Disclosing crystal nucleation mechanism in lithium disilicate glass through molecular dynamics simulations and free-energy calculations

Abstract

Unraveling detailed mechanism of crystal nucleation from amorphous materials is challenging for both experimental and theoretical approaches. In this study, we have examined two methods to understand the initial stage of crystal precipitation from lithium disilicate glasses using molecular dynamics simulations. One of the methods is a modified exploring method to find structurally similar crystalline clusters in the glass models, enabling us to find three different embryos, such as Li₂Si₂O₅ (LS₂), Li₂SiO₃ (LS) and Li₃PO₄ (LP), in the 33Li₂O·66SiO₂·1P₂O₅ glass (LS₂P1), in which P₂O₅ is added as a nucleating agent. Interestingly, LS₂ and LP crystals were found inside the LS₂P1 glass while LS crystal appeared on the glass surface, which agrees with experimental observations. The other method is free energy calculation using a subnano-scale spherical crystal embedded in the glass model. This method, which we called Free-Energy Seeding Method (FESM), allows us to evaluate free energy change as a function of crystal radius and to identify critical size of the crystal precipitation. The free energy profiles for LS and LS₂ crystal nuclei in the LS₂ glass models possess maximum energy at a critical radius as expected by classical nucleation theory. Furthermore, the critical radius and the energy barrier height agree well with recent experimental investigation, proving the applicability of this method to design glass-ceramics by atomistic modeling.

Figure 1

Structure of the LS and LS₂ crystals along different orientations and unit cell parameters. Blue tetrahedral represents silicon, red and green spheres represent oxygen and lithium ions, respectively.

Figure 2

Snapshot of the MD-derived bulk structural model of the LS₂ glass showing all the ions in the box (a) and Li ions only (b). Snapshot of the LS₂P1 glass showing all the ions in the box (c) and Li (cyan spheres) and PO₄ tetrahedra only (d).

Figure 3

Li–Li Pair Distribution Functions of the LS₂ and LS₂P1 Glasses compared to that of the LS₂ and LS crystals.

Figure 4

Distribution of cumulative distances (with respect to Li₂SiO₃, Li₂Si₂O₅ and Li₃PO₄ crystals) of clusters of radii 3.6, 4.0 and 4.6 Å centered on Silicon (left) and Lithium (middle) and Phosphorous (right) for the LS₂ and LS₂P1 glasses.

Figure 5

Embryos of Li₂Si₂O₅ (LS₂), Li₂SiO₃ (LS) and Li₃PO₄ (LP) found in the LS₂P1 glass and structures of the three crystals.

Figure 6

Top and lateral view of the surface of the LS₂ and LS₂P1 glasses. Li, Si and O ions are, respectively, represented by violet, yellow and red spheres. Orthophosphate units are represented as green tetrahedral.

Figure 7

Z-depth profiles of the atomic fraction of Li, Si, P and O ions and Qⁿ distributions of Si ions in the LS₂ and LS₂P1 glass surface models.

Figure 8

Structure of boxes with critical size nuclei. On the left, glass with LS₂ composition with the critical nucleus of Li₂Si₂O₅ crystal. On the right, glass with LS₂ composition with the critical nucleus of Li₂SiO₃ crystal.

Figure 9

Free energy of nucleation for (a) the LS and LS₂ crystals in the LS₂ glass at 800 K and (b) the LS₂ crystals in the LS₂ glass at 800 K and 1000 K with relative standard deviation.

Figure 10

(a) Q₆ Steinhardt parameter of silicon atoms from the center of the LS or LS₂ crystal nuclei to the glass matrix at 800 K. (b) Computed local order Q₆ parameter for silicon atoms from the center of the LS₂ crystal nuclei (of 10 Å) to the glass matrix at 800 K, 1000 K and 1200 K. (c) Glass with LS₂ composition with a nucleus of Li₂Si₂O₅ crystal with radius of 10 Å equilibrated at 800 K. (d) Glass with LS₂ composition with a nucleus of Li₂Si₂O₅ crystal with radius of 10 Å equilibrated at 1200 K.