{"knowledge_schema": {"broad_category": "Materials Science \u2192 Crystallography \u2192 Interplanar Distances", "refinement": "This problem involves calculating the interplanar distance for a specific crystallographic plane in a rhombohedral crystal structure.", "specific_scope": "The focus is on the (111) plane of a rhombohedral crystal with given interatomic distances and angles.", "goal": "Calculate the interplanar distance of the (111) plane using the provided parameters."}, "summary": "This problem requires understanding the relationship between crystal structure and interplanar distances in crystallography. Specifically, it involves calculating the interplanar distance for the (111) plane in a rhombohedral crystal with specified interatomic distances and angles. The goal is to apply the appropriate formula for interplanar spacing in a rhombohedral lattice to find the correct distance, which will help in identifying the correct answer from the provided options."}