Investigation of the Chemical Disorder of LiNi0.5Mn1.5O4 Lattice by

Article pubs.acs.org/JPCC

Investigation of the Chemical Disorder of LiNi0.5Mn1.5O4 Lattice by Means of Extended X‑ray Absorption Fine Structure Spectroscopy G. Greco,*,†,‡ S. Brutti,¶,§ F. M. Vitucci,‡,§ L. Lombardo,†,‡ M. Köntje,∥ A. Savoini,⊥ A. Paolone,‡,§ and S. Panero†,‡ †

Chemistry Department, Sapienza University of Rome, Piazzale A. Moro 5, I-00185 Roma, Italy Research Center Hydro-Eco, Sapienza University of Rome, Via A. Scarpa 14, I-00161 Roma, Italy ¶ Department of Science, University of Basilicata, V.le Ateneo Lucano 10, 85100 Potenza, Italy § CNR-ISC, UOS Sapienza, P.le A. Moro 5, I-00185 Rome, Italy ∥ ZSW Zentrum für Sonnenenergie und Wasserstoff-Forschung, Baden-Württemberg, Helmholtzstrasse 8, D-89081 Ulm, Germany ⊥ Research Center for Non-Conventional Energies, Istituto ENI Donegani, ENI S.p.A. via Fauser 4, I-28100 Novara, Italy ‡

ABSTRACT: This work reports on a characterization methodology for investigating the transition-metal site disorder in the LiNi0.5Mn1.5O4 spinel structure (LNMO, Fd3̅m space group, cF56 lattice). This approach, previously adopted on simple intermetallic ordered solid solutions, is here applied to a complex lattice. The LNMO material synthesized by us has been investigated by advanced techniques such as X-ray absorption spectroscopy (XAS), X-ray diffraction, scanning electron microscopy, and high-resolution transmission electron microscopy. High-quality XAS spectra measured at both the Ni K-edge and the Mn K-edge have been analyzed using double-edge multiple-scattering data analysis. Computer simulations, based on structural lattice models describing substitutional disorder between Ni and Mn in the 16d site of the LNMO lattice, have been carried out by varying the order parameter s of the site occupancy from 0 (completely disordered) to 1 (completely ordered). These simulations allow us to predict the evolution of the two- and three-body structural parameters versus the order parameter s. The chemical ordering in the transition-metal 16d atomic site of the primitive LNMO cell has been analyzed by coupling computer simulations and extended X-ray absorption fine structure (EXAFS) data analysis results. The EXAFS signals are sensitive to the surrounding substitutional disorder, and their intensities, especially those of the collinear three-atom configurations, can be used to evaluate the ordering level of the transition metals in the lattice. The final refined order parameter value (s = 0.0) suggests that only negligible ordering occurs in this lattice between Ni and Mn, and the structure is therefore completely disordered.

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INTRODUCTION

The synthesis procedure deeply influences both the crystal structure and the performance of this compound.5,6,10,14−17 It is known that samples synthesized above 700 °C have a facecentered cubic spinel structure (Fd3m ̅ space group, cF56 lattice). In addition, all materials produced above 650 °C display a Ni content lower than the nominal one and contain, as an impurity, a LiNi1−xO1−x/2 phase (Fd3̅m space group, cF8 lattice).10 The crystallization of this undesired contaminant has been observed by many authors, and it is commonly recognized as an apparently unavoidable byproduct of all syntheses carried out above 700 °C (see discussion in refs 18 and 25). However, despite this drawback, high-temperature synthesis is usually used because the growth of the spinel phase at low temperatures is extremely slow.19,20,23 There is a general consensus about the random distribution of the manganese and nickel ions in the 16d sites in the Fd3m ̅ lattice. On the other

Material science (sensu lato) literature is rich in papers dealing with the structural, physical, and chemical properties of phases belonging to the spinel structure type. End members and solid solutions within these chemical systems are easily synthesized, and because of their physical and electronic properties, they are very widely used as technological materials, for example in magnetic recording media, lithium ion batteries, catalysts, and pigments.1 LiMxMn2−xO4 spinels phases with x = 0.5 and M = Mg, Cr, Mn, Fe, Ni, Zn2−4 have recently attracted huge interest as innovative cathodes for lithium batteries. They are environmental friendly, inexpensive, and have good theoretical properties in lithium cells. In particular, LiNi0.5Mn1.5O4 is able to reversibly cycle lithium in electrochemical cells for hundreds of times at high current rates,5 and use in full lithium ion cells has been demonstrated.8,9 It displays a high charge− discharge potential of about 5 V with minor irreversible losses upon cycling.6 © XXXX American Chemical Society

