The discussion centers on the factors influencing whether a solid adopts a crystalline or amorphous structure, emphasizing that the crystal structure is determined by the substance's composition, similar to how molecular structures in gases depend on their atomic makeup. While crystalline structures can be categorized into various types such as cubic, tetragonal, and hexagonal, predicting which structure a solid will take remains complex and challenging. Current mathematical methods for determining crystal structures are limited, as there are infinitely many possible configurations. Techniques like ab initio calculations and density functional theory can help identify likely structures when the possibilities are narrowed down. However, proving that a specific structure is the global minimum energy configuration is difficult, with even basic packing problems recently resolved. Additionally, minor changes in temperature or pressure can significantly alter crystal structures, as seen in substances like water ice and elemental sulfur. Overall, accurately predicting crystal structures from chemical compositions is still largely unattainable, particularly for complex systems.
