Possible Existence of a Monovalent Coordination for Nitrogen Atoms

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Article

On the Possible Existence of a Monovalent Coordination for Nitrogen Atoms in LiPON Solid Electrolyte : Modelling of XPS and Raman Spectra x

y

z

Émilie Guille, Germain Vallverdu, Yann Tison, Didier Bégué, and Isabelle Baraille J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b08427 • Publication Date (Web): 25 Sep 2015 Downloaded from http://pubs.acs.org on September 29, 2015

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The Journal of Physical Chemistry

On the Possible Existence of a Monovalent Coordination for Nitrogen Atoms in LixPOyNz Solid Electrolyte: Modelling of XPS and Raman Spectra ´ Emilie Guille, Germain Vallverdu,∗ Yann Tison, Didier Bégué, and Isabelle Baraille Université de Pau et des Pays de l’Adour, IPREM - ECP CNRS UMR 5254, Technopole Hélioparc, 2 av. du Président Pierre Angot, 64053 Pau cedex 9, France E-mail: [email protected] Phone: +33 (0)559407851. Fax: +33 (0)559407622

∗

To whom correspondence should be addressed

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ACS Paragon Plus Environment


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Abstract Lix POy Nz is an amorphous solid electrolyte widely used in microbattery devices. The present study, based on a confrontation between experiment and theory, aims at providing new knowledge regarding the ionic conductivity model of such systems in correlation with its structure. The computational strategy involved molecular dynamic simulations and first-principle calculations on molecular and periodic models. The experimental target data involve electronic and vibrational properties and were considered through the simulation of Raman and X-ray photoemission spectra in order to identify characteristic patterns of Lix POy Nz . In particular, the presence of short phosphate chains is suggested by molecular dynamic calculations and the simulation of Raman spectra clearly evidenced a new coordination for nitrogen atoms in the amorphous state, not considered until now in the experimental structural model of the electrolyte and initially hypothesized based on core level binding energy computations. Monovalent nitrogen atoms together with short phosphate chains were used to build a structural model of the electrolyte and appeared to lead to a better reproduction of the target experimental results, while it implies a necessary refinement of the diffusion schemes commonly considered for lithium ions.

Keywords First-principle, solid electrolyte, LiPON, core level, vibrational The authors declare no competing financial interests.

1

Introduction

The increasing demand for electronic portable devices requires an important research effort on energy storage, those technologies being demanding in terms of mass capacity, size and

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battery life. As a complementary solution to conventional lithium-ion batteries, microbatteries are electrochemical systems built of several stacked solid layers (thin films), including the active part which consists of two electrodes separated by a solid electrolyte ; current collectors, insulating and lithium diffusion barrier layers as well as thin film encapsulation constitute the remaining ”inactive” part. The total thickness of the device does not exceed 15 µm, which allows diversifying the fields of application of lithium-ion batteries. The performances of microbatteries are well-known to depend upon phenomena occurring at electrode/electrolyte interfaces. 1 Those interfaces have been largely studied in the case of liquid electrolytes, because of the formation of a solid-electrolyte interface (SEI) which appears necessary for the protection of the electrode as well as limiting for lithium-ion diffusion through the interface. 2 Conversely, the experimental characterization of solid-solid interfaces appear more complex, due to their low thickness and difficulty of access from bulk or surface techniques. Modelling then appears as a suitable way to understand the limiting phenomena likely to occur at the atomic scale, as computational strategies can be performed to solve thermodynamics issues. 3,4 Both crystalline and amorphous solid electrolytes (as an example, Lix POy and Lix POy Nz materials, respectively) are used in modern microbatteries and they generally present lower ionic conductivities than their liquid analogues (about 10−6 vs 10−3 S.cm−1 ). Amorphous systems consist of oxide glasses, and the partial substitution of oxygen atoms by nitrogen atoms appears as a way to improve their ionic conductivity properties. Lix POy Nz systems have been synthesized (RF magnetron sputtering) for the first time by Bates et al. 5 from γ-Li3 PO4 as the target material and are nowadays among the most frequently used solid electrolytes, which explains why they were chosen as systems of interest in the present study. Beyond their great stability, Lix POy Nz shows an ionic conductivity of 3.10−6 S.cm−1 (for a material with chemical composition Li2.9 PO3.3 N0.46 ), much larger than that of Li2.7 PO3.9 (3.10−7 S.cm−1 , for a bulk material, to 7.10−8 S.cm−1 , for the corresponding thin-film material 5,6 ).

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The synthesis of Lix POy Nz materials can be achieved either through Physical Vapor Deposition (PVD), 7 Plasma-Assisted Direct Vapor Deposition (PA-DVD), 8 or solid-phase reactions. 9,10 The partial substitution of oxygen atoms by nitrogen atoms leads to modifications of the vitreous network and therefore to an enhanced ionic conductivity for Lix POy Nz systems. In an XPS investigation of Nax POy Nz systems, Marchand et al. 11 proposed to assign the two components observed on the XPS N 1s core peaks to divalent and trivalent nitrogen atoms; based on the study of Veprek et al., 12 who worked on P3 N5 Hx systems. Later, the similarity with Lix POy Nz materials allowed to generalize such an interpretation, as shown by Fleutot et al. 7 through XPS and Raman measurements. Based on the work of Marchand et al., 11 it was proposed that the substitution of oxygen atoms by nitrogen atoms in those amorphous systems leads to both divalent and trivalent kinds of nitrogen atoms. Substitution schemes commonly considered in the literature, following the work by Marchand et al., are depicted in Figure 1.

