J. Phys. Chem. C 2008, 112, 20481–20490
20481
Direct Correlation between the 31P MAS NMR Response and the Electronic Structure of Some Transition Metal Phosphides E. Bekaert,† J. Bernardi,‡ S. Boyanov,‡ L. Monconduit,‡ M.-L. Doublet,*,‡ and M. Me´ne´trier*,† CNRS, ICMCB, UniVersite´ de Bordeaux, 87 AV. Schweitzer, 33608 Pessac cedex, France, and Institut Charles Gerhardt, CNRS, UMII, ENSCM, UMI, Place Euge`ne Bataillon F-34095 Montpellier Cedex 5, France ReceiVed: September 12, 2008
A series of binary transition metal phosphides (Ni3P, Ni12P5, Ni2P, Ni5P4, NiP, NiP2, FeP, FeP2, FeP4, VP2, CoP) were investigated by solid state 31P MAS NMR, leading to rather different lineshapes, shifts, relaxation times, and temperature dependences. The electronic structures of these compounds were computed using various DFT codes, based either on plane wave PAW potentials (VASP) or on all-electron basis sets in the FPLAPW formalism (Wien2K). Depending on the electronic features of the phosphide, self-interaction corrected formalisms (DFT+U or PBE0 hybrid functional) were also used to reach a better description of the electronic ground state and to establish a correlation with the shape and the nature of the NMR signals. As a result of the analysis, the main categories are diamagnetic compounds (FeP4, NiP2) and metallic ones, either real (VP2) or with some electronic localization in band tails (Ni12P5, Ni2P, Ni5P4, NiP) or with spin-polarized conduction bands (CoP, FeP). FeP2 appears somewhat ambiguous, both based on the various computational results and on the NMR characteristics. Besides, FeP4 is the only compound for which very clear J couplings resulting from P-P bonds were observed. Introduction Binary transition metal phosphides are studied in particular for their catalytic properties, as well as more recently for their reactivity with Li. The latter property has been evidenced by different groups, either based on classical Li insertion processes like LixMP41,2 and MnP43 or based on more complex conversion processes like CoP3,4,5 Cu3P,6,7 NiP2,8 FeP, 9 and MnP4,10 a concept first proposed by Poizot and Tarascon in the case of oxides.11 Upon electrochemical reaction of Li on such phosphides, quite complex and diverse processes may indeed occur, depending on the system: lithium insertion forming a ternary Li-TM-P compound (TM: transition metal) and decomposition (conversion) of the phosphide (or lithiated phosphide) into other ones combining different TM/P ratios and different lithium contents or even into nanocomposite electrodes consisting of nanoparticles of TM at the metallic state embedded in an Li3P matrix. What is particularly remarkable is that the global lithiation-delithiation process is reversible, leading to good rechargeability of the batteries using such materials as negative electrode, with quite attractive energy densities compared to the presently used lithiated carbons. This global faradic reversibility, however, is not always present in the mechanisms, in the sense that the compounds formed during the lithiation (in particular before the full conversion reaction) are not necessarily reformed during delithiation, while the original phosphide may also not be reformed upon full delithiation. A peculiarity of these phenomena is that they lead to the formation of mixtures of compounds with nanometric particle sizes, often covered by thin layers of products of parasitic reactions with the electrolytic medium, making them particularly difficult to characterize using diffraction techniques. * Corresponding authors. E-mail adresses:
[email protected] (M.M.) and
[email protected] (M.L.D.). † Universite´ de Bordeaux. ‡ Institut Charles Gerhardt.
Li and P NMR are therefore potentially of interest to characterize such materials and to further give better insights into the complex lithiation-delithiation processes. To our knowledge, only few 31P MAS NMR characterization reports of TM phosphides exist in the literature, namely, Ni3P and Cu3P,12 as well as Ni2P and Ni12P5.13 All these compounds exhibit relatively large 31P NMR shifts that were considered as Knight shifts in relation with the metallic character assigned to these compounds. Transition metal phosphides, however, may exhibit very different electronic structures and properties that are expected to lead to very different 31P NMR characteristics, including absence of signal or impossibility to carry out such characterization. Facing the need to establish a correlation between the NMR characteristics and the electronic structures, we have therefore prepared a selection of V, Fe, Co, and Ni phosphides, characterized them using 31P MAS NMR, and computed their electronic structures by means of first-principles density functional theory (DFT) calculations. In principle, pure metals (i.e., delocalized electronic ground states) and diamagnetic semiconductors with large gaps should be well described by conventional DFT, even though gaps of semiconductors are underestimated. For more complex systems such as paramagnetic systems or Mott-Hubbard semiconductors, the well-known self-interaction error of DFT can become large (especially when strongly correlated M(3d) orbitals are involved), and it may be necessary to use self-interaction corrected (SIC) formalisms to overcome this shortcoming. The DFT+U approach is one of these SIC methods. It provides a better treatment of the electron correlation by the introduction of an effective Hubbard parameter (Ueff ) U - J) that penalizes the fractional (or double) occupation of the metallic 3d orbitals.14,15 In the same spirit, the hybrid DFT/HF (Hartree-Fock) approach is based on a weighted mixing of the DFT exchange and correlation energy with the purely nonlocal (exact) Hartree-Fock exchange energy. Compared to the DFT+U approach, the hybrid DFT/HF can be seen as a “parameter-free” method although the weight of
10.1021/jp808122q CCC: $40.75 2008 American Chemical Society Published on Web 12/03/2008
