{"knowledge_schema": {"broad_category": "Physics \u2192 Crystallography \u2192 Crystal Structures", "refinement": "This problem pertains to the calculation of interplanar spacing in a specific type of crystal lattice, namely a rhombohedral lattice.", "specific_scope": "The focus is on determining the distance between the (111) planes in a rhombohedral crystal with given interatomic spacing and angles.", "goal": "Calculate the interplanar distance for the (111) planes using the provided parameters."}, "summary": "This problem involves crystallography, specifically the calculation of the distance between specific crystal planes in a rhombohedral lattice. Given the interatomic spacing and the angles of the crystal, the task is to apply the appropriate formula for interplanar spacing to find the distance between the (111) planes. The correct answer, based on the calculations, is 9.54 \u00c5."}