Final answer:
The coordinates of tetrahedral and octahedral interstitial sites in close-packed crystal structures are (1/4, 1/4, 1/4) and (1/2, 1/2, 1/2) respectively, with the tetrahedral sites having a coordination number of 4 and octahedral sites having a coordination number of 6.
Step-by-step explanation:
The coordinates of tetrahedral and octahedral interstitial sites can be defined based on their positions within a crystal lattice structure, particularly in face-centered cubic (fcc) or close-packed arrays. A tetrahedral hole is located between one atom at a corner of the unit cell and the three atoms at the centers of the adjacent faces, and has a coordination number of 4, indicating an atom at this site would be in contact with 4 other atoms.
An octahedral hole, however, is located in positions where the centers of spheres form the six corners of an octahedron. Octahedral holes are generally larger than tetrahedral holes and an atom in such a site would have a coordination number of 6.
Referencing the options provided for the coordinates, the correct coordinates for a tetrahedral hole in a close-packed structure would be (1/4, 1/4, 1/4), while for an octahedral hole, the correct coordinates are (1/2, 1/2, 1/2). Thus, the answer to the question is 1) (1/4, 1/4, 1/4) for tetrahedral sites and (1/2, 1/2, 1/2) for octahedral sites.