O O

P

Li+

O O

O−

P

O

O

O− Li

+

N

P

O

O− + Li

O Li

P

P

+

O O

Li+ O−

O−

O O

O

P

N

O−

O− Li

Li+

+

Figure 1: Commonly accepted scheme for the substitution of oxygen atoms by nitrogen ones during the synthesis of Lix POy Nz : (top) leading to a divalent nitrogen atom, (bottom) leading to a trivalent nitrogen atom. Those substitution schemes, based on experimental interpretations, have been used to propose a migration mechanism for lithium-ions: i- the introduction of divalent nitrogen atoms leads to the formation of P=O− Li+ interactions, ii- the lithium ions bound to P=O− groups are less mobile, iii- as a consequence, the mobility of the remaining lithium ions is 4


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increased, due to fewer collisions between ions. 7 The present study aims at dealing with the role of nitrogen substitution. In this view, we first modelled the structure of amorphous Lix POy Nz materials. The search for a suitable model for this solid electrolyte was guided by confrontations between simulated and both XPS and Raman experimental spectra and constitutes the first step for a future work on Lix POy Nz /electrode interfaces. The computational strategy we followed involved several theoretical methods (molecular dynamics and quantum mechanics methods : molecular or periodical) in order to identify the relevant patterns in the amorphous state. In that scope, electronic and vibrational properties of investigated systems were simulated in relation with the target experimental results available in the literature : XPS and Raman spectra. 7 This report is organized as follows. First, we consider the doping of Lix POy crystalline by nitrogen through the computation of the corresponding core-level binding energies. Then we present numerical experiments, using molecular dynamics simulations which aim at identifying the recurring patterns likely to be found in the amorphous Lix POy phases, thus completing the schemes reported in Figure 1. These patterns were used to build original models for which we report the calculated electronic and vibrational properties. Finally, we compare the computed data to the corresponding target experimental results, 7 discuss of the physical reality of a monovalent coordination for nitrogen in those amorphous materials and propose a model for the electrolyte and an alternative migration scheme for lithium ions. As the present study involves various kind of coordinations, for both oxygen and nitrogen atoms, we will use a unique notation. Monovalent, divalent and trivalent coordinations for nitrogen atoms will be labelled as Nm , Nd and Nt , respectively. Likewise, monovalent and divalent oxygen atoms will be refered to as Om and Od respectively.

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2

Doping of LixPOy crystalline structures : calculation of XPS core level binding energies

In the search for a suitable model of Lix POy Nz , we first considered the nitrogen doping of three Lix POy crystalline structures well described in the literature, namely γ-Li3 PO4 , LiPO3 and Li4 P2 O7 (see Figure 2). These structures were chosen because of their specific tetrahedral organizations : • γ-Li3 PO4 , 10 target material for the synthesis of Lix POy Nz , exclusively made of isolated phosphate tetrahedra ; • Li4 P2 O7 , 13 constituted of phosphate dimers ; • LiPO3 , 14 made of infinite phosphate chains. In order to distinguish between those structures after nitrogen doping, we label them with respect to their tetrahedral structuration : • Mono. Lix POy Nz in the case of doped γ-Li3 PO4 ; the doping leads to monovalent nitrogen atoms (Nm ), the chemical composition then obtained being Li3.0 P(Om )3.75 (Nm )0.25 . • Dim. Lix POy Nz in the case of doped Li4 P2 O7 ; nitrogen atoms are exclusively inserted in a divalent coordination (Nd ), leading to Li2.5 P(Om )3 (Nd )0.5 . • Chain Lix POy Nz in the case of doped LiPO3 ; once again, nitrogen atoms are exclusively considered in a divalent (Nd ) coordination and the resulting doped crystalline structure is Li1.0 PO2.8 (Nd )0.2 . The computation of core-level binding energies was carried out for all these structures for a further confrontation with experimental XPS core peaks reported for Lix POy Nz materials. 7 The following paragraphs respectively details the computational methodology followed for core peaks computations and the discussion on computed results. 6


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a) γ-Li3PO4

b) Li4P2O7

c) LiPO3

Figure 2: Representations of the three crystalline Lix POy structures : a) γ-Li3 PO4 (Pmnb), b) Li4 P2 O7 (P-1) and c) LiPO3 (P2/n). Red and green atoms refer to oxygen and lithium atoms, respectively. Phosphorus atoms constitute the centers of the tetrahedra. The structures are projected in the [001] direction, except for LiPO3 ([010]). See supporting information for structural details.

