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The use of the superspace formalism is extended to the description and refinement of the homologous series of modular structures with two symmetry-related modules with different orientations. The lillianite homologous series has been taken as a study case. Starting from a commensurate modulated composite description with two basic subsystems corresponding to the two different modules, it is shown how a more efficient description can be achieved using so-called zigzag modulation functions. These linear zigzag modulations, newly implemented in the program JANA2006, have very large fixed amplitudes and introduce in the starting model the two orientations of the underlying module sublattices. We show that a composite approach with this type of function, which treats the cations and anions as two separate subsystems forming a misfit compound, is the most appropriate and robust method for the refinements.

Supporting information


Crystallographic Information File (CIF)
Contains datablocks global, I


Structure factor file (CIF format)
Contains datablock I

Computing details top

Program(s) used to refine structure: Jana2006 (Petricek, Dusek & Palatinus, 2006); software used to prepare material for publication: Jana2006 (Petricek, Dusek & Palatinus, 2006).

(I) top
Crystal data top
PbSZ = 16
Mr = 239.2F(000) = 214
Orthorhombic, Bmmm(0β0)s00†Dx = 63.789 Mg m3
q = 0.05556b*Mo Kα radiation, λ = 0.71069 Å
a = 13.737 ŵ = 77.24 mm1
b = 1.7496 ÅT = 293 K
c = 4.1448 ÅPlaty, black
V = 99.62 Å30.10 × 0.05 × 0.02 mm
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, −x2, x3, −x4; (3) −x1, x2, −x3, x4+1/2; (4) x1, −x2, −x3, −x4+1/2; (5) −x1, −x2, −x3, −x4; (6) x1, x2, −x3, x4; (7) x1, −x2, x3, −x4+1/2; (8) −x1, x2, x3, x4+1/2; (9) x1+1/2, x2, x3+1/2, x4; (10) −x1+1/2, −x2, x3+1/2, −x4; (11) −x1+1/2, x2, −x3+1/2, x4+1/2; (12) x1+1/2, −x2, −x3+1/2, −x4+1/2; (13) −x1+1/2, −x2, −x3+1/2, −x4; (14) x1+1/2, x2, −x3+1/2, x4; (15) x1+1/2, −x2, x3+1/2, −x4+1/2; (16) −x1+1/2, x2, x3+1/2, x4+1/2.

Data collection top
Radiation source: X-ray tube756 independent reflections
Absorption correction: empirical (using intensity measurements)454 reflections with I > 3σ(I)
Tmin = 0.037, Tmax = 0.187
Refinement top
Refinement on F24 parameters
R[F2 > 2σ(F2)] = 0.043Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
wR(F2) = 0.051(Δ/σ)max = 0.049
S = 1.42Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
756 reflectionsExtinction coefficient: 243 (28)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Pb00.92118 (19)0.500.0443 (11)0.0555
S10.50.500.0199 (14)0.5
Pb10000.0174 (3)0.5
Atomic displacement parameters (Å2) top
Pb00.0341 (16)0.068 (2)0.0310 (19)000
S10.024 (2)0.018 (3)0.019 (2)000
Pb10.0184 (5)0.0163 (5)0.0175 (5)000

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