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It is often very difficult to analyze structures of crystals with sinusoid-like modulations of lattice based on diffraction data, because the number of measurable superlattice reflection is not sufficient to determine atomic coordinates in the large unit cell of modulated structure. The structure of the Bi_2Sr_2(Ca_<1-x>Ln_x)Cu_2O_<8+delta> (Ln=rare earth metal) substitution system is a member of the family of the modulated structures.The present study aims to resolve the modulated structure of the substitution systems of Ln=Y,Nd,Pr and Tb by means of the analyses of  high-resolution image and electron diffraction pattern, and then, to show the Ln-concentration dependencies of the modulation period and the substitution effects of the elements to the concentration dependence. The results are summarized as follows.
1.A long-period modulated structure model was proposed, consisting of ordered alignments of domains with extent b_1=4.5b_0 and b_2=5b_0 or b_3=4b_0. The model shows the co
nsistency with the intensity distribution of electron diffraction.
2.An analysis was carried out based on photometric density distribution curves of one-dimensional contrast modulation of  high-resolution image and computer simulations of the density distribution curve. The result of analysis has elucidated that the ordered alignment of the domains ( domain configuration ) in the crystal has been determined from the density distribution curve directly.
3.The modulation period decreases with the Ln-concentration. The Pr and Tb elements have a larger substitution effect to the concentration dependence of period than the Y and Nd elements. Taking the 2 valence of Ca and 3 of Y as the standard ones, the Nd and Pr or Tb elements serve as the 3 and 3.2-3.3 valences in the crystals, respectively.
The modulation period prefers to show a stairswise decrease with the Ln-concentration. The study on the details of the stairs is in progress newly. The domain configurations found in density distribution curves are equivalent those of the ground states of the one-dimensionally competitive system.
1. T. Onozuka, et al., (1991). Phys. Rev. B 43, 13066-13073.
2. T. Onozuka and Y. Hirotsu, (1991). submitted to Acta Cryst.
3. T. Onozuka, (1993). J. APPL. Cryst. 26, in the prees. Less