If the crystal structure of a compound is known and a twin must be used for refinement of the structure, then the twinning relation can be used to interpret the observed intensity values. The problem becomes the task of calculating the crystal-volume ratio, which may be defined as the ratio K=Vβ/Vα of the volume Vβ of the smaller crystal to the volume Vα of the larger crystal, O <K <1. If the twin produces two sets of reflections, each set self-consistent within its own indexing, then the crystal-volume ratio can be calculated by direct comparison of equivalent reflections from each set. If the two twinned crystals produce reflections that are superimposed on each other, then a least-squares solution can be employed as described below. This method has been used successfully (Freed and Peacor, 1967) for a case which yielded the value K = 0.07.

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