Received: June 26, 2014 Revised: October 21, 2014

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dx.doi.org/10.1021/jp5063622 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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hand, prolonged annealing below 700 °C, after the first calcination at higher temeprature, leads to the ordering of Mn and Ni and the formation of a superstructure, thus transforming the Fd3m ̅ face-centered structure (disordered) to the primitive cubic lattice P4332 (ordered).21,22 Infrared spectroscopy is the more often used method for distinguishing these two structures and can be used qualitatively to evaluate ordering percentage in spinel which contains both ordered and disordered LiNi0.5Mn1.5O4.23 The Li intercalation path is greatly influenced by the Ni and Mn ordering that form an electrostatic repulsion. This repulsion is different in the two ordered and disordered phases; therefore, the Li migration activation barriers will be different from each other. Previous studies showed that disordered LiNi0.5Mn1.5O4 exhibited cycling performance better than that of ordered LiNi0.5Mn1.5O4 at high rates.24,25 A synthesis procedure for LiNi0.5Mn1.5O4 (LNMO) has been developed in our lab: the samples obtained by wet chemistry, starting from acetate precursors and synthesized at 800 °C,5,6 show the lowest contamination, highest crystallinity, and best electrochemical response in terms of stability and high current rate in a Li-ion cell (100 mAh g1 for more than 400 cycles at 146 mA g1 (1C)).5 Combining different techniques including X-ray absorption spectroscopy (XAS), X-ray diffraction (XRD), scanning electron microscopy (SEM), and high-resolution transmission electron microscopy (TEM), we present a deep quantitative structural characterization never performed up to now in a complex structure such as LiNi0.5Mn1.5O4 spinel. In particular, we address the issue of chemical disorder in the 16d sites (0.6250, 0.6250, 0.6250), as both Ni and Mn ions reside on these positions. Our goal is to clarify definitively the atomic structure and thus the influence of chemical disorder on the electrochemical performances of this complex material, giving an effective quantitative characterization method that can be applied in principle to every active material. Instrumental for this task was the use of extended X-ray absorption fine structure (EXAFS) techniques. In fact, it has been shown that the EXAFS signals due to multiple scattering between different atoms occupying identical crystal sites (partial occupancies) allow the estimate of the probability of finding the same chemical species on the same position in each unit cell.26−30 Double-edge EXAFS analysis coupled with computer simulations has been recently used31 to study the chemical disorder of a PtxCo solid solution. This approach is apparently capable of revealing unique quantitative information about the distribution of different chemical species among equivalent crystallite sites. Here we extend this model to a complex cubic lattice with 56 atoms (8 Li, 12 Mn, 4 Ni, and 32 O) in the face-centered unit cell. The paper is organized as follows: the first section is dedicated to sample characterization by using TEM and XRD techniques. XAS experimental details and preliminary data are reported in the second section. The third section is focused on the methodology of the XAS data analysis using an advanced technique based on the GNXAS method32,33 and statistical computer simulation. In the fourth section the main conclusions of this work are given.

Figure 1. (a) SEM images of LiMn2xNixO4. (b) Metallic particle size distribution obtained from the analysis of the SEM image in panel a. (c) High-resolution TEM (HRTEM) image of the crystalline agglomerates; (inset) fast Fourier transformation of HRTEM.

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EXPERIMENTAL DETAILS AND PRELIMINARY CHARACTERIZATION BY DIFFRACTION AND ELECTRON MICROSCOPY LiNi0.5Mn1.5O4 spinel samples have been synthesized accordingly to ref 5 by our standard wet chemistry route followed by high-temperature annealing in air at 800 °C degrees. Conventional Cu Kα X-ray diffraction (Rigaku Ultima+ diffractometer) confirmed the formation of the cF56 structure with a minor contamination by LiNi1−xO1−x/2 (∼2.7 wt %) due to the precipitation of the expected cF8 phase.5 The composition of the sample has been confirmed by elemental analysis using inductively coupled plasma mass spectrometry (ICP-MS) on B



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Table 1. Lattice Parameter (a), Mean (dmean) and Maximum (dmax) Diameter of Crystallites, Broadening of the Diameter Distribution (σ), Oxidation State of Manganese Ion (Os), and the Ratio between Mn and Ni Atoms (Mn:Ni) LNMO

a (Å)

dmax (×100 nm)

dmean (×100 nm)

