Which of the following characteristic features match(es) with the crystal systems: cubic and tetragonal?

Options

A. Both have the cell parameters a = b = c and `alpha=beta=gamma`
B. Both belong to different crystal systems
C. Both have only two crystallographic angles of `90^(@)`
D. Both belong to same crystal system

Answer

To solve the question regarding the characteristic features that match with the crystal systems cubic and tetragonal, we need to analyze the properties of each crystal system step by step.

### Step 1: Understand the Cubic Crystal System
- In the cubic crystal system, all three edge lengths (a, b, c) are equal.
- The angles between the edges are all 90 degrees (α = β = γ = 90°).

### Step 2: Understand the Tetragonal Crystal System
- In the tetragonal crystal system, two edge lengths are equal (let's say a = b) while the third edge length (c) is different (c ≠ a).
- The angles between the edges in the tetragonal system are also all 90 degrees (α = β = γ = 90°).

### Step 3: Compare the Two Systems
- Both cubic and tetragonal systems have angles that are all 90 degrees.
- However, the edge lengths differ: cubic has all edges equal, while tetragonal has two edges equal and one different.

### Step 4: Identify the Correct Characteristic Feature
- The key characteristic that matches both cubic and tetragonal systems is that they both have angles of 90 degrees.
- However, they belong to different crystal systems due to the differences in edge lengths.

### Conclusion
Based on the analysis:
- The correct answer is that both cubic and tetragonal belong to different crystal groups, but they share the characteristic of having angles of 90 degrees.

### Final Answer
The characteristic feature that matches with the cubic and tetragonal crystal systems is that both have angles of 90 degrees, but they belong to different crystal groups.

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