Linking Local Environments and Hyperfine Shifts: A Combined Experimental and Theoretical³¹P and⁷Li Solid-State NMR Study of Paramagnetic Fe(III) Phosphates

Abstract

Iron phosphates (FePO(4)) are among the most promising candidate materials for advanced Li-ion battery cathodes. This work reports upon a combined nuclear magnetic resonance (NMR) experimental and periodic density functional theory (DFT) computational study of the environments and electronic structures occurring in a range of paramagnetic Fe(III) phosphates comprising FePO(4) (heterosite), monoclinic Li(3)Fe(2)(PO(4))(3) (anti-NASICON A type), rhombohedral Li(3)Fe(2)(PO(4))(3) (NASICON B type), LiFeP(2)O(7), orthorhombic FePO(4)·2H(2)O (strengite), monoclinic FePO(4)·2H(2)O (phosphosiderite), and the dehydrated forms of the latter two phases. Many of these materials serve as model compounds relevant to battery chemistry. The (31)P spin-echo mapping and (7)Li magic angle spinning NMR techniques yield the hyperfine shifts of the species of interest, complemented by periodic hybrid functional DFT calculations of the respective hyperfine and quadrupolar tensors. A Curie-Weiss-based magnetic model scaling the DFT-calculated hyperfine parameters from the ferromagnetic into the experimentally relevant paramagnetic state is derived and applied, providing quantitative finite temperature values for each phase. The sensitivity of the hyperfine parameters to the composition of the DFT exchange functional is characterized by the application of hybrid Hamiltonians containing admixtures 0%, 20%, and 35% of Fock exchange. Good agreement between experimental and calculated values is obtained, provided that the residual magnetic couplings persisting in the paramagnetic state are included. The potential applications of a similar combined experimental and theoretical NMR approach to a wider range of cathode materials are discussed.

DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

“…Focusing on the dipolar component of the hyperfine tensor, A dip , there is a decrease along the series from Mn to Ni, hence giving a progressively smaller contribution to the shift anisotropy, as seen by comparing terms (e) of Table IV. The calculated tensor with no spin-orbit coupling inclusion corresponds to the dipolar interaction between the magnetic moments of the observed nucleus and magnetic moment of the TM ion [29,36]. the considered ions reported in Table II, a progressively weaker dipolar interaction is observed when going from Mn 2+ towards Ni 2+ .…”

“…Furthermore, as derived in Ref. 29, the bulk magnetic properties of the materials affect the paramagnetic shift. These effects are included in the treatment by modifying the temperature dependence of the shift via the inclusion of the Weiss constant Θ.…”

“…For solids in which the TM ions are a major constituent of the lattice, the total paramagnetic shielding at the OC is the combination of the various contributions to the isotropic shift and shift anisotropy from all the TM sites. Solidstate density functional theory (DFT) calculations have been shown to be extremely helpful in unravelling the NMR response of paramagnetic solids containing multiple paramagnetic centres [13,29,37,38]. The approach for the calculation of the Fermi contact shifts and shift anisotropy in paramagnetic solids [12] is here extended to include the spin-orbit coupling effect.…”

“…After the pioneering work of Kurland and McGarvey [16], Moon and Patchkovski derived a formalism to describe the entire shift tensor including the effects of spin-orbit coupling [19], later ex-tended to the presence of zero-field splitting by Vaara et al [20,21] and Soncini and Van den Heuvel [22], with the consequent extensive study of the NMR shift of paramagnetic molecules [23][24][25][26][27][28]. The shift mechanisms in paramagnetic transition metal-containing extended solids have been studied by Carlier, Grey and co-workers and the effects of multiple paramagnetic centres on the isotropic Fermi contact shift and its relation to the bulk magnetic properties of the solid have been qualitatively [13], and subsequently more quantitatively [29], rationalised. In their work the spin-orbit coupling effects on the NMR shift are included in an empirical effective magnetic moment.…”

Review—Manganese-Based P2-Type Transition Metal Oxides as Sodium-Ion Battery Cathode Materials

“…ssNMR can be used in situ to study dynamic processes occurring on the NMR timescale. 106,107 To date, in situ NMR is difficult to combine with sample rotation, i.e. Magic Angle Spinning (MAS), which is crucial for chemical (and hyperfine) shift resolution enhancement of paramagnetic materials in ssNMR.…”