Why carbon has more solubility in FCC structure?

Carbon has more solubility in face-centered cubic (FCC) structures primarily due to the larger interstitial sites available in the FCC lattice compared to body-centered cubic (BCC) structures. The FCC structure has a higher coordination number, allowing more carbon atoms to fit into the interstitial spaces. Additionally, the close-packed arrangement of atoms in FCC provides greater stability for the carbon atoms when dissolved, enhancing solubility. This is particularly important in alloys, such as steel, where carbon plays a significant role in modifying mechanical properties.