20482 J. Phys. Chem. C, Vol. 112, No. 51, 2008 the on-site two electron Hartree-Fock integrals is imposed in the functional (for a recent review, see ref 16). While the DFT+U method has already been widely experienced in transition metal oxides (leading to accurate Ueff parameters for most of the first-row TM),17-19 there are only few reports on more covalent (therefore more delocalized) systems, such as antimonides20 or sulfides21 for instance. This paper aims at a systematic study of the NMR response of a large variety of MPy phases, not only to point the 31P NMR as a method of choice to distinguish between the various electronic behaviours of transition metal phosphides, but also to decide which of the computational methodology (DFT, DFT+U or hybrid) is the most adapted one to properly and accurately reproduce their electronic structure. Background: 31P NMR Shifts. 31P being a (100% naturally abundant) spin 1/2 nucleus, no contribution to the NMR shift can come from quadrupolar effects. Its usual chemical shift range (screening effect of the electronic surrounding on the applied field) is relatively large, approximately from +300 to -200 ppm, in relation with the diversity of the bonds that P can establish. It is not our aim in the present report to discuss these effects, and one can suppose that decisive analysis of chemical shifts in (diamagnetic) phosphorus-containing compounds using first-principles density functional theory (DFT) calculations will soon shed light on the matter. In transition metal phosphides, however, it is expected that additional so-called hyperfine (actually very strong) interactions will be exerted by electron spins or delocalized electrons and will govern the NMR shift and line width. If electron spins are present, like in paramagnetic compounds, they will first cause a strong dipolar interaction on the nuclear spins, a through-space interaction that decreases with the third power of the distance, leading to possibly very broad NMR lines. Magic angle spinning should average out this interaction to some extent, but residual broadening of the signal is expected to remain at practical spinning speeds. In addition, if a suitable orbital overlap permits, the electron spin formally carried by a TM-ion d-orbital can be partially transferred to the P nucleus site (more precisely to an s-type spherical orbital of P covering the nucleus). The nucleus will then feel an additional field either adding or subtracting to the applied field, so that the NMR resonance will occur for quite different applied field, leading to a so-called Fermi contact shift for the 31P NMR signal. In the case of Li in transition metal oxides, some of us have paid some attention to the mechanisms that prevail to this effect.22 Since whatever the nucleus studied it originates from the presence of electron spins whose polarization in the applied field will depend on temperature (like the bulk susceptibility of the sample), the Fermi contact shift will follow this temperature dependence. Thus, for strictly paramagnetic samples obeying a Curie-Weiss law, the Fermi contact will scale to the reciprocal absolute temperature. For compounds with metallic conduction, there are no electron spins as such, but the electrons of the conduction band at the Fermi level have a partial unpaired spin character that leads to the Pauli paramagnetism characteristic of such compounds. If an s orbital of P participates to this band in the DOS at the Fermi level, the nucleus will again feel an additional field, leading in this case to a Knight (contact) shift of the 31P NMR signal. The Pauli paramagnetism being (in first approximation) temperature independent, so is the Knight shift for real metals. Another significant effect of the presence of electron spins (and, to a lesser extent, of delocalized conduction electrons) is the drastic decrease of the T1 “spin-lattice” relaxation time due
Bekaert et al. to transfer of the energy quantum associated to the (nonradiative) de-excitation of the nuclear spin to the electron spin system, essentially through dipolar interaction. Computational Methods and Details. As already mentioned, the MPy phases (M ) V, Fe, Co, Ni) show very different electronic behaviors (diamagnetic, paramagnetic, metallic, etc.) depending on both the transition metal and the M/P ratio. Such electronic properties arise from a strong covalent character of the M-P and P-P bonds that makes these systems very different from oxides regarding their electronic ground-state and their reactivity with respect to lithium. Despite the recent development of computational methods for NMR shielding parameter calculations (chemical shifts),23-25 the case of paramagnetic periodic systems including transition metals still remains difficult to handle. Nevertheless, it can be meaningful to correlate the 31P NMR signals to both the crystal structure and the electronic structures of the MPy compounds and more specifically to the general features of their density of states, as a starting point. Density functional calculations including full structural relaxations were then carried out on a wide series of transition metal phosphides, using the plane-wave based Vienna ab initio program package VASP. 26,27 within the generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE) approximation for the exchange and correlation potential.28,29 The electron wave functions were described using the projector augmented wave (PAW) method of Blo¨chl30 in the implementation of Kresse and Joubert.31 The convergence of the calculations was checked with respect to both the energy cutoff (up to 700 eV) and the k-points grid used for the Brillouin zone integration (up to 150 k-points in the irreducible Brillouin zone). The ionic convergence was done with respect to both the atomic forces (less than 10-3 eV/ Å) and the energies (less than 1 meV/atom). Spin polarized calculations were considered to seek any possible magnetic interaction in the binary MPy phases. As already mentioned, a peculiar attention was paid to the electronic structure in the vicinity of the Fermi level, i.e., to the band nature and its dependence on the exchange and correlation potential used in the calculations. The DFT+U formalism 14,15 was then used to account for the strongly correlated character of the middle-row transition metals (M ) Fe, Co, and Ni) and to study the changes in the MPy electronic structures when the effective Ueff ) U - J (J ) 1 eV) parameter is increased from the DFT limit (Ueff ) 0 eV) to a more strongly correlated limit Ueff > 0 eV. When specified, the PBE0 hybrid functional 32,33 recently implemented in the WIEN2K code34 was also used as a comparison with the DFT+U formalism. Total and partial densities of states (DOS and PDOS) were computed in large k-point grids for the (most stable) relaxed MPy phases. While PAW potentials30 provide a more rigorous description of the core region than the ultrasoft pseudopotentials35 (through the reconstruction of the total wave function including all nodes in the core region), they are still treated within the frozen-core approximation. We then chose to use all electron methods such as the full-potential linearized augmented plane-wave (FPLAPW) method as implemented in the Wien2K program package36 to compute accurate s, p, d angular momentum contributions to the total DOS. Experimental Section Materials Preparation. The samples were characterized by X-ray diffraction (XRD) on a Philips θ-2θ diffractometer using Cu KR radiation (λ ) 1.5418Å) and a nickel filter. The data were recorded in continuous mode for 2θ angles ranging from
