Multinuclear NMR and DFT Calculations on the LiFePO4·OH and

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Multinuclear NMR and DFT Calculations on the LiFePO4 3 OH and FePO4 3 H2O Homeotypic Phases

A. Castets,†,‡ D. Carlier,*,†,‡ Y. Zhang,§ F. Boucher,§ N. Marx,†,‡ L. Croguennec,†,‡ and M. M
en
etrier†,‡ †

CNRS, Universit
e de Bordeaux, ICMCB, 87 avenue du Dr. A. Schweitzer, 33608 Pessac Cedex, France CNRS, IPB-ENSCBP, ICMCB, 87 avenue du Dr. A. Schweitzer, 33608 Pessac Cedex, France § Institut des Mat
eriaux Jean Rouxel (IMN), Universit
e de Nantes, CNRS, 2 rue de la Houssiniere, BP 32229, 44322 Nantes Cedex, France ‡

bS Supporting Information ABSTRACT: 7Li, 31P, and 1H MAS NMR spectra and magnetic properties are reported for LiFePO4 3 OH and FePO4 3 H2O. The former shows no Curie
Weiss-type behavior up to room temperature, while the latter tends to such a behavior in a restricted temperature range. Calculation strategies are discussed for the NMR shifts that result from Fermi contact interaction with the high spin Fe3+ ions. Zero Kelvin electron spin densities obtained by averaging over the ion size using VASP (with PAW potentials) range with those obtained at the nucleus from WIEN2k, with the GGA and GGA+U methods. The latter values have been scaled with the temperature of the NMR measurement by using the experimental magnetic susceptibility, yielding calculated NMR shifts. The agreement is quite satisfactory, but very much dependent on the exchange correlation potential used for the calculation. Possible reasons for this are discussed, also considering the difference in magnetic behaviors.

’ INTRODUCTION In the scope of the search of new materials as electrodes for lithium-ion batteries, three-dimensional transition metal phosphates are rather interesting.1
9 In particular, LiFePO4 exhibits high thermal and chemical stability as shown by Padhi et al.10 In this context, LiFePO4 3 OH and FePO4 3 H2O were recently studied in our group.11,12 While the tavorite LiFePO4 3 OH phase was obtained by hydrothermal reaction, FePO4 3 H2O was prepared by H+/Li+ ion-exchange from previously synthesized LiFePO4 3 OH. The two phases are homeotypic; they consist of chains of FeO6 octahedra interconnected by PO4 tetrahedra, thus forming several types of tunnels. Figure 1 shows the structures of the two materials.11,12 The differences between the two structures reside in the distortion of FeO6 octahedra along the chains, those being responsible for a change in the unit cell symmetry described by a triclinic (P-1 LiFePO4 3 OH) or a monoclinic (C2/ c FePO4 3 H2O) space group. These phases were studied by X-ray and neutron diffraction, and two positions for Fe in LiFePO4 3 OH were found, whereas there is only one in FePO4 3 H2O. In LiFePO4 3 OH, the Li atoms are located in the tunnels along the c axis and occupy a single site. In the two structures, the P atoms occupy also a single site. The H atoms in FePO4 3 H2O and the one in LiFePO4 3 OH were all shown to be bound to the oxygen atoms bridging two adjacent FeO6 octahedra in the chains; in FePO4 3 H2O, they induce a strong weakening of the antagonistic Fe
O bonds leading to a strong distortion of the FeO6 octahedra as compared to those in LiFePO4 3 OH. These phases r 2011 American Chemical Society

with Fe3+ ions were tested as positive electrode material in lithium-ion batteries.11,12 The initial aim of the present NMR study was to check the number of Li, P, and H sites (in parallel with the neutron diffraction experiment) in this system, and possibly to evidence some defects or remaining lithium ions during the exchange reaction. As discussed in the following, different shifts magnitude and/or sign were interestingly observed for the various 31P and 1H NMR signals, despite the great similarity in the structures of the two compounds. We therefore wish to understand these differences. Like most battery materials, these compounds are magnetic, and their NMR spectra are consequently dominated by interactions between nuclear and electron spins (hyperfine interactions). The presence of electron spin density at a given nucleus site induces a local magnetization, which results in the so-called Fermi contact shift for the NMR signal of this nucleus. The sign and magnitude of the Fermi contact shift produced are usually expressed using the so-called contact coupling constant Ai for this nucleus as:13 δiiso ¼

