Practical Electron Microscopy and Database

The general formula A_1-pCr₂X_4-p (A =ˆ Ba, Sr, Eu, Pb, X = ˆS, Se) [1 - 3] represents an unusual average structure formed by the intergrowth of three different substructures that are mutually incommensurate along one direction.

The structure [4] shown in Figure 3474a is formed by a three-dimensional (3-D) Cr₇S₁₂ framework raising the strips of edge-sharing octahedra {CrX₆} as a triple twinning {111} of NaCl-type and thus, resulting in a hexagonal symmetry sublattice. This 3-D framework forms two different types of tunnels with hexagonal and trigonal geometry. The columns with composition A₃CrX₃ located in the hexagonal tunnels and the columns with composition A₃X located in the trigonal tunnels. There are one hexagonal tunnel and two trigonal tunnels in an unit cell. Both types of columns present hexagonal lattices with the same lattice parameters.

Figure 3474b shows the SAED (selected-area electron diffraction) patterns of A_1-pCr₂X_4-p crystals along the [0001] zone axis, revealing only the Bragg reflections hk0, which are common to the three sublattices.

Surprisingly, the high-resolution images along [0001] (given in Figure 3474c) does not correspond to the expected six-fold symmetry as indicated in Figure 3474b, but to three-fold symmetry.

Figure 3474d shows the electron diffraction pattern along any [hki0] zone axis. The reflection spots originate from the 3-D framework Cr₂₁S₃₆, while the diffuse diffraction lines originate from the two columnar substructures Pb₆Cr₂S₆ and Pb₃S. The lack of correlation between columns of the same type results in planes of diffuse intensity instead of well-defined reflections, even though some degree of correlation between the columns still exist since the diffuse intensity of the planes are not uniform in the figure.

[1] Brouwer, R., and Jellinek, F., 1977. Multiple order in sulfides and selenides. Journal de Physique C7 38, 36 - 41.
[2] Brouwer, R., and Jellinek, F., 1977. Intergrowth structure of Eu_1-pCr₂Se_4-p (…p ˆ =0.29)† and isotypic compounds. A novel type of crystal structure with three incommensurate periodicities in one direction: X-ray study. J.C.S. Chem. Commun., 879 - 881.
[3] Brouwer, R., and Jellinek, F., 1979. Modulation of the intergrowth structures of A_1-pCr₂X_4-p (A =ˆ Ba, Sr, Eu, Pb, X = ˆS, Se, p ≈ 0.29). Modulated structures - 1979. AIP Conf Proceedings No. 53, pp. 114 - 116.
[4] Hyde, B.G., Andersson, S., 1989. Inorganic Crystal Structures. Wiley, New York.
[5] Landa-Cánovas, A.R., Gómez-Herrero, A., and Carlos Otero-Díaz, L. Electron microscopy study of incommensurate modulated structures in misfit ternary chalcogenides, Micron 32 (2001) 481 - 495.