for comparison. The inset shows the volumeexpansion of the Nax M phases as a function of Na concentration.

3. Results and discussion

3.1. Electrochemical properties of NaeM alloy anodes

The electrode potential profiles with respect to Na/Naþ for NaxM (M ¼ P, As, Sb and Bi) alloys obtained from our DFT calculationsare shown in Fig. 1. Experimentally measured potential valuesavailable in the literature for NaeP [13], NaeBi [14] and NaeSb [19]systems are also shown for comparison. Our calculated potentialprofiles are consistent with the experimental data. The calculatedelectrode potential varies within the range of 0.4e1.2 V for NaePsystem, 0.5e1.0 V for NaeAs, and within a narrow range of0.58e0.62 V and 0.50e0.62 V for NaeSb and NaeBi, respectively.While the measured electrochemical potentials can vary with anumber of parameters such as temperature, electrolyte type andconcentration, and cell environment, the predicted potentialsshown in Fig. 1 represent the intrinsic electrode potentials of Nax M

(M ¼ P, As, Sb and Bi) alloys under typical NIB conditions [8]. Anarrow range and lowmagnitudes of the electrode potentials pointto the suitability of group-15 Nax M alloys as anodes for NIBs.

Fig. 2 shows calculated volumetric energy densities of Nax Mphases as a function of the volume expansion upon increasingsodiation. It is clear that the volumetric energy densities for Naalloys with all group-15 elements follow a similar path. Thisobservation can be attributed to the similar volume occupied by Naions in all Nax M alloys, as given by the slopes of the volumeexpansion versus Na concentration curves shown in the inset ofFig. 2. It is also evident from Fig. 2 that a maximum volumetricenergy density of ~3.5 Wh cc�1 can be achieved for all group-15alloy anodes at full sodiation. This maximum volumetric energydensity exceeds that of hard carbons as the high capacity carbo-naceous material for anodes of NIBs (1.75 Wh cc�1 [51]), while it iscomparable to group-14 alloy anodes such as Sn [15]. The volu-metric energy densities of group-15 alloys for Na ions, however, aremuch lower than those of Si and Sn for Li ions due to the twofoldlarger volume occupied by Na ions compared to Li ions [15].Nevertheless, these results suggest that in order to achieve largevolumetric energy densities and low electrode potentials for group-15 alloys shown in Figs. 1e2, strategies to mitigate the effects oflarge volume changes in phases with higher Na fractions will needto be identified. Therefore, a knowledge of the mechanisticbehavior of the group-15 alloys with increasing sodiation will becritical for their practical application as active materials for high

Table 3

M. Mortazavi et al. / Journal of Power Sources 285 (2015) 29e3632

capacity anodes of NIBs.

Bulk modulus (B), Young's modulus (E), shear modulus (G) and Poisson's ratio (n) ofpolycrystalline Nax M alloys obtained using Hill's averaging method. AU denotes theuniversal anisotropy factor. All moduli are in GPa.

Phase y BH EH GH n BH/GH AU

NaePP 0.00 37.4 67.6 28.4 0.21 1.3 5.9Na3 P11 0.21 14.0 18.1 7.08 0.28 2.0 0.4NaP 0.50 26.8 33.1 12.8 0.30 2.1 0.8Na3 P 0.75 24.7 40.3 16.4 0.22 1.5 0.5Na 1.00 7.40 7.15 2.70 0.33 2.7 6.4NaeAsAs 0.00 37.8 63.4 26.0 0.21 1.4 5.1Na3 As7 0.30 8.4 19.2 9.2 0.12 0.9 3.2NaAs 0.50 23.9 19.4 7.2 0.36 3.3 4.4Na3 As 0.75 18.3 24.8 9.8 0.27 1.8 1.5Na 1.00 7.40 7.15 2.70 0.33 2.7 6.4NaeSbSb 0.00 34.9 58.8 22.7 0.22 1.4 2.4NaSb 0.50 18.6 23.7 9.2 0.28 2.0 0.5Na3 Sb 0.75 19.4 31.4 12.7 0.23 1.5 0.7Na 1.00 7.40 7.15 2.70 0.33 2.7 6.4NaeBiBi 0.00 30.0 28.4 10.6 0.34 2.8 3.9NaBi 0.50 27.3 29.7 11.3 0.32 2.4 0.2Na3 Bi 0.75 17.2 26.4 10.6 0.24 1.6 0.6Na 1.00 7.40 7.15 2.70 0.33 2.7 6.4

Table 4Experimental values of the elastic moduli and the Poisson's ratios for polycrystallineNa, Sb and Bi [53] and As [55]. All moduli are in GPa.