σ (×100 nm)

Os

Mn:Ni

XRD SEM, TEM XAS

8.172(2) 7.9(5) −

− 3(1) −

− 4(1.5) −

− 1.2(5) −

3.96 − 3.93

1.50:0.51 − 1.57:0.43

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XAS EXPERIMENTAL DETAILS AND RESULTS EXAFS measurements have been performed in transmission mode at room temperature at the beamline XAFS of the

solid pellets of the starting material. A Li:Mn:Ni ratio of 1.01:1.50:0.51 with an estimated accuracy of 0.01 on each stoichiometric coefficient was determined. The structural refinement by Rietveld method was carried out by the GSAS program11,12 following a constrained approach proposed in ref 5. The overall stoichiometry of the sample has been determined from ICP-MS data. Similarly, the Mn:Ni and Li:Ni ratios in the cF56 and cF8 phases, respectively, have been postulated by a preliminary determination of the cubic lattice parameter of the two phases on the basis of the benchmark data by Dahn and coworkers10 and Toussaint.13 Because all these parameters were kept constant, with the additional assumption of a unitary occupancy of the oxygen atoms in the atomic sites of both the cF8 and cF56 lattices, the lithium stoichiometric coefficient in the cF56 lattice results by the sole optimization by the Rietveld method of the relative amount of cF8 phase in the sample. This indirect and constrained approach is applied to circumvent the limitations of the XRD technique to correctly evaluate compositions, in particular in the case of similar heavy nuclei (like manganese and nickel) or for light elements (like lithium). As a final point it is important to underline that in the refinement the Debye−Waller factor has been assumed equal to B = 1 Å2 for all the atomic species in all lattices. Our constrained Rietveld refinement of the XRD pattern suggests for the LNMO cF56 lattice a cubic parameter of a = 8.172 ± 0.002 Å, a slight lithium deficiency, a final stoichiometry of Li0.98Mn1.54Ni0.46O4 with estimated s = 0.02 inaccuracies on the stoichiometric coefficients. The estimated manganese oxidation state estimated from this stoichiometry is 3.96 to be compared with the 3.98 value derived by electrochemical analysis (see refs 5 and 6). The scanning electron microscopy (JEOL JSM 7600F) investigation suggests a highly homogeneous morphology of the sample (see Figure 1a). It is constituted by wellformed octahedral-like crystallites with regular shapes and sharp edges. The image analysis of 100 randomly selected quasioctahedron-shaped particles observed in several SEM images has been carried out by the ImageJ program34 to derive the mean particle geometrical properties. Crystallites have been assumed to be regular octahedral, and the reported size distribution plot shows the diameters of the corresponding outer sphere (Figure 1b). The crystallite size distribution is peaked at approximately 300 nm; as expected, it is asymmetric and shows a tail extended to larger-sized particles. The apparent mean crystallite size is about 400 nm. The size distribution can be reproduced rather accurately through a log−normal model.35,36 The size distribution maximum and mean values (dmax and dmean, respectively) and the distribution broadening (σ) are summarized in Table 1. TEM investigation (JM-3010 HR TEM) confirmed the long-range crystalline ordering of the particles (Figure 1c). Fast Fourier transform (FFT) analysis of several high-resolution TEM (HRTEM) images confirmed the formation of a face-centered cubic lattice with a cell parameter of approximately 7.9−8.0 Å (Table 1).

Figure 2. (a) Comparison of Mn K and Ni K near-edge XAS spectra of LNMO powder; Eo, edge energy. Experimental χ(k) signals and its FT of LNMO powder (panels b and c, respectively) for Mn K-edge and Ni K-edge.

ELETTRA Synchrotron Light Laboratory (Trieste, Italy) using a double-crystal monochromator equipped with a Si(111) crystal.37 The sample powder has been mixed with graphite in the proper ratio to give an optimized absorption step of ∼1.1 at the Mn K-edge and ∼0.4 at the Ni K-edge.32,33 The same pellet has been used for acquisition at both absorption edges to avoid possible inhomogeneities of the powders. The raw XAS data at the Mn and Ni K-edges are reported in Figure 2. The X-ray absorption near-edge spectroscopy C



