One-dimensional contrast modulations in [001] high-resolution reverse images of Bi₂Sr₂(Ca_1−xNd_x)Cu₂O_8+δ ceramics

The one-dimensional contrast modulation along the b axis of [001] high-resolution reverse images of the compounds Bi₂Sr₂(Ca_{1 − x}Nd_x)Cu₂O_{8 + δ} (x = 0.05 + 0.1n; n = 1, 2, 6 and 7) is examined closely using the density distribution recorded from a wide area of the negative film by microphotometric densitometry. Three typical short units of the density distribution, of lengths 4.5b₀, 5b₀ and 4b₀, characterized by twin peaks or a single maximum peak with subpeaks in the middle of the unit, are discerned. The density distributions of the three units and the contrast modulations of their images are reproduced well by computer simulations, using three structure models modulated with longitudinal displacement waves along the b axis of the metal atoms. The one-dimensional contrast modulation is attributed to sinusoidal changes in the effective scattering amplitudes for the [001] electron beam of the metal-atom chains along the c axis. The results of the simulation are applied to investigation of the (2, 1)₅ and (3, 1)₄ modulation modes in the modulated structure.