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Chapter 12: Problem 26

Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (a) triclinic, (e) both rhombohedral and triclinic.

Short Answer

Expert verified
Only a rhombohedral unit cell has equal edge lengths, where a = b = c. Therefore, the correct answer is (c) Rhombohedral.

Step by step solution

01

1. Check if Orthorhombic unit cell has equal edge lengths

In an orthorhombic unit cell, the cell edges are not necessarily equal in length. The angles between the edges are 90 degrees, but the edges can have different lengths. So, the orthorhombic unit cell does not meet the criteria.
02

2. Check if Hexagonal unit cell has equal edge lengths

A hexagonal unit cell has equal edge lengths a, b and, c, where a = b. However, the edge length c is not equal to a and b. So, the hexagonal unit cell does not meet the criteria either.
03

3. Check if Rhombohedral unit cell has equal edge lengths

A rhombohedral unit cell has equal edge lengths a, with a = b = c. Additionally, the angles α, β, and γ are equal but not equal to 90 degrees. Thus, a rhombohedral unit cell meets the criteria.
04

4. Check if Triclinic unit cell has equal edge lengths

In a triclinic unit cell, the edge lengths and angles are all different. The edges a, b, and c are different in length, and the angles α, β, and γ are also different from each other. So, the triclinic unit cell does not meet the criteria.
05

5. Conclusion

Based on our analysis of the different types of unit cells, only a rhombohedral unit cell has equal edge lengths. Therefore, the correct answer is (c) Rhombohedral.

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