On structure refinement using data from a twinned crystal

Refinements leading to accurate structural parameters are possible by using the measured data F2o of a twinned crystal with exactly superimposed reciprocal lattices and accumulating the sum for the n twin domains, Σniαi|kFci|2, of the calculated squared structure factors, |kFci|2, weighted according to the fractional contribution αi of twin i to the total squared structure factor |kFc|2. The derivatives with respect to structural parameters and the overall scale factor (k) may be accumulated similarly. The (n - 1) independent αi should also be refined; here the derivatives are of the form ∂|kFc|2/∂αi = |kFci|2 - |kFcn|2 since αn = 1 -- Σn-1i αi. These procedures have been incorporated into a standard least-squares program for the successful refinement of the low-temperature structure of Ni(en)3SO4. Two domain systems with partial overlap of reciprocal lattices may also be handled.