An expression for the temperature factor of a librating atom

The temperature factor for an atom undergoing librational motion is usually expressed in the form of the Debye-Waller factor appropriate to a translational oscillation with an equivalent root-mean-square amplitude. As a result of this the atomic positions may depart significantly from their true positions, and in an X-ray structure analysis the effect on the final difference density hinders the study of bonding electron distributions. A new form of the temperature factor for thermal librations which obviates these difficulties is proposed.