Ai χM p μ0 γi ge μB

ð1Þ

where χM is the magnetic susceptibility referred to one mole of magnetic ions (and therefore identical to the molar magnetic Received: May 23, 2011 Revised: July 11, 2011 Published: July 12, 2011 16234

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Figure 1. Structures of (a) LiFePO4 3 H11 and (b) FePO4 3 H2O.12

susceptibility for both compounds), p is the Planck constant, μ0 is the magnetic constant, γi is the nuclear gyromagnetic ratio of the probed nucleus, ge is the electron g factor, and μB is the Bohr magneton. This coupling constant is related to the portion of the global magnetization that is present at the site of the nucleus. Thus, it is proportional to the electron spin density at the nucleus site (as being transferred in effect from the various magnetic ions in the surrounding of the atom considered) with:14 μ Ai ¼ 0 pγi ge μB Fi ð0Þ ð2Þ 3S where S is the spin quantum number of the magnetic transition metal ion, and Fi(0) is the spin density at or near the nucleus considered. Therefore, the contact shift can be expressed as: 1 i F ð0ÞχM ð3Þ 3S Progress in the understanding of these interactions involves the analysis of local geometries and their suitability for electron spin transfers based either on delocalization or on polarizationtype mechanisms leading to positive or negative Fermi contact shifts, respectively.15 This effort is greatly supported by calculation strategies. In periodic (inorganic) materials, the first approach was based on DFT methods using plane waves and δiiso ¼

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pseudopotentials using the VASP code. Although the polarization and the amount of electron spins at the site of the nucleus site of interest were approximated by integrating over a quite large sphere (with a radius equal to the ionic one), this qualitative approach allowed assigning decisively the resonances to the different Li sites in a given compound. In addition, spin density maps drawn from the output of these calculations revealed the orbital pathway and the mechanism by which the electron spin transfer takes place.15
17 Other paramagnetic phosphates were also extensively studied by NMR with discussion of the shifts based on the local environment or bonding.18
22 Recently, calculation codes providing a direct access to the unpaired spin density at the nucleus were applied in periodic systems to this aim, and the effect of temperature was furthermore taken into account. Thus, the PAW reconstruction used in the “GIPAW” package of the Quantum Espresso code was used by Mali et al. for Li2MnSiO4 polymorphs.23 Assuming an ideal Curie behavior and using the hyperfine coupling constant thus provided, the authors calculated the finite temperature NMR shift. In a very recent study on phosphate compounds, Grey and co-workers22 used an all-electron LCAO code, Crystal06 with B3LYP hybrid exchange-correlation functionals, to compute the electron spin density at the Li nucleus. Room temperature NMR shifts were then deduced by scaling with a “calculated” magnetic susceptibility where χcalc(T) is obtained by assuming Curie
Weiss type behavior and using experimentally derived C and θ parameters. In this work, we first report the magnetic properties and the 1 H, 7Li, and 31P NMR characterization of LiFePO4 3 OH and FePO4 3 H2O. In a first qualitative approach, we apply the pseudopotential method developed earlier to estimate electron spin densities. Those values are compared to the ones computed in the full potential/all-electron LAPW method. We finally compute the finite temperature NMR shifts from the latter approach using the experimental magnetic susceptibility. In a forthcoming paper, we will focus on understanding and describing the spin transfer mechanisms.

