Comparison of Superstructure Phases of Rb 2 ZnBr 4 Type Compounds
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COMPARISON OF SUPERSTRUCTURE PHASES OF Rb 2 ZnBr
4
TYPE COMPOUNDS
A.C.R. HOGERVORST Delft University of Technology, Laboratory of Applied Physics, 1, 2628 CJ Delft, The Netherlands.
Lorentzweg
ABSTRACT Nine crystal structures, taken from literature, are compared with each other and with the room temperature structure of Rb 2 ZnBr 4 . Compared are the modulation functions and some pronounced local distortions. It appears that the ten structures have strikingly similar cooperative rotations of the anion tetrahedra.
INTRODUCTION The crystal structures discussed are distorted 8-K2SO4 type structures. The 3-K2SO4 structure is orthorhombic with space group Pcmn. In this paper the crystallographic axes are chosen such that the S-axis is the pseudohexagonal axis and a=-/b. The Rb2ZnBr 4 ty 4 structures contain a displacive modulation wave with wave vector q=yc . c is the reciprocal lattice vector of the average structure. The modulation wave can be either commensurate or incommensurate with the lattice of the average structure. If the modulation is commensurate, y can be written as u/v, with u and v mutually prime integers. The structure is then a v-fold superstructure. If the modulation is incommensurate it is not possible to write y as a rational fraction. In a structure with an incommensurate or a commensurate displacive modulation, the coordinates of the atoms with respect to the lattice vectors of the average structure can be written as x i =xoi+Wi(t)
for i=1,2,3
where the xoi's are the average coordinates, wi(t) the modulation functions and t=Xo.q. The modulation functions can be written as a Fourier series: wi(t)=Z ain. cos2nn(t-•in), where ain is the amplitude and ýin the phase of a cosine. The general formula of the compounds discussed is A2 BX4 . The structures consist of two kinds of chains parallel to 5: chains of alternatingly BX4 groups and A atoms (from now on called A2 atoms) and chains of only A atoms (A1 atoms). The data discussed are taken from literature. These data contain atomic coordinates which have not been corrected for thermal motion. This correction is however unimportant for the purpose of the present paper. In Table I some information is given about the structures. For NZC2 two structure determinations are reported. The one by Van Koningsveld is preferred because his standard deviations of the atomic coordinates are much smaller. The room temperature structure of Rb 2 XnBr 4 was believed to be incommensurate until recently. There is strong evidence now that it is a 17-fold superstructure (see [10]. The structure is still under investigation by the author but is known accurately enough to be compared with the other structures. In this investigation, the structure is treated as incommensurate with a higher symmetry than the space group mentioned in the table.
Mat. Res. Soc. Symp. Proc. Vol. 21 (1984) QElsevier Science Publishing Co., Inc.
138
TABLE I. The compound name, a code to denote the structure, y, the space group, the temperature at which the structure is determined and the ph
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