Calculations Involving Unit Cell Dimensions

Because it is not practical to draw or directly measure a three-dimensional crystal lattice at the atomic scale, the actual dimensions of a unit cell are worked out indirectly, using X-ray diffraction analysis -- the single most powerful experimental tool for determining crystal structure.

When X-rays strike the successive, evenly-spaced planes of atoms inside a crystal, they are diffracted according to Bragg's equation:

where d is the spacing (interplanar distance) between two successive planes of atoms, lambda is the wavelength of the X-rays used, theta is the angle of diffraction at which a diffraction peak is observed, and n is the order of diffraction (a positive integer: 1, 2, 3, ...).

Rearranging Bragg's equation to solve for the interplanar spacing gives:

$d = \dfrac{n\lambda}{2\sin\theta}$ …