To determine which statement is incorrect regarding the packing structures of hcp (hexagonal close-packed) and ccp (cubic close-packed), let’s analyze each option carefully.
Understanding the Structures
Both hcp and ccp are types of close-packed structures where spheres (atoms or ions) are arranged to maximize space efficiency. The coordination number, which indicates how many nearest neighbors each sphere has, plays a crucial role in these structures.
Evaluating Each Statement
- (a) In hcp and ccp the sphere is in contact with 6 spheres of its own layer.
This statement is correct. In both hcp and ccp arrangements, each sphere is indeed in contact with six other spheres in the same layer.
- (b) In both hcp and ccp the sphere has 3 spheres above it and 3 below it.
This statement is also correct. In both structures, a sphere is surrounded by three spheres in the layer above and three in the layer below, contributing to the overall coordination number.
- (c) In both hcp and ccp the coordination number is 12.
This statement is accurate as well. The coordination number for both hcp and ccp structures is indeed 12, meaning each sphere is in contact with 12 other spheres.
- (d) In inverse spinel (e.g., magnetite, Fe3O4) only.
This statement is incomplete and misleading. Inverse spinel structures do not relate directly to the coordination numbers or arrangements of hcp and ccp. Instead, they refer to a specific type of crystal structure where cations occupy different lattice sites, which is not applicable to the previous statements about hcp and ccp.
Conclusion on the Incorrect Statement
Based on the analysis, the incorrect statement is (d). It lacks context and does not accurately describe the relationship between inverse spinel structures and the coordination or packing of spheres in hcp and ccp arrangements. Understanding these distinctions is crucial for grasping the complexities of crystal structures in materials science.
