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Ch.12 - Solids and Modern Materials
Chapter 12, Problem 23

Imagine the primitive cubic lattice. Now imagine grabbing the top of it and stretching it straight up. All angles remain 90. What kind of primitive lattice have you made?
Illustration showing a primitive cubic lattice being stretched into a rectangular prism.

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Key Concepts

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

Primitive Cubic Lattice

A primitive cubic lattice is a type of crystal structure where atoms are located at the corners of a cube. Each unit cell contains one atom, as the corner atoms are shared among adjacent cells. This arrangement is characterized by its simple geometry and is the basis for understanding more complex lattice structures.
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Lattice Distortion

Lattice distortion refers to the alteration of the regular arrangement of atoms in a crystal lattice. In this scenario, stretching the primitive cubic lattice vertically while maintaining 90-degree angles transforms it into a rectangular prism, indicating a change in the unit cell dimensions while preserving the overall symmetry of the structure.
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Unit Cell

The unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. In the case of the stretched primitive cubic lattice, the unit cell changes from a cube to a rectangular prism, which affects the properties of the material, such as density and symmetry.
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