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

Verified step by step guidance

Step 1: Understand the concept of a unit cell in crystallography, which is the smallest repeating unit in a crystal lattice that shows the entire structure's symmetry.

Step 2: Recall that a cubic unit cell has all edges of equal length and all angles at 90 degrees.

Step 3: Analyze the characteristics of each given unit cell type: (a) Orthorhombic has unequal edge lengths and all angles at 90 degrees. (b) Hexagonal has two equal edge lengths and one different, with angles of 90 and 120 degrees. (c) Rhombohedral has all equal edge lengths with angles that are not 90 degrees. (d) Triclinic has unequal edge lengths and angles that are not 90 degrees.

Step 4: Identify which unit cell types have all edge lengths equal. From the analysis, the rhombohedral unit cell has this property.

Step 5: Conclude that the rhombohedral unit cell is the only one among the options that has all edge lengths equal to each other.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Cell Types

In crystallography, a unit cell is the smallest repeating unit that defines the structure of a crystal lattice. Different types of unit cells, such as cubic, orthorhombic, hexagonal, rhombohedral, and triclinic, have distinct geometric properties. Understanding these types is essential for identifying their edge lengths and angles.

Edge Lengths in Crystals

Edge lengths refer to the dimensions of the unit cell along its axes. In cubic unit cells, all edge lengths are equal, while in other types, such as orthorhombic and rhombohedral, edge lengths can vary. Recognizing which unit cells have equal edge lengths helps in determining their classification and properties.

Rhombohedral and Triclinic Structures

Rhombohedral unit cells have equal edge lengths but differ in angles, while triclinic unit cells have unequal edge lengths and angles. Both structures are less symmetric than cubic cells, making their identification based on edge lengths and angles crucial for understanding their crystallographic properties.

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