# The Effect of the Chemical Composition on Mechanical Properties of CMAS Diopside Glass Ceramics
## 2 Sample Preparation and Simulation Method  
In the study, we used the force field in the CMAS94 model, as below, to capture the interactions for the Ca, Mg, Al, Si and O atoms [28]. \[V_{r_{(ij)}}=q_{i}q_{j}r_{ij}^{-1}-C_{i}C_{j}r_{ij}^{-6}+f\left(B_{i}+B_{j} \right)\times\exp\left[\left(A_{i}+A_{j}-r_{ij}\right)/\left(B_{i}+B_{j} \right)\right]\]  
where the terms represent Coulomb, van der Wals and repulsion interactions, respectively. The subscripts \(i\) and \(j\) are two interactive atoms. \(A\), \(B\), \(C\) and \(q\) are repulsive radii, softness parameters, van der Wals coefficients and net charges for ion \(i\). The CMAS94 potential is successful in reproducing 27 crystal structures (including the diopside crystal) with a stable structure during MD simulation at appropriate temperatures. The fidelity of the potential in capturing the mechanical properties of the CMAS diopside GCs is substantiated by the good agreement of the bulk and elastic modulus for the between-simulation and experimental values. The glass-ceramic samples in this study were prepared following these steps:1. To create the glass structure, a slab simulation box with dimensions near 20 nm \(\times\) 20 nm \(\times\) 2 nm was set, and then the Ca, Mg, Si and O ions were placed in the simulation box, following the diopside crystal structure, as shown in Figure 1b. The diopside cell structure belongs to the space symmetry group of C12/C1 (as shown in Figure 1a) and the lattice parameters were calculated based on the ab initio calculation, so the structure was optimized to find the ground state before MD simulation [29]. The diopside structure is also stable in the MD simulation with the CMAS94 potential. The system first minimized the energy using the conjugated gradient method, and then heated up to about 3000 K for 2 ns in NVT (canonical ensemble) [30]. A temperature of 3000 K is sufficient to melt the diopside crystal into an amorphous form. As shown in Figure 1c, as the temperature raised to about 2500 K, the average displacement vector magnitude for ions increased significantly, which means that the diopside crystal converted to amorphous melting. Finally, we cooled down the melt to 300 K over a period of 8 ns in NPT (Nose/Hoover isobaric-isothermal ensemble) with zero pressure in all three dimensions. 2. To create the diopside GCs, we first created the CMS diopside crystal structure and then the structure was subsequently cut into ellipsoids with a radius of 4 nm. Then, we created an ellipsoid void with the same shape in the glass by deleting ions and refilled with the pre-made diopside crystal, so the diopside GCs structure was created. The total ion number in CGs samples is the same as the glass sample, to make the comparison reasonable. Finally, to relax the interface between the glass and the inserted ellipsoid crystals, the assembled samples were heated up to 1000 K and relaxed for 2 ns in the NPT ensemble with zero pressure and then cooled down to 300 K to relax for another 2 ns. 3. To create different CMAS diopside GCs samples, we adjusted the atom type in the glass phase and relaxed the system for 2 ns at 1000 K and 300 K. The total ion number for the samples in the simulation box was about 100,000. In this study, we investigated the effect of Mg, Ca and Al ion ratios, so the O and Si ion ratios would not change. The influence of the glass phase composition in diopside GCs was studied by MD simulation. The MD simulations were performed using the LAMMPS code and the timestep  
Figure 1: (**a**) The CaMgSi\({}_{2}\)O\({}_{6}\) diopside cell (red for O, yellow for Si and green for Mg and Ca); (**b**) the CMS diopside sample; (**c**) plot of temperature versus average displacement vector magnitude during melting; (**d**) the CMS glass sample; (**e**) the CMS diopside GCs sample. Each ion is colored by its element type. was 1 fs [31]. Periodic boundary conditions were applied in all directions for all samples. The NPT ensemble was used to control the temperature and pressure.