Transition Metal Phosphide 31P NMR/Electronic Structure 10 to 70°. Unless otherwise stated, the patterns matched those for the structures briefly described in the following for each compound, without additional impurity lines. Nickel phosphides as well as FeP and CoP were prepared at high temperature. In an argon-filled glovebox, red phosphorus (99%, 100 mesh, Alfa Aesar) and nickel (99.99%, 100 mesh, Aldrich) or iron (99+ %, 200 mesh, Alfa Aesar) were mixed in stoichiometric amounts of metal and red phosphorus powders and sealed in a silica tube. The temperature was increased to reach 700 °C for FeP, CoP, Ni3P, Ni2P, Ni5P4, and Ni12P5, 900 °C for NiP2, and 1000 °C for NiP using a ramp of 20 °C/h. The final temperature was then kept for two weeks. Finally, the samples were air or water quenched.37 FeP2 and FeP4 were synthesized using a tin flux method:38,39 iron powder, red phosphorus, and tin (99.8%, 325 mesh, Alfa Aesar) were mixed in a molar ratio 1:4:10 or 1:10:40 for the preparation of FeP2 and FeP4, respectively. The samples were heated at 650 °C for one week and then slowly cooled to 250 °C and air quenched. The products were then washed several times with diluted HCl (6 M) to remove the tin rich matrix. The VP2 phase 40,41 was prepared by ball-milling vanadium (99%, Aldrich) and red phosphorus (Alfa Aesar, 100 mesh, 99%). Stoichiometric amounts of the powdery elements were placed in a stainless steel reactor, which inside is coated with a tungsten carbide layer. The reactor was then placed onto a planetary grinder (Retsch 100), and the grinding was performed with 10 mm diameter stainless steel balls, the ball to powder weight ratio being equal to 10. After 50 h grinding at 600 rpm, the X-ray diffraction pattern revealed a very badly crystallized VP2 phase. A single annealing of the as-obtained phase at 600 °C for 4 days in a sealed stainless steel tube followed by air quenching led to a well-crystallized VP2 product. Powders morphologies were investigated by scanning electron microscopy (SEM). In all cases shapeless aggregates having an average size ranging from 5 to 30 µm were noted. Except for FeP4, the aggregates have the MPx nominal stoichiometry and were exempt of any impurity as deduced from energy dispersive X-ray (EDS) analysis. NMR. 31P MAS NMR spectra were recorded at 120 MHz using a Bruker Avance300 solid state spectrometer. The spinning speed was varied up to 30 kHz using a standard 2.5 mm Bruker MAS probe. Single pulse experiments at various spinning speeds and Hahn echo type experiments at 30 kHz (one rotor period as echo delay) were used with a 1 µs 90° pulse, with identical results unless otherwise stated. The repetition time was varied until full observation of the spectrum is achieved. The spectra were referenced to H3PO4 (85%) set at 0 ppm, using the secondary solid state reference Al(PO3)3 (-50.8 ppm). Decomposition and simulation of the spectra were achieved using the DMfit program.42 Results and Discussion For each compound, the structure will be briefly described; for a complete description the reader is referred to the structural parameters given in the references cited, to be visualized in any dedicated software. The crystallographic data obtained from full structural relaxations are listed in Table 1 and compared to experimental data. The NMR spectra will be reported and brief comments will be presented, and then the electronic structure will be discussed in relation to the former. VP2. V in VP2 sits in VP9 capped distorted cubes sharing rectangular and triangular faces, leading to two types of P, namely, P1 and P2.40 A static NMR spectrum of VP2 is shown in Figure 1. It clearly contains three components, with rather
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20483 TABLE 1: Space Group and Experimental and Relaxed Unit Cell Parameters for the Studied Transition Metal Phosphides
MPy
space group
VP2a
monoclinic C12/m1 (No. 12)
FePb
orthorhombic Pnma (No. 62)
FeP2c
orthorhombic Pnnm (No. 58)
FeP4d
monoclinic P121/c1 (n°14)
Ni3Pe
tetragonal I4j (No. 82) hexagonal P6j2m (No. 189) orthorhombic Pbca (No. 61)
Ni2Pe NiPe NiP2e
monoclinic C12/c1 (No. 15)
CoPf
orthorhombic Pnma (No. 62)
a
e
exp. unit cell parameters, distances (Å), and angles (deg)
relaxed unit cell parameters, distances (Å), and angles (deg)
a ) 8.4641 b ) 3.1054 c ) 7.1698 β ) 119.26 a ) 5.193(1) b ) 3.099 (1) c ) 5.792(1) a ) 4.9729(7) b ) 5.6568(8) c ) 2.7230(4) a ) 4.619(1) b ) 13.670(2) c ) 7.002(1) β ) 101.48(2) a ) 8.954(4) c ) 4.386(2) a ) 5.8590 c ) 3.3820 a ) 6.050(3) b ) 4.881(2) c ) 6.890(3) a ) 6.352(1) b ) 5.6042(9) c ) 5.621(1) β ) 119.62(2) a ) 5.077(1) b ) 3.281(1) c ) 5.587(1)
a ) 8.4449 b ) 3.1048 c ) 7.1641 β ) 119.18 a ) 5.1352 b ) 3.0454 c ) 5.7701 a ) 4.9666 b ) 5.6470 c ) 2.7245 a ) 4.6203 b ) 13.6905 c ) 7.0181 β ) 101.47 a ) 8.9630 c ) 4.3938 a ) 5.8691 c ) 3.3938 a ) 6.0532 b ) 4.8858 c ) 6.9259 a ) 6.4642 b ) 5.6147 c ) 5.6330 β ) 119.33 a ) 5.0738 b ) 3.2685 c ) 5.5591
Reference 40. b Reference 48. Reference 37. f Reference 49.
c
Reference 47.
d
Reference 39.
Figure 1. Static 31P NMR spectrum of VP2. The dotted lines shows the simulation discussed in the text, with the isotropic position of the two anisotropic contributions found.
different anisotropies. Based on the intensities, the signal at 324 ppm is assigned to an unidentified impurity. MAS spectra (Figure 2) fully confirm this decomposition; the isotropic signal is strictly identical in position for the various spinning speeds, despite the unavoidable temperature difference due to friction of the spinning gas flow. Note however that full relaxation is obtained for a 10 s accumulation delay. The computed DOS (Figure 3) shows the absence of an energy gap at the Fermi level suggesting a delocalized metallic type material. This is confirmed by the absence of any difference between spin-up and spin-down densities using spin polarized calculations (not shown here) and by the magnetic data by Alemany.41 VP2 is therefore a textbook case of a metallic sample with real temperature independent Knight shift contribution to the NMR
20484 J. Phys. Chem. C, Vol. 112, No. 51, 2008
Figure 2. MAS 31P NMR spectra of VP2 for 10, 20, and 30 kHz spinning. The isotropic positions are indicated.