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(XANES) signal intensity after removal of the pre-edge absorption and without normalization (Figure 2a) is directly proportional to the Mn and Ni quantities in the sample. The Mn K-edge XANES signal is typical of the spinel phase with prepeak features between 6540 and 6545 eV.7 This preedge features result from transitions to bound final state in 3d orbital and are proportional to the Mn oxidation state.7 The obtained stoichiometry and oxidation state is reported in Table 1, in good agreement with XRD and electrochemical results. The analysis of the XAS signals has been performed by means of the GNXAS program.32,33 The k-weighted EXAFS oscillations, kχ(k), have been extracted from the experimental data and are shown in Figure 2b. Good signals have been obtained up to 15 and 13.5 Å−1 for the Mn and Ni K-edge, respectively. The k-weighted χ(k) data have been Fourier transformed (FT) in the k range between 3.5 and 14.9 Å−1 for the Mn K-edge and between 3.5 and 13.4 Å−1 for the Ni Kedge. The Fourier transform obtained shows many correlation peaks up to R = 6 Å, as expected for a crystalline structure. The FT signals are reported in Figure 2c. In the following analysis we do not take into account the secondary LixNi1−xO1−x/2 (cF8) phase. Indeed, the results obtained on the Mn K-edge are not affected by this impurity phase because the cF8 does not contain manganese. Moreover, the content of the secondary phase is so low (≤4%) that also the Ni K-edge is only very weakly influenced by the presence of this contamination. It is likely that an increase of the Debye−Waller factor could occur, as in the case of manganites with a low concentration (≤2%) of spurious Mn3O4.38 Therefore, a good starting point for the analysis of the EXAFS data is the bulk structure of the spinel LiNi0.5Mn1.5O4, (cF56 cell, cubic lattice parameter a = 8.16 Å, and space group Fd3m ̅ , #227) in which the lithium ions are located at the 8a sites (0, 0, 0), the oxygen atoms reside on the 32e positions (0.3792, 0.3792, 0.3792), and the manganese and nickel ions are distributed in the 16d sites (0.6250, 0.6250, 0.6250).

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COMPUTER SIMULATION TO MODEL EXAFS SIGNAL OF DISORDERED STRUCTURE Recently, it has been proven that the analysis of the scattering of triangular configurations is a valuable tool for evaluating the ordering of simple cubic alloys, such as PtxCo.31 In particular, the presence of chemical disorder affects the geometrical parameters such as the coordination numbers of neighboring atoms. Here, we discuss the extension of such an analysis method to a more complex structure compared to a simple cubic alloy to investigate capabilities and limits of this approach. To evaluate the effect on the EXAFS signals of the chemical disorder on the 16d crystal site of the spinel structure, occupied alternatively by the two transition metals (Mn and Ni), we focused our attention only on the Mn/Ni sublattice in the conventional unit cell (cF56 lattice, cubic lattice parameter a = 8.16 Å, space group Fd3̅m, metal atoms in the 16d atomic site in (0.625, 0.625, 0.625)). In Figure 3a, the hypothetical ordered cell made by 16 atoms of Mn and Ni is shown; the atomic ratio Mn:Ni is 3:1. Substitutional disorder is simulated introducing a finite probability p for the occupancy of selected lattice sites with Ni atoms. In particular, p is taken as the probability that a Ni atom occupies the same site position in each unit cell, see Figure 3a. The range 0.25 ≤ p ≤ 1 describes all possible levels of chemical disorder, spanning from a completely ordered structure (p = 1) to a completely disordered one (p = 0.25, for which no preferential position can be defined for Ni). We

Figure 3. Structural representation of (a) Mn−Ni primitive cell (only 16d sites are shown) and (b, c, and d) three different Mn−Ni supercells (Mn, blue; Ni, yellow) with a cubic structure and with a different degree of chemical disorder; s = 1.00, ordered, and s = 0.45 and s = 0.00, random structure, respectively.

calculate the multiplicity and coordination numbers of the main two- and three-body contributions to the EXAFS signals as a function of chemical disorder by means of a computer simulation scheme, previously discussed in ref 31. The effects of the finite size of the calculation have been minimized by considering a supercell 4 × 4 × 4 replica of the conventional spinel cell, which contained 64 cubic structures and a total of 1024 atoms. For each supercell we preserve the stoichiometry, maintaining the Mn:Ni ratio at 3:1. In the following, the results of the computer simulations are presented introducing the order parameter s for the disorder, defined as D



