Which one of the following schemes of ordering closed packed sheets of equal sized spheres does not generate close packed lattice?

Options

A. ABCABC
B. ABACABAC
C. ABBAABBA
D. ABCBCABCBC

Answer

To determine which scheme of ordering closed packed sheets of equal-sized spheres does not generate a close packed lattice, we need to analyze the arrangements provided in the options.

### Step-by-Step Solution:

1. **Understanding Close Packed Structures**:
- Close packed structures are formed by arranging layers of spheres in such a way that they occupy the maximum possible volume. The most common types of close packed structures are face-centered cubic (FCC) and hexagonal close packing (HCP).

2. **Analyzing the Given Options**:
- We need to evaluate each arrangement to see if it meets the criteria for a close packed lattice, which requires that the same type of spheres (or layers) should not be adjacent to each other.

3. **Option 1: ABC-ABC**:
- This arrangement alternates layers of spheres (A, B, C). Each layer is different from the adjacent layers, which allows for optimal packing.
- **Conclusion**: This arrangement does form a close packed lattice.

4. **Option 2: ABAC-ABAC**:
- In this arrangement, the layers alternate between A and B, with A appearing twice in a row before switching to B. However, the pattern still maintains a separation between the same types of layers.
- **Conclusion**: This arrangement also forms a close packed lattice.

5. **Option 3: ABBA-ABBA**:
- Here, the arrangement has two A layers followed by two B layers (AA and BB). This means that the same type of layers are adjacent to each other (AA and BB), which violates the close packing rule.
- **Conclusion**: This arrangement does not form a close packed lattice.

6. **Option 4: ABC-BCA-BCB**:
- Similar to the first option, this arrangement ensures that no two layers of the same type are adjacent. The layers are arranged in a way that maintains the separation of different types.
- **Conclusion**: This arrangement forms a close packed lattice.

### Final Answer:
The scheme of ordering that does not generate a close packed lattice is **ABBA-ABBA**.