Figure 3. V(d), P(s), and P(p) partial density of states (states/eV) for the VP2 compound from a GGA-PBE spin nonpolarized calculation. The inset shows the P(s) contribution of the two crystallographically independent P1 and P2 around the Fermi level.
shift. From the projected DOS, no significant difference can be found between the 3s participation of the two P in the unit cell to the DOS at the Fermi level, which suggests that the Knight shift contribution is very similar for both. However, the chemical shift contribution can be significant in this ppm range so that the two contributions to the NMR shift can hardly be discussed separately. Ni3P. The tetragonal structure of Ni3P is rather close-packed and contains three types of Ni (namely, Ni1, Ni2, and Ni3) with complex P coordination (triangles or distorted tetrahedra) leading to a single type of P.37 The P atom has 9 Ni neighbors at an averaged distance of 2.30 Å. The MAS NMR spectrum reported in Figure 4 together with all the other NMR spectra for global comparison shows one narrow signal around 2000 ppm, with a very short relaxation time (shorter acquisition delays were not attempted in order to protect the probe). Increasing the spinning speed from 20 to 30 kHz surprisingly causes a slight but definite positive shift of the position by 8 ppm (not shown). The computed DOS (Figure 5) is clearly dominated by the metallic states and shows that the Fermi level lies in the tail of the conduction band. This should correspond to a metallic situation but the narrowness of the band at eF is likely to induce more or less localized electronic states. Indeed, it is quite common that metals with nearly filled (respectively nearly empty) band are susceptible of undergoing hole (respectively electron) localization due to some random potential created by
Bekaert et al.
Figure 4. Compilation of the 31P MAS NMR spectra (30 kHz) for the phosphide samples investigated.
Figure 5. Ni(d), P(s), and P(p) partial density of states (states/eV) for the Ni3P compound from a GGA-PBE spin nonpolarized calculation. All crystallographically independent atoms (3 Ni and 1 P) are shown separately.
defects. As concerns the NMR, such localized electron spins are expected to strongly shorten the T1 (as observed) and possibly to induce Fermi contact shifts if such states overlap with the P nucleus (as also observed from the very strong shift). Temperature is however an important parameter in that case, since the nature of the localized states (as felt by the P nuclei) can be very different at the measuring temperature from the calculated T ) 0 K situation and also at different temperatures like when spinning at different speeds (hence the unusual temperature effect suggesting more electron spins on the P nuclei at higher temperature). The temperature dependence of the magnetic moment of Ni3P has been previously investigated and indicates that Ni3P has a temperature-independent Pauli-type paramagnetism.43 It therefore appears that the localized (paramagnetic) electron states in the tail of the conduction band very strongly influence the 31P NMR characteristics through dipolar (inducing a short T1) and contact interactions (inducing a strong shift of the line), while the global conductivity characteristic remains that of a metal. This is a consequence of the very local nature of the situation to which NMR is sensitive, namely, the site of the P nucleus, as compared to a macroscopic physical property such as electronic conductivity. NiyP (y g 1). The three-dimensional NiP structure consists of edge- and corner-shared NiP5 polyhedra with one P and one Ni in the unit cell. Ni5P4 (4 Ni with pyramidal and tetrahedral P coordination and 4 P in the unit cell) as well as Ni12P5 (2 Ni with octahedral and tetrahedral P coordination and 2 P in the unit cell) offer a similar situation to NiP and to the case of Ni3P discussed above as concerns their electronic structure, namely,
Transition Metal Phosphide 31P NMR/Electronic Structure
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20485
Figure 7. Fe(d), P(s), and P(p) partial density of states (states/eV) for the FeP compound from a GGA-PBE spin-polarized calculation. Figure 6. Ni(d), P(s), and P(p) partial density of states (states/eV) for the Ni2P compound from a GGA-PBE spin nonpolarized calculation. A magnification of the P(s) contribution to the total DOS around eF is given in inset for the two independent P1 and P2 atoms.
a Fermi level lying in the tail of the conduction band (see Supporting Information). These compact phases show a globally delocalized behavior with localized electron spin states that influence the P nuclei in a complex way, consistent with broadened and shifted NMR signals (Figure 4) and a positive shift effect upon heating. Note that impurity lines of Ni5P4 are clearly identified in NiP. Ni2P. Ni2P (SG) is an interesting case, since the two P in the unit cell (namely, P1 and P2) have very different NMR shifts (Figure 4). One of them belongs to the common edge of two NiP4 tetrahedra, and the other (multiplicity 2) belongs to the common edge of a NiP4 tetrahedron and a NiP5 square-based pyramid.37 The computed DOS (Figure 6) again reveals a metallic situation with possible electron localization in the tail of the conduction band. If now one looks at the projected DOS on the 3s orbitals of P1 and P2 (Figure 6), they clearly reveal different participations to the DOS at the Fermi level. In a metallic situation, the Knight shift is directly proportional to this quantity and seems to be therefore the dominant contribution for the NMR shift of the two P, although electron localization once again can also induce a Fermi contact contribution. Ni2P is indeed given in the literature as a temperature-independent, Pauli-paramagnetic compound.44,45 FeP. Like NiP, FeP is built on closely packed FeP6 octahedra sharing one edge in two directions of the crystal lattice and one face in the third one (one Fe and one P in the unit cell). The NMR signal (Figure 4) is very broad compared to all other ones discussed above, but weakly shifted. Unfortunately, spinning at a lower speed leads to an overlap of the spinning sidebands and does not allow showing whether the isotropic position remains at the same position or not. The calculated DOS (Figure 7) shows the Fermi level in the top portion of the conduction band, which should lead to a metallic situation (without electron localization), but the key is in the spinpolarized calculation that indeed shows different spin-up and spin-down contributions. This spin polarization of the whole conduction band results in a net magnetic moment so that the compound is a paramagnetic metal. These resulting unpaired spins exert a strong dipolar interaction on the P nuclei, which can explain the strong residual broadening of the NMR line despite MAS. As discussed above, such unpaired spins can also lead to a Fermi contact shift of the NMR line, but this is clearly not the case here, which suggests there is no overlap of the polarized orbital with an s orbital of P (or, in slightly different terms, no participation of the s orbital of P to the polarized conduction band). This is indeed consistent with the PDOS
Figure 8. Co(d), P(s), and P(p) partial density of states (states/eV) for the CoP from a GGA-PBE spin-polarized calculation using the DFT (top) and DFT+U (bottom) formalism.