’ EXPERIMENTAL SECTION LiFePO4 3 OH was obtained by hydrothermal synthesis.24 FePO4 3 4H2O (97%, Fluka) and CH3COOLi 3 2H2O (97%, Fluka) were used as starting materials. They were mixed as described by Marx et al.11 with the molar ratio 1:4 in water in a 600 mL Parr reactor at 170 °C for 24 h. The obtained yellowgreen powder was dried at 80 °C overnight. FePO4 3 H2O was obtained from LiFePO4 3 OH through an Li+/H+ exchange as described by Marx et al.12 A suspension of LiFePO4 3 OH powder was prepared in water and maintained at a moderate temperature (∼60 °C), with an excess (H+/Li+ ≈ 4) of nitric acid (65%, J.T. Baker), during 1 week. After filtration and drying at 80 °C overnight, a light gray-green solid was then obtained, consisting of pure FePO4 3 H2O. This exchange is moreover completely reversible. Static magnetic susceptibilities of the two materials (χ(T) = M(T)/H (H = 1 T)) were measured between 5 and 350 K using a SQUID magnetometer (Quantum Design) for the two materials. The zero-field cooled χ values were obtained by cooling the sample in zero field down to 5 K and then heating them under the measuring field. The diamagnetic contribution was corrected using the atomic values from Bain et al.,25 yielding the χM paramagnetic susceptibility contribution. 16235

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Li, 31P, and 1H MAS NMR spectra were recorded at 38, 40, and 100 MHz, respectively, using a Bruker Avance solid state spectrometer with a Wide Bore Bruker magnet activated to 2.35 T. The spinning speed was varied up to 30 kHz using a standard 2.5 mm Bruker MAS probe. Single pulse and Hahn echo type experiments at 30 kHz (one rotor period as echo delay) were used with a 1.2 μs 90° pulse (for the three nuclei). The spectra were referenced to a 1 M aqueous solution of LiCl set at 0 ppm for 7Li, to an aqueous solution of Al(PO3)3 set at
50.8 ppm for 31P (secondary reference for H3PO4 85%), and to H2O set at 4.7 ppm for 1H (secondary reference for TMS). The recycle time used for 1H, 31P, and 7Li NMR, D0 = 1 s, is long enough to avoid T1 saturation effects for the studied nuclei in the paramagnetic phases. First principles calculations were all performed using Density Functional Theory in the generalized gradient approximation (GGA). Two types of calculations were used: (i) pseudopotential method with projector augmented waves as implemented in the Vienna ab initio simulation package (VASP),26 and (ii) allelectron/full-potential linearized augmented plane wave (FLAPW) using the WIEN2k package.27 The unit cells contain 18 and 36 atoms for LiFePO4 3 OH (P-1 space group) and FePO4 3 H2O (C2/c space group), respectively. The reciprocal space sampling was performed with the same Monkhorst pack k-point grids the two compounds (4  4  4 for the VASP code and 3  2  3 with the more demanding WIEN2k code). The structures were fully relaxed with VASP (cell parameters and atomic positions) using a cutoff energy of 450 eV for the plane wave basis sets. Relaxed structures were further imported within the WIEN2k code. LAPW calculations were done using the following muffintin spheres radii for LiFePO4 3 OH, Li, 1.86; Fe, 1.95; P, 1.46; O, 1.23; H, 0.66; and FePO4 3 H2O, Fe, 1.91; P, 1.45; O, 1.26; H, 0.68. The RMTKmax parameter, which is the product of the smallest muffin-tin radius by the wave cutoff, was fixed to 3.5 for the two compounds. All calculations were spin polarized type with a ferromagnetic type ordering, which is considered appropriate as described in ref 15. The GGA and GGA+U approximations of the local density were used. An Ueff (U
J) value of 4.9 eV was used, being previously ab initio determined for high spin Fe3+ in the olivine FePO4.28 The aim of comparing GGA and GGA+U calculations was to evidence the effect of electron localization on the predicted amount and polarization of spin transferred on the Li nucleus. So, even if the Ueff value chosen in this study is not the optimum one, the main effects of the electron localization on the calculated parameters will be observed. In the VASP method, the electron spin density around the nucleus, Fi (ri), is extracted from calculations (integration of the number of spins in a sphere using the ionic radius of each element as found in Shannon’s table,29 0.7, 0.45, and 0.2 Å for Li, P, and H, respectively, divided by the volume). Because the Fermi contact shift (at a given temperature) is proportional to the spin density at the nucleus (eq 2), this approach should provide a rather good estimation for the relative values of NMR shifts for a given compound and, to some extent (as will be discussed), for a comparison between the two compounds. In WIEN2k, two outputs of the electron spin density at the nucleus are available: (i) the spin density at the first radial grid point (closest to the nucleus) at the nucleus, and (ii) the average spin density FHFFi(0) within a crown going from this first radial grid point to its Thomas radius. This last quantity is used to

