Mean-Squared Displacement of Si and O Atoms in Original Lithium Disilicate Glass
Motions of Si and 0 of this system are shown in the lower panel of Fig. 6.3. For both 600 and 800 K, they are immobile for a long time and hence the cage is stable during this time period. A slight increase in the mobility for these species is found at ~1 ns at 800 K.
Diffusion coefficients are fundamental transport properties, which are closely related to other ones such as conductivity [47-50] as already discussed in Chapter 5.
Dynamical changes toward the maximum of the diffusion coefficient with the expansion of the system
The MSD of porous systems obtained in NVE condition shows a remarkable difference from the original glass. In Fig. 6.4, the time dependence of the MSD of Li ions for porous systems is compared with the original glassy system. In the porous systems, MSDs levels off earlier than that in the original glass and hence the NCL region is shortened. That is, the change in the dynamics of ions starts at the early time region for caged ion dynamics.
It is worth to mention that the motion affected by introducing pore is not only for Li ions but also for network-forming atoms as shown in the bottom part of the figure. In porous systems showing high-diffusivity of Li ions, levels of Si and О are found to be larger than the original system and no flat region of О atoms is observed after 1 ps. Motions of network-forming atoms are then non-negligible even in the short time region. Because these atoms are forming cages for Li ions, this result also means that the loosening of the cage is contributing to the enhancement of mobility of Li ions. Such changes in coordination polyhedra naturally increased in the jump rate. These features are consistent with the observation in trajectories shown in Fig. 6.2 and accompanied with the decrease in the coordination number Nv [= x
in LiOx structure), as shown in Fig. 6.5a. In this figure, the position of the maximum of the peak is found at 5 before the expansion of the system and gradually decreases. This change accompanied with the increase of the diffusivity.
Figure 6.4 Shortening of the caging (NCL) region in porous systems. Top: MSD of ions and atoms in lithium disilicate in porous systems at 800 К (upper curves). Upper panel: Li ions for p = 2.47 (black) (original), 2.30 (green), 2.13 (blue) and 1.98 (red) from lower to upper. The diffusivity of the system increases in this order. In this figure, long-time data for the p = 2.47, which were obtained by a larger time step (4 fs), are smoothly connected to those for short time scales (dashed curves) obtained by a smaller time step (1 fs). Bottom: MSD of Si (lower four curves in the beginning part) and 0 (upper four curves in the beginning part) of the same systems. The same color as that for MSD of Li ions is used for each atom. Reprinted from Habasaki, J. (2016), Molecular dynamics study of nano-porous materials—Enhancement of mobility of Li ions in lithium disilicate in NVE conditions, /. Chem. Phys., 145, 204503(1-11), with the permission of A1P Publishing.
Figure 6.5 Topological change of the coordination polyhedra (0 atoms around Li ion) by introducing pores with decreasing density, (a) Changes of the distribution of the coordination number (Nv) at 800 K. Green (solid) line: for the original lithium disilicate glass. Pale green (dashed) line: for the porous system with p = 2.30, orange (dotted) line: for p = 2.13 and red (thick solid) line: for p = 1.98. An arrow (blue) in this figure means the trend with decreasing density, (b) Further changes in the coordination number. The red one is the same one as in (a). The distribution connected by dotted dashed lines is for p = 1, and that connected by two dotted dashed lines is for p = 1.58. The trend shown by the arrow is just opposite to that found in (a). That is, the loosening of the cage (by decreasing overlaps of polyhedra occurs in (a), while the tightening of it occurs in (b). Reprinted from Habasaki, J. (2016), Molecular dynamics study of nano-porous materials—Enhancement of mobility of Li ions in lithium disilicate in NVE conditions,/. Chem. Phys., 145, 204503(1-11), with the permission of AIP Publishing.
Further decrease of the dynamics with the expansion of the system
With the further decrease of the density (p = 1.84 and 1.58), the coordination number of LiOA. structure tends to increase (Fig. 6.5b).
With this structural change, the decrease of the MSD is found (see Fig. 6.6). That is, MSDs of Li ions, Si and 0 atoms decrease and the NCL region of these species becomes longer again. This slowing down also starts from the early time region, implying the tightening of the cage. This structural change is accompanied with the gradual structural changes with a formation of larger voids as shown later.
Figure 6.6 Dependence of MSD on density (porosity) of Li2Si205 systems at 800 K. Upper panel: Li ions for p = 1.98, 1.84 and 1.58 from upper to lower. The diffusivity of the system decreases in this order. Lower panel: Si (lower three curves) and 0 atoms (upper three curves) Density is 1.98, 1.84, and 1.58 from upper to lower for each species. Reprinted from Habasaki, J. (2016), Molecular dynamics study of nano-porous materials—Enhancement of mobility of Li ions in lithium disilicate in NVE conditions, / Chem. Phys., 145, 204503 (1-11), with the permission of A1P Publishing.