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which corresponds to 16 different s values spanning from 0 ≤ s ≤ 1, with steps of s = 0.0625. In panels b, c, and d of Figure 3 we report three supercells, which are representative of three chemical orderings: s = 1.00, 0.45, and 0.00, respectively. Moreover, in Tables 2 and 3 we report the parameters of the two- and three-body configurations for the ideal ordered structure. In Figure 4 the calculated coordination numbers (Nc) for the first (c = 1), second (c = 2), third (c = 3), and fourth (c = 4) shells g2 are reported as a function of s. In Figure 5 we report the calculated g3 coordination numbers (N3(s)) which correspond to the scattering of three atoms connected by two bonds forming an angle of 120° or 180°. These simulations highlight that the chemical disorder affects the coordination numbers of the transition metal sublattice. In particular, at s < 0.4 (order structures), it is possible to find marked differences in the g2 Nc(s), even for little variation of s, whereas the coordination number N3(s) of the three-body configurations g3 can probe even the limited ordering at s < 0.4. In Figure 6 the calculated FT both at the Mn and Ni edges are shown for four different values of the order parameter s. It can be noted that the peak related to the Mn−M path (M = Mn or Ni) centered around 2.9 Å and the peak around 5.6 Å which is due to the three-body scattering are the features more affected by the chemical disorder.

Table 2. Two-Atom (g2) Configurations in a Hypothetical Mn−Ni Ordered Structurea atoms

shell

Nc

R1 (Å)

atoms

shell

Nc

R2 (Å)

Mn−Mn Mn−Ni Mn−Mn Mn−Ni Mn−Ni Mn−Mn Mn−Ni Mn−Mn

I I II II III III IV IV

4 2 10 2 4 8 4 8

2.86 2.86 4.96 4.96 5.72 5.72 6.40 6.40

Ni−Mn Ni−Ni Ni−Mn Ni−Ni Ni−Mn Ni−Ni Ni−Mn Ni−Ni

I I II II III III IV IV

5 1 10 2 8 4 10 2

2.86 2.86 4.96 4.96 5.72 5.72 6.40 6.40

a

Only 16d positions in a LNMO Fd3̅m spinel structure have been considered, see Figure 3a,b. R1 is the mean distance between atoms Mn−M (M = Mn or Ni), and R2 is the mean distance between atoms Ni−M (M = Mn or Ni). NC is the number of neighbors M.

s=

p − Ca 1 − Ca

(1)

where p is the occupation probability defined above and Ca is the atomic concentration of the selected species (Ca = 1/4 for Ni). Therefore, s = 0 corresponds to the random distribution of Mn and Ni atoms in the 16d sites, whereas s = 1 describes a perfectly ordered crystal. We calculate by computer simulations the coordination numbers and degeneracy of the two-body (g2) and three-body (g3) configurations on 3000 different supercells,

Table 3. Three-Atom (g3) Configurations in a Hypothetical Mn−Ni Ordered Structurea atoms

degeneracy

R01=R02 (Å)

Ni−Mn−Mn(ph2) Mn−Mn−Mn Mn−Ni−Ni Ni−Ni−Mn(ph2) Mn−Ni−Mn(ph2) Mn−Mn−Mn Mn−Mn−Mn(ph2) Ni−Ni−Mn(ph2) Ni−Mn−Mn(ph2) Mn−Ni−Mn Mn−Ni−Mn Mn−Mn−Mn Mn−Mn−Mn(ph2)

4 2 1 1 2 3 7 1 1 2 1 1 1

2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86

Ni−Ni−Mn Ni−Mn−Mn Ni−Ni−Mn Mn−Ni−Ni(ph2) Ni−Mn−Mn Mn−Ni−Mn(ph2) Ni−Ni−Mn Ni−Ni−Mn(ph2) Mn−Ni−Ni(ph2) Ni−Mn−Mn Mn−Ni−Mn(ph2)

2 4 2 2 4 8 1 1 2 2 3

2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86 2.86

R03 (Å)

Θ (deg)

freq (Å)

Mn−Mn I shell − − Mn−Ni II shell Mn−Ni II shell − Mn−Mn II shell Mn−Ni III shell Mn−Mn III shell Mn−Ni III shell Mn−Ni III shell − Mn−Mn III shell

60 60 120 120 120 120 120 180 180 180 180 180 180

4.29 4.29 5.34 5.34 5.34 5.34 5.34 5.72 5.72 5.72 5.72 5.72 5.72

− − Ni−Mn II shell Ni−Ni II shell − Ni−Mn II shell − Ni−Mn III shell Ni−Ni III shell − Ni−Mn III shell

