Step 1: Determine the coordination number for each crystal structure. The coordination number is defined as the count of immediate neighboring atoms in a crystal lattice.
A. Diamond: The diamond cubic structure features carbon atoms bonded tetrahedrally to four other carbon atoms, resulting in a coordination number of 4.
B. Sodium Chloride (NaCl): In the rock salt structure, each ion (e.g., Na\(^+\)) is surrounded by six oppositely charged ions (e.g., Cl\(^-\)) in an octahedral configuration. The coordination number is 6.
C. Cesium Chloride (CsCl): The CsCl structure places each ion at the center of a cube formed by eight oppositely charged ions. The coordination number is 8.
D. Zinc (HCP): Zinc adopts a Hexagonal Close-Packed (HCP) structure. In any close-packed structure (HCP or FCC), an atom is in contact with 12 other atoms (6 in its own plane, 3 above, and 3 below). The coordination number is 12.
Step 2: Arrange the crystal structures based on their coordination numbers in ascending order.
The coordination numbers are as follows:
- Diamond (A): 4
- Sodium Chloride (B): 6
- Cesium Chloride (C): 8
- Zinc (HCP) (D): 12
Arranging these in ascending order yields the sequence: A (4)<B (6)<C (8)<D (12).
The resulting order is A, B, C, D.