shown, since P participates significantly to the conduction band essentially in non-spin-polarized energy regions. CoP. It is interesting in this respect to compare this situation with CoP, which is iso-structural to FeP. The NMR spectrum of CoP is rather similar in width to that of FeP, but with a much stronger shift (Figure 4). Like for FeP, lower spinning speed does not allow the isotropic position to be resolved clearly. The DOS of CoP is shown in Figure 8 for Ueff ) 0 and 2 eV. In opposition to what was observed for FeP, the DFT+U formalism is here required to reproduce the spin-polarized metallic groundstate of CoP, as obtained from the NMR spectrum. This is not surprising since the cobalt 3d-orbitals are known to be more correlated than the iron 3d-ones, thus requiring larger Ueff values to cancel the self-interaction error of DFT. In cobalt and iron oxides, these values vary in the range 4.9 e Ueff (Co) e 6.34 eV and 3.71 e Ueff (Fe) e 4.90 eV) depending on their environment and oxidation state, as reported by Ceder et al.18 Nevertheless, as a result of the strong covalent character of the M-P bonds compared to the ionic M-O ones, the metallic (localized) 3d-electrons are more efficiently screened by the conducting (delocalized) electrons in TM-phosphides than in TM-oxides, thus resulting in smaller self-interaction error and therefore in smaller Ueff values (for one given transition metal in one given environment and one given oxidation state), as found in this work. A simple electron count allows understanding the difference observed on the NMR signal shifts between FeP and CoP. In both systems, the TM local Oh symmetry leads to t2g-like and
20486 J. Phys. Chem. C, Vol. 112, No. 51, 2008
Bekaert et al.
Figure 9. Static 31P NMR spectrum of NiP2. The dotted lines shows the simulation discussed in the text, with the isotropic position of the anisotropic contribution found.
Figure 11. Ni(d), P(s),and P(p) partial density of states (states/eV) for the NiP2 compound from a GGA-PBE spin nonpolarized calculation using the DFT (top) and the DFT+U (bottom) formalism.
Figure 10. MAS 31P NMR spectra of NiP2 for 10, 20, and 30 kHz spinning. The isotropic position is indicated.
eg-like orbitals at the Fermi level. These orbitals correspond to antibonding π-type and σ-type overlaps between the metallic 3d orbitals and the phosphorus 3p and 3s/3p orbitals, respectively. Considering the total number of electrons in the two systems, the Fermi level lies in the bottom portion of the eglike band for CoP and in the top portion of the t2g-like band for FeP. A stronger Co(3d)/P(3s) overlap is then expected for CoP in agreement with the greater P(s) contribution to its total DOS (see Figure 8)and with the stronger shift of its NMR signal compared to that of FeP. NiP2 (Monoclinic). The crystal structure of NiP2 consists of corner-sharing NiP4 square planes forming slightly corrugated layers, leading to one type of Ni and one type of P in the unit cell. A static NMR spectrum of monoclinic NiP2 is shown in Figure 9. It reveals a signal with a line shape characteristic of chemical shift anisotropy as confirmed by the simulation shown (dotted line). The nonzero asymmetry parameter suggests a nonaxially symmetrical shielding tensor, which is in good agreement with the nature of the P crystallographic site. Besides, another narrower signal is observed with a Gaussian line shape. Note that a very long repetition time (160 s) is required for full relaxation. MAS spectra are shown in Figure 10, with a very clear averaging of the anisotropy and dipolar broadening. The isotropic signal is strictly identical in position for the various spinning speeds and, therefore, temperature-independent. This is not true for the position of the second signal, which suggests it is due to an unidentified not-diamagnetic compound.
The electronic structure of the monoclinic NiP2 phase is shown in Figure 11 and reveals an energy band gap, indicative of a neatly diamagnetic compound. A crystal orbital analysis previously reported for this compound reveals that Ni ions adopt a Ni2+ (d8) configuration consistent with its square planar environment.8,46 This is fully confirmed by the magnetic susceptibility, which is slightly negative (-1.5 × 10-6 emu/mol) and rather temperature independent. The monoclinic form of NiP2 is therefore a very straightforward case of a strictly diamagnetic phosphide, with a single temperature-independent 31P NMR shift well in the usual chemical shift range for this nucleus. As expected, the conventional DFT method is well-adapted to reproduce the electronic ground-state of diamagnetic semiconductors, even though it is known to systematically underestimate energy band gaps. According to the literature,18 the Ueff values reported for Ni in TM-oxides lie in the range 5.1 e Ueff(Ni) e 6.93 eV depending on the TM environment and oxidation state. A possible way to extract the “true” Ueff value for the nickel diphosphide is to compare the energy band gaps obtained within the DFT+U formalism to the one obtained with the “parameter-free” PBE0 hybrid functional, assuming the latter provides an accurate correction of the selfinteraction error. Interestingly, the gap of NiP2 increases from Eg ) 0.56 to 0.67 eV when Ueff is increased from 0 to 2 eV and does not change significantly above this value. A gap of Eg ) 0.65 eV is obtained with the PBE0 functional (see Supporting Information), suggesting that Ueff ) 2 eV is the appropriate parameter to reproduce the energy band gap of NiP2. As expected from the less atomic-like character of the 3d metal orbitals in (covalent) transition metal phosphides compared to (ionic) transition metal oxides, smaller selfinteraction errors arise in the DFT limit, thus implying smaller Ueff value to properly reproduce their electronic structures. FeP2. Fe in FeP2 sits in FeP6 octahedra forming parallel edgesharing chains interconnected by corners (one type of Fe and one type of P).47 The MAS NMR spectrum (Figure 12) accordingly consists of one signal. Its isotropic position at 664.5 ppm does not change with temperature. This would suggest a Knight shift like for the VP2 case discussed above, but the relaxation time around 10 s seems somewhat long for a metallic compound.
