 Atomic displacement parameter

An atomic displacement parameter describes the spread of an atom's modeled position about its mean in a crystal structure. An isotropic atomic displacement parameter represents equal spread in all directions; an anisotropic atomic displacement parameter uses a directional matrix. These parameters can reflect thermal motion, unresolved static variation and limitations of the refinement model, rather than temperature alone.

For isotropic Cartesian displacement, let $U_{\mathrm{iso}}$ be the mean-square displacement of one component, in squared angstroms. The conventional alternative parameter isThe IUCr dictionary gives both conventions and prefers reporting $U$.^[ref]

For an original numerical example, $U_{\mathrm{iso}}=0.010{\mathring{\mathrm{A}}}^2$ givesThe second value is the root-mean-square spread along one Cartesian direction. Under isotropy the three-dimensional mean-square displacement is $3U_{\mathrm{iso}}$, so the corresponding radial root-mean-square spread is about $0.173\mathring{\mathrm{A}}$.

This spread is not the same as uncertainty in the refined mean coordinate. Nor does doubling $B$ by itself prove that an atom's temperature doubled. Crystallographic disorder, imperfect data and a different structural model can affect the fitted parameter. Interpretation requires the experimental and modeling context.