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2.1

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Computational details

All calculations were performed using the plane wave DFT code available in the Vienna Ab Initio Simulation Package (VASP) 15,16 within the generalized gradient approximation, using the PBE 17 functional. The electronic wave-functions were described in the Projected Augmented Wave (PAW) formalism 18,19 and a realspace projection was further used for the total wavefunction analysis. We checked the quality of the basis set by increasing the plane wave energy cut-off from 300 to 700 eV. The plane wave energy cut-off was set to 500 eV, which appeared to be a converged value for all of the crystalline systems studied. The Brillouin zone integration was done on a k-point grid distributed uniformly around the origin using a mesh of 4×4×4 for all the systems considered throughout this paper. Cell parameters and atomic positions were fully relaxed. Core-level binding energies (BE) were computed using a modified PAW approach implemented in VASP which allows the generation of the corresponding core excited ionic potential during the calculations. 20,21 This approach follows the so-called ”(Z+1) approximation”, the core hole is modeled by adding the corresponding amount of removed electron to the nuclear charge. In order to avoid spurious interactions between the core hole created during the calculations and its periodic images, supercells of the materials investigated were considered. Dimensions of the supercells used for all the materials studied are given in the supporting information. The same method was used in previous works which deal with surface science or catalysis. 22–24 However, the absolute value of the BE cannot be compared directly to experiment because two different reference energies are used. Experimentally, in particular, the work function of the material is included in the BE. To account for it, we used the following equation 23,24 : ref ref mat BEi,corr = BEi,exp + (ǫmat i,calc − ǫi,calc )

8


(1)

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ref in which BEi,exp stands for the experimental binding energy related to the core orbital i ref of interest, measured on the reference material. ǫmater i,calc and ǫi,calc stand for the computed

eigenenergy of the core orbital i, in the studied material and in the reference material, respectively. The work function of the material of interest is included in the energy difference ref (BEi,exp − ǫref i,calc ). As long as the reference material and the material of interest show close

electronic and structural properties, their respective work functions can be considered as equivalent, so that the work function of the studied material is effectively taken into account. Besides, equation 1 leads to absolute core-level binding energies, which allows for a direct comparison between computed values and experimental XPS data. We previously showed that this approach leads to an effective error of at most 500 meV in the computation of N1s BE on Lix POy Nz related materials. 25 The use of equation 1 requires the choice of reference materials, which have to be structurally as well as electronically close to the material of interest, so as to guess that their respective workfunctions can be supposed as equivalent. The XPS technique is very sensitive to the chemical environment surrounding each atom, therefore reference materials need to be chosen for each kind of chemical environment observed in Lix POy Nz materials : 1. P2 O5 for O1s core orbitals in a bridge type environment (Od atom type); 2. P3 N5 for N1s core orbitals (Nd and Nt atom types); 3. KH2 PO4 for the particular case of O1s core orbitals in a tetrahedral type environment (Om atom type).

2.2

Results

Core-level binding energies computed on doped Lix POy structures are reported in Table 1. Computed eigenenergies for all the systems studied throughout this work are also available in the Supporting Information. In Table 1 are also reported, for comparison, the results we previously obtained for Li2 PO2 N systems 25 proposed by Du et al. 26 as periodic mod9



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els of original chemical composition and later synthesized and characterized by Holzwarth’s group. 27 It should be noted that the core peak position doesn’t depend upon chemical composition, 7,25 which justifies that the target experimental value is unique for each kind of core peak, independently of the stoichiometry considered for the calculation on model structures. Table 1: Calculated O1s and N1s core orbital energies (in eV) for doped crystalline Lix POy compounds as well as Li2 PO2 N systems. 25 Experimental values refer to the work by Fleutot et al. 7 Xm and Xd (X=O,N) refer to monovalent and divalent coordinences, respectively. We used the following reference materials (cf. equation 1) : (α) P2 O5 and (β) P3 N5 .

Dim. Lix POy Nz Chain Lix POy Nz s1-Li2 PO2 N s2-Li2 PO2 N s3-Li2 PO2 N Experiment

O1s (Od ) 532.6(α) 532.0(α) 533.3(α) 533.3(α) 532.1(α) 532.3

O1s (Od ) 533.2(α)

533.5

N1s (Nd ) 395.6(β) 394.8(β) 395.7(β) 395.7(β) 394.7(β) 397.9

At first, O1s core-level binding energies lead to proper results for both Om and Od types of oxygen atoms, as computed core peaks reproduce the experimental values with a deviation of 0.3 eV, leading to a better reproduction of the experimental data than the results previously obtained on s1 and s2-Li2 PO2 N structures. Despite the agreement for O1s core peaks, the models considered do not properly simulate the N1s core-level binding energies, for which systematic deviations of more than 2 eV are obtained. A significant difference can be noticed between the computed core peaks of Dim. Lix POy Nz and Chain Lix POy Nz systems. Because of the sensitivity of core-level binding energies to the close chemical environment of the atom of interest, 25 this energy difference can be at least partially attributed to a chain length effect, as the major structural parameter that differs from one structure to another. Doping γ-Li3 PO4 exclusively leads to the formation of Nm kind of atoms. This coordination is not considered in the structural model of the electrolyte, proposed on the basis of XPS interpretations. Besides, there is no reference material available for the calculation of the corresponding N1s core peak, i.e. there is no well-characterized material showing a P-Nm 10