60 60 120 120 120 120 180 180 180 180 180

4.29 5.34 5.34 5.34 5.34 5.34 5.72 5.72 5.72 5.72 5.72

Mn K

Ni K

a

Only 16d positions in a LNMO Fd3̅m spinel structure have been considered, see Figure 3a,b for Mn and Ni K-edges. Degeneracy is specified for each configuration, with the photoabsorber placed at the vertex between two shortest bonds (e.g., Mn−Ni−Ni, Mn atom is at the vertex). R01 and R02, mean distances of two shortest bonds with angle Θ between; R03, corresponding atoms and belonging shell; freq (frequency), half of the length of the triangle perimeter corresponding to the peak leading frequency in Fourier spectrum; phN, the photoabsorber is positioned in position N (side of the triangle, not the triangle vertex). E



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Figure 6. Fourier Transforms of the Mn and Ni K theoretical XAS signals calculated for different values of the disorder parameter s.

Figure 4. Two-body coordination numbers as a function of s (chemical order) parameter for the LNMO phase, calculated in this work. Topleft panel, first g2 shell; top-right panel, second g2 shell; bottom-left panel, third g2 shell; and bottom-right panel, fourth g2 shell.

Figure 7. Best-fit results of GNXAS analysis performed for LiNi0.5Mn1.5O4 at Mn (left-hand panel) and Ni K-edge (right-hand panel) (k3 weighted); dashed line, the experimental signal; solid line, sum of all theoretical components of the signal. Upper curves represent components of the model signal, vertically shifted for clarity; solid line, model signal; dashed line, experimental signal. The scale is indicated within the figure. Figure 5. Calculated degeneracy (Nc) for three-body configurations (g3) with 120° or 180° vertex angle as a function of s parameter.

• Third neighbors: we consider both the two- and threebody signals due to the scattering of the Mn−O−O and Ni−O−O triangular configurations formed by two firstneighbor bonds. The value of the angle formed by the bonds was imposed to be 180°. Also, the coordination number and the degeneracy of these paths have been fixed in the analysis. • Fourth and fifth neighbors: we include both the two- and the three-body signals using Ni−Ni−Ni, Ni−Ni−Mn, Ni−Mn−Mn, and Mn−Mn−Mn triangular configurations formed only by two first-neighbor bonds with bond angles of 120° and 180° (fixed values), as the signals related to 60° configuration are negligible. Nc and degeneracy of the triangular configurations have been varied according to the chemical order parameter s (see Figures 4 and 5). Diagonal covariance matrices for the thermal average have been used, and only the bond-

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EXAFS DATA ANALYSIS AND DISCUSSION The fitting of the EXAFS χ(k) signals has been performed considering the two- and three-body main contributions listed below. The other possible scattering paths give much weaker signals and therefore have been neglected. • First and second neighbors: in the range of distances between 1.5 and 3.2 Å, the two-body scattering due to the Mn−O or Ni−O (I shell) and to the Mn−Mn, Mn− Ni, Ni−Mn, and Ni−Ni (II shell) paths are modeled by usual Gaussian distributions. The coordination numbers (Nc) for the four contributions of the II shell have been allowed to vary according to the chemical order parameter s, imposing, however, the constraint that the sum of the coordination numbers of the Mn−Mn (Ni− Ni) and Mn−Ni (Ni−Mn) shells equals 6. F



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found in a range between 0 and 1°, whereas the bond−bond correlation of the collinear configuration is negative ρr,r′ ∼ −0.26 as found in other systems.30,31 The bond variance, σ2, around Mn atoms is in good agreement with previous works, i.e., σ2 = 0.0034−0.0050 Å2 for Mn−O and Mn−Mn first and second shell signals.7,40 Around the Ni atom, the variance is σ2 = 0.005−0.006 Å2 for both Ni−O and Ni−Ni bonds. These values are larger than those in the literature (σ2(Ni−O) = 0.0039 Å2 and σ2(Ni−Ni) = 0.0023 Å2),41 probably because of the presence of the secondary LixNi1−xO1−x/2 phase described in the first section. The same holds for the second and higher shells in which the distance variances approach the uncorrelated limit of 2u2 = 0.01 Å2, where u2 is the fluctuation around the equilibrium positions. As discussed before, the increase of the Debye−Waller factor was already observed in other compounds with secondary phases, such as in manganites with a low concentration (

Investigation of the Chemical Disorder of LiNi0.5Mn1.5O4 Lattice by

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