Transition Metal Phosphide 31P NMR/Electronic Structure
Figure 12. MAS 31P NMR spectra of FeP2 for 20 and 30 kHz spinning. The isotropic position is indicated.
Figure 13. Fe(d), P(s), and P(p) partial density of states (states/eV) for the FeP2 compound computed in spin-polarized DFT+U calculations with Ueff ) 0 eV (top) and Ueff ) 3 eV (bottom).
The DOS (Figure 13) computed for FeP2 shows a very small energy band gap, smaller than that of NiP2. Compared to FeP, the less compact and more anisotropic crystal structure of FeP2 leads to a more localized electronic structure (narrower bands). This suggests that the Fe(3d) electrons are more correlated in FeP2 than in FeP (i.e., the self-interaction is less efficiently screened by the conducting electrons than in a metal), and that the DFT+U formalism should be required to properly cancel the self-interaction error arising from the DFT limit (Ueff ) 0 eV). Surprisingly, the energy band gap of FeP2 does not increase with the increase of the correlation parameter, as previously shown for NiP2. Instead, spin fluctuations occur when Ueff is increased from 0 to 2 eV, and a semiconducting to magnetic phase transition is observed at Ueff ) 3 eV. This results in the cancelation of the energy band gap of FeP2 when going from Ueff ) 0 to 3 eV (see Figure 13), as already reported for the homologous iso-structural FeSb2.20 This is confirmed by the PBE0 calculations (not shown here) that show very close energies but very different electronic structures for the ferromagnetic (no gap) and antiferromagnetic (small gap) structures, sug-
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20487 gesting a quasi-degenerated ground-state for that system. Considering the Ueff value reported in the literature for the iron disulfide (Ueff ) 2 eV)21 it is likely that FeP2 does not undergo the magnetic phase transition observed at Ueff ) 3 eV but that low-energy excitations are responsible for its ambiguous NMR response. The NMR shift of FeP2 is therefore close to that of VP2 and far from that of NiP2 due to the narrowness of the gap and to the dynamical electronic excitations, but the relaxation time is way too long compared to that of a real metal, as there is no Pauli paramagnetism (that would strongly decrease the relaxation time). The NMR line shape of FeP2 is close to that of NiP2 and far from that of FeP as a result of the weak occurrence of the electronic spin states in the total wave function of FeP2 therefore avoiding strong dipolar interactions. A Fermi contact rather than a Knight shift is thus expected for FeP2. In this respect, it is significant that the NMR characteristics of FeP2 are somewhat ambiguous between those of a diamagnetic (or semiconducting with significant gap) compound like NiP2 and of a metallic compound like VP2 and that the DOS characteristics of FeP2 are somewhat ambiguous between a small gap semiconductor and a localized magnet. FeP2 is therefore a nearly ferromagnetic small gap semiconductor, as its homologous FeSb2.20 At this stage, it is interesting to correlate the different behaviors of NiP2 and FeP2 to their crystal structure. As shown in Figure 14, NiP2 and FeP2 structures compare well in their in-plane layers, showing corner-shared NiP4 squareplanes or FeP6 octahedra. However, they are very different regarding the interlayer direction. While the NiP2 layers are shifted from one to another in the interlayer a-direction, leading to almost disconnected NiP4 square-planes associated with long Ni-Ni distances (Ni-Ni ) 3.03 Å and 4.24 Å), the FeP2 layers are perfectly superimposed in the interlayer c-direction, thus forming chains of edge-shared FeP6 octahedra with short Fe-Fe distances (Fe-Fe ) 2.72 Å). Exchange integrals being very sensitive to the transition metal local environment, it is expected that very different (phosphorus mediated) M-M interactions occur in these two systems. From the M+2 oxidation state expected in NiP2 (d8) and FeP2 (d6), it is pretty straightforward that the first empty band in both MP2 electronic structures is mainly built on the local eg-like metallic orbitals, and more precisely on the Ni(dy2-z2) for NiP2 and on both the Fe(dx2-y2) and the Fe(dz2) for FeP2. As shown in Figure 14, the spatial orientation of these orbitals leads to very weak δ-type interactions along the interlayer a-direction for NiP2 and to strong π-type interactions mediated by two phosphorus 3p-orbitals for FeP2. The latter are likely responsible for the spin fluctuations (quasi-degenerated electronic ground state) occurring in that system and explains why its electronic structure is very sensitive to the way exchange integrals are treated in the calculations. FeP4. XRD shows the presence of FeP2 impurity. The structure of FeP4 consists of corrugated monolayers of Fe atoms (perpendicular to the (100) direction) separated by double layers of P atoms, leading to two types of Fe and six types of P in the unit cell.39 The Fe atoms sit in FeP6 octahedra sharing some of their edges and/or corners, and the P atoms form a 3D network of P-P bonds within each double layer. The MAS NMR spectrum of FeP4 (Figure 15) is rather busy, but the signals of FeP2 and also of FeP (not detected by XRD) can clearly be identified; there is also a weak signal at around 300 ppm which must correspond to some unidenti-
20488 J. Phys. Chem. C, Vol. 112, No. 51, 2008
Bekaert et al.
Figure 14. Projection views of the NiP2 (left) and FeP2 (right) crystal structures in the interlayer direction (top) and in the chain direction (bottom). The successive layers in NiP2 are illustrated by gray and white square-planes. For both systems the eg-like orbitals and their interactions along the chain direction are illustrated.
