Polaron-ion correlations inLixFePO4studied by x-ray nuclear resonant forward scattering at elevated pressure and temperature

Abstract

Valence fluctuations of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ were studied in a solid solution of ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ by nuclear resonant forward scattering of synchrotron x rays while the sample was heated in a diamond-anvil pressure cell. The spectra acquired at different temperatures and pressures were analyzed for the frequencies of valence changes using the Blume-Tjon model of a system with a fluctuating Hamiltonian. These frequencies were analyzed to obtain activation enthalpies and an activation volume for polaron hopping. There was a large suppression of hopping frequency with pressure, giving an activation volume for polaron hopping of $5.8\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.28em}{0ex}}0.7 {\AA{}}^{3}$. This large, positive value is typical of ion diffusion, which indicates correlated motions of polarons and ${\mathrm{Li}}^{+}$ ions that alter the dynamics of both. Monte Carlo simulations were used to estimate the strength of the polaron-ion interaction energy.