Calculation of Compactness in a Simple Cubic Structure

This page details the process of calculating the compacité (compactness) in a structure cubique simple (simple cubic structure). The concept is fundamental in crystallography and materials science.

The compactness is defined as the ratio of the volume occupied by atoms to the total volume of the unit cell. For a simple cubic structure, this calculation involves comparing the volume of a single atom to the volume of the cubic unit cell.

Formula: Compacité = (Volume of atom) / (Volume of unit cell)

The document provides the specific formula for calculating compactness in a simple cubic structure:

Highlight: Compacité = (4πR³/3) / (2R)³ = π / 6 ≈ 52.36%

Where R is the radius of an atom in the structure.

Example: In a simple cubic structure, the edge length of the unit cell (a) is equal to twice the atomic radius (2R).

The page includes a visual representation of a face of the cubic structure, illustrating that the edge length (a) is indeed equal to 2R.

Vocabulary:

• Maille: Unit cell
• Rayon d'un atome: Atomic radius

This calculation demonstrates that in a simple cubic structure, only about 52.36% of the total volume is occupied by atoms, leaving a significant amount of empty space. This relatively low compactness is one reason why simple cubic structures are less common in nature compared to more efficiently packed structures like face-centered cubic or body-centered cubic.

Understanding compactness is crucial for studying material properties, as it affects characteristics such as density, melting point, and mechanical strength. This knowledge is essential for students in fields like materials science, physics, and chemistry.