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arrangement. Reasoning in Koopmans’ formalism (ie only taking into account the initial state effects), the absolute value of the computed eigenenergy (ǫmat i,calc. term in equation 1) associated with Nm (400.87 eV for Mono. Lix POy Nz ) evidences that the peak associated with monovalent nitrogen atoms should appear at a lower binding energy than the corresponding peak (402.26 eV in the case of Dim. Lix POy Nz ) associated with Nd nitrogen atoms. In fact, as the environment around Nm nitrogen atoms (P=N− ) is electron enriched, it implies that extracting a N1s electron requires less energy, the corresponding binding energy is thus lower than that of Nd (=N–) nitrogen atoms. This accounts for the relative position of the N1s core peak that should be associated with monovalent nitrogen atoms on the scale of binding energies. In our previous study, 25 we considered the structural modifications to be applied on Li2 PO2 N systems, leading to monovalent nitrogen atoms. Calculations of core-level binding energies have then been performed for Nd atoms in order to evaluate the influence of Nm atoms lying in their vicinity. Computed core peaks appeared significantly shifted towards the experimental value (396.5, 396.2 and 395.0 eV for s1, s2 and s3, respectively), leading us to ask as for the possible existence of monovalent nitrogen atoms in amorphous Lix POy Nz systems. Therefore, periodic structures lead to unsatisfactory results, which can be attributed to various structural parameters, unsuitable for properly simulating the recurring patterns that characterize the amorphous state. The study of doped Lix POy structures evidenced the influence of the chain length on the computed N1s core peak. In addition, our previous work on Li2 PO2 N systems highlighted the possible existence of monovalent nitrogen atoms. 25 Considering those two parameters as essential, we built original models of Lix POy Nz materials.

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3 3.1

Original models based on phosphate dimers A numerical experiment using molecular dynamics (MD) simulations

Since XPS measurements are highly sensitive to the local chemical environment of the atom of interest, various structural parameters can be responsible for the core peak position. Facing the unsatisfactory results obtained for doped crystalline structures as well as for Li2 PO2 N systems, we used molecular dynamics simulations in order to identify the recurring structural patterns occurring in amorphous Lix POy Nz materials. More precisely, we made numerical experiments to simulate the amorphization of γ-Li3 PO4 , as the target material used for the synthesis of the electrolyte. Indeed, the commonly used plasma-induced synthesis route leads to an amorphous form of Lix POy Nz , thus MD simulations are expected to help characterizing the different kind of environments encountered in the amorphous state. An analysis of the recurring patterns likely to characterize the amorphous structure will help us to build original models for Lix POy Nz systems. 3.1.1


All molecular dynamics simulations have been conducted with the DL POLY code. 28 We performed constant pressure (NPT) molecular dynamics simulations with Noose-Hoover thermostat and barostat, starting from LiPO3 and γ-Li3 PO4 crystalline structures. For all simulations, we used 1 fs time steps as well as a cut-off of 8 ˚ A to account for long-range interactions. Simulation boxes contained 2400 atoms, for each structure, which corresponds to 2×6×2 and 3×3×5 supercells (approximately 30×30×30 ˚ A) for LiPO3 and γ-Li3 PO4 , respectively. As those simulations aim at reproducing the structural parameters of amorphous Li3 PO4 , the target material for the synthesis of Lix POy Nz , approximately ten configurations of each of those systems were heated from 300K to 900K (in the case of LiPO3 ) or 1000 K (in the case of γ- Li3 PO4 ) with temperature steps of 100K, in order to achieve vitreous 12


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structures. From 300K to 400K, a total simulation time of 1 ns was applied, until convergence of the total energy. At higher temperatures, a simulation time of at least 2 ns was necessary, because of a higher materials’ disorganization, linked to difficult convergence of the total energy. Once again, about ten configurations of each system were then rapidly cooled, from 1000 K (900 K in the case of LiPO3 ) to 200 K and equilibrated for 2 ns. Thus, the amorphous patterns obtained by this dynamical thermal treatment was preserved. We used a Born-Mayer 29,30 type pair potential :

φij =

Zi Zj e 2 −rij + Aij exp rij ρij

(2)

where Zi is the atomic charge of atom i and rij the atomic distance between atoms i and j. The force field parameters are reported in the supporting information. These data were taken from the work of Prasada Rao et al. 31,32 who optimized a force field for the study of ternary glasses xLiCl-(1-x)(0.6Li2 O-0.4P2 O5 ), which includes the study of LiPO3 . The use of this Born-Mayer potential was validated on the basis of structural data, as reported in Table 2. The calculated structural parameters are in agreement with the experiment by less than 5% error. 3.1.2

Results

Molecular dynamics simulations have been performed on γ-Li3 PO4 and on LiPO3 for comparison. The γ-Li3 PO4 structure was heated to 1000K, beyond its glass transition (Tg =875 K). Phosphate dimers appeared starting from a heating temperature of about 500K. The number of dimers and, more rarely, of trimers in the supercell then increases with temperature. After the cooling step, the amorphization process of γ-Li3 PO4 leads to the formation of short chains, of two to three PO− 4 tetrahedra, mixed with isolated tetrahedra. Similar results have been observed in the case of LiPO3 , for which ”infinite” phosphate chains are broken into short chains.