Phase BH EH GH n BH/GH

Na 7.3 7.9 3.0 0.32 2.4As 52.8 50.4 20.0 0.33 2.6Sb 37.8 56.8 24.1 0.25 1.4Bi 34.8 33.1 12.4 0.33 2.8

3.2. Elastic properties of NaeM alloy anodes upon sodiation

Table 2 presents second order elastic constants of crystalline NaxM (M ¼ P, As, Sb and Bi) phases as obtained from our calculationsalong with the experimental measurements for pure Na, P, As, Sband Bi phases [52e55]. Our calculated elastic constants are in anexcellent agreement with experimental values for Na, and arewithin 10% of the experimental values for P, As, Sb and Bi. It shouldbe noted that the elastic constants given in Table 2 correspond to asingle crystal structure of the Nax M phases, while the microstruc-ture of an active anode material is polycrystalline [56]. Therefore wehave obtained Young's modulus (E), shear modulus (G) and bulkmodulus (B) as well as Poisson's ratio (n) for polycrystalline Nax Mphases using Hill's averaging method [50], as shown in Table 3. Forcompleteness, the experimental values of elastic moduli and Pois-son's ratios for pure polycrystalline Na, P, As, Sb and Bi are alsogiven in Table 4 [52e55]. Our results for the elastic properties ofpure, polycrystalline phases obtained from first principles calcual-tions are also in a reasonably good agreement with the experi-mental measurements.

In order to gain an insight into the concentration-dependentelastic behavior of Nax M phases, the Young's and shear moduliare plotted as a function of the Na fraction y in Fig. 3. Here, y¼ 0 andy¼ 1 represent pure M and Na, respectively. While increasingsodiation generally leads to elastic softening in all M phases, thisbehavior is characterized by two remarkable observations: (i)Young's and shear moduli vary in a non-monotonic manner withincreasing Na fraction, and (ii) fully-sodiated phases are generallynot the most elastically soft phases. For example, upon initialsodiation of P leading to the formation of Na3 P11 phase (y~ 0.21),the Young's and shear modulus decreases abruptly by 75%. Uponfurther increasing sodium concentration, moduli gradually increasefor subsequent phases. At full sodiation (Na3 P, y~ 0.75), the moduliare larger by more than 120% with respect to Na3 P11, the weakest

Table 2Second order elastic constants Cij s (in GPa) for single crystal Nax M (M¼ P, As, Sb and Bi) phases obtained from our DFT calculations. Experimental values of Cij s for pure Na, P,As, Sb and Bi phases are also included.

Phase C11 C22 C33 C44 C55 C66 C12 C13 C23 C15 C25 C35 C46 C14

NaePP 179.8 70.5 48.1 5.4 65.0 46.72 10.5 42.8 1.6P (Exp [52]) 178.6 55.1 53.6 5.5 14.5Na3 P11 32.2 21.3 19.2 8.5 5.9 7.5 11.0 6.3 10.5NaP 51.8 42.4 43.5 7.4 24.4 9.5 18.2 19.5 15.4Na3 P 52.0 52.0 58.8 11.8 17.7 16.5 6.6Na 8.4 8.4 8.4 5.7 5.7 5.7 6.8 6.8 6.8Na (Exp [53]) 8.2 8.2 8.2 5.7 5.7 5.7 6.8 6.8 6.8NaeAsAs 126.0 24.8 31.3 43.2 39.0 26.0 20.4As (Exp [55]) 123.6 59.1 22.6 51.9 19.7 62.3 �4.1Na3 As7 12.4 14.4 15.5 4.5 4.4 6.0 �4.0 12.8 8.0 �2.3 0.7 3.2 2.2NaAs 41.5 35.1 40.1 1.5 14.8 8.3 15.6 20.0 14.3Na3 As 36.0 36.0 49.5 5.4 11.4 13.0 4.3Na 8.4 8.4 8.4 5.7 5.7 5.7 6.8 6.8 6.8NaeSbSb 89.9 36.7 29.7 32.6 24.7 19.7 17.4Sb (Exp [53]) 90.2 43.9 35.2 32.4 25.2 27.2 17.8NaSb 31.3 38.3 31.2 7.3 9.9 10.0 14.1 13.8 12.2 3.2 �0.4 �2.0 �0.20Na3 Sb 42.2 42.2 47.2 8.4 14.6 12.9 4.3Na 8.4 8.4 8.4 5.7 5.7 5.7 6.8 6.8 6.8NaeBiBi 70.2 31.4 5.6 20.0 30.3 16.5 �4.7Bi (Exp [53]) 63.3 38.0 11.0 19.4 24.5 25.0 7.3NaBi 47.8 43.2 8.9 11.8 23.0 15.5Na3 Bi 36.0 36.0 39.8 7.2 11.7 12.5 4.5Na 8.4 8.4 8.4 5.7 5.7 5.7 6.8 6.8 6.8

Fig. 3. Young's modulus (EH) and shear modulus (GH) of Nax M alloys as a function of Na fraction y¼ x/(xþ 1).