Figure 15. MAS 31P NMR spectrum of FeP4 for 30 kHz spinning. The spectra of FeP and FeP2 are recalled in dotted lines to show their presence as impurity in the FeP4 sample.
fied impurity. Six signals remain for FeP4, two of them being superimposed in the 120 ppm peak, in agreement with the 6 crystallographically independent P atoms of the unit cell. Again, their isotropic positions lie in the usual chemical shift range and are not temperature sensitive (Figure 16), but the most interesting feature is the splitting of the lines, which indicates unusually strong J couplings as high as 280 Hz clearly visible in the solid state. They are fully consistent with the existence of very covalent P-P bonds. Careful analysis of the P-P distances suggests that P1 and P5, each with two rather similar P-P bonds (P1-P4: 2.189 Å; P1-P2: 2.218 Å and P5-P3: 2.220 Å; P5-P6: 2.241 Å) should lead to well defined triplets, one of which might correspond to the signal at 175 ppm while P2 has two more different P-P bonds (P2-P6: 2.165 Å; P2-P1: 2.218 Å) which should lead to a less well defined triplet (most probably the 65 ppm signal). Besides, the other three P atoms have three more or less different P-P bonds, which should lead to more or less well defined quadruplets. The best defined one at 90 ppm might correspond to P3 on that basis. It is however difficult at the present point to go much deeper in this analysis, since
Figure 16. Expansion of the MAS 31P NMR spectra of FeP4 for 20 and 30 kHz spinning showing the five multiplets discussed in the text.
Figure 17. Fe(d), P(s), and P(p) partial density of states (states/eV) for the FeP4 compound computed in non-spin-polarized calculations (the most stable). The projection over the crystallographically independent atoms (2 Fe and 6 P per unit cell) is not shown separately for the sake of clarity.
decomposition of the 125 ppm peak is ambiguous. The computed electronic structure (Figure 17) again confirms a diamagnetic behavior for FeP4, in good agreement with the NMR observations above. Interestingly, the P(s) contribution
Transition Metal Phosphide 31P NMR/Electronic Structure to the total density of states is much larger above the Fermi level (conduction band) than below the Fermi level (valence band), in full agreement with the destabilization of the P(s) electronic levels (strongly antibonding P(s)-P(s) local interactions) due to the short P-P distances occurring in that system. Concluding Remarks In this report, we have established a hand waving-type discussion of the correlation between the computed electronic structures and the 31P NMR characteristics of a series of TM phosphides, which leads to the following classification of compounds: Diamagnetic (or semiconducing with large gap) like FeP4 or NiP2 with no electron spin influence on the NMR signal (only chemical shift arises, with very long T1 relaxation time). Metallic like VP2, with a moderate temperature independent Knight shift. Paramagnetic metals with a spin-polarized conduction band like FeP and CoP, leading to very strong residual dipolar interactions despite MAS. Depending on the case, electron spin density can be transferred to the s orbital of P (CoP) or not (FeP), establishing a clear correlation between the NMR shift and the electronic structure features. It should be noted here that reproducing the 31P NMR data with first-principles calculations has been found to be a key criterion for selecting the appropriate calculation methodology to be used in such (more or less) correlated systems. Provided that the strong covalent character of the M-P bonds is considered as an efficient screening of the TM on-site electron repulsions, the Ueff values proposed in this work for FeP (Ueff ) 0) and CoP (Ueff ) 2 eV) are fully consistent with those obtained in the more ioniclike cobalt and iron oxides. More complex (and interesting) cases obviously arise as follows: FeP2 first appeared somewhat ambiguous between the first two categories (diamagnetic or metal), as concerns both its NMR signal (metallic-like characteristics except for a somewhat long relaxation time) and its electronic structure. This apparent ambiguity has been attributed to the very complex and nearly degenerated electronic ground-state of that system. DFT+U calculations with Ueff less than 3 eV clearly show that spin fluctuations may occur in that system due to the occurrence of different (energy close) local minima associated with different iron magnetization (e1 µB). Metallic-type cases with the Fermi level in a tail of the conduction band like Ni3P, Ni2P, NiP, Ni5P4, and Ni12P5, leading to metallic-type conduction, still with some localized electron spin states. The P NMR signals then result from the combined influence of a Knight shift (exemplified by Ni2P, with a rather clear correlation between the participation of s orbitals of the two types of P in the unit cell to the DOS in the Fermi level and their NMR shift) and of local electron spin states leading to very short T1 and to contact shifts with unusual temperature effects. Finally a remarkable feature is also the clear observation of J-coupling for the case of FeP4, which is very well correlated with the existence of P-P bonds (either as pairs or as triplets) with distances in the range of 2.18 Å. However, it is striking that although similar P-P distances are also found in many of the other compounds studied in this work, such J couplings were not observed, for reasons not clearly understood by us yet. Acknowledgment. This research was performed in the framework of the ALISTORE Network of Excellence (Contract
