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Ch.12 - Solids and Modern Materials
Chapter 12, Problem 26

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
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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.