On structure refinement using data from a twinned crystal

Refinements leading to accurate structural parameters are possible by using the measured data F²_o of a twinned crystal with exactly superimposed reciprocal lattices and accumulating the sum for the n twin domains, Σⁿ_iα_i|kF_ci|², of the calculated squared structure factors, |kF_ci|², weighted according to the fractional contribution α_i of twin i to the total squared structure factor |kF_c|². The derivatives with respect to structural parameters and the overall scale factor (k) may be accumulated similarly. The (n - 1) independent α_i should also be refined; here the derivatives are of the form ∂|kF_c|²/∂α_i = |kF_ci|² - |kF_cn|² since α_n = 1 -- Σ^n-1_i α_i. 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.