= Atomic displacement parameter
{title2=$U,\ B$}
An \b[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 is
$$
B=8\pi^2U_{\mathrm{iso}}.
$$
The IUCr dictionary gives both conventions and prefers reporting $U$.<Atomic displacement parameters in the IUCr core CIF dictionary>[Definitions of U/B isotropic or equivalent displacement parameters and their conversion]{ref}
For an original numerical example, $U_{\mathrm{iso}}=0.010\,\mathrm{\mathring A^2}$ gives
$$
B\approx0.790\,\mathrm{\mathring A^2},\qquad
\sqrt{U_{\mathrm{iso}}}=0.100\,\mathrm{\mathring A}.
$$
The 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 $0.173\,\mathrm{\mathring A}$.
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.
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