M. Mortazavi et al. / Journal of Power Sources 285 (2015) 29e36 33

phase. Over the whole concentration range, the elastic modulideteriorate by 40% at full sodiation with respect to pure P phase,pointing to a significant elastic softening. As shown in Fig. 3, theelastic moduli of As and Sb also behave in a similar manner. Fullysodiated As shows 60% elastic softening with respect to pure As,whereas the moduli of the fully sodiated Sb phase are only 50% ofthe elastic moduli of pure Sb.

The increase in Youngs and shear moduli for Nax M (M ¼ P, Asand Sb) at full sodiation as shown in Fig. 3 can be attributed to theelastic anisotropy of the monoclinic crystal structures of thesephases. From the data presented in Table 2, it is evident that thebulk moduli of the phases at full sodiation are lower than thephases with intermediate Na content in all three systems. Thisdiscrepancy between the trends of various elastic moduli at fullsodiation is due to the averaging methods used to obtain themoduli of polycrystalline sample, where the effect of anisotropy ismore pronounced on Young's and shear modulus than the bulkmodulus. A similar divergence between the variation of variouselastic moduli has also been reported in case of anisotropic struc-tures of LieSn phases [57]. The observations of abrupt reduction inelastic moduli of Nax M (M ¼ P, As and Sb) phases at low Na con-centrations shown in Fig. 3 are in contrast with group-14 elementswhere elastic softening upon increasing sodiation is monotonic andthe fully-sodiated phases are the weakest phases [16]. As the var-iations in elastic moduli during progressive sodiation can causebuild-up of severe internal stresses in host particles, this observa-tion suggests that the sodiation-induced structural transformationsin these materials are unlikely to be gradual. Nevertheless, thedegree of elastic softening at full sodiation in Nax M (M ¼ P, As andSb) alloys (40e60%) is lower than in group-14 alloys (~ 75%) [16].

In contrast to P, As and Sb, Bi shows a different mechanicalresponse to sodiation (Fig. 3 b,d). The elastic moduli of Bi nearlystay constant upon any degree of sodiation. This behavior, togetherwith the least volume expansion among group-15 alloys, impliesthat Bi will likely to be immune from severe mechanical stressesthat lead to the loss of electrochemical reversibility and capacity.Recent reports of a good reversibility of Na ions in Bi anodes for anonaqueous NIB could be associated with the concentration-independent elastic behavior of NaeBi system as shown in Fig. 3b,d [14]. Finally, Table 4 also shows the values for the ratio ofbulk modulus to shear modulus (B/G), which characterizes a

material's susceptibility to brittle fracture under mechanicalstresses. According to Pugh, B/G ratios lower than 1.75 typicallyindicate a low resistance to brittle failure [58]. Our calculationsshow that phases Na3 P11, NaP, NaAs, Na3 As, NaSb and NaBi aresusceptible to ductile plastic flow, while the rest are likely to fail viabrittle fracture. Consequently, all NaeM systems are expected toundergo a transition from brittle failure to plastic flow, and viceversa during cycles of sodiation and desodiation, though this effectis marginal for NaeBi system.

3.3. Atomic-level origins of elastic softening in NaeM alloys uponsodiation

To elucidate atomic-level origins of the elastic softening ingroup-15 Nax M phases upon increasing sodiation, we next studytheir electronic structures obtained from our first principles cal-culations. The evolution of the electronic charge distribution in NaxM phases is shown in Figs. 4e6. We explain the relationship be-tween the elastic softening and the interatomic bonding byconsidering the NaeP system as an illustrative example (Fig. 4). Inpure P, the electronic orbitals of every P atom overlap with threeneighboring P atoms, resulting in relatively strong network of co-valent PeP bonding. This electronic bonding structure is brokenduring the initial stage of sodiation leading to the formation of Na3P11 phase. The atomic structure of this phase is characterized byisolated P11 clusters separated by Na atoms. The mechanical prop-erties of such structure are therefore controlled by a fewer numberof weak ionic NaeP bonds, giving rise to a dramatic degradation ofthe elastic moduli as seen in Fig. 3. Upon formation of NaP phase,the network of covalent PeP bonds is reformed, albeit with onlytwo PeP and five NaeP bonds per P atom, resulting in a small in-crease in elastic strength compared to Na3 P11. In fully sodiated Na3P phase, no covalent PeP bonds exist as all P atoms are surroundedby Na atoms. A similar transition from strong, covalent bonding toweak, ionic bonding is also seen for NaeAs, NaeSb and NaeBisystems as shown in Figs. 5 and 6. The analysis of the evolution ofthe electronic structure presented here illustrates that sodiation-induced elastic softening in NaeM phases can be associated withan increasing proportion of the relatively weak ionic NaeMbonding. This analysis of the crystal structures and the associatedelectronic charge distributions also explains the origins of the

