Finite-size effect of antiferromagnetic transition and electronic structure in LiFePO4

Abstract

The finite-size effect on the antiferromagnetic (AF) transition and electronic configuration of iron has been observed in LiFePO4. Determination of the scaling behavior of the AF transition temperature (TN ) vs. the particle size dimension (L) in the critical regime, 1 −∼ L −1 , reveals that the activation nature of the AF ordering strongly depends on the surface energy. In addition, the effective magnetic moment that reflects the electronic configuration of iron in LiFePO4 is found sensitive to the particle size. An alternative structural view based on the polyatomic ion groups of PO 3− 4 is proposed. LiFePO 4 has been considered as an ideal cathode electrode material with a workable redox potential of 3.45 V and a high theoretical capacity of 170 mAh/g.[1] LiFePO 4 is a band insulator in bulk crystal form in agreement with the calculated large band gap,[2] however, the fast electron/ion charge/discharge process has been shown to be possible only when the particle size is reduced to below ∼100 nm.[3] While significant progress has been made to demonstrate the impact of nanoscaling on defect chemistry, electrochemical behavior, electron-ion conductivity, lithium ion diffusion, and the charge/discharge rate in general,[4-6] the fundamental question of "why nano-scaling matters?" remains. Generally, there have been two major approaches to interpret the property improvement for LiFePO 4 using nano-scaling induced electron/ion transport: the first is called the "domino-cascade" model, which describes a fast anisotropic lithium insertion/extraction action coupled to the LiFePO 4 -FePO 4 interface movement through an electron polaronic hopping mechanism in nano-crystallites, [5] and the second focuses on the surface effect with carbon coating and miscibility gap size reduction as a result of nano-scaling. [4,7] Conventionally, the iron ion has been viewed as Fe 2+with oxygen ligands to form the octahedral crystal electric field (CEF) of e g -t 2g splitting.[8] However, the magnitude of the effective magnetic moment (µ ef f ) obtained from the Curie-Weiss law fitting was inconsistent and spread in the range of µ ef f ∼4.7-5.5 µ B , which has been interpreted that Fe 2+ must be in the high-spin state (HS) as t 4 2g e 2 g of S=2 with a spin-only value of µ ef f = 4.9µ B , and the inconsistent moment above 4.9 µ B has often been described by incomplete orbital-quenching, i.e., the theoretically calculated value from the Lande g-factor with J=L+S (S=2, L=2) without orbital quenching should be µ ef f =6.7µ B .[9, 10] Considering a typical iron ion in the crystal field composed of oxygen ligands with high electronegativity, the HS choice of d 6 implies an unexpectedly small crystal field splitting between e g − t 2g , unless the influence of the nearby PO 3− 4 phosphate groups are included. In addition, within the explanation of in-

“Hydrotriphylites” Li1-xFe1+x(PO4)1-y(OH)4y as Cathode Materials for Li-ion Batteries

“…The particle size may affect the Néel temperature too. For example, a slight decrease of T N from 52 to 49K has been reported for LiFePO 4 when the particle size was reduced from 315 m to 50 nm, 56 but in our case the #1 and #2 samples feature very similar particle size of few hundred nm (Supporting Information Fig. S5, S6, S9), whereas T N 's differ remarkably.…”

Heat capacity (C) and entropy of olivine-type LiFePO4 in the temperature range (2 to 773) K

“…materials, in contrast to metals, l eff decreases with decreasing crystallite size [32,33] which leads to smaller entropies of the magnetic transition. The attenuation of the effective magnetic moment for nanoparticles can be interpreted as a result of the minimization of the Gibbs free energy.…”

“…The attenuation of the effective magnetic moment for nanoparticles can be interpreted as a result of the minimization of the Gibbs free energy. The deviation from the perfect crystal for the nano-sized powder leads to an increase of the surface free energy by c DA, partially compensated by the magnetic energy B DM [32].…”

“…The experimental value 10.1 J Á K À1 Á mol À1 corresponds to 75% of the expected entropy which is, on a first view, a reasonable agreement. However, it is known from literature, that the effective magnetic moment depends on the ''particle size'' [32] or more precisely crystallite size. For ferrimagnetic and antiferromagnetic Standard uncertainties u are: u(T) = 0.01 K for 2 < T/K < 20, u(T) = 0.02 K for 20 < T/ K < 100, u(T) = 0.05 K for 100 < T/K < 300, u(T) = 0.1 K for 300 < T/K < 770; u(p) = 5 kPa; Relative combined expanded uncertainty with level of confidence 0.95: U r (C p,m ) = 0.07Á for 2 < T/K < 20 and U r (C p,m ) = 0.02Á for 20 < T/K < 773. a PPMS (Quantum Design).…”

“…Besides the magnetic entropy, the Néel-temperature for the magnetic transition is also a function of crystallite size [32]. The Néel-temperature varies from 52 K for single crystals to 49 K for LFP nano-particles ($50 nm).…”