# The Effect of the Chemical Composition on Mechanical Properties of CMAS Diopside Glass Ceramics
## 3 Results and Discussion
### Effect of the Ca/Mg Ratio in Glass Composition  
To investigate how glass composition in GCs influences their mechanical properties, the ion ratios in the glass region were modified. The original atomic ratio of Ca:Mg:Si:O for the CMS diopside crystal (CaMgSi\({}_{2}\)O\({}_{6}\)) is 1:1:2:6. Oxygen ions in the system are used for the charged balance, and the coordinate number for the Si ion is significantly different for Mg and Ca ions. Therefore, for convenience, we focused on changing the Ca/Mg ion ratio. Since the Ca and Mg ions have the same charge, the creation of different GC samples was implemented by replacing certain Mg ions with Ca ions, and vice versa. As larger deviation from the standard composition may cause the failure of nucleation of diopside crystals in real experiments, the maximum replacement percentage in this study was 20%. After relaxation, all samples suffered uniaxial tension, as in the previous simulation. Three samples were created for each composition to avoid contingency, and the stress-strain curves were taken and averaged. Firstly, we replaced 5%, 10% and 20% Mg ions with Ca ions, and the stress-strain curves for the three compositions and the original samples are shown in Figure 4a. It was found that the composition variation has no significant effect on the strength of the GCs samples, but it was still detected that increasing the Ca ions could decrease the flow stress, especially for the case of maximum percentage of Ca ion replacement. Then, 5%, 10% and 20% Ca ions were replaced with Mg ions, and the stress-strain curves of these Mg-rich samples are shown in Figure 4b. With the increase in  
Figure 3: Deformation map for glass sample (**a**) and CMS diopside GCs sample (**b**) at 0.18 strain. Each ion is colored according to its displacement vector magnitude; red regions represent high displacement and blue regions represent low displacement. The homogenous cell deformations are not included in the calculation, which means that the elastic displacement is not included. Mg content, the strength increases slightly. Previous experimental results also showed that the addition of MgO would increase the Young's modulus of glass [34]. The strengthening effect was too small to be observed for the 5% and 10% Mg-replaced samples. To show the trend of strength benefits from the high Mg content ratio clearly, the stress-strain curves comparing the original sample and another two 20% replacement samples are presented in Figure 4c. It has been noticed that replacing 20% Mg with Ca would reduce the flow stress decrease by about 10%. Interestingly, compared to the original sample, the Mg-rich samples showed high flow stress until about 0.14 strain and the enhancement was very small. These results reveal that the strength of the glass would be affected by the Ca/Mg ratio and a low Ca ratio is preferred. One obvious difference between Ca\({}^{2+}\) and Mg\({}^{2+}\) is their radii. Since Mg\({}^{2+}\) has a relatively smaller radius, the coordination number for Mg\({}^{2+}\) (4.5-5) is smaller than that of Ca\({}^{2+}\) (6) [35]. As the MgO and CaO cannot form glass, the low coordination number means that Mg\({}^{2+}\) is a better glass network modifier than Ca\({}^{2+}\), which may improve the mechanical properties of glass. A previous NMR study by [PERSON] et al. [36] showed that the high crack-resistant 60 SiO\({}_{2}\)-10 Al\({}_{2}\)O\({}_{3}\)-10B\({}_{2}\)O\({}_{3}\)-10 MgO-10 Na\({}_{2}\)O glasses benefit from the network formation role of Mg\({}^{2+}\). A recent MD simulation performed by [PERSON] et al. [37] also revealed the MgO plays a dual role as a glass network modifier/charge compensator and a network former. In addition, the machine learning model developed by the [PERSON] groups can predict the correlations between atomic radius and the hardness [38]. The tendency for higher Mg\({}^{2+}\) ratio lead towards higher hardness compared with Ca\({}^{2+}\) may be further analyzed with reference to their model in future work.