How to Calculate Planar Density

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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.