Symmetrical Staircase in the Profile of Lattice-Modulation Period versus Pr-Concentration in Bi₂Sr₂(Ca_1-xPr_x)Cu₂O_8+δ

Abstract

Variation of the lattice-modulation period p_a of the “incommensurate” phase Bi₂Br₂(Ca_1-xPr_x)Cu₂O_8+δ (0≤ x≤ 0.72) with Pr-concentration x was examined by electron diffraction. The plot of p_a versus x exhibits roughly a linear decrease but it has a staircase structure. The period of each stair, p_a, agrees with a value expected for a commensurate structure. We observed nine stairs which are symmetrically arranged; the central stair corresponds to the primary structure with a simple modulation, and a stair on the left (or right) corresponds to a structure which is derived from the primary structure by introducing an advanced (or delayed) discommensuration. The observed structures cover a full range of commensurate structures predicted theoretically.