= Crystallographic disorder
\b[Crystallographic disorder] is variation in atomic positions, orientations or chemical occupation that is represented by an average <crystal structure> rather than one perfectly repeated local arrangement. A <split-site disorder model> can describe alternative positions with fractional <crystallographic site occupancies>. The IUCr disorder-group convention distinguishes atoms present together in one configuration from mutually alternative configurations.<Atom-site symmetry and disorder in the IUCr core CIF dictionary>[`_atom_site_disorder_group`, jointly occupied sites and alternative groups]{ref}
For an original single-atom model, suppose an atom occupies position0 along an axis with probability0.6 and position $d$ with probability0.4. Then
$$
\mathbb E[X]=0.4d,\qquad
\operatorname{Var}(X)=0.6(0-0.4d)^2+0.4(d-0.4d)^2=0.24d^2.
$$
At $d=1\,\mathrm{\mathring A}$, the mean is $0.4\,\mathrm{\mathring A}$ and the variance is $0.24\,\mathrm{\mathring A^2}$. There need be no atom at the mean position in any individual configuration. Fitting only an average position with a large <atomic displacement parameter> can conceal this distinction.
The same average occupation could arise from different unit cells adopting different configurations, from motion among configurations during measurement, or from a mixture of these effects. A static average alone does not determine an interchange rate.
Experimental interpretation therefore combines the <electron density map>, the allowed chemical geometry, occupation constraints and other evidence. Weak or broadened density should not automatically be assigned one specific dynamic mechanism.
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