Mullite is an important ceramic material with a solid solution series between alumina (\( \text{Al}_2\text{O}_3 \)) and silica (\( \text{SiO}_2 \)). The limiting compositions of mullite in this solid solution series are 3:2 and 2:1.
Step 1: Understanding the Mullite Composition
- Mullite exists in a range of compositions between 3Al\(_2\)O\(_3\)·2SiO\(_2\) (3:2) and 2Al\(_2\)O\(_3\)·SiO\(_2\) (2:1).
- This range defines the mullite solid solution series.
- These compositions influence the thermal stability, mechanical properties, and phase stability of mullite.
Step 2: Evaluating the Options
- Option (A) - Incorrect: 1:2 is not a composition in the mullite series.
- Option (B) - Incorrect: 2:1 is correct, but 3:1 is not part of the mullite series.
- Option (C) - Correct: The 3:2 and 2:1 ratios correctly represent the limiting compositions of mullite.
- Option (D) - Incorrect: 3:1 is not a correct composition in the mullite phase.
Step 3: Conclusion
Since the limiting compositions of mullite solid solution are 3:2 and 2:1, the correct answer is option (C).