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compute the hyperfine field HFF following eq 4:30 HFFi ¼

8π0 FHFF i ð0Þ μ e 3 B

ð4Þ

where e is the electron charge. Both values were considered in this study, but as negligible differences were observed (less than 3.6%), only FHFFi(0) is now used in the following. The Fermi contact shift can now be deduced from eq 3, provided that the magnetic susceptibility is known. The following parameters are used in our calculation: ge = 2, T = 320 K, and S = 5/2 (for Fe3+).

’ RESULTS AND DISCUSSION Magnetism. The evolution of the inverse molar susceptibility versus temperature, recorded under a 1 T magnetic field, is plotted in Figure 2; it shows the appearance of antiferromagnetic interactions at low temperature for both compounds, but the transition to a paramagnetic regime is rather complex as already mentioned by Pizzaro et al. in the case of LiFePO4 3 OH.31 It is clear that up to 350 K, this compound still does not exhibit a Curie
Weiss behavior. Therefore, no Curie constant can be given for this material. For FePO4 3 H2O, a Curie
Weiss type paramagnetism appears for temperatures higher than 180 K, yielding a Curie constant equal to around 2.7, significantly lower than the theoretical value for HS octahedral Fe3+ (Ctheo = [n(n + 2)/ 8] 3 nFe3+ with n = 5 yields 4.4), but much larger than 1.9, the theoretical value for a hypothetical intermediate spin configuration that might result from the elongation of the FeO6 octahedra ([dxzdyz]3dxy1dz21; n = 3). Note that this compound starts to decompose before 400 K,32 so that extension of the magnetic measurements to higher temperatures (requiring a different experimental setup) was not tempted. For the two materials, considering the one-dimensional character of the FeO6 chains, it is therefore likely that the spin-only model is not appropriate, and further analysis of the magnetism is not within the scope of this Article. However, we conclude that the magnetic characterization for both materials is in agreement with the existence of high spin Fe3+ ions, as suggested by M€ossbauer characterization.11,32 The important observation is that the complex magnetic behavior makes it difficult, in particular for LiFePO4 3 OH, to compute the susceptibility, or even to model it as a Curie
Weiss type law, at the temperature of the NMR experiments. NMR. 7Li MAS NMR spectra using single pulse and Hahn Echo sequences are identical and very well resolved. Figure 3 shows the 7Li MAS NMR spectrum of LiFePO4 3 OH recorded using a Hahn echo sequence. The position of the isotropic signal at 214 ppm is unambiguous and corresponds to the only Li site in this structure. 31 P MAS NMR spectra obtained for FePO4 3 H2O and for LiFePO4 3 OH using Hahn echo sequences are shown in Figure 4a. As expected from the structure, a single signal is observed for the two materials. We can note, however, that despite the great similarities between the structures of these compounds, the 31P shifts are significantly different: 11 066 ppm for FePO4 3 H2O and 7498 ppm for LiFePO4 3 OH. In Figure 4a, the spectra are plotted with a scaling factor taking into account the molecular mass, the sample mass, the number of probed atoms present in the chemical formula, the receiver gain, and the number of scans. Surprisingly then, the LiFePO4 3 OH 16236

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Figure 2. Inverse magnetic susceptibility data (1/χM) between 5 and 350 K for FePO4 3 H2O and LiFePO4 3 OH. The Curie
Weiss fit (dashed line) and table of parameters are also shown for FePO4 3 H2O.

