Probabilistic theory of the structure invariants: extension to the unequal atom case with application to neutron diffraction

Abstract

Recent methods in the probabilistic theory of the structure invariants and seminvariants are here generalized to include the case that not all atoms in the unit cell are identical. The presence of unequal atoms, in particular a few heavy atoms, is thus clearly seen to enhance the power of the direct method. Since the method permits the presence of negative scatterers, the application to neutron diffraction is immediate. Only the conditional probability distributions associated with the first neighborhood of the three-phase structure invariant and the first two neighborhoods of the four-phase structure invariant in P1 and P{\bar 1} are treated here. However the methods are clearly sufficiently general to cope with structure invariants and seminvariants in general.