Ba1-pCr2X4-p (X = ˆS, Se)
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The general formula A1-pCr2X4-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 3477a 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.

Idealized structure model of PbCr2S4 projected onto (0001)

Figure 3477a. (a) Ideal structure of PbCr2S4 projected onto (0001). Pb, Cr and S atoms are drawn as medium black, small black and big gray circles. (b) The triangular tunnels. Black spheres represent Pb atoms and the gray ones located in the center of the face sharing Pb-prisms are S atoms. (c) The hexagonal tunnels. The black spheres represent Pb atoms and the S atoms are located at the corners of the face-sharing octahedra which are centered by Cr atoms. [5]

Furthermore, as mentioned above the Ba1-pCr2X4-p (X = ˆS, Se) crystal structure is similar to that of PbCr2S4 structure investigated by TEM and electron diffraction.

 

 

 

 

[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 Eu1-pCr2Se4-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 A1-pCr2X4-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.

 

 

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