Figure 3. 7Li MAS NMR spectrum (Hahn echo) of LiFePO4 3 OH at 38 MHz (spinning 30 kHz). The spinning sidebands are marked with asterisks.

spectrum is much higher in intensity than that of FePO4 3 H2O. To understand such a difference, T2 relaxation time measurements were performed, varying the refocusing delay of the Hahn echo experiment either in static or in MAS experiments. As shown in Figure 4b, this leads to a much shorter T2 value for FePO4 3 H2O (T2
30 μs) than for LiFePO4 3 OH (T2
70 μs). Because the refocusing delay used for the MAS spectra of Figure 4a (one rotor period) is 33.33 μs for a 30 kHz spinning

rate, a value close to the T2 relaxation time of 31P in FePO4 3 H2O, the intensity of the echo recorded for this compound is weak. The one recorded for LiFePO4 3 OH, which exhibits a longer T2 relaxation time, is correspondingly much higher. Considering that the T2 relaxation process is mostly due to homonuclear dipolar interactions, a larger T2 value is indeed expected for LiFePO4 3 OH, because it exhibits much longer P
P distances than FePO4 3 H2O (dP
P (LiFePO4 3 OH) = 4.77 Å and dP
P (FePO4 3 H2O) = 3.93 Å11,12). 1 H MAS NMR spectra of FePO4 3 H2O and LiFePO4 3 OH are shown on Figure 5. Hahn echo experiments allow one to obtain well-resolved spectra. Note that a parasitic signal is always present even if the probe is empty, mostly due to surface OH groups in the environment of the coil. Two different spinning rates were used to determine the position of the isotropic signals for the two materials (see Figure S1 in the Supporting Information): 161.6 ppm for LiFePO4 3 OH and
59.8 ppm for FePO4 3 H2O, spinning at 30 kHz (Figure 5). A single line is observed for LiFePO4 3 OH and FePO4 3 H2O as expected from the neutron diffraction studies.11,12 In FePO4 3 H2O, the main peak was therefore assigned to this H environment. We notice, moreover, the presence of a second peak, very weak in intensity, located around 161 ppm that corresponds to the 1H signal in LiFePO4 3 OH. This signal can be due to the presence of residual precursor phase LiFePO4 3 OH that was not detected by X-ray or neutron diffraction, or to residual Li+ ions locally due to an incomplete H+/Li+ ion exchange. We note that no Li was observed by NMR in FePO4 3 H2O. Calculations. Table 1 gives relaxed cell parameters of the triclinic (P-1) space group of LiFePO4 3 OH and the monoclinic (C2/c) space group of FePO4 3 H2O obtained by the GGA and GGA+U methods with the VASP code as compared to the experimental cells. The cell parameters are slightly overestimated in the two phases. For the two cases, the GGA+U calculation gives closer cell parameters than GGA, but calculations are done at 0 K, whereas experimental values are obtained at room 16237

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Figure 5. 1H MAS NMR spectra (Hahn echo) of LiFePO4 3 OH and FePO4 3 H2O at 100 MHz (30 kHz spinning). The spinning sidebands are marked with asterisks. The parasitic probe signal is marked with “#”. The dashed line shows the suggested trace of LiFePO4 3 OH impurity in FePO4 3 H2O.

Figure 4. (a) 31P MAS NMR spectra (Hahn echo) of LiFePO4 3 OH and FePO4 3 H2O at 40 MHz (spinning 30 kHz). The spinning sidebands are marked with asterisks. (b) T2 measurements from 31P NMR static and MAS experiments. The dashed line shows the echo delay used in synchronized Hahn echo MAS experiments (33.33 μs).

