Representational surfaces for thermal motion

Representational surfaces for the mean-square displacement, and the root-mean-square displacement, are derived for atomic thermal motion in the harmonic approximation. It is shown how the form of these surfaces depends on the way in which `mean-square displacement' is defined. It is concluded that to represent atomic thermal motion a different surface may be required from the second-order (ellipsoidal) surface usually presented in reports of crystal structure determinations.