MD Simulations and Modeling of Porous Systems
The system examined is lithium disilicate, which is located in the silica-rich region of Li20-Si02 systems, and pores are introduced by the scaling of volume and positions [13, 14]. So far, several compositions of lithium silicates such as lithium disilicate and lithium metasilicate in the molten, glassy, crystalline states have been examined successfully from many points of view by several groups, where our potential model previously developed based on the ab initio MO calculations  was commonly used. The model has been tested for several polymorphs of crystals under atmospheric pressure. The diffusivity and/or viscosity of the simulated system using our potential model are comparable to the experiments in several conditions . Since the model covers a wide range of potential surfaces, it will be useful for further systematical comparison of systems with different states including the porous ones.
Each original and porous lithium disilicate (Li2Si205) system examined contains 3456 atoms (768 Li ions, 768 Si atoms, and 1920 oxygen atoms) in the basic MD box with a periodic boundary condition. The following model function was used:
The model potential consists of the Coulombic term, the pair potential function of the Gilbert-Ida type [76, 77] with the r6 for correction of the softness of the oxygen atom. The value r is the distance between atoms and a,- is the effective radius and fo, is the softness parameters of the atom / with a constant /о (=1 kcal A"1 mol-1 = 4.184 kj A'1 mol'1). The Ewald method was used for the calculation of the Coulomnbic force. A cut-off distance was chosen to be 12 A for the calculation of both the repulsive force and that for the real space term of the Coulombic force.
The present model seems to be good enough for discussing the trend caused by the changes in the density (and porosity) of the system and changes in dynamics in different states based on the same potential model.
Preparation of Porous Lithium Disilicate and Porous Lithium Metasilicate
The procedure for preparing porous systems is as follows. First, lithium disilicate in the glassy state was obtained by the rapid cooling (~1 К ps"1) from the melt at 3000 К with the combination of constant pressure condition and temperature scaling to the target temperatures (2000, 1700, 1400, 1200, 1000, 800, 700, and 600 K). Systems were quasi-equilibrated at each temperature in the NPT condition and then the following runs in the NVE condition were done. Then porous systems were prepared by the scaling of the volume and position of particles at 600 K. Similar methods had been previously used to prepare the porous silica . After the expansion of the system, each system was equilibrated during 300,000 steps run in the NVT condition and the following NVE runs are used for analyses. The time step used in the MD run was 1 fs for almost of porous systems. The densities p examined are 2.47 (original), 2.30, 2.13, 1.98, 1.84 and 1.58 in g cm"3 for lithium disilicate. Simulations at several temperatures (700, 800, and 1000 K) in the porous systems have been done using the same volume as systems at 600 K. The results for NPT conditions of MD are partly described in  and in Chapter 7. Interestingly, the self-healing process is found in this condition, even after the relatively large voids are formed. Because the porous system was prepared by the expansion of the original system in NVE conditions, observed enhancement may be correlated to the residual stress in the system. Therefore, the relation between such mechanical properties and dynamics in porous systems is also worthy to examine. The result in the subsequent NPT run related to this problem will be discussed in Chapter 7.