temperature, and one cannot consider these agreements as a better accuracy of any other method. Whatever the calculation type (VASP or WIEN2k) and the approximation (GGA or GGA+U), HS Fe3+ ions are produced, as shown by partial DOS plots in the Supporting Information (Figure S2). Table 2 gives the values of the spin densities calculated by VASP and WIEN2k for the nuclei of interest. They are expressed in units of Bohr radius (1/a03). The VASP densities being average in larger spheres, they are obviously much lower than the WIEN2k ones. Adding a U term to the calculations leads, for the two methods, to a decrease of the spin density values around the 7Li and 31P nuclei, which was expected from the increase of electrons localization in the d orbitals of the Fe3+ ions, thus reducing the delocalization-type mechanism. For the 1H nucleus, this is also true, except for the WIEN2k calculations for the LiFePO4 3 OH phase, where the GGA+U method leads to a slightly higher spin density value than pure GGA. Figure 6 shows the same data as in Table 2, for the nuclei common to the two compounds, in a graphical manner, together with a comparison with the experimental NMR shifts (of course, with an arbitrary scale with respect to the spin densities). Because the calculated spin densities reflect a hypothetical 0 K situation with saturated magnetization (all spins aligned ferromagnetically), one can obviously not expect them to simulate the room temperature situation in a quantitative manner. Indeed, at the NMR measurement temperature, the situation is within the transition from AF interactions to a paramagnetic state, this transition being clearly

more advanced for FePO4 3 H2O. Nevertheless, it is clear that these spin densities provide the right sign for the Fermi contact shifts in all of the cases. Furthermore, we note (Figure 6) for all nuclei that the values obtained for the two phases are very consistent for the two methods, with and without the U parameter, because they lead to similar ranking of the spin densities. This validates the strategy consisting in using the less computer resources demanding VASP code with PAW potentials, and integrating over the full cation size around the nucleus, to rank the electron spin density at the nucleus for a given nucleus (although the absolute value is meaningless) as we have discussed earlier,16 and as was also pointed out by Grey and coworkers.22 The second set of results is the calculation of NMR Fermi contact shifts following eqs 3 and 4 by using the FHFFi(0) output from WIEN2k and taking into account the experimentally known magnetic susceptibilities at a given temperature. The NMR shift deduced from the GGA and GGA+U (Ueff = 4.9 eV) calculations are shown in Table 3 and Figure 7. In our experimental conditions, the sample temperature in a rotor spinning at 30 kHz was estimated to be 320 K. A Pb(NO3)2 powder sample with the calibration process earlier described17 was used for this estimation (there is actually a rather large temperature gradient by about 20 K, but 320 K corresponds to the most part of the signal). For comparison and to use the same approach as Mali et al.,23 we also performed NMR shift calculations assuming spinonly Curie-type magnetization. The following equation was then used: δi ¼

μ0 ge 2 μB 2 ðS þ 1Þ i F ð0Þ 9kT

ð5Þ

where k is the Boltzmann constant. We first discuss the results for LiFePO4 3 OH as follows. For the 7Li nucleus, the calculated values of the NMR shift at 320 K (Figure 7a and Table 3) yield a much better agreement with the experimental value when the experimental magnetic susceptibility is taken into account (with eqs 3,4), which is expected because the magnetic behavior is indeed far from a Curie-type one. In addition, the GGA+U method clearly improves the agreement. 16238

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Table 1. Relaxed Cell Parameters of LiFePO4 3 OH (P-l Triclinic Space Group) and FePO4 3 H2O(C2/c Monoclinic Space Group) Obtained by the GGA and GGA+U Methods with VASP in Comparison with the Experimental Ones from Refs 11,12

LiFePO4 3 OH

FePO4 3 H2O

a (Å)

b (Å)

c (Å)

R (deg)

β (deg)

γ (deg)

V (Å3)

exp.

5.352(8)

7.289 (6)

5.118 (7)

109.35 (9)

GGA GGA+U

5.432 5.407

7.416 7.363

5.161 5.150

109.07 108.98

97.73 (3)

106.35 (9)

174.98(3)

98.28 98.15

106.16 106.32

182.29 179.84

exp.

