Synchrotron x-ray diffraction study of a charge stripe order in $\frac{1}{8}$-doped ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$

Lattice distortions associated with charge stripe order in $\frac{1}{8}$ hole-doped ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ are studied using synchrotron x-ray diffraction for $x=0.05\mathrm{}$ and $x=\mathrm{0.075.}\mathrm{}$ The propagation wave-vector and charge order correlation lengths are determined with a high accuracy, revealing that the oblique charge stripes in orthorhombic $x=0.075\mathrm{}$ crystal are more disordered than the aligned stripes in tetragonal $x=0.05\mathrm{}$ crystal. The twofold periodicity of lattice modulations along the c axis is explained by long-range Coulomb interactions between holes on neighboring ${\mathrm{CuO}}_2$ planes.