How to Calculate Planar Density

••• Jupiterimages/Pixland/Getty Images

Atoms can be packed together densely or loosely. In crystalline materials such as metals, atoms are packed on periodic, three-dimensional arrays. In non-crystalline materials such as silicon oxide, atoms are not subject to periodic packing. The basic component of a crystal structure is a unit cell. Planar density is a measure of packing density in crystals. The planar density of a face centered cubic unit cell can be calculated with a few simple steps.

    Calculate the number of atoms centered on a given plane. As an example, there are 2 atoms on a (1 1 0) plane of an FCC crystal.

    Find the area of the plane. As an example, the area of a (1 1 0) plane of an FCC crystal is 8_sqrt(2)_R^2 where "R" is the radius of an atom within the plane.

    Calculate planar density with the formula:

    PD = Number of atoms centered on a given plane / Area of the plane.

    Substitute the value calculated in step 1 for the numerator and the value calculated in step 2 for the denominator.


About the Author

Paige Turner started writing professionally in 2009. Her articles on business, health, technology and travel have been published on various websites ever since. She holds a Master of Science in engineering from New York University.

Photo Credits

  • Jupiterimages/Pixland/Getty Images