6.708(2)

7.761 (2)

7.382 (2)

115.08(2)

348.1 (2)

GGA

6.678

7.964

7.513

113.90

365.32

GGA+U

6.650

7.922

7.461

114.25

358.41

Table 2. Spin Densities Calculated with VASP (Integration Radii: ri(31P) = 0.85 a0, ri(1H) = 0.38 ao, and ri(7Li) = 1.32 a0) and WIEN2k for the Nuclei Probed in the Two Materials and with GGA or GGA+U (Ueff = 4.9 eV) Methods spin density F(ri) (VASP) (1/a03)

spin density FHFF(0) (Wien2k) (1/a03)

8.76  10
5

3.30  10
3

GGA+U GGA


5

5.62  10 4.34  10
4

2.44  10
3 8.13  10
2

GGA+U

3.34  10
4

6.95  10
2


4

1.44  10
3


4

1.56  10
3


4

9.19  10
2


4

7.86  10
2


4


4.11  10
4


4


1.98  10
4

nucleus LiFePO4 3 OH

7

Li

31

P

1

H

GGA

GGA GGA+U

FePO4 3 H2O

31

P

GGA GGA+U

1

H

GGA GGA+U

6.98  10

5.88  10

4.80  10 3.37  10


2.34  10
1.55  10

experimental ones. The magnetic behavior for this compound is actually less far from a Curie
Weiss type one, and tentative fitting leads to Cexp significantly different from Cth and a rather large Weiss term, which is in any case very different from a pure Curie type behavior. Not surprisingly then, agreement is again better when using the experimental susceptibility, but, in contrast with the LiFePO4 3 OH compound, the best agreement is with the pure GGA. Another difference is that the calculated value is lower than the experimental one, and therefore U worsens the agreement by further decreasing the value. For the 1H nucleus, the remarkable feature is the reproducing of the negative sign (as already mentioned from the spin densities), and, like for 31P, the best (and rather good) agreement is obtained with pure GGA. However, the situation is rather complex because, possibly fortuitously, GGA+U with (unphysical) Curie magnetism leads to apparent agreement, and, as for LiFePO4 3 OH, the effect of U is to add a positive polarization on the proton. Figure 6. Spin densities around each nucleus (a) 31P and (b) 1H obtained with GGA and GGA+U methods and with VASP (integration radii ri(31P) = 0.85 a0 and ri(1H) = 0.38 a0) and WIEN2k codes for the two materials with an arbitrary scale comparison with experimental NMR results.

For the 31P nucleus, similar observations hold: using the experimental susceptibility and the U term leads to satisfactory agreement of NMR shift with experiment (Figure 7b and Table 3). For the 1H nucleus, we note that the effect of U is opposite to the case of the other two nuclei, and the agreement appears satisfactory without the use of U. As concerns FePO4 3 H2O, the following observations can be made. For the 31P nucleus, the values calculated assuming Curie type magnetism are again in very bad agreement with the

’ GENERAL DISCUSSION For the LiFePO4 3 OH phase, the agreement is therefore generally quite good when calculating the shift from the experimental susceptibility and using GGA+U with a value of U that was shown to be adequate to HS Fe3+ in octahedral site in the FePO4 olivine.33 Although the effect of U for the protons is not intuitive, this tends to validate this calculation strategy. In particular, it is important to recall that the complex behavior of the macroscopic magnetization of this compound precludes any calculation of the susceptibility. In contrast, for FePO4 3 H2O, better agreement is obtained using the experimental susceptibility with pure GGA. A possible explanation would be that, in this compound, the nature of the Fe3+ ions does not require the use of U, but it is not clear why an 16239

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Table 3. Calculated Values for the NMR Fermi Contact Shift Obtained from the Spin Density Values Calculated with the WIEN2k Code (GHFFi(0)) for the Two Materialsa nucleus LiFePO4 3 OH

7

Li

31

1

FePO4 3 H2O

H

31

1

P

P

H

experimental δ (ppm) 214 7498 161.6 11 066
59.8

δ (ppm) assuming Curie law GGA

δ (ppm) with experimental susceptibility

848

396

GGA+U GGA

627 20 873

293 9752

GGA+U

17 835

8333

GGA

371

173

GGA+U

400

187

GGA

23 618

9653

GGA+U

20 177

8245


106


43


51


21

GGA GGA+U

a

The calculations have been performed at 320 K assuming the Curie law or including the experimental susceptibility and with GGA and GGA+U approximations.