Fig. 4. Electronic charge density distribution in Nax P alloys. Yellow isosurfaces are plotted at a density of 0.04 e/bohr3. Orange and black spheres denote Na and P atoms,respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Electronic charge density distribution in Nax As alloys. Yellow isosurfaces are plotted at a density of 0.04 e/bohr3. Orange and green spheres denote Na and As atoms,respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

M. Mortazavi et al. / Journal of Power Sources 285 (2015) 29e3634

Fig. 6. Electronic charge density distribution in Nax Sb and Nax Bi alloys. Yellow isosurfaces are plotted at a density of 0.03 e/bohr3. Orange, cyan and purple spheres denote Na, Sband Bi atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

M. Mortazavi et al. / Journal of Power Sources 285 (2015) 29e36 35

abrupt decrease in the elastic moduli of group 15 elements at lowNa content, in contrast to group 14-elements where the variation inelectronic structures as well as the elasticmoduli with Na content ismore gradual [16].

From the electronic charge distribution, the net charge on eachatom was obtained using Bader charge population analysis [44].Our calculated net charges are given in Table 5. In all Nax M phases,Na donates a majority of its valence electron (0.74� 0.85 e). Thismagnitude of charge transfer is smaller than in the lithiated alloyanodes due to the larger size of the Na ion [30]. In each phase, Matoms assume distinct charge states depending on their localbonding environment. For example, in Na3 P11, P atoms take distinctcharge states in the range of �0:12 e to �0:46 e depending on thenumber of NaeP and PeP bonds participated by P atoms. In NaPphase, P atoms adopt either�0:78 e or a�0:87 e charge state owingto two non-equivalent P coordinations in the crystal structure. Atfull sodiation in Na3 P phase, P atoms adopt a single charge state aslarge as �2:26 e as they are all equivalently coordinated and sur-rounded by Na atoms. This investigation into charge states onceagain confirms that relatively strong, covalent MeM bonds at lowNa concentrations are replaced with the weak, ionic NaeM bondsat higher Na concentrations. Such analysis illustrates how themacroscopic elastic properties of polycrystalline Nax M (M ¼ P, As,Sb, Bi) alloy anode materials presented in Fig. 4 are governed bytheir local electronic charge distribution.

Table 5Net charges on Na and M atoms in Nax M phases obtained using the Bader chargepopulation analysis.

Phase Net charge on (e)

Na atoms M atoms

Na3 P11 0.85 P: �0.12 to �0.46NaP 0.82 P(1): �0.78, P(2): �0.87Na3 P 0.75 P: �2.26Na3 As7 0.84 As: �0.15 to �0.62NaAs 0.82 As(1): �0.76, As(2): �0.88Na3 As 0.75 As: �2.25NaSb 0.81 Sb(1): �0.79, Sb(2): �0.83Na3 Sb 0.75 Sb: �2.26NaBi 0.79 Bi: �0.79Na3 Bi 0.74 Bi: �2.22

4. Conclusions

We have obtained a complete description of the intrinsic elec-trochemical and elastic properties for polycrystalline Na alloys withP, As, Sb and Bi using first principles quantum mechanical simula-tions. While these alloys demonstrate attractive electrochemicalproperties for high-performance anodes under typical operatingconditions of NIBs (maximum specific capacity 385e2560 mA h/g,volumetric energy density 1.2e3.5 Wh cc�1 and electrode potential0.4e1.2 V with respect to Na/Naþ), Na intercalation in them isaccompanied by a drastic volume expansion in the range of40e400%. Our results show that although P, As and Sb undergo asignificant elastic softening by upto 60% at full sodiation, the Naintercalation of Bi leads to only a marginal reduction in its elasticstrength. Moreover, for P, As and Sb, the phases with lowNa contentdemonstrate largest weakening of their elastic moduli. Thisobserved elastic behavior can be attributed to the evolution ofelectronic charge distribution, which shows an increasing popula-tion of weak ionic bonds that replace strong covalent bonds. Theaccurate description of the concentration-dependent electro-chemical and elastic properties presented here provides theessential, preliminary information for developing analytical modelsof themechanistic behavior during cyclic sodiation and desodiationof group-15 alloys. Since Na-induced deterioration of the me-chanical properties of these materials may prove to be a significantbarrier for their practical application as high capacity anodes ofNIBs, such models could be crucial in designing mechanical buffers,binders and appropriate battery architectures that may help miti-gate the structural stability issues [36,59].

Acknowledgment

Authors gratefully acknowledge computational support fromMonash University Campus Cluster, Multi-modal Australian Sci-ences Imaging and Visualisation Environment, iVEC at iVEC@Mur-doch and the Australian National Computing Infrastructure.

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