Oxygen ordering and strain-related morphology inYBa2Cu3−xMxO7systems, whereMis a trivalent atom

Monte Carlo simulations were performed on an anisotropic lattice-gas model which well represents the interactions between oxygen atoms in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ systems doped with trivalent impurity atoms M such as Fe or Al. Concentration wave amplitudes obtained from these simulations were used to calculate the diffuse x-ray scattering intensity caused by the resulting displacement field using a concentration-wave–displacement-wave approach, and the results are compared with x-ray and electron diffraction data. The results suggest that the small orthorhombic domains (short-range ordering) associated with the oxygen ‘‘cross-links’’ around impurity atoms M cause the diffuse scattering intensity to fall off with the scattering wave-vector difference q from a Bragg peak as 1/${\mathit{q}}^2$ for small q and as 1/${\mathit{q}}^4$ for larger q. We show that the average size of such domains can be obtained from diffuse x-ray scattering data.