Figure 7. Comparison between experimental and calculated values for the NMR Fermi contact shift obtained from the spin density values calculated with the WIEN2k code (FHFF(0)) for the two materials. The calculations have been performed at 320 K assuming a Curie law or including the experimental susceptibility and with the GGA and GGA +U approximations.

elongation of the FeO6 octahedra should lead to such a situation, but it can be proposed that the shortening of some Fe
O bonds is the evidence of more covalent Fe
O interactions. Consequently, a less correlated method (without a U value) seems to be more appropriated for the description of the exchangecorrelation potential. Another explanation would be that, in this

compound, and despite a behavior of the macroscopic magnetization closer to Curie
Weiss type, the transfer of electron spin density responsible for the contact shift of the P and H nuclei does not arise through a coupling with the macroscopic magnetization, as implied in eq 1. Actually, the P and H nuclei are indeed coupled to (i.e., receive electron spin density from) a sum of individual Fe3+ ions of their neighborhood. If the latter possess electron spins with polarization that does not reflect the average macroscopic magnetization, which is expected if local interactions between the Fe3+ ions remain, then the NMR shifts cannot follow the macroscopic magnetization, and the concept of hyperfine coupling constant as defined in eq 1 needs to be revised. A possible, but not necessarily conclusive, check for this would be comparison of the temperature variations of the individual NMR shifts and of the macroscopic magnetization. The question as to whether the paramagnetic ions that are coupled to the nucleus probed by NMR individually follow or not the macroscopic magnetization is of course crucial to the contact shift calculation strategy. Actually, considering the rather complex magnetic behavior of the LiFePO4 3 OH phase, it even appears somewhat surprising in retrospect that the contact shifts calculated using the macroscopic magnetization reproduce so closely the experimental values. Because many parameters can be adjusted in any calculation process (in particular the U parameter in our case, although it was not adjusted but chosen on the basis mentioned above), one has to be very cautious about the possibility that such an agreement be due to fortuitous cancellation of various errors. In consequence, it appears important that further efforts be devoted to apply such strategies to various systems to strengthen the analysis. The origin of the very different NMR shifts magnitude observed (and for the most part reproduced by the calculations) for both 1H and 31P MAS NMR spectra for LiFePO4 3 OH and FePO4 3 H2O is striking because the two materials possess the same HS Fe3+ electronic configuration and similar structures. Indeed, P in the two materials is surrounded by four FeO6 octahedra with environments not so different geometrically. Similarly, the geometries of the Fe3+ ions around the protons are not very different in the two compounds, although they receive electron spins with opposite polarization. It is therefore important to understand how the nature of the chemical bonds in each case leads to different electron spin transfer mechanisms as was previously done for other compounds. This can be 16240

dx.doi.org/10.1021/jp204767c |J. Phys. Chem. C 2011, 115, 16234–16241

The Journal of Physical Chemistry C approached by analyzing the local geometries and bonding, in particular by studying spin density maps established by the calculations, and will be reported in a subsequent paper.

’ ASSOCIATED CONTENT

bS Supporting Information. Additional figures. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author

*Phone: +33 (0) 5 40 00 35 69. Fax: +33 (0) 5 40 00 27 61. E-mail: [email protected].

’ ACKNOWLEDGMENT This work benefited from a grant from Agence Nationale de la Recherche (ANR-09-BLAN-0186-01). We thank Laurent Le Polles for fruitful discussions. R
egion Aquitaine (2007/2013 CPER Contract: 2.3.1-08012000) is acknowledged for financial support of NMR equipment, as well as M3PEC (Bordeaux) and IMN (Nantes) for computing facilities.

ARTICLE

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