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Table 2: Structural parameters obtained through DFT (using the VASP code) and MD treatments, facing experimental values 9,14 (collected at 295K) ; for MD simulations, average values are reported together with the standard deviations observed throughout the simulation System

γ-Li3 PO4

LiPO3

(˚ A) a b c P-Om a b c β P-Om P-Od

MD 11.03 (0.14) 6.44 (0.14) 5.30 (0.07) 1.50 (0.11) 14.22 (0.11) 5.66 (0.25) 18.15 (0.11) 101.6 (0.43) 1.45 (0.07) 1.57 (0.07)

DFT calculations 10.61 6.17 4.99 1.56 13.31 5.49 16.74 99.0 1.50-1.51 1.62-1.64

Experiment 10.46 6.11 4.92 1.53-1.55 13.07 5.41 16.45 99.0 1.47-1.49 1.57-1.62

As a result, it appears that short chains, and mostly phosphate dimers, are a recurring pattern representative of the structure of Lix POy amorphous materials. Those results are in reasonable agreement with the HPLC measurements reported by Wang and coworkers, 10 which showed that Lix POy and Lix POy Nz structures are mainly made of short phosphate chains (about 3 to 4 tetrahedra). On the basis of those simulations and given the hypothesis of the possible existence of monovalent nitrogen atoms, we built original models and computed their core-level binding energies. The following paragraph will describe these models and discuss the computed results obtained on those new systems. 3.1.3

Building the original models

Based on the results of MD simulations, we first built aggregates containing the recurring patterns encountered for the amorphous state. These aggregates, depicted in Figure 3, take into account both the three possible coordinations for nitrogen atoms and the chain length effects.

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Aggregates C1 to C3 account for all the possible coordinations of nitrogen atoms, i.e. divalent, trivalent and monovalent, respectively. Aggregate C4 has then been built to evaluate some potential cooperative effects of Nm and Nd types of atoms on both electronic and vibrational properties. Finally, aggregate C5 contains three tetrahedral units to evaluate the influence of the chain length, whereas C0 corresponds to an undoped system and constitutes the reference material, to evaluate the doping effects. These aggregates were used to build original periodic models. In agreement with the molecular dynamics results, which suggest that the amorphous state is mainly made of short phosphate chains mixed with isolated tetrahedra, we started with a supercell of γ-Li3 PO4 . Central atoms were judiciously removed to insert the previously described aggregates, so that aggregates are actually surrounded by a matrix of Li3 PO4 (see Figure 4). The N 1s and O 1s core-level binding energies have been calculated for these original periodic models (the structural parameters as well as the dimensions of the supercells used for computations are reported in the Supporting information) and are discussed in the following paragraph. It should be noted that, as core-level binding energy can only be calculated for Nd and Nt types of nitrogen atoms, aggregate C3 has not been inserted in a matrix of Li3 PO4 to form an M3 periodic structure.

3.2

Calculation of core-level binding energies

The core-level binding energies calculated for M1, M2, M4 and M5 according to the previously described methodology are reported in Table 3, for a confrontation with the corresponding target experimental data. Once again, all N 1s core peaks refer to calculations performed for divalent nitrogen atoms. The core-level binding energies computed on the O 1s core state of Om oxygen atoms appear in good agreement with the experimental value, for all the systems considered. Besides, it is worth noting that the computed N 1s binding energies obtained for M1 are closer to the experimental XPS data than any of the values determined for the previous 15



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C0

C1 (Nd)

C2 (Nt)

C3 (Nm)

C4 (Nm, Nd)

C5 (Nd)

Figure 3: Aggregates considered to reproduce all possible coordinations for nitrogen atoms (given in parenthesis) and evaluate the effect of the chain length.

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M1

M2

M4

M5

Figure 4: Original models M1, M2, M4 and M5, including C1, C2, C4 and C5 aggregates, respectively ; red, green, purple and blue atoms refer to oxygen, lithium, phosphorus and nitrogen atoms, respectively.

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structures (see table 1). Moreover, the computed N1s core peak appears rather improved through the insertion of a monovalent nitrogen atom to the dimer, corresponding to the M4 model. Regarding the effect of the chain length, evaluated through the M5 aggregate, this model appears penalized by the presence, in the first coordination sphere around Nd , of a lithium atom which lies closer (1.59 ˚ A) to the nitrogen atom than the generally observed Li–N interactions (1.97 to 2.11 ˚ A). In this case, Nd is electron enriched, implying that its core-level binding energy is lowered. On the contrary, in the case of M4, lithium atoms lying in the vicinity of Nd appear at slightly longer distances (1.97-2.11 ˚ A) compared to the M1 system (2.00-2.01 ˚ A), as they tend to move towards the neighboring Nm atom. This can account for the small shift observed on the N1s core peak position between those two systems. Computed N 1s binding energy obtained on M2 also leads to satisfactory results. Table 3: Computed O 1s and N 1s core orbital energies (eV) for M1, M2, M4 and M5 model ; we used the following reference materials (cf. equation 1) : (α) P2 O5 and (β) P3 N5 . Core orbital M1 M2 M4 M5 Experiment 7

O1s (Om ) 532.9(α) 533.2(α) 533.5(α) 532.1(α) 532.3

N1s (Nd ) 396.5(β)

N1s (Nt ) 398.0(β)

396.9(β) 395.3(β) 397.9

399.3

Finally, M2 and M4 periodic structures which contain the three possible coordinations for nitrogen atoms, appear as the best systems, among the investigated models, to reproduce the target N 1s core peaks,energies with a reasonable agreement. Nevertheless, the reality of a monovalent coordination for the nitrogen atom (M4 model) needs to be investigated to ensure that this computed shift is not an artifact. Indeed, this nitrogen coordination has not yet been experimentally considered and the N1s core peak energy is sensitive to the presence of lithium atoms in the first coordination sphere. As a consequence, our study was extended to the computation of Raman vibrational properties, for a further comparison with the corresponding experimental data. 7 18