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20489 No. SES6- CT-2003-503532) founded by the EC. We would like to thank the ADEME (Agence de l’Environnement et de la Maıˆtrise de l’Energie, France) for its financial support through the Ph.D. grants of S.B. and J.B. Supporting Information Available: Computed density of states mentioned but not shown in the document. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Doublet, M. L.; Lemoigno, F.; Gillot, F.; Monconduit, L. Chem. Mater. 2002, 14, 4126–4133. (2) Bichat, M. P.; Gillot, F.; Monconduit, L.; Favier, F.; Morcrette, M.; Lemoigno, F.; Doublet, M. L. Chem. Mater. 2004, 16, 1002–1013. (3) Souza, D. C. S.; Pralong, V.; Jacobson, A. J.; Nazar, L. F. Science 2002, 296, 2012–2015. (4) Alcantara, R.; Tirado, J. L.; Jumas, J. C.; Monconduit, L.; Olivier Fourcade, J. J. Power Sources 2002, 109, 308–312. (5) Pralong, V.; Souza, D. C. S.; Leung, K. T.; Nazar, L. F. Electrochem. Commun. 2002, 4, 516–520. (6) Bichat, M. P.; Politova, T.; Pascal, J. L.; Favier, F.; Monconduit, L. J. Electrochem. Soc. 2004, 151, A2074–A2081. (7) Crosnier, O.; Nazar, L. F. Electrochem. Solid State Lett. 2004, 7, A187–A189. (8) Gillot, F.; Boyanov, S.; Dupont, L.; Doublet, M. L.; Morcrette, M.; Monconduit, L.; Tarascon, J. M. Chem. Mater. 2005, 17, 6327–6337. (9) Boyanov, S.; Bernardi, J.; Gillot, F.; Dupont, L.; Womes, M.; Tarascon, J. M.; Monconduit, L.; Doublet, M. L. Chem. Mater. 2006, 18, 3531–3538. (10) Gillot, F.; Monconduit, L.; Doublet, M. L. Chem. Mater. 2005, 17, 5817–5823. (11) Poizot, P.; Laruelle, S.; Grugeon, S.; Dupont, L.; Tarascon, J.-M. Nature 2000, 407, 496. (12) Furo, I.; Bakonyi, I.; Tompa, K.; Zsoldos, E.; Heinmaa, I.; Alla, M.; Lippmaa, E. J. Phys.: Condens. Matter 1990, 2, 4217–4225. (13) Stinner, C.; Tang, Z.; Haouas, M.; Th, W.; Prins, R. J. Catal. 2002, 208, 456–466. (14) Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Phys. ReV. B 1991, 44, 943–954. (15) Anisimov, V. I.; Aryasestiawan, V.; Liechtenstein, A. I. J. Phys.: Condens. Matter 1997, 9, 767–809. (16) Cora`, F.; Alfredsson, M.; Mallia, G.; Middlemiss, D. S.; Mackrodt, W. C.; Dovesi, R.; Orlando, R. Density Functional Theory in Inorganic Chemistry, Structure and Bonding; Springer: Heidelberg, 2004; Vol. XX. (17) Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A.; Czyzyk, M. T.; Sawatzky, G. A. Phys. ReV. B 1993, 48, 16929–16934. (18) Zhou, F.; Cococcioni, M.; Marianetti, C. A.; Morgan, D.; Ceder, G. Phys. ReV. B 2004, 70, 235121. (19) Wang, L.; Maxisch, T.; Ceder, G. Phys. ReV. B 2006, 73, 195107.1195107.6. (20) Lukoyanov, A. V.; Mazurenko, V. V.; Anisimov, V. I.; Sigrist, M.; Rice, T. M. Eur. Phys. J. B 2006, 53, 205–207. (21) Persson, K.; Ceder, G.; Morgan, D. Phys. ReV. B 2006, 73, 115201.1115201.8. (22) Carlier, D.; Me´ne´trier, M.; Grey, C. P.; Delmas, C.; Ceder, G. Phys. ReV. B 2003, 67, 174103 1–14. (23) Pickard, C. J.; Mauri, F. Phys. ReV. B 2001, 63, 245101.1245101.13. (24) Gonze, X. Phys. ReV. A 1995, 52, 1086–1095. (25) Mauri, F.; Pfrommer, B. G.; Louie, S. G. Phys. ReV. Letters. 1996, 77, 5300–5303. (26) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169–11186. (27) Kresse, G.; Furthmuller, J. Computat. Mater. Sci. 1996, 6, 15–50. (28) Perdew, J. P.; Burke, K.; Wang, Y. Phys. ReV. B 1996, 54, 16533– 16539. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (30) Blochl, P. E. Phys. ReV. B 1994, 50, 17953–17979. (31) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758–1775. (32) Ernzerhof, M.; Scuseria, G. E. J. Chem. Phys. 1999, 110, 5029– 5036. (33) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158–6170. (34) Tran, F.; Blaha, P.; Schwarz, K.; Novak, P. Phys. ReV. B 2006, 74, 155108.1155108.10. (35) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892–7895. (36) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. Wien2k, An Augmented Plane WaVe + Local Orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Techn; Universita¨t Wien: Austria: 2001 (ISBN 3-9501031-1-2). (37) Larsson, E. ArkiV fo¨r Kemi 1964, 23, 335.
20490 J. Phys. Chem. C, Vol. 112, No. 51, 2008 (38) Grandjean, F.; Ge´rard, A.; Krieger, U.; Heiden, C.; Braun, D. J.; Jeitschko, W. Solid State Commun. 1979, 33, 261. (39) Jeitschko, W.; Braun, D. J. Acta Crystallogr., Sect. B 1978, 34, 3196–3201. (40) Goelin, M.; Carlsson, B.; Rundqvist, S. Acta Chem. Scand. 1975, 29, 706–708. (41) Alemany, P.; Alvarez, S. Inorg. Chem. 1992, 31, 3007–3010. (42) Massiot, D.; Fayon, F.; Capron, M.; King, I.; Le Calve, S.; Alonso, B.; Durand, J. O.; Bujoli, B.; Gan, Z. H.; Hoatson, G. Magn. Reson. Chem. 2002, 40, 70–76. (43) Gambino, R. J.; McGuire, T. R.; Nakamura, Y. J. Appl. Phys. 1967, 38, 1253.
Bekaert et al. (44) Shirotani, I.; Takahashi, E.; Mukai, N.; Nozowa, K.; Kinoshita, M.; Yagi, T.; Suzuki, K.; Enoki, T.; Hino, S. Jpn. J. Appl. Phys. Part 1 1993, 32, 294. (45) Zeppenfeld, K.; Jeitschko, W. J. Phys. Chem. Solids 1993, 54, 1527. (46) Bernardi, J.; Lemoigno, F.; Doublet, M.-L. Ionics 2008, 14, 197. (47) Dahl, E. Acta Chem. Scand. 1969, 23, 2677. (48) Fjellvag, H.; Kjekshus, A.; Andersen, A. F. Acta Chem. Scand., Ser. A 1986, 40, 227. (49) Rundqvist, S. Acta Chem. Scand. 1962, 16, 287.
JP808122Q
