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Condens. Matter 2019, 4, 86 4 of 15 being the elementary charge and nuclear quadrupole moment, respectively). The quadrupole moment of the excited 57Fe nucleus was taken from Reference [22] to be Q = 0.16 barn. If an external magnetic field (Bext) is applied, then it sums up with Bhf in the vectorial way, i.e., one gets an effective magnetic field Beff = |Beff| = |Bhf + Bext|, which determines the overall magnetic splitting of the 57Fe nuclear levels. For powder samples, ∆Beff, the distribution width of the effective magnetic field, is another useful parameter to characterize Mössbauer spectra. When such spectra are fitted, it is yet important to obtain the geometrical relationship of Beff or Bhf and the EFG tensor. This relationship is defined using the parameter θ, the polar angle between the direction of Beff and the principal axis of the main component Vzz of the EFG, and parameter φ, the azimuthal angle between Beff and the Vxx’s principal axis. Finally, the isomer shift, IS, characterizes the change of the 57Fe nucleus’ chemical environment with respect to a pure α-iron sample. A negligible spectral component with an intensity of ∼1 % corresponding likely to Fe3+ ions was subtracted from the measured spectra. This component can be due to a minor content of other phases and/or presence of point defects (in the vicinity of Fe ions, misplaced Fe ions, e.g., at Li sites) [23]. The origin of this spectral component will be studied in the future. The subtraction of the component does not affect the current evaluation of the magnetic structure in powdered LiFePO4. In order to calculate hyperfine parameters that are related to the electronic and magnetic structure of the studied material, a DFT-based approach was employed. In particular, the WIEN2k code [24], which is an implementation of the augmented plane wave plus local orbital [25,26] concept for electronic structure calculations for crystalline solids. In the course of calculations, the spin-polarized exchange-correlation functional—within the generalized gradient approximation [27]—after Perdew, Burke and Ernzerhof (PBE) [28] is used. The spin-orbit coupling (SOC) is also taken into account in specific investigations. The WIEN2k implementation is described in Reference [29], though in the present study the p1/2 local orbitals were not considered in SOC calculations. The calculations of the EFG and magnetic hyperfine field follows References [30,31] and [32,33], respectively. 3. Results and Discussion 3.1. Structural and Magnetic Measurements Figure 2 shows the XRD patterns of the LiFePO4 sample. According to the powder XRD Rietveld analysis, the sample was assigned to be a single phase of an orthorhombic symmetry with the space group Pnma (No. 62). The observed lattice parameters a = 10.3234(3) Å, b = 6.0045(2) Å and c = 4.6915(1) Å is are in a good agreement with the previous data [1,3,34,35] summarized also in Reference [2]. In this way, the expected structure of the investigated sample was confirmed. Moreover, we can infer that the Li stoichiometry of the sample is likely good since reduced Li content results in a decrease of the parameters a and b and an increase of the parameter c.PDF Image | Mossbauer Spectroscopy of Triphylite (LiFePO4) at Low Temperatures
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