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The general formula A1-pCr2X4-p (A = Ba, Sr, Eu, Pb, X = S, 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 3473a 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)](image1/3473.gif)
Figure 3473a. (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]
Figure 3473b shows the SAED (selected-area electron diffraction) patterns of A1-pCr2X4-p crystals along the [0001] zone axis, revealing only the Bragg reflections hk0, which are common to the three sublattices.
![SAED pattern of PbCr2S4 crystals oriented along the [0001] zone axis](image1/3477b.jpg)
Figure 3473b. SAED pattern of PbCr2S4 crystals oriented along the [0001] zone axis. [5]
Surprisingly, the high-resolution images along [0001] (given in Figure 3473c) does not correspond to the expected six-fold symmetry as indicated in Figure 3473b, but to three-fold symmetry.
![HRTEM image of a crystal of a PbCr2S4 crystal imaged along the [0001] zone axis](image1/3477d.jpg)
Figure 3473c. HRTEM image of a crystal of a PbCr2S4 crystal imaged along the [0001] zone axis. The unit cell is outlined.
Figure 3473d 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.
![Electron diffraction pattern of a PbCr2S4 crystal oriented along the [2 -1 -1 0] zone axis](image1/3477c.jpg)
Figure 3473d. Electron diffraction pattern of a PbCr2S4 crystal oriented along the [2 -1 -1 0] zone axis.
[5]
[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 =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 = Ba, Sr, Eu, Pb, X = S, 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.
[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 =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 = Ba, Sr, Eu, Pb, X = S, Se, p ≈ 0.29). Modulated
structures - 1979. AIP Conf Proceedings No. 53, pp. 114 - 116.
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