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3.3

Raman spectra : molecular calculations on phosphate dimers

The extended study conducted on Lix POy Nz models highlights the possibility of encountering monovalent nitrogen atoms in the amorphous state, as the presence of such nitrogen atoms shifts the position of the N1s core peak associated with divalent nitrogen atoms towards the experimental value. Following the work of Fleutot et al. 7 , we computed the vibrational properties of the previously depicted aggregates (see Figure 3), in order to interpret the experimental Raman spectra obtained on real Lix POy Nz systems in the light of computed data. 3.3.1


Calculations of structures, energies and vibrational Raman spectra of aggregates were performed using the PBE functional together with a 6-31G* basis set, as implemented in Gaussian09 C01. 33 For the whole systems studied, several structures were investigated to ensure an adequate sampling of the potential energy surface and allow the identification of the global minimum. Additionally, the aug-cc-pVTZ basis set was used in order to control the accuracy of the calculations. Basis set effects appear practically negligible for the vibrational frequencies, leading to values separated by 10 cm−1 at most (see supporting informations, section 3). Raman intensities were obtained at the same level of theory and will be expressed in terms of normalized units. The first and second derivatives of the polarizabiliy were obtained by finite difference with the Placzek theory. 34 3.3.2

Simulation of Raman spectra

Experimental Raman spectra 7 are shown in Figure 5, top panel. LiPON-0 refers to an amorphous form of γ-Li3 PO4 , which is then gradually doped by nitrogen atoms from LiPON2 to LiPON-40, according to the nomenclature used by Fleutot et al. 7 Concerning vibrational spectroscopy of the phosphate network, it is generally assumed that vibrational optic modes are rather localized and that the symmetry of the basic build19



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ing structural element (Elementary Structural Units, ESU) is expected to govern the optical spectroscopic activity. 35 As a consequence, the qualitative interpretation of the Raman spectra of the amorphous Lix POy Nz systems only requires the calculation of the vibrational properties of the aggregates presented in 3. Following those assumptions, we first considered C0, representative of the amorphous form of Li3 PO4 , according to both HPLC measurements 10 and molecular dynamics study presented in this work. This amorphous Li3 PO4 , labeled as ”LiPON-0” on Figure 5, should allow to further characterize the influence of nitrogen atoms as well as to evaluate the relevance of the computational models used compared to the vibrational properties we attempt to calculate. Table 4 summarizes the computed wavenumbers and their corresponding assignments and intensities, while the simulated spectrum, labelled C0, is depicted in Figure 5. Table 4: Computed wavenumbers (cm−1 ) and their corresponding assignments and intensities for C0 ; (s) strong, (m) medium, (w) weak, (vw) very weak. Computed wavenumber 1166–1138 1012 944 (comb. mode) 876 824 655 (comb. mode) 635–626 (comb. mode)

experimental 7 1025 950 800 695

Intensity (w) (m) (s) (vw) (w) (vw) (vw), (w)

Assignment νas (P-Om ) νas (P-Om ) νs (P-Om )+νas (P-Od -P) νs (P-Om ) νas (P-Od -P) νs (P-Od -P)+δ (P(Om )3 ) δ (P-Od -P)+α (P(Om )3 )

This phosphate dimer presents a characteristic signature at 944 cm−1 , corresponding to a combination mode between the stretching vibrations of P-Om and P-Od -P bonds. Another distinctive feature is the peak located at 1012 cm−1 , which corresponds to the asymmetrical stretching vibrations of P-Om bonds. Those two computed peaks are in good agreement with the experimental spectra, reproducing the bands observed at 950 and 1025 cm−1 , respectively. Other computed wavenumbers appear far too weak to be properly characterized, even in the area ranging from 1200 to 1170 cm−1 , corresponding to the stretching vibrations of P-Om bonds. Much care needs to be taken for the vibrational study of amorphous struc20


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tures, for which micro-structuring can occur and modify both the shape and the intensity of the peaks. 35 However, our computational conditions appear to properly reproduce the experimental Raman spectra, suggesting that both method and models are suitable for the vibrational study of Lix POy Nz patterns. Significant modifications can be noted on the experimental spectra (cf. Figure 5) further to the nitrogen doping 7 : • the signal between 600 and 640 cm−1 is extinguished • the peak ranging from 695 to 850 cm−1 appears exalted and broadened • the intensity of the distinctive mode located at 950 cm−1 decreases • the peak centered at 1025 cm−1 is broadened We considered the previously built aggregates (see Figure 3), as systems likely to be representative of Lix POy Nz patterns. Raman frequencies were computed for each aggregates considered, leading to the calculated spectra reported in Figure 5, bottom panel. In this figure, each peak is reported with its corresponding assignment. For all the studied aggregates, except C2, the peak spreading between 600 and 640 cm−1 can be attributed to bending vibrations of the network (δ(P-X-P) or δ(X-P-X), X=O,N). According to the modifications induced on Raman spectra by the nitrogen doping process, Figure 5 first reveals that aggregates C2, C3 and C4 show a peak in the spectral area located between 695 and 850 cm−1 . This peak corresponds either to (i) an antisymmetrical stretching vibration of the three P−Nt bonds in C2, or to (ii) an antisymmetrical stretching vibration of P-Od bonds in C3, or to (iii) a symmetrical stretching vibration of the two P–Om bonds close to P−Nm , in C4. In the case of C4, this peak presents a far more significant relative intensity, while the corresponding signal appears lower in the case of C2 and C3. Secondly, the peak experimentally located at 950 cm−1 appears on the simulated spectra of C0, C2 and C3. In the case of C0, it corresponds to a combination mode between the stretching

