R factors in X-ray fiber diffraction. III. Asymptotic approximations to largest likely R factors

The largest likely R factor is useful for evaluating the significance of R factors obtained in structure determinations, and is smaller in fiber diffraction than in traditional crystallography. Very simple approximations to functions used to calculate the largest likely R factor in fiber diffraction are derived. For example, the largest R factor (R_m) for m overlapping terms is very well approximated by R_m ≃ (2/π)^1/2 m ^-1/2. These are a useful alternative to the exact, but quite complicated, expressions derived previously. More significantly, they provide insight into the behavior of R factors in fiber diffraction and may be useful in further analysis.