| dc.description.abstract | In summary, a new interionic potential function for Li? with the Zr?(PO?)? framework of the LiZr?(PO?)? system, consisting of three terms-Coulombic, repulsive, and charge-polarizability interaction-has been proposed. Molecular dynamics (MD) simulation employing this potential suggests that the model accurately describes several aspects of Li? motion in LiZr?(PO?)?, in good agreement with experimental observations. The occupancy of Li? ions in site 1 and site 2, the radial distribution functions (RDFs), variation of specific heat, conductivity, and density contours all agree with experiments. The conductivity shows the expected transition from normal to superionic conductor (SIC) at the experimentally observed temperature of 550–600 K. The spread of the density around site 1 and site 2 matches that found in X-ray studies [4,24]. Our results also suggest the presence of a mid-Li site, consistent with the recent neutron diffraction study by Catti and Stramare [13]. However, the population of Li? at the mid-Li site predicted by MD is significantly smaller than that reported by Catti and Stramare. The activation energy for Li? ion migration above the transition is 0.39 eV, compared to the experimentally observed values of 0.42 eV or 0.44 eV. In fact, the success of the present MD study suggests that ion transport over a wide range of temperatures, including the normal-to-SIC transition in NASICON-type systems, can be realistically simulated within a rigid framework approximation. However, framework motion may become important under certain conditions.
MD study of ion diffusion through the pores of the rigid structure formed by PO? tetrahedra and ZrO? octahedra suggests that the diffusion coefficient (D) reaches a maximum at a particular ion size. These results indicate that the levitation effect exists even when the dominant interaction between the ion and the NASICON framework is long-range. This finding is of considerable importance in many areas: battery materials, ion diffusion across membranes, sensors, among others. The existence of an optimum size for ion diffusion suggests that an ion diffusing through a biomembrane will diffuse faster and with lower activation energy when the channel size is optimum. This could provide a way to achieve optimum mobility in complex systems.
The proposed interionic potential (Equation 4.1 and Table 4.1) has been found to predict known quantities relating to structure, conductivity, and other properties in good agreement with experiments. In view of this agreement, it appears reasonable to expect that other properties obtained using this model will be reliable and correct. Many results are in excellent agreement with the X-ray diffraction results of Boilot et al. [9]. For example, the sum of sodium occupancy at Na(1) and mid-Na sites adds up to unity. The preferred conduction channel is the one connecting Na(1) and Na(2) sites. The free energy profiles and Na? density contours between Na(1) and Na(2) sites suggest that the mid-Na site is a “delocalized” one. At 600 K, the mid-Na site is energetically more favorable than Na(1) and Na(2) sites for almost all compositions. The higher occupancy observed at Na(1) and Na(2) sites for most compositions is due to the larger entropic contributions to the free energy from these sites. The larger Na-O distance at Na(1) and Na(2) sites compared to that at the mid-Na site also supports this argument.
Interesting (Si/P)O?-tetrahedra orientational disorder proposed by Kohler and Schulz [11] as well as Didisheim et al. [41] is supported by the present simulation results. The orientational disorder is found to be dynamic rather than static or frozen-in, in agreement with Colomban et al. [26]. The (Si/P)O?-tetrahedra rotations are associated with rotations of ZrO? octahedra around the c-axis. The present simulation results suggest that the most important single factor for the high conductivity of Na?Zr?Si?PO?? is the framework motion, which assists Na? hops between Na(1) and Na(2) sites. Ion–ion correlation and widening of bottlenecks could be other factors enhancing conductivity in Na?Zr?Si?PO??.
The important framework motion that assists high ionic mobility could be a dynamic breathing-like mode of the bottleneck oxygens coupled with Na? hops between Na(1) and Na(2) sites. This aspect requires further, more detailed analysis of the NVE–MD trajectories.
Starting from the low-temperature monoclinic structure of Na?Zr?Si?PO??, thermodynamic quantities such as average energy, average volume, heat capacity at constant pressure, and isothermal compressibility have been calculated at various temperatures in the range of 300–1000 K. Three phase transitions are observed in the system at 450 K, 600 K, and 650 K. The transition at 450 K is accompanied by a sharp volume change and peaks in heat capacity and isothermal compressibility. The Arrhenius plot of conductivity confirms that this transition (at 450 K) is due to the monoclinic ? rhombohedral structural change. The activation energy for conduction in the rhombohedral phase of Na?Zr?Si?PO?? is in excellent agreement with experimental studies on high-temperature-sintered samples [8]. Structural characterization of the two phases using radial distribution functions and bond angle distribution functions indicates no significant structural change above and below the transition. The absence of structural evidence for this transition is attributed to extremely small atomic displacements involved during the transition [7]. The monoclinic ? rhombohedral transition temperature from simulation studies is also in good agreement with experiments [4–9].
The transition at 600 K is accompanied by changes in volume and a peak in isothermal compressibility. The slow convergence of the mean squared displacement of oxygen atoms with time indicates the presence of some low-frequency modes of the polyhedral-possibly dynamic orientational disorder of the (Si/P)O?-tetrahedra first proposed by Colomban [8,13]. The transition at 600 K is a manifestation of spontaneous excitation of the low-frequency polyhedral mode. The absence of a peak in heat capacity at 600 K suggests that this low-frequency mode is energetically inexpensive.
The transition at 650 K is characterized by a peak in heat capacity. A similar feature was observed by Colomban [8] in differential scanning calorimetric experiments on well-sintered samples. The reason for this transition remains to be probed. It is interesting to note that while most experimental studies [4–6,9] observe only one transition around 423 K in the 300–1000 K range, high-temperature-sintered samples studied by Colomban [8] showed three transitions at comparable temperatures. The present simulation results on phase transitions in Na?Zr?Si?PO?? are in good agreement with previous experimental studies on high-temperature-sintered samples by Colomban [8].
The study also discusses interesting aspects of ionic motion in the monoclinic and rhombohedral phases of Na?Zr?Si?PO??. Most notably, Na(1)–Na(2) and Na(1)–Na(3) hops are found to be equally preferred for Na? ions, and the larger transport of Na? through the Na(1)–Na(3) channel is mainly due to the greater number of such channels compared to Na(1)–Na(2) channels. | |
