Describe the geometries of the following cubic cells: simple...

Name: Problem 34, Chapter 11: Chemistry
Uploaded: 2023-03-22T15:54:39-08:00
Duration: 1 min 41 s
Channel: Anand Jangid
Description: Describe the geometries of the following cubic cells: simple cubic, body-centered cubic, facecentered cubic. Which of these structures would give the highest density for the same type of atoms? Which the lowest?

Describe the geometries of the following cubic cells: simple cubic, body-centered cubic, facecentered cubic. Which of these structures would give the highest density for the same type of atoms? Which the lowest?

Key Concepts

Atomic Packing Efficiency and Density

The concept of atomic packing efficiency relates to how closely atoms are packed within a unit cell and is a key factor in determining the density of a material. Structures with higher packing fractions, such as the face-centered cubic arrangement, generally yield higher material densities, whereas structures with lower packing fractions, like the simple cubic, result in lower densities when the atomic size remains constant.

Simple Cubic Structure

This structure features atoms positioned only at the corners of a cube. Each corner atom is shared among adjacent cubes, resulting in a low coordination number and minimal space-filling efficiency. It serves as one of the simplest models in crystallography despite its relatively poor packing efficiency compared to other cubic arrangements.

Body-Centered Cubic Structure

In a body-centered cubic arrangement, atoms are positioned at each of the cube’s corners with an additional atom placed at the center of the cube. This arrangement enhances the coordination number and packing efficiency relative to the simple cubic structure, and it is commonly encountered in metals that benefit from a balance of density and symmetry in their crystal lattice.

Face-Centered Cubic Structure

This structure has atoms located at each corner and at the center of all cube faces. It exhibits one of the highest packing efficiencies among cubic lattices, leading to greater density for a given atomic type. The high coordination number and efficient atomic arrangement make this structure prevalent in many metallic crystals.

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