21



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vibrations of P-Om and P-Od bonds, while this band appears slightly shifted towards higher wavenumbers when considering C2, due to the substitution of an Od atom by a Nt one. An analysis of the frequencies computed for C3 reveals that this band can no longer be attributed to a combination mode but to the stretching vibrations of the P−Nm group. Once again, it is shifted towards higher wavenumbers, by comparison with the base C0 aggregate. Finally, the peak experimentally centered at 1025 cm−1 appears on all computed spectra with the exception of C2. It corresponds (i) to the stretching vibrations of P-Om bonds in the case of C0 and C1, (ii) to a combination mode between the stretching vibrations of P-Om and P−Nm bonds in the case of C3 and (iii) to a stretching vibration of the Nd −P−Nm arrangement in the case of C4, which implies a cooperative effects of both Nm and Nd atoms. To complete the interpretation of the experimental spectra in a more quantitative manner, the previously computed spectra were then weighted, using the compositions reported by Fleutot et al. 7 on the basis of XPS interpretations (the weight are given section 5 in the supporting informations). This strategy allows for a direct comparison between computed and experimental spectra. Three simulations were thus conducted : 1. was based on the structural model commonly considered for Lix POy Nz materials, as proposed on the basis of XPS interpretations, 7 and involved C1, C2 as well as C0. This simulation thus involves both Nd and Nt types of nitrogen atoms ; 2. was quite similar, except that C1 was substituted by C3, to evaluate the influence of monovalent nitrogen atoms on the vibrational properties ; 3. was simulated based on the results we get through the simulation of XPS spectra. It considered C2, C4 and C0, to account for all the possible coordinations for nitrogen atoms. Simulated spectra corresponding to the LiPON-40 composition are depicted in Figure 6 along with the corresponding experimental spectrum. This figure clearly evidences that the common experimental structural model (case 1), which mainly consider C1 and C2, doesn’t 22


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00

25

Intensity (counts)

695 cm

-1

800 cm

-1

950 cm

-1

1025 cm

a)

-1

LiPON-40

0

LiPON-20

0 20

LiPON-5

00

LiPON-2

15

0

0 10

LiPON-0

b)

νs(Nd-P-Nm)

δ(Nd-P-Nm) νs(P(Om)2)

Relative intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


νs(P-Nm) δ(Om-P-Om) νas(P-Od-P)

νas(P-Nm)+ νas(P-Om) νas(P-Om)

νs(P-Nt)-νs(P-Om) νas(P-Nt) δ(Om-P-Om) δ(P-Nd-P) δ(P-Od-P)+ α(P-Om)

600

700

C4

C3 νas(P-Om)

C2 νas(P-Om) νs(P-Om)

νs(P-Om)

C1

νs(P-Om)+νas(P-Od-P) νas(P-Om)

800 900 1000 -1 wavenumber (cm )

1100

C0 1200

Figure 5: a) Experimental Raman spectra of Li4.43 PO4.35 (LiPON-0), Li4.02 PO3.91 N0.37 (LiPON-2), Li3.65 PO3.42 N0.71 (LiPON-5), Li3.43 PO3.09 N0.89 (LiPON-20) and Li3.25 PO3.00 N1.00 (LiPON-40), as reported by Fleutot et al. 7 . b) Computed Raman spectra for each aggregate (C0, C1, C2, C3 and C4) as depicted in 3 considered throughout the vibrational study.

23



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lead to the appearance or enhancement of the experimentally observed peaks when increasing the nitrogen rate. This observation appears true both in the spectral area ranging from 695 to 850 cm−1 and for the peak experimentally centered at 1025 cm−1 . The second simulation (case 2) also fails at displaying a peak between 695 and 850 cm−1 . However, the intensity ratio between the peaks located at 950 and 1025 cm−1 appears to better reproduce the behavior experimentally observed upon doping. Finally, the third simulated spectra (case 3), which accounts for all the types of nitrogen atom coordinations, leads to a good reproduction of experimental observations, i.e. the peak located between 695 and 850 cm−1 appears upon doping while the peak located at 1025 cm−1 widens. Thanks to the assignments reported on Figure 5, this latter peak corresponds to a combination mode, induced by a cooperative effect of Nd and Nm types of nitrogen atoms (νas (P−Nd −P)+ν (P−Nm )). This observation tends to demonstrate that the characteristic features appearing while increasing the nitrogen rate have to be attributed to combination modes, due to the joint presence of monovalent, divalent and trivalent types of nitrogen atoms.

