Synchrotron X-ray diffraction study of a charge stripe order in 1/8-doped La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$

Lattice distortions associated with charge stripe order in 1/8 hole-doped La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$ are studied using synchrotron X-ray diffraction for $x=0.05$ and $x=0.075$. The propagation wave vector and charge order correlation lengths are determined with a high accuracy, revealing that the oblique charge stripes in orthorhombic $x=0.075$ crystal are more disordered than the aligned stripes in tetragonal $x=0.05$ crystal. The twofold periodicity of lattice modulations along the c-axis is explained by long-range Coulomb interactions between holes on neighboring CuO$_{2}$ planes.