Linearization routines for the parameter space concept to determine crystal structures without Fourier inversion

Vallinayagam, M.; Nentwich, M.; Meyer, D.C.; Zschornak, M.

doi:10.1107/S1600576725001955

Journal of Applied Crystallography Journal of Applied
Crystallography

IUCr IT WDC

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Figure 3
The definition of asymmetric units upon specific sets of f values is shown in (a)–(c). The $[{\cal A}^{3}]$ in (a) is defined for the EPA framework where all f_i are equal. The $[{\cal A}^{3}]$ in (b) and (c) are defined for the non-EPA framework. In (b) it is assumed that two fs (along the z₁ and z₂ directions) are the same and f₃ is different. In (c) it is assumed that all fs are different and hence $[{\cal A}^{3}]$ is equivalent to $[{\cal P}^{3}]$ . In (d) $[{\cal G}[l = 1,g_{0}(l)]]$ are given for the EPA case representing the magnitude of g₀(l) from

to 3 in color code. The zero isosurface $[{\cal G}[l = 1,g_{0}(l) = 0]]$ separates the PS into two halves containing isosurfaces $[{\cal G}[l = 1,g_{0}(l)]]$ of positive or negative signs. When applying the choice of origin symmetry, the origin is fixed at [0,0,0]. Then the asymmetric unit reduces to half under the zero isosurface, containing only the positive signs