4

Discussion : an alternative scheme for lithium-ion migration

Both the molecular dynamics simulations presented here and earlier HPLC measurements 10 pointed out that the structural organization in amorphous forms of Lix POy and Lix POy Nz materials mainly consists of short chains. Besides, all computations reported throughout this paper tend to demonstrate the physical possibility of a P=N− coordination for nitrogen atoms. The presence of monovalent nitrogen atoms first leads to a shift of the N1s core peak energy associated with divalent nitrogen atoms, because of the structural reorganization which tends to take lithium ions away from divalent nitrogen atoms, making them slightly electron deficient. 24


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-1

695 cm

-1

800 cm

-1

950 cm

1025 cm

-1

1.5 Relative intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LiPON-40 (exp)

1 C0, C2, C4 C0, C2, C3

0.5

C0, C1, C2 0 600

700

800 900 1000 -1 wavenumber (cm )

1100

case 3 case 2

case 1 1200

Figure 6: Experimental and simulated Raman spectra corresponding to case 1, 2 and 3 as described in the text. Only the composition of LiPON-40 (see figure 5) was plotted. The computation of Raman spectra further evidenced this assessment on the possible existence of monovalent nitrogen atoms. Indeed, in a confrontation between experiment and theory, we showed that the experimental Raman spectrum 7 is consistent with a model structure built on dimer involving trivalent, divalent and monovalent nitrogen atoms. Experimental vibrational features cannot be properly reproduced without taking into account the three possible coordinations of nitrogen atoms, as the characteristic peaks appearing upon doping can be unambiguously assign to combination modes, due to the joint presence of divalent and monovalent nitrogen atoms. All those observations thus point out the possible existence of monovalent nitrogen atoms in the amorphous state. Besides, such a coordination requires to refine the commonly used lithium ions’ diffusion scheme. The study of the structural organization is essential to build a consistent model for the diffusion of lithium ion through the electrolyte. The diffusion model commonly considered is based on the assumption that nitrogen doping implies a 25



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Page 26 of 32

reduction of the number of mobile lithium ions. 7 Therefore, the remaining mobile ions can diffuse more efficiently throughout the electrolyte. This can be easily understood thanks to the substitution models depicted in Figure 1, which lead to divalent and trivalent nitrogen atoms. The presence of divalent nitrogen atoms leads to the creation of additional -Om + Li type of oxygen atoms. Thus, as ionic interactions bind parts of the oxygen and lithium atoms and consequently reduce the amount of mobile lithium ions, the diffusion of unbounded lithium ions is made easier. Besides, trivalent nitrogen atoms partly lead to a network reorganization, through cross-linking, which enhance the ionic conductivity as long as the amount of trivalent nitrogen atoms remains limited, so as to avoid the creation of preferential pathways. The formation of non-bridging nitrogen atoms could be explained thanks to the substitution model depicted in Figure 7.

Figure 7: Substitution model leading to the formation of non-bridging nitrogen atom. Considering the commonly used diffusion scheme, 7,11 the presence of non-bridging nitrogen atoms could both (i) regulate the amount of mobile lithium ions and (ii) allow more efficient jumps between sites. Indeed, the energy of the -Nm

+

Li ionic bond is lower than

the energy of the -Om + Li interaction. Lithium ions are thus less tightly bound to nitrogen atoms, so that this interaction can be easily formed and broken, allowing ions to hop from one site to another. This assumption should be consistent with the reduction of the activation energy, observed when doping Lix POy with nitrogen to form Lix POy Nz materials. 7 As this activation energy is correlated to the stabilization of lithium ions during migration, we can assume that the presence of non-bridging nitrogen atoms is responsible for the reduction of the activation energy. 26


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5

Conclusion

We have demonstrated the possible existence of non-bridging nitrogen atoms in amorphous Lix POy Nz . The calculation of electronic and vibrational properties allow arguing in favor of the existence of a -P=N−

+

Li coordination. Those structural evidences will have to be

taken into account for further studies on this type of materials, from both experimental and theoretical points of view. Indeed, such a structural result should allow to refine diffusion models and thus help to find solutions to the limiting phenomenons likely to influence lithium ion diffusion. Moreover, two other structural parameters have been highlighted to play a significant role on electronic properties, i.e. the chain length and the neighboring presence of lithium ions. These three factors allow to explain the unsatisfactory results obtained on Li2 PO2 N models proposed by Du and co-worker, 26 and lead us to build original models. Among the four models tested, all built starting from the crystalline structure of γ-Li3 PO4 , our modified dimer model appears as the best model to reproduce the electronic properties of Lix POy Nz . Its size and structure make it a good candidate for the study of solid electrode/electrolyte interfaces.

Acknowledgement This work was performed using HPC resources from GENCI-CINES (Grant 2014 – c2014086920) and from the Mesocentre de Calcul Intensif Aquitain. Structural pictures were done with VESTA 3 software. 36 We would like to thank Hervé Martinez and Benoˆıt Fleutot for fruitful discussions and Brigitte Pecquenard for providing the raw data of raman spectra extracted from Fleutot et al. 7 .

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Supporting Information Available Supporting information is available and contains computed eigenenergies and experimental binding energies, structural data, basis set effects on Raman spectra and forcefield parameters. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry Raman Spectra

Core Level Binding Energy Z 0 ε(η)dη El = 1

600

700

800

900

1000

-1

1100 σ (cm )

32


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Possible Existence of a Monovalent Coordination for Nitrogen Atoms

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