Debye Temperature Evaluation for Secondary Battery Cathode of α-Sn _x Fe_{1- x}OOH Nanoparticles Derived from the ⁵⁷Fe- and ¹¹⁹Sn-Mössbauer Spectra

Debye temperatures of α-Sn_xFe_1-xOOH nanoparticles (x = 0, 0.05, 0.10, 0.15 and 0.20, abbreviated as Sn100x NPs) prepared by hydrothermal reaction were estimated with ⁵⁷Fe- and ¹¹⁹Sn-Mössbauer spectra measured by varying the temperature from 20 to 300 K. Electrical properties were studied by solid-state impedance spectroscopy (SS-IS). Together, the charge-discharge capacity of Li- and Na-ion batteries containing Sn100x NPs as a cathode were evaluated. ⁵⁷Fe-Mössbauer spectra of Sn10, Sn15, and Sn20 measured at 300 K showed only one doublet due to the superparamagnetic doublet, while the doublet decomposed into a sextet due to goethite at the temperature below 50 K for Sn 10, 200 K for Sn15, and 100 K for Sn20. These results suggest that Sn10, Sn15 and Sn20 had smaller particles than Sn0. On the other hand, 20 K ¹¹⁹Sn-Mössbauer spectra of Sn15 were composed of a paramagnetic doublet with an isomer shift (δ) of 0.24 mm s^-1 and quadrupole splitting (∆) of 3.52 mm s^-1. These values were larger than those of Sn10 (δ: 0.08 mm s^-1, ∆: 0.00 mm s^-1) and Sn20 (δ: 0.10 mm s^-1, ∆: 0.00 mm s^-1), suggesting that the Sn^IV-O chemical bond is shorter and the distortion of octahedral SnO₆ is larger in Sn15 than in Sn10 and Sn20 due to the increase in the covalency and polarization of the Sn^IV-O chemical bond. Debye temperatures determined from ⁵⁷Fe-Mössbauer spectra measured at the low temperature were 210 K, 228 K, and 250 K for Sn10, Sn15, and Sn20, while that of α-Fe₂O₃ was 324 K. Similarly, the Debye temperature of 199, 251, and 269 K for Sn10, Sn15, and Sn20 were estimated from the temperature-dependent ¹¹⁹Sn-Mössbauer spectra, which were significantly smaller than that of BaSnO₃ (=658 K) and SnO₂ (=382 K). These results suggest that Fe and Sn are a weakly bound lattice in goethite NPs with low crystallinity. Modification of NPs and addition of Sn has a positive effect, resulting in an increase in DC conductivity of almost 5 orders of magnitude, from a σ_DC value of 9.37 × 10^-7 (Ω cm)^-1 for pure goethite Sn (Sn0) up to DC plateau for samples containing 0.15 and 0.20 Sn (Sn15 and Sn20) with a DC value of ~4 × 10^-7 (Ω cm)^-1 @423 K. This non-linear conductivity pattern and levelling at a higher Sn content suggests that structural modifications have a notable impact on electron transport, which is primarily governed by the thermally activated via three-dimensional hopping of small polarons (SPH). Measurements of SIB performance, including the Sn100x cathode under a current density of 50 mA g^-1, showed initial capacities of 81 and 85 mAh g^-1 for Sn0 and Sn15, which were larger than the others. The large initial capacities were measured at a current density of 5 mA g^-1 found at 170 and 182 mAh g^-1 for Sn15 and Sn20, respectively. It is concluded that tin-goethite NPs are an excellent material for a secondary battery cathode and that Sn